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    Fatigue handbook2 Fatigue handbook2 Document Transcript

    • FATIGUE HANDBOOK Offshore Steel Structures Edited by A. Almar-Naess I B TAPIR 1985
    • Editorial Committee Jan R. Getz Professor, MARINTEK, Trondheim, Chairman of Committee. A. Alrnar-Naess Professor, Norges tekniske hogskole, Trondheim. Carl A. Carlsen Dr.ing., Senior Principal Surveyor, Det norske Veritas, Oslo. Kristian Haslum Sivilingenior, MAROTEC A/S, Oslo. Torgeir Moan Professor, Dr-ing., Norges tekniske hogskole, Trondheim. Per Tenge M-Sc., Chief Surveyor, Det norske Veritas, Oslo. Harold S. Tyler B.Sc. (M.E.), Principal Metallurgical and Corrosion Engineer, Phillips Petroleum Company Norway, Stavanger.Authors A. Alrnar-Naess Professor, Norges tekniske hogskole, Trondheim. Hiikan Andersson M.Sc., Structural Analyst, VERITEC, Oslo Einar Bardal Professor, Dr.ing., SINTEF, Trondheim. Stig Berge Professor, Dr .ing., Norges tekniske hogskole, Trondheim. Knut Engesvik Dr.ing., Senior Research Engineer, SINTEF, Trondheim. StAle Fines Sivilingenior, Senior Engineer, A.S VERITEC, Oslo. M.B. Gibstein M.Sc., Senior Principal Engineer, A.S VERITEC, Oslo. Per J. Haagensen M.Sc.A., Senior Research Engineer, SINTEF, Trondheim. Agnar Karlsen Sivilingenior, Principal Surveyor, Det norske Veritas, Oslo. Jon Lereim M.Eng., Principal Surveyor, Det norske Veritas, Oslo. Inge Lotsberg Dr .ing., Principal Engineer, A.S VERITEC, Oslo. Torgeir Moan Professor, Dr.ing., Norges tekniske hogskole, Trondheim. Einar T. Moe M.Sc., Senior Project Engineer, A.S VERITEC, Oslo. Stephen Slatcher M.A., Ph.D., Research Engineer, A.S VERITAS RESEARCH, Oslo. Stig Wastberg Ph.D., Principal Engineer, A.S VERITEC, Oslo.
    • PREFACE Soon after oil and gas exploration and production began in the North Sea in the19603, it became apparent that the steel structure design developed for offshore activitiesin the Gulf of Mexico was not adequate when transferred to the more rigorous North Seaenvironment. In particular, fatigue cracks evolved as a result of wave action during thesevere winter storms. There were no serious accidents, but it was evident that there was agreat need for better understanding of the fatigue phenomenon so that safer structurescould be built. In Norway, a vigorous effort to collect wave, wind and current data, and to developmethods for calculating static and dynamic response in offshore structures started in theearly 1970s. A corresponding, but less intensive activity to determine fatigue capacityof materials and welded joints in air and sea water, was initiated some years later, However,everyone concerned recognized that a much greater effort was needed to keep up withthe rapidly developing construction work in progress in the North Sea. In 1977, concerned materials scientists at SINTEF and Det norske Veritas prepareda 5 year program for intensified research on fatigue of offshore steel structures. This wasapproved by the Royal Norwegian Council for Scientific and Industrial Research in 1979.In 1981, it became the National 5 Year Program for Fatigue of Offshore Steel Structures. The stated objective of the program:Establishing a more reliable basis for design of welded marine structures with respect tofatigue, thus contributing to an improved and better defined safety level for such struc-tures, and developing a basic understanding of mechanisms and conditions governing thefatigue life of steel structures. A steering committee was named with responsibility for the organization andexecution of the program. Present members are: Bjom Lian, Statoil, Chairman A. Almar-Naess, Norges tekniske hogskole Einar Horn, Det norske Veritas Per Tenge, Det norske Veritas Harold S. Tyler, Phillips Petroleum Company Norway.
    • During 1981-1985, research work was performed in laboratories at Norges tekniskehogskole, SINTEF, and Det norske Veritas. This work generally followed the originalprogram at a total cost of about 25 million Nkr. The main contributors to the program arethe Norwegian Council for Scientific and Industrial Research and Phillips PetroleumCompany Norway. Supplementary funding is coming from Statoil, Oljedirektoratet, NorskHydro A/S, and Kvaerner Industrier A/S. Close cooperation was established with similarprograms organized by the European Coal and Steel Community and National programswithin the Community. In order to satisfy the objective of the program, it is important that results areavailable to engineering industries, oil companies and certifying authorities without delay,and in a form that can be understood and utilized by those responsible for the differentstages in engineering, design, fabrication and service of offshore structures. Therefore,this book was written as one of the projects within the program. A six member committee with Mr. Kristian Haslum as editor drafted the outlineand gave the initial instructions to the authors. At the final stage of the book, the editorialwork was undertaken by Professor A. Almar-Niess. It is intended that the book should cover the most important subjects related tofatigue of steel structures, to an extent and depth which will give the reader a correctunderstanding of the main problems, and enable transfer of knowledge into practicaldesign. Examples of calculation of fatigue stresses and fatigue lives have been includedto illustrate the text. Much of the editorial work has been to coordinate the eleven chapters so that thedifferent topics are dealt with in a logical order without unnecessary recurrences, and withnomenclature and symbols that are essentially consistent. In this, the editor has been onlypartially successful. The editorial work has been a joint effort between the authors, Mrs. Vera Almar-Naess, who has composed the book and corrected the proofs, Mr. Per Molde and Mr. IngarGraneggen, who have drawn the figures, and myself. I want to thank them all for a re-warding cooperation. I would also like to acknowledge the positive connection withProfessor Jan R. Getz, chairman of the drafting committee, and Mr. Nils Ostlyng, directorof Tapir. Trondheim May 1985 A. Alrnar-Naess
    • CONTENTS1 OVERVIEW OF OFFSHORE STEEL STRUCTURES. . . . . . . . . . . . . . . . . . 1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Types of offshore steel structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 System layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Design requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Loads and load effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Ultimate strength design check. . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.4 Fatigue design check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.5 Progressive failure design check . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3 Practical implications of design criteria . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Semi-submersibles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.2 Tension leg platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.3 Jackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 1.4 Lessons learned from fatigue failures. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.2 Fatigue failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.3 Implications of service failures . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .352 LOADS ON OCEAN STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3 Dynamic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.2 Single-degree-of-freedom system . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.3 Physical properties used for dynamic analysis . . . . . . . . . . . . . . . . 50 2.3.4 Natural frequencies of common structural elements . . . . . . . . . . . . 52 2.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.2 Regularwaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.3 Irregular waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.4 Long-term wave statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
    • Contents 2.5 Hydrodynamic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.2 Loads on small-volume bodies - Morisons equation . . . . . . . . . . . 63 2.5.3 Loads on large-volume bodies . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.5.4 Deterministic calculation of response to hydrodynamic loads. . . . . . 69 2.5.5 Spectral method for calculation of response to hydrodynamic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.5.6 Slamming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.5.7 Vortex-induced oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.6 Long-term stress range distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.2 Deterministic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.3 Stochastic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.6.4 Simplified long-term distribution . . . . . . . . . . . . . . . . . . . . . . . . 87 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3 FRACTURE MECHANICS AS A TOOL IN FATIGUE ANALYSIS . . . . . . . 91 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 r 3.1 Fundamentals of fracture mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 94I I .. 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.1.2 Analytical basis of LEFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.1.3 Evaluation of stress intensity factors . . . . . . . . . . . . . . . . . . . . . . 98 3.2 Fracture mechanics applied to fatigue problems . . . . . . . . . . . . . . . . . . . 113 3.2.1 Estimation of crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 3.2.2 Estimation of fatigue life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.2.3 Fracture mechanics applied in the calculation of SN-curves . . . . . . . 130 3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Appendix 3 .A. Conversion tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Appendix 3.B. General references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 Appendix 3.C. A small compendium of stress intensity factors . . . . . . . . . . . . . 144 Two-dimensional edge crack problems . . . . . . . . . . . . . . . . . . . 144 Elliptical cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4 BASIC FATIGUE PROPERTIES OF WELDED JOINTS. . . . . . . . . . . . . . . - 1 5 7 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 ....... ; List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 .. 4.1 Basic fatigue mechanisms and characteristics . . . . . . . . . . . . . . . . . . . . . . 159 4.1.1 Fatigue initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 4.1.2 Crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 4.1.3 Final failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168 4.1.4 Characteristics of fatigue failures . . . . . . . . . . . . . . . . . . . . . . . . 168 4.1.5 Fatigue capacity assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.2 Constant amplitude SN testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 4.2.1 SN testing versus crack growth testing . . . . . . . . . . . . . . . . . . . . .176 . VIII .
    • Contents 4.2.2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.2.3 TypesofSNtests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.2.4 Fatigue failure criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.2.5 Fatigue limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.2.6 Real structures versus test specimens. . . . . . . . . . . . . . . . . . . . . . 187 4.3 Cyclic strain and material response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.3.2 Monotonic stress and strain . . . . . . . . . . . . . . . . . . . . . . . . . . . .189 4.3.3 Cyclic stress and strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 4.3.4 Cyclic stress and strain resistance . . . . . . . . . . . . . . . . . . . . . . . . 192 4.3.5 Fatigue of notched members . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4.4 Variable amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 4.4.1 Characterization of fatigue loading . . . . . . . . . . . . . . . . . . . . . . . 196 4.4.2 Cycle counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 4.4.3 Load spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 4.5 Cumulative damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208 4.5.1 The Miner summation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 4.5.2 Equivalent stress range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4.5.3 Stress interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 4.6 Fatigue of welded joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 4.6.1. Crack initiation versus crack growth . . . . . . . . . . . . . . . . . . . . . . 212 4.6.2 SN-curve - low cycle and lugh cycle fatigue . . . . . . . . . . . . . . . . . 214 4.6.3 The effect of geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215 4.6.4. Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 4.6.5 Material properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 4.7 SN data for welded joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.2 Classification of SN data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 4.7.3 Assessment of design SN-curves . . . . . . . . . . . . . . . . . . . . . . . . . 227 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2335 SIGNIFICANCE OF DEFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.2 Classification of defects according to origin . . . . . . . . . . . . . . . . . . . . . . 237 5.2.1 Fabrication defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 5.2.2 In-senice defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .241 5.3 Other faults in fusion welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 5.4 Statistical description of weld quality . . . . . . . . . . . . . . . . . . . . . . . . . . 244 5.5 Non-destructive inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 5.5.1 Non-destructive inspection methods . . . . . . . . . . . . . . . . . . . . . .247 5.5.2 Nondestructive inspection reliability . . . . . . . . . . . . . . . . . . . . . 249 5.6 Assessment of defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.6.1 Fitness-for-purpose approach . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.6.2 Defect severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 . IX-
    • Contents6 IMPROVING THE FATIGUE STRENGTH OF WELDED JOINTS . . . . . . . . 259 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .259 6.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.1.2 The potential for improving fatigue strength . . . . . . . . . . . . . . . . . 260 6.1.3 Improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 6.2 Weld geometry modification and defect removal methods . . . . . . . . . . . . . 264 6.2.1 Grinding techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 6.2.2 Weld toe remelting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 6.2.3 Improved welding techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 6.3 Residual stress methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .273 6.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3.2 Hammer peening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3.3 Shot peening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 6.4 Combination of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . 276 6.5 Test on large scale components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 6.6 Comparison of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . 278 6.7 Cost of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 6.8 Applying improvement methods to offshore structures . . . . . . . . . . . . . . .283 6.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 6.8.2 Effects of size and stress distribution in improved joints . . . . . . . . . 283 6.8.3 Inspection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2867 EFFECTS OF MARINE ENVIRONMENT AND CATHODIC PROTECTION ON FATIGUE OF STRUCTURAL STEELS . . . . . . . . . . . . . . . . . . . . . . . . 291 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7.1 Qualitative presentation of effects. mechanisms and important factors. . . . . 291 7.2 Effects of corrosion and cathodic protection on experimentally determined SNdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 7.2.1 Plain specimens and different types and qualities of welded joints . . . 294 7.2.2 Significance of environmental factors and corrosion protection measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 7.2.3 Significance of loading variables and materials properties . . . . . . . . 299 7.3 Effects of corrosion and cathodic protection on crack growth . . . . . . . . . . 300 7.3.1 Different effects at different levels of crack growth . . . . . . . . . . . . 300 7.3.2 Significance of loading variables and materials properties . . . . . . . . 301 7.3.3 Significance of environmental factors . . . . . . . . . . . . . . . . . . . . . 302 7.4 Prediction of effects of corrosion and cathodic protection on fatigue life by means of crack growth data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304 7.5 Design guide-lines, British proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 7.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309
    • Contents 8 FATIGUE OF TUBULAR JOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 8.2 Types of tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-315 8.3 Simple welded tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 8.3.1 Definitions and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3182 ! 3 -3Y 9 8.3.2 Definition of the hot spot stress, and stress and strain concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 8.3.3 Methods for stress analysis of tubular joints . . . . . . . . . . . . . . . . . 326 8.3.4 Stress concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 8.3.5 Fatigue testing, experimental results and establishment of SN-curves 339 8.3.6 Joint design and fabrication. . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 8.3.7 Procedurg for fatigue evaluation of tubular joints . . . . . . . . . . . . .346 8.3.8 In-senice experience. Repair . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 8.3.9 Fracture mechanics analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 8.4 Heavy duty joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 8.4.1 Overlapping joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 8.4.2 Complex joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .353 8.4.3 Cast steel nodes (CSN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Appendix A: Parametric formulas for stress concentration factors. . . . . . . . . . . . 363 9 UNSTABLE FRACTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 9.1 Failure modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .371 . 9.2 Modes of unstable fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 . 9.3 Toughness parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 9.3.1 Charpy toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .374 9.3.2 Fracture mechanics parameters to characterise unstable fracture . . . -375 9.4 Fracture toughness (KIC and CTOD) testing . . . . . . . . . . . . . . . . . . . . . . 376 9.4.1 KIC testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 . 9.4.2 CTOD testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 9.5 Application of fracture mechanics to unstable fracture . . . . . . . . . . . . . . .382 9.5.1 The stress intensity factor approach . . . . . . . . . . . . . . . . . . . . . . 382 9.5.2 The CTOD design curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 9.5.3 The R6 failure assessment diagram . . . . . . . . . . . . . . . . . . . . . . .389 9.5.4 Stress concentrations and residual stresses . . . . . . . . . . . . . . . . . . 393 9.6 Factors affecting fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . . . .396 9.6.1 Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 . 9.6.2 Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 9.6.3 Strain rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 9.6.4 Metallurgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .401 .
    • Contents10 FATIGUE LIFE CALCULATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405 10.1 Importance of fatigue life estimation at the design stage . . . . . . . . . . . . . . 405 10.2 Prediction of fatigue life by use of SN data and the Miner-Palmgren approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 10.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .406 10.2.2 Closed form fatigue life equations. . . . . . . . . . . . . . . . . . . . . . . . 409 10.2.3 Calculation of equivalent stress range . . . . . . . . . . . . . . . . . . . . .413 10.2.4 Stresses to be considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 10.2.5 SN-curves and joint classifications . . . . . . . . . . . . . . . . . . . . . . .421 10.3 Prediction of crack propagation by use of da/dN-AK curves . . . . . . . . . . . 422 10.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 10.3.2 Constant amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . .423 10.3.3 Variable amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . .425 10.3.4 Geometry functions and crack growth integrals . . . . . . . . . . . . . . . 425 10.4 Sensitivity and uncertainty analysis of fatigue life . . . . . . . . . . . . . . . . . . 427 10.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .427 10.4.2 Load calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428 10.4.3 Stress calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 10.4.4 SN data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 10.4.5 Fabrication tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .433 10.4.6 Cumulative damage hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.4.7 Probability of failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.5 Design formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .437 10.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .437 10.5.2 Allowable stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 10.5.3 Allowable cumulative damage ratio . . . . . . . . . . . . . . . . . . . . . . . 440 10.5.4 Comments on the design formats . . . . . . . . . . . . . . . . . . . . . . . .443 10.6 Allowable stress format for pre-engineering design check . . . . . . . . . . . . . 443 10.6.1 Design chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443 10.6.2 Considerations on the Weibull parameter h . . . . . . . . . . . . . . . . . . 445 10.7 Considerations on yield strength and relieving of residual stresses . . . . . . . . 447 10.7.1 Yield strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 10.7.2 Post weld heat treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 10.8 Example 9 . Redesigning of cross joint in a loading buoy . Discussion on the choice of SN-curve and possible use of stress relief heat treatment . . . . . . . 448 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45611 FATIGUE IN BUILDING CODES .BACKGROUND AND APPLICATIONS . . 459 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 11.1 The various codes on fatigue requirements . . . . . . . . . . . . . . . . . . . . . . .459 11.2 Fatigue design regulations based on fatigue strength tests . . . . . . . . . . . . . 462 11.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 11.2.2 Stresses to be considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .462 11.2.3 SN-curves and joint classifications . . . . . . . . . . . . . . . . . . . . . . . 463
    • Contents 11.2.4 Thickness effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 11.2.5 Fatigue failure criteria inherent the SN-curves. . . . . . . . . . . . . . . . 468 11.3 Stress concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 11.4 Examples of fatigue design based on fatigue strength tests . . . . . . . . . . . . . 468 11.5 Fatigue design regulations based on crack growth rate tests and fracture mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 11.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .481 11.5.2 Crack growth parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 1 1 -5.3 Crack growth calculation for butt welds, cruciform joints and tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 11.6 Examples of crack growth calculation based on crack growth rate tests and fracture mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 11.7 Fatigue failure criteria in connection with repair of defects . . . . . . . . . . . . 495 11.8 Notes on damages and methods for making repairs . . . . . . . . . . . . . . . . . . 496 11.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 11.8.2 Repair and reinforcing methods . . . . . . . . . . . . . . . . . . . . . . . . . 497 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 Appendix A. Joint classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502SUBJECT INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
    • CHAPTER 1 OVERVIEW OF OFFSHORE STEEL STRUCTURES Torgeir Moan Norges tekniske hsgskole, TrondheirnABSTRACTThe main features of various types of offshore steel structures are outlined.Their construction and fabrication are discussed in relation to their fatiguestrength. Design requirements for offshore platforms are reviewed, with emphasison those concerned with structural integrity. The practical implications ofdesign requirements are shown, with a semi-submersible being used as theprincipal example. In particular, the factors that determine the relative im-portance of the fatigue design criterion have been discussed. Lessons learnt from service failures of structures are used to illustratehow fatigue failures may be avoided by proper design, fabrication and opera-tion.1.1 TYPES OF OFFSHORE STEEL STRUCTURES1.1.1 System layoutsFig. 1.1 shows typical floating and bottom supported offshore platforms.All these structures are made of steel, except the one in Fig. 1 . l e, which is aconcrete platform with a steel deck. Semi-submersibles, or column-stabilized units differ radically in appear-ance from traditional vessels. They have a platform or deck area that mightbe square, rectangular or triangular in general configuration. This platformis supported by columns connected to large underwater displacement hulls,or it is mounted on large vertical caissons. The basic purpose of this design
    • Section 1.1.1Fig. 1.1 Selected offshore structures. a) Semi-submersible platform; b) Tension leg platform; c) Buoy- type platform; d) Jack-up; e) Gravity platform; f) Jacket; g) Steel tripod; h) Articulated tower; i) Guyed tower.
    • Section 1.1.1t--I- I t ?
    • Section 1.1.1is to reduce the effects of wave forces by locating the major buoyancy mem-bers beneath the surface and therewith the wave action. Sufficient stabilityis provided by the columns. Their operation displacement ranges from 15 000-30 000 metric tons. The ratio between minimum (transit) and maximum dis-placement is 112 - 213. Several semi-submersible designs have the basicfeatures displayed in Fig. 1.1 a - b, with a deck supported by two rows ofcolumns, each connected to a "longitudinal" pontoon. The slender bracingarrangement varies. Semi-submersibles are commonly used in exploratorydrilling, but also serve as production units in "marginal" oil fields. The buoy-type platform in Fig. I . 1c is self-explanatory. Floating platforms are kept on location either by a conventional spreadmooring, or a taut mooring system or a dynamic positioning system. Up tonow spread mooring systems consisting of 6-12 lines with anchors at the endshave been used. The tension leg platform, Fig. 1.1b, is a semi-submersible typeplatform with buoyancy that exceeds its weight, and hence causes a pre-tension force in the vertical cables. The first tension leg production platformwas installed in the Hutton field in the summer of 1984. The jack-up is characterized by 3-4 (or more) legs that can be loweredto serve as bottom support, see Fig. 1.ld. The main platform deck will thus beraised out of the water on location during drilling. However, the deck unit iswatertight and has buoyancy and stability to serve as a transport unit withelevated legs during ocean or field transit. The legs may be pipes perforatedwith holes, or a truss-work. The jack-up is commonly used as a drillingplat form. A (concrete) gravity platform essentially consists of a large cellularcaisson supporting 3-4 towers with a deck on the top, see Fig. 1.1 e. To date,the upper part of the superstructure has been exclusively a steel grillage,built of plate girders or as a truss-work, the main reason being the desire forlow self-weight during tow-out. This makes it possible to install more equip-ment before tow-out, and thus reduce the offshore installation time. Thebasic concept of the gravity platform is to attain stability in the permanentlocation without special piling. The jacket or "template" platform is a truss-work tower consisting oftubular members with a deck on the top and piles into the sea-bed, see Fig. 1.1 f. The deck loads (and environmental loads) are transferred to the founda-tion through the legs, of which there may be 4 to 16. The legs are stiffenedby a bracing, w h c h will also carry resultant horizontal forces. Most of thesome 2500 jackets in the world are located in shallow waters. There are onlyabout 50 in water depths over 100 meters.
    • Section 1.1.1 Smaller jackets are transported to the field location on a barge andlifted into position by a crane. Heavier jackets are towed self-floating andpositioned by a weight-buoyancy system. The large legs on one broad-sideof the jacket, illustrated in Fig. 1.1 f, served as buoyancy volume during tow-out. The installation phase is sensitive to the weather, and several weeks mayelapse before the structure is safely pinned to the sea-bed. As an alternative to the conventional truss-work platform, steel orconcrete tripod platforms have been suggested for deep water applications,Fig. 1.1 g. The use of inclined legs makes the global transfer of wave loadsto the seafloor very effective, mainly by axial forces. The articulated tower shown in Fig. 1.l h, consists of a deck, a buoy-ancy chamber and a load bearing truss-work structure linked to the sea-bedby a joint. Alternative structural layouts are envisaged. So far, this type ofplatform has been used as loading buoys, but its potential as a productionplatform is being investigated. The guyed tower in Fig. 1.1i is a truss-work tower resting on a spud can(or piles) and is moored by some 20-24 pre-tensioned cables. A buoyancychamber located below the mean water level may be used to relieve the spudcan or piles of some of the vertical loads. The first guyed tower has beensuccessfully installed in the Lena field of the Gulf of Mexico. T-joint Y -joint K-joint Heavy wall can joint D T joint Fig. 1.2 Simple tubular welded joints. a) Simple plane joints; b) Multiplane joints.
    • Section 1.1.21.1.2 JointsOffshore steel structures are commonly composed of thin tubular membersbecause their closed sections provide buoyancy and high torsional rigidity,minimum surface for painting and corrosion attack, simplicity of shape andpleasing appearance. In submerged parts of the structures, circular tubesare preferred because they result in smaller hydrodynamic forces than mem-bers with square cross-sections. However, fabrication is easier for the lattertype. Above the splash-zone, hollow rectangular sections or other sectionalshapes may be used. Colu shell a)I II I I Fig. 1.3 Welded joints of circular tubular members.
    • Section 1.1.2 Possible ringstiffener/bulkheadFig. 1.4 Transition components for a) small diameter tubes and b) large dia- meter tubes. Possible vertical T-shape stiffeners are not shown. Welded Cast Fig. 1.5 Difference in layout of a) welded and b) cast tubular joints. Fig. 1.2 a shows typical configurations of tubular joints for memberslying in one plane. In Fig. 1.2 b more complex three dimensional situationsare displayed. Depending on the relative diameters of the members and theirplate thicknesses, stiffening of the joint may be used. The simplest form ofstiffening is to increase the plate thicknesses in the joint area. Other possi-
    • Section 1.1.2Fig. 1.6 Various types of welded joints. a) Between tubes with rectangular cross sections, b) and c) between plates, d) attachment welds.bilities include the use of internal bulkheads and stiffeners as shown in Fig.1.3. Fig. 1.3 a shows a layout applicable when members of very different sizesare to be joined. Fabricating joints with internal stiffeners obviously requiresa minimum space and thus a minimum diameter of the tubes. Sometimes, a transition component is introduced between the memberand the joint itself. This may be done to increase the diameter or t o change
    • Section 1.2.1the cross-sectional shape as shown in Fig. 1.4 a. Ring-stiffeners may be intro-duced at the juncture between the circular tube and the transition compo-nent. Cast joints may be used instead of joints built-up by welding, Fig. 1.5.The advantage is that the geometry may be smoothly shaped to keep stressconcentrations low. In the connection between the column and pontoon inFig. 1.3 b, a cast piece was used to reduce stress concentrations and avoidwelds in the highly stressed region. However, costs and proneness to brittlefracture are disadvantages that should be considered. Rectangular members may be joined as shown in Fig. 1.6 a, possiblywith internal stiffening. Such joints tend to be planar joints or complex jointsin planes which make right angles to each other. Members having equal widthsand lying in one plane can be effectively joined as shown in Fig. 1.6a. Jointsbetween rectangular tubes may offer advantages with respect to analysis andfabrication. Various joints between plates are shown in Fig. 1.6b and c. Other struc-tural details may have to be introduced in offshore structures for differentreasons. Holes for penetrating pipes, water drainage, attachment of anodes,etc. are examples of such details, Fig. 1.6 d.1.2 DESIGN REQUIREMENTS1.2.1 General remarksIn general, a structure is designed so as to serve its function with an adequatesafety and economy. For instance, the main layout (pontoons, columns,deck) of a floating platform as shown in Fig. 1.7 used in drilling operations,is determined by the requirement for a stable platform having a large deck-load capacity combined with limited motions, sufficient mobility and overallstrength. To fulfill most effectively the requirements of structural strength, itmay be necessary to introduce bracings or other members. The local layout,i.e. the plate thicknesses, use of brackets etc. and materials, are determinedon the basis of strength, fabrication and inspection, and maintenance require-ments. Strength criteria refer to failure modes such as rupture by overloading,or to fatigue failure of individual structural components or by the progressivefailure of the system. Rupture may occur as an unstable fracture or a ductilebuckling.
    • Section 1.2.1 Fig. 1.7 Semi-submersible drilling plat form. Unstable fracture, which reveals itself as a fishbone pattern (Fig. 1.8a),is primarily avoided by proper selection of material qualities, depending uponambient temperature, plate thickness and triaxiality of the stress pattern(Refs. / 1/, 120. A ductile collapse occurs by excessive yielding or buckling(Fig. 1.8 b) under a single extreme load. A fatigue failure is caused by the cumulative effect of many loadcycles (Fig. 4.8). The region surrounding the origin of the fatigue fracturehas a smooth, silky appearance. As the crack progresses, the texture becomesrougher. Careful examination of this smooth part frequently reveals con-centric rings or beach marks around the fracture nucleus. On a microscopiclevel, lines corresponding to each load cycle or group of cycles may be ob-served (Fig. 4.8). Design criteria for ductile collapse and fatigue may be stated moreexplicitly in terms of stresses (load effects) caused by the external loadson one hand and the capacity of the structural components on the other.Before stating these criteria, a brief description of loads and load effects isprovided. A full discussion is given in Chapter 2.
    • Section 1.2.2Fig. 1.8 Appearance of overload failures. a) Unstable fracture surface (Ref. 131); b) Ductile collapse of a cylin- der (Ref. 141).1.2.2 Loads and load effectsLoads on platforms mainly consist of two categories: - Functional loads due to steel weight, ballast, deck loads, and the reac- tion forces: Buoyancy for floating platforms, and foundation reactions for fixed ones. These loads are quasi-static (slowly varying over time). - Environmental loads due to waves, currents and wind. The correspond- ing reaction forces are primarily inertia forces due to the dynamic wave and wind forces, mooring forces due to steady currents together with wind forces for floating platforms, and foundation reactions for fixed platforms.
    • Section 1.2.2 The forces and stresses due to external loads are commonly determinedby separately calculating their local and global effects. For instance, theeffect of the distributed hydrostatic pressure on the pontoon plate, stiffenersand frames of the semi-submersible in Fig. 1.7 are determined by consideringthe direct pressure on the pontoon plates. In addition, the hydrostatic pressureyields a resultant load per unit length of the pontoons , i.e. the buoyancy,which will balance the own weight of the platform. The global behaviour of most types of platforms, such as semi-submer-sibles and jackets is determined by using a frame model of the platform.The functional loads are directly applied t o the frame. The wave (and wind)loads fluctuate in a stochastic manner. However, experience has shown thatthe extreme effects (stresses, forces) due to waves can be determined accu-rately enough by the so-called design wave method. The wave forces arethen determined with the platform in a regular extreme wave of appropriatelength and height. In practice, several design wave load conditions (waveheight/-length, direction) have to be applied to obtain the maximum forcesand stresses in each member or joint. Fig. 1.9 a shows how the stress may vary at a weld joint in an offshorestructure. In welded structures it is the stress reversal o r stress range, Ao, thatcauses the crack to grow. Normally, the effect of the sequence of the rever-sals is not accounted for. Therefore, the stress history in Fig. 1.9 a may be re-presented by the number of cycles, ni associated with each stress range inter-val [noi; Aoi + A(Ao)] in a time period T, as shown in Fig. 1.9 b. If the time period is long e.g. several years, a probability density func-tion fA,(Ao) may be defined on the basis of relative frequency and informa-tion of the type given in Fig. 1.9 b. Time Stress r a n g e Ao Fig. 1.9 Fatigue load effects. a) Stress history; b) Frequency of stress ranges.
    • Section 1.2.3where No is the number of stress cycles in the period T. For many marinestructures, fA,(AO) can be closely represented by the Weibull distribution:where: h = Aoo /[ lnNo 1 = the scale parameter (1.3) Aoo = expected maximum stress range in the period T p = the shape parameter 0 is a good indicator for the relative importance of the stresses inducingfatigue and those inducing overload in the structure. This is because P indi-cates the relative magnitude between the stress occurring once in the lifetimeof the structure and stresses occurring, say, lo4 times within the same life. The Weibull distribution Eq. (1.2) has been generally verified, but theparameters p and h (or Aoo) have yet to be determined. For a wide class of semi-submersible platforms, P varies in the range 1.0 to 1.2. If Aoo is determined conservatively by a design wave approach,0 can be assumed equal to 1.0. Hence, when the extreme wave load effect,i.e. the stress oo, at a weld joint has been determined as mentioned above, theextreme stress range Aoo is obtained as 2u0. The value of the shape parameter 0 is further discussed in Sec. 10.6.2.More information regarding P and Auo is available in Refs. /5/and / 6 / .1.2.3 Ultimate strength design checkAs previously indicated, the occurrence of unstable fracture due to over-loads is avoided by proper selection of material properties, weld layout,welding procedures etc. Criteria for ultimate ductile failure are usually expressed by a loadeffect Q, in terms of a stress resultant or stress, due to the various types ofloads, and the associated strength R of the structural component. The charac-teristic strength, R , is required to be greater than the characteristic load ,effect, Q,, by a certain safety factor 7
    • Section 1-2.4 The characteristic value of the strength R, is determined as a valuewhich R will exceed in 95-98% of the cases. Characteristic values of thefunctional loads are specified values, and characteristic values of environ-mental loads correspond to an occurrence on the average once every 100years. The safety factor y is introduced to ensure that failure does not occurtoo frequently, due to the inherent uncertainties in Q, and R,. For, e.g. abrace in axial tension or compression, the design check in terms of stresses,is simply (Ref. / 1/) :where o, and o,, are the load effect (axial stress due to external loads) andthe strength, respectively. For tensile stresses o,, = Re (yield strength). Forcompressive stresses o,, decreases with increasing slenderness ratio, A, due tobuckling. Here, h is L/ri, where L and ri are the buckling length of the braceand radius of inertia of its cross section, respectively. In many cases a more general design check than Eq. (1.4) must beapplied. For instance, when a brace is subjected to both axial stresses due toan axial force (0,) and bending moments (ab), the design check for a semi-submersible drilling platform may be stated as (Ref. /I/): k o, + ob < Y Re - 1 where k = Re/oUaThe stresses o, and ob are obtained for an extreme load condition, i.e. by adesign wave approach. For production platforms, slightly different formats for design checksare applied (Ref. 121).1.2.4 Fatigue design checkThe fatigue phenomenon.Fatigue fracture goes through three stages: initiation, slow growth, and onsetof unstable fracture, see Refs. 171 and 181. Fatigue cracks usually originateat the surface. Once a crack is initiated, it grows slowly as the stress cyclesare repeated, even if the stress level is below yield. In offshore structures thecyclic stress variations are primarily caused by waves and wind loading. Whenthe crack size becomes critical, an unstable fracture occurs. In welded structures fatigue cracks almost always start at a weld defect,and the growth period accounts for more than 90 percent of the fatigue life. The crack growth depends on the stress conditions at the crack tip asfurther discussed in Secs, 3.2 and 4.1. The crack grows when opened by ten-sile stresses. Under a compressive loading the two surfaces may be forced into
    • Section 1.2.4 b V) E *- V) v, - - : R e v e TimeFig. 1.10 a) Stress variation due b) Stress variation due to external load- to external loading. ing and extreme residual stresses.contact and can then transmit forces without activating the notch at thecrack tip. It is still a matter of discussion whether a compressive stress (i.e.below the time axis in Fig. 1.10a) should be considered to contribute to thefatigue damage. In the presence of residual tensile stresses it is the combinedstresses due t o fabrication and external loads that matter. Residual stressesadjacent to welds are commonly assumed to be tensile and amount to yieldstress level. In the case of a one dimensional stress condition, the yield stress repre-sents the upper limit of stress, and a constant amplitude loading will thenresult in stress variations adjacent to a weld, as shown in Fig. 1.10 b. In thiscase Ao will be the significant parameter to describe the time variation of thestress. In weldments with careful stress relief treatment and in cast nodeswhere initiation will contribute to the fatigue life, the mean stress om mayalso be a fatigue load parameter. The fatigue crack propagates in a direction normal to the maximumprincipal (tensile) stress. This has been observed by comparing fracturedstructures and calculated stress distributions. Fatigue crack growth follows different laws depending upon the levelof the stress reversals. We therefore distinguish between: - low-stress, high-cycle fatigue - high-stress, low-cycle fatigue Fatigue failures that occur after only 1O4 to lo5 cycles are usuallydenoted low-cycle. The endurance in high-cycle fatigue is usually severalmillions cycles. Since only the latter phenomenon has been of real concernin offshore platforms t o date, this section will be concerned with high-cyclefatigue.
    • Section 1.2.4 The fatigue capacity of a welded joint subjected to constant amplitudeuniaxial loading, is expressed in terms of an SN diagram. For welded structures the SN-curve is independent of the yield strength.This is because welded joints contain crack-type defects and the fatigue lifeconsists of crack growth, which is independent of the yield strength. The crack growth depends on the very local cyclic stress at the cracktip. Hence, fatigue is governed by the geometry, especially any change in thegeometry which introduces a concentration of the stress flow. The geome-trical effects associated with the weld profile and inevitable weld defectsare normally accounted for in the SN (capacity) data. Other geometricaleffects should be considered in the calculation of local stress ranges, see Fig.1.1 1. The effect of geometry on the local stress is further discussed in Secs.4.6.3 and 10.2.4, and in Chapter 8 for tubular joints. Plate a) Ring I stiffen-LA A-A LA A -A b Plate thickness Crack o r undercut c)Fig. 1.11 Stress concentrations due to macroscopic changes of geometry. Order of magnitude of concentrator: a) Plate widthlmember dia- meter; b) Fraction of plate widthlstiffener height; c) Plate thick- ness.
    • Section 1.2.4Failure criterion - variable amplitude loading.The failure criterion is commonly expressed by the Miner-Palmgren hypo-thesis aswhere the cumulative damage, D, is determined on the basis of the number ofcycles, ni, in the local stress range interval between Aoi and A U ~ +Ni .is the ~number of cycles to failure at stress range A u ~ +according to the SN-curve. ~ , ~S is a constant of magnitude between 0.5 and 1.O.Design check.The fatigue design check may be performed with a different degree of refine-ment, namely : 1. Judgement, more or less qualitative, based on experience. 2. Calculation of acceptable fatigue life based on the SN Miner-Palmgren approach. 3. Fracture mechanics analysis. As discussed earlier, the first approach should be used with caution, ifit is not supported by significant quantitative experience from similar cases.Underestimation of the fatigue hazard has led to several accidents. The second method may be expressed as: Bearing in mind the uncertainties in the factors involved in Eq. (1.8),the acceptable cumulative damage A is chosen as a value smaller than 6 toensure an adequate margin of safety. Eq. (1.8) may be approximated by assuming that ni is represented byEqs. (1.1 a) and (1.2) and by using an SN-curve of the formThe result for the damage:where No is the number of cycles in the design life of the structure (e.g. 20or 50 years), Aao is the expected maximum value of the stress range in thedesign lifetime, and I( ) is the gamma function. Clearly, Eq. ( 1.lo) is based on approximations and should be used withcaution.
    • Section 1.2.5The format expressed by Eq. (1 .lo) may be reformulated aswhich resembles Eqs. (1.5) and (1.6) for the ultimate limit state (ULS) check.The principal differences are that Eq. (1 .l Oa) refers to an extreme stress rangedue to wave and wind loading, while Eqs. (1.5) and (1.6) involve extremestresses due to functional as well as environmental loads. Furthermore, Eqs.(1.5) and (1.6) refer t o nominal stresses in braces due to beam theory whilethe stress range in Eq. (1 .lOa) includes the magnification due to local changesin the geometry. Finally it is noted that Oo will depend on the shape para-meter, p, of the distribution of stress-ranges, and hence the total load history. As in the ULS check, a characteristic value of Ni is applied in Eq. (1.9).Usually, SN-curves corresponding to a probability of 97.5% of survival areused. ni in Eq. (1.8) is taken as the expected long-term distribution. Thevalue of A is chosen such that the probability of failure due to the uncertain-ties of ni and Ni in Eq. (1.8) is acceptably small. In practice, A lies between0.1 and 1.0. The third approach by fracture mechanics may be viewed as a refine-ment in the determination of Ni in Eq. (1 3).1.2.5 Progressive failure design checkProgressive failure may develop after a local damage if the structure has littlereserve strength. The initial damage may be ductile collapse due to collisionor other abnormal loads; or it may be a fracture due to fabrication faults, ora fatigue fracture. Since it can obviously take some time before such damageis detected and repaired, the structure ought to survive a certain period oftime in the damaged state. The philosophy applied by e.g . the Norwegian Petroleum Directorate(NPD), Ref. 121, for production platforms is that system failure should notoccur due to local damage. The design check is accomplished by assuming acertain degree of damage, as specified in the code, and primarily applyingan ULS type criterion to check that there is adequate strength to resist theloads acting on the structure in the damaged condition. The loads used inthe residual strength check depend upon the anticipated time to repair.As repairs are often only possible in the summer, the structure should survivea winter storm. The NPD specifies environmental loads that occur once in 100 years. However, the required safety factors are less than in the ordinaryultimate strength check and generally equal to 1.O.
    • Section 1.3.1 The "Alexander L. Kielland" accident initiated progressive strengthcriteria for semi-submersibles and other mobile platforms classified by Detnorske Veritas. Semi-submersibles are hence required to have adequatereserve strength after the failure of any one brace. In this case environmentalloads with an annual occurrence and a safety factor of 1.2 are applied.1.3 PRACTICAL IMPLICATIONS OF DESIGN CRITERIAIn this section the influence of fatigue criteria on layout, dimensions, localdetailing of structural components and on materials selection will be dis-cussed.1.3.1 Semi-submersiblesIn the design of semi-submersible platforms for exploratory drilling opera-tions in the North Sea (Fig. 1.7), the overall layout is determined on thebasis of requirements to floatability/stability, limited motion and strengthfor resisting progressive failure. The scantlings of the deck, columns and pontoons are governed byultimate strength criteria. For the braces the situation is different as fatiguecriteria may be important. The procedure will normally be first to determinethe plate thickness of the braces so that the ultimate strength requirementin Eq. (1.6) is fulfilled, and thereafter check for fatigue. The typical locationsinvestigated, by applying formulas like Eq. ( 1.1O), are : - the brace to column connections - possible transitions in cross-section properties - longitudinal or transversal stiffeners on the braces - cut-outs for equipment, port holes etc. - attachments for equipment If the fatigue criterion is not satisfied, one or more of the followingremedies may be applied : - change of overall layout to reduce the fatigue loading - increase of overall plate thickness in the brace or at areas with high local stresses, or introduction of stiffeners - make the local geometry more smooth, e.g. by applying: brackets at hard points fully penetrated welds rather than fillet welds grinding butt welds and the toes of fillet welds
    • Section 1.3.1 Deck / I ? - Column 0 - - - A - W a v e length I I Fig. 1.12 Semi-submersible platform subjected to a regular beam wave. To illustrate that the overall layout may have an important effecton the fatigue loads and hence the susceptibility to fatigue cracking, con-sider the platform shown in Fig. 1.12. Extreme waves occurring once in 100years, may be 30 m high, and about 400 m long with a wave period of 16 s.Waves that induce fatigue occur more frequently, and have lengths of 100 mto 220 m and periods of 8 to 12 s. The extreme stresses in platforms do not necessarily occur for extremewaves, hence, the condition shown in Fig. 1.12 can often be the most criticalfor the horizontal braces in semi-submersible plat forms. The length of thewave in Fig. 1.12 is 100 m, and occurs quite frequently, so in this case theamplitude of the stresses, occurring many thousand times, will not be verymuch less than the one occurring once during the lifetime. Therefore, thefatigue criteria rather than ultimate strength criteria will dominate for thesebraces. However, the significant change of main dimensions required to achievereduced fatigue loads introduces other disadvantages, e.g. regarding thestrength of the deck. This approach is therefore practised rarely in semi-submersibles, though in other types of platforms, such as jackets, the choiceof layout to limit fatigue loads is of more interest (Ref. 191). If it is assumed that an increase in plate thickness affects the nominalstress level and not the stress concentration, then an increase in plate thick-ness by a factor of a will reduce the fatigue damage, D, by a factor a-0.75m,where m lies between 3 and 5. Hence doubling the plate thickness, resultsin a D which is between 20% and 8% of the reference value. The reductionwill be greater if the possible effect of increased plate thickness on the stressconcentration is considered. If larger plate thicknesses are introduced for
    • Section 1.3.1fatigue reasons, it is also natural to use steel with a lower yield strength, Re.This is because the fatigue strength does not depend upon the yield strength,and the ultimate strength criterion, Eq. (1.6), will be satisfied by a lower Rewhen o, and ob are reduced by increased thicknesses. Also, steels with loweryield strengths usually have better weldability. The extra steel weight inbraces does not represent a serious penalty because their centre of gravityis low. However, increased thicknesses themselves may cause weldabilityproblems, and imply more costly fit-up, welding and welding procedures. By smoothing the geometry as shown in Fig. 1.13, the stress concen-tration factors (SCFs) are reduced. A reduction of SCF to SCFIa implies areduction of the fatigue damage from D to D/am. According to recent fatigue codes (Ref. /8/), grinding of the weld toeimplies a reduction of D by about 50%. However, grinding should preferablynot be used as a design measure but rather kept as a last resort of improve-ment after fabrication when for any reason tlus would be necessary. Such a G r o u n d flush Im l m proved M l m proved l m proved Improved P l a t e a i s continuous l m proved through p l a t e bFig. 1.13 Improvement of fatigue life by changes of geometry. a) Butt weld, b) fillet weld, c) plates, d) plane plates in a 3-D joint.
    • Section 1.3.1measure might be accepted by the authorities, but the benefit might not makeup for the costs. Different methods for improving the fatigue strength ofwelded joints are discussed in Chapter 6. When fatigue requirements, with A in Eq. (1.8) equal to 1.O, are im-posed on braces in actual semi-submersibles which have been designed tofulfill ULS requirements, the results have been increases of plate thicknessesby as much as 50%, local smoothing of brace-column connections by bracketsand cut-outs (Fig. 1-13), and improvements of the weld geometry and quality. As the requirements have been tightened recently, changes on existingplatforms have also been undertaken, obviously at much higher costs thanwhen implemented during the initial design and fabrication.1.3.2 Tension leg platformsFor tension leg platforms (Fig. 1.1 b), fatigue criteria in particular may in-fluence the layout and scantlings relating to the pontoon-column connec-tions. In the Hutton platform in the North Sea, fatigue requirements with Ain Eq. (1.8) equal to 1.O, were governing for in-board sections of the columnshell and the pontoon (Ref. /lo/). As in the case of semi-submersibles, it wasfound that relatively short waves, with periods of 10 to 12 s, were equallyimportant as the extreme 100 year wave of greater length. The fatigue crite-rion led to a 10% increase of steel weight of a hull designed according ULScriteria. In addition, fatigue considerations implied careful design of geome-trical transition areas and weld connections together with restrictive fabri-cation procedures and control. A special design feature that evolved from the fatigue analysis was theintroduction of a cast steel transition piece as shown in Fig. 1.3 b. The objec-tives of this were to : -improve the stress concentration - move critical welds away from the hot spots - solve the geometrical problem of tapering the curved pontoon to the column shell. - improve the SN weld class in the area The cast joint improved the fatigue life by a factor of 9 compared t oa conventional welded joint.1.3-3 JacketsIn the design of the Mau jacket platform offshore New Zealand (Ref. 11I/), thefatigue criterion was found to increase the weight of the jacket by about 4%.
    • Section 1-4.1For North Sea jackets in up to 180 m water depths, such as the Murchisonjacket (Ref. /12/), fatigue governs plate thicknesses in some joints. For mostplatforms in the Gulf of Mexico, fatigue criteria are not governing becausethe wave climate is dominated by rarely occurring hurricanes, which inducelarge extreme loads, but few stress reversals. However, for the Cognac plat-form in 300 m of water, fatigue had some influence on the design of sometubular joints due to dynamic magnification of the response (Ref. 191). In the first two cases mentioned above, the A in Eq. (1.8) was setequal to 1 .O, in the latter to 0.5. If A is reduced to 0.1 for joints wherefatigue is governing, then the plate thickness must be increased by 30-50%. Increasing the thickness may cause fabrication problems and stiffeners mayhave to be used.1.4 LESSONS LEARNED FROM FATIGUE FAILURES1.4.1 General remarksWe learn more from failures than successes. The phenomenon which is todayknown as fatigue was itself discovered prior to 1850 by observing railwayaxles failing without apparent cause. The understanding of the phenomenonwas brought a big step forward by Wohlers intensive and systematic studiesin the 1850s. Many times afterwards the fatigue phenomenon has been moreor less rediscovered for various types of structures, i.e. bridges, ships, aircraftand offshore platforms. In the popular literature, Kipling was presumably the first to exploitthe dramatic possibilities of fatigue. In "Bread Upon the Waters" in 1895he described how the Grotkau lost a propellor due to a fatigue crack in thetailshaft. Kipling went out of fashion, but public interest in fatigue was re-viewed in 1948 by Nevi1 Shutes "No Highway", a few years before the threeComet aeroplane disasters, which were initiated by fatigue cracks. We can still learn from fatigue failures. For instance, the appearanceof the crack surface may provide information about the rate of crack propa-gation. On the microscopic level the distance between striations, which aremarks set up by each load cycle, may give such insight. In case of variableamplitude loading, beach marks on the crack surface may also give clues tothe load history and crack propagation rate. Another source of information is the location of crack initiation,which may be roughly determined from the beach mark pattern (Fig. 4.8).Both the shape and size of the weld defect initiating the crack and the sur-rounding geometry may contribute to the understanding of how the failurehas been affected by factors relating to design and fabrication.
    • Section 1.4.2 Only in relatively few cases has the physical cause of the failure, e.g.,the type of cracking (hydrogen induced, lamellar tearing, fatigue, stress corro-sion, brittle fracture) been determined. This information can only be revealedwhen there is access to the fracture surface. The crack appearance on theplate surface does not even allow judgement as to whether the crack is fatigueor otherwise. Where it is possible for repairs to be effected in situ, failures are fre-quently not removed from the installation for investigation, so that eitherno specific cause is recorded, or where the cause is stated, its veracity mustbe open to question. In certain cases, removal of the failed parts for investi-gation may enhance the existing hazard or create a new one. In any case,establishing the causes of failures frequently requires quite extensive andlaborous investigations in competent laboratories, together with reanalysesof fatigue loading etc. Some case histories and more general experiences regarding fatiguefailures are briefly described in the following section.1.4.2 Fatigue failuresSemi-submersibles and jack-ups.An early example of fatigue damage occurred in the original "Sedco 135",a triangular semi-submersible drilling rig, illustrated in Fig. 1.14 a, whichbegan working in the Gulf of Mexico in 1965. By the end of 1967 fatiguefailures were experienced in an aft horizontal brace in the same type of rigsoperating in the North Sea, the South China Sea, the Canadian Pacific Ocean,and offshore Australia. The North Sea case is particularly illustrative, becausethe axial stress in the failed horizontal member was recorded during the fewmonths before failure. The stress concentration factor measured on the proto-type was 4.7 for the critical cylinder-to-flare knuckle transition. A cumula-tive fatigue damage calculation using curve X in AWS Code Dl .l-72 yields aMiner-Palmgren damage ratio of 2.18 for the North Sea platform (Ref. 1131).By using the mean value of more recent SN data, the expected damage ratiois found to be nearly an order of magnitude less than shown in Ref. 1131.Recognizing the scatter in fatigue life estimates, the above results imply areasonable correlation between calculated and actual performance. However,abnormal weld defects or other deficiencies may also have contributed to thefailure. This failure occurred in 1967 in a platform designed a few yearsearlier, at a time when fatigue design checks were not routine, and also be-fore the severity of the fatigue loading of the North Sea was fully recognized. Other examples of occurrences of cracks which were published early,appear in Refs. / 141 and / 151.
    • Section 1.4.2 In May 1979 the jack-up drilling rig "Ranger I" (Fig. 1.14b) collapsedin the Gulf of Mexico (Ref. /16/). The accident occurred because a crackinitiated and propagated in the aft leglstiffener weld and stiffenerlmat filletweld. The cracks were coincident with the leg/mat bulkhead and structuralbulkheads. This suggests that considerable rigidity in this region resulted instress concentration. The approximately 500 mm long fatigue crack appa-rently developed at position 270 and to a lesser degree at position 90° inthe course of the lifetime of the structure, and led to the collapse of the leg,with the subsequent falling down of the aft deck, and bending and separationof the forward legs. Crack indications were also observed near the same loca-tions on the forward legs. The fatigue crack already existed when the plat-form entered a shipyard for repairs three months before the accident, butremained undetected. The rules of the Classification Society involved, wereamended subsequent to the accident, demanding non-destructive testing ofcritical connections of support legs at periodic intervals. In March 1980 the accomodation platform "Alexander L. Kielland"(Fig. 1.14 c) with 2 12 men onboard capsized in the North Sea (Ref. 1171).The primary reason for the accident was the failure of a brace mainly due toa fatigue crack starting from a hydrophone support, followed by a rapid,unstable fracture. The fillet welds between the hydrophone support and thebrace had a poor shape. Inspections had been performed during fabricationas well as during operation without discovering the 70 mm long cracks presentalready at the time of fabrication. Fatigue life calculations have been carriedout based on Miners rule as well as on the Paris equation, and the fatigue lifeof the brace could be verified within reasonable limits of uncertainty. Frac-ture mechanics analysis showed that the crack growth in the brace had accele-rated very quickly from the initial stage. With a through-thickness crack ofabout 30 mm length, the remaining life of the brace was found to be lessthan one year. Cracks were observed at hydrophone supports in other rigs ofsimilar design during inspections after the accident. The failure of this brace was rapidly followed by the failure of otherbraces supporting column D. The subsequent loss of column D led to floodingand capsizing within 20 min. It is noted that also the design of this platform was conceived in the 1960s when fatigue design checks were not as routinely done as they aretoday. However, when the actual platform was built in 1975-76, the generalpractice in the offshore industry regarding fatigue design check was different.But no fatigue checks had been made for "Alexander L. Kielland". Besides the above cases, where members actually parted, several cases of
    • Section 1.4.2 /F o r w a r d I 6 9 A f t horizontal ,Plate o f brace D 6 marks Drainage /hole rnm - F i l l e t weldFig. 1.14 Mobile platforms suffering fatigue failures. a) "Sedco 135" (Ref. 1131); c) "Alexander L. Kielland" (Ref. 1171).
    • Section 1.4.2 F r a c t u r e i n a f t leg - m a t connection Fig. 1.14 b) "Ranger I" (Ref. /16/).cracks have been detected in semi-submersible and jack-up platforms (Refs./18/ and /19/). Most cracks have been repaired without further examinationand circulation of information. For instance, Lloyds list contains only oneof the many cracks detected at brace-leg connections, manholes etc. duringthe extraordinary surveys carried out especially on rigs in the North Seaafter the "Alexander L. Kielland" accident. This incident was, however,widely published in the press. There are incidents that ought to have been reported and investigated,but were not. For instance, it is known that in a number of semi-submer-sibles, weld failures were so extensive that the safe operation of the rig wasin jeopardy (Ref. / 181).
    • Section 1.4.2Jackets.A case of partial failure of a fixed offshore platform in the North Sea isreported by Harrison (Ref. 1201). A plan view of the platform, a tubularstructure with four legs joined by sundry tubular bracing members, is illu-strated in Fig. 1.15 a. The failure involved the complete failure of threejoints between the diagonal bracing and the main legs situated at a levelapproximately 0.6 m below the lowest astronomical tide level. Fig. 1.15 ashows the location of the fractures and cracks. At corners A8, A9 and B9, the300 mm dia. 12 mm thick bracing tubes were completely detached from thelegs, the failures having occurred through the bracing tubes and initiatedat the toes of the tube-to-leg welds. At corner B8 the fracture had occurredin the leg material so that a disc of the leg had come off with the bracing.Cracks were also found at the crossing points of the diagonal members ini-tiating at the toes of the welds. The welds between the bracing tubes and thelegs were nominally full penetration welds made from the outside and builtup with external fillets of about 10 mm leg length. Observations of thefracture surfaces revealed that the fractures were initiated at the outsidecircumference at the weld toe, by low stress-high cycle bending in the verticalplane. Underestimation of vertical wave loads seems to be a cause of thefailure. Unusually large amount of marine growth surrounding the members,which had not been accounted for, was the main underlying cause. Themarine growth amounted to 200 mm at the time of failure, so that the origi-nal 300 mm dia. bracing tubes were increased t o 700 mm. Taking the marinegrowth into account, the fatigue life was calculated t o 4.5-5.5 years. Ref. /2 1/ reports recent Findings of fatigue cracks at two levels (-6 m,- 20 m) in the horizontal conductor frame of an eight-leg platform in 110 mwater depth, Fig. 1.15 b. Two reasons were found for the premature appear-ance of these cracks: Firstly horizontal wave forces had been fully consideredin the original design but only limited allowance had been made for verticalforces, which were now found to be significant. Secondly, the original ana-lysis used low stress concentration factors. A reanalysis was performed basedon the new SN T-curve proposed by DOE for tubular joints, and up-to-dateknowledge about loads and stress concentration factors. Good correlationwas obtained for many of the cracked joints. Other incidents of fatigue crack propagation are referred to in generalterms, for instance, in Refs. 1181 and 1231. Because these cases have beeninvestigated less, our knowledge is incomplete and yields little informationfor the present purpose. The files of the Norwegian Petroleum Directorate reveal that 163 .. , a---Aeue--m,.aes. -- I" "- ".- -- A " --e"""w"+m*
    • Section 1.4.2 Fracture Fracture plane C = Crack .-------. ----- --------- Crack - .-- ------. ----- --------Fig. 1.15 Jackets suffering fatigue damage. a) Horizontal truss-work of West Sole jacket (Ref. 1201); b) Hori- zontal conductor frame in eight leg platform (horizontal plane) (Ref. 1211); c) Typical cracked tubular joint.cracks, fairly evenly distributed over the water depth, were detected in 27North Sea jackets in the four-year period 1980-83. The actual number ofcracks may be greater, as only 5-10% of the nodes are inspected in a four tofive years cyclus. The cause of the cracks is hard to judge, but they are most
    • Section 1.4.2likely due to fabrication defects. Most cracks were found to be non-propagat-ing. In another survey (Ref. 1231) only 3 out of 33 cracks were reported topropagate. Also, most cracks are shallow and are easily repaired by grinding.Finally, most cracks affect secondary structures, such as the conductor framein Fig. 1.15 b. A particular case worth noting is of a crack that was initiated and grewfrom a sharp dent caused by collision. In another case, a severe offset andpoor weld between components which were assembled offshore, led rapidlyto failure. Finally it is observed that malfunction of the corrosion protectionsystem may lead to reduced plate thicknesses, and hence increased crackgrowth, or accelerated crack growth due to corrosion-fatigue. Such mal-functions of impressed current corrosion protection systems have beenexperienced (Refs. 1231 and 1241).Other structures.Fatigue failure experiences in other structures such as ships, bridges, towers,etc., may provide useful insight into the fatigue problem for offshore plat-forms. Due to the greater structural redundancy in ships, fatigue damage hasgenerally less severe consequences than in offshore structures. However,the economical losses may be considerable. It has been found that fatiguecracks are a dominating type of damage in ships, the total number beinglarger in oil tankers than in other types of ships (Ref. 1251). A very interesting survey of damages in large tankers is given in Ref.1261, where types and frequency of damages are related to hull areas andtypes of constructional details. Most damages occur in the midship part.Cracks in brackets, at bulkheads and at notches dominate, see Fig. 1.16 a.No case was found where a crack could be related to an internal weld defect,although a rather large number of internal planar defects had been found byNDT. The cause of the surface defects observed was bad workmanship, whichin many cases could be traced back to difficult working conditions for thewelders (bad access). In some cases poorly designed structural details withexcessive stress concentration had been the cause of cracking. Most crackswere initiated at structural discontinuities. Improvement in design practicehad reduced the earlier experienced rate of such cracks. Another extensive investigation by the American Ship Structure Com-mittee is reported in Ref. 1271. Over a long period Commission XI11 of the Int. Institute of Welding
    • Section 1.4.2Longitudinalstiffener, h, i Cracks I. Side shell Fig. 1.16 Cracks in ship details. a) Longitudinal-transverse stiffener connection, b) bracket in trans- verse frame. has collected information about fatigue failures in welded structures and their interpretation. Conclusions are drawn in Ref. 1281. The major part of failures are initiated at details of classes F, F2 and G according to Ref. 171. Details concerned are amongst others butt welds with backing bars, trans- verse and longitudinal fillet welded attachments, and load carrying transverse fillet welds. Incorrect design dominates as a primary reason, although other reasons such as bad workmanship and unexpected sources of fatigue loading may contribute to the failure. In particular, vortex shedding induced by a moving fluid has caused cyclic loading, and hence fatigue damage in bridges, offshore platforms, etc. Attention is drawn to the very high frequency in- volved. Fatigue failures can therefore occur, even if the damaging conditions are experienced only for short periods during either fabrication or delivery. It is further worth mentioning that fatigue cracks are rarely reported to start from internal weld defects. Several cases of fatigue failures in bridges are presented in Ref. 1291. A primary cause seems to be secondary stresses due to local bending, which have not been designed for. Large fabrication defects or cracks make up the next largest category of cracked members and components. Cracks occurring in planes parallel to the tensile stresses considered in the design, may not be
    • Section 1.4.3detrimental to the performance of the structure, provided they are discoveredand repaired before turning perpendicular to the tensile stresses producedby the loads on the structure. In several cases the defect was due to poorquality welds which were produced before non-destructive test methodswere well developed. A large number of these cracks occurred because thecomponent was considered a secondary member or attachment, so no weldquality criteria were established, nor were nondestructive test requirementsimposed on the weldment . For some bridges an increased traffic intensityalso increased the failure likelihood.1.4.3 Implications of service failuresDesign precautions.Fatigue crack growth especially occurs when the loading is predominantlydynamic, local stresses are relatively high, high-strength steels are applied,and when crack-type fabrication defects are likely. In some situations thedesign check may easily be overlooked, even if one or more of these factorsare present. Some examples of such situations will be mentioned in thefollowing. For instance, it should be noted that fatigue damage may be accumu-lated in temporary phases of the platform, such as during towing. In factsome components may be more stressed in temporary phases than in thein-service condition. Vortex-shedding phenomena may especially lead t o signi-ficant fatigue loads. Fatigue may occur even in components which are not introduced inthe structure for strength purposes, such as installation lugs etc. Cracks may grow even in areas where the stresses due to the externalloading are predominantly compressive, due to the presence of tensile resi-dual stresses. Fatigue depends critically on stress concentrations, and every effortshould be made to make geometrical transitions smooth and locate weldsoutside the areas of the highest stress concentrations. Use of cast componentsmay facilitate this objective. Fillet welds have often been the cause of fatigue failures because ofunderdimensioning of the throat thickness, and improper weld shapes. The local geometry (alignment of plates, shape of weld profiles, size ofweld defects) depends to a large extent on the execution of fabrication.The designer should have a realistic understanding of geometrical tolerancesand the use of them in the design calculations and specifications for fabri-cation, see Fig. 1.17.
    • - t I Unrealistic v Unrealistic r - Realistic Realistic Section 1.4.3 Un- realistic Stiffener % plate Section A-A Realistic Stiffener Gap Section A-A Fig. 1.17 Geometric tolerances. a) Plate connection, b) stiffened plate. It is important t o limit the susceptibility to cracking during fabricationand afterwards, including lamellar tearing, by specification of adequatematerials properties and fabrication procedures, to achieve good weldability.Choice of a simple layout is important because it simplifies the fabricationand inspection, and thus reduces the probability of defects. In some cases the design check is done simply by copying previousdesign practice. However, great caution should be exercised when this prac-tice is employed, since environmental conditions, material qualities, fatigueaccept criteria etc. may differ, compared with previous cases. The designer should not focuse just on the direct satisfaction of thedesign criteria, but should consider other factors that could affect the fatiguerisk indirectly. For instance, choice of layout is important for the accessduring fabrication. Good access is a necessary condition to avoid weldingdefects, as shown in Fig..l .l8. Also, overhead welding is more difficult andprone to faults than downhand or horizontal welding. Obviously access is also necessary to accomplish inspection. It is espe-cially noted that some regulations and codes for fatigue design include fatigueacceptance criteria, which are dependent upon accessibility. Specificationof fatigue prone areas which should be scrutinized during inspection, con-stitutes a part of the design documentation.
    • Section 1.4.3 J StiffenerFig. 1.18 Difficult access for the welding stick may increase the suscepti- bility to welding defects. a) Steel-plated structure; b) Tubular joint.Fabrication precautions.Clearly, the fabrication should closely follow the specifications. However,brackets and stiffeners are sometimes chosen with more material than speci-fied at the ends, because it might ease fabrication by reducing the weldingdeformations (Fig. 1.19). Such liberty in interpretation of the specificationsmight have a significant effect on the stress concentrations, and is not re-commended. Stiffener Fig. 1.19 Deviation between a) specified and b) as-fabricated details. The design specifications do not define all the factors that influencethe fatigue strength. For instance, start-stop positions of welds are decidedduring fabrication. As weld defects frequently occur at start-stop points,they should be located outside areas with high dynamic stresses as far aspossible. In general, the quality of workmanship plays an important role forthe fatigue life.
    • Chapter 1. ReferencesPrecautions during operation.During operation the main aspect of fracture control involves reliable detec-tion of cracks, judgement of their significance and the decision to repair. The time to failure of a cracked structure must be assessed by a fracturemechanics approach, or by experimental investigations. Repair of any damagemust be carefully planned with due consideration of possible defects andstress concentrations. Repair welds, particularly when made under water orin other difficult circumstances, are unlikely to be better than those thathave failed. Repaired cracked welds often fail again after a relatively shortperiod. Sometimes some form of reinforcement is applied, but this often hasthe effect of moving the point of failure from one location to another.REFERENCES 1. "Rules for Classification of Mobile Offshore Units", Det norske Veritas, Oslo, 1981. 2. "Regulations for the structural design of fixed structures on the Norwegian Conti- nental Shelf (with guidance notes), Norwegian Petroleum Directorate, Stavanger, 1984. 3. "The Alexander L. Kielland Accident", NOU report 1981:11, (in Norwegian with English summary), Oslo, 19 8 1. 4. Cottrill, A.: "Crumpled Frigg Jacket Begins to Recover its Lost Buoyancy: Offshore Engineer, May 1975. 5. Marshall, P.W. Luyties, W.H. : and "Allowable stresses for fatigue design", Proc. BOSS Conf., MIT, 1982. 6. Odland, J.: "Response and Strength Analysis of Jack-up Platforms", Norwegian Maritime Re- search, Vol. 10, No. 4,1982. 7. Gurney, T.R.: "Fatigue of Welded Structures", Cambridge University Press, Cambridge, 1979. 8. "Guidance on Design and Construction", 1977, with Amendment No. 8, Fatigue, Department of Energy, London, 1984. 9. Kinra, R.K. and Marshall, P.W. : "Fatigue Analysis of the Cognac Platform", Paper No. 3378, Proc. Offshore Techno- logy Conference, 1979.
    • Chapter 1 . References10. Ellis, N.: "Hutton Tension Leg Platform. Structural Design and Configuration", Proc. "Ocean Structural Dynamics Symposium", September 8.-10. 1982.1 1. Kallaby, J. and Price, J.B.: "Evaluation of Fatigue Considerations in the Design of Framed Offshore Structures", Paper No. 2609, Proc. Offshore Technology Conference, 1976.12. Hallam, M.G. et al.: "Dynamic .and Fatigue Analysis of Murchison Tower Structure", Paper No. 3163, Proc. Offshore Technology Conf., 1978.13. Marshall, P.W. : "Basic Considerations for Tubular Joint Design in Offshore Construction", Int. Con- ference on Welding in Offshore Construction, The Welding Institute, Newcastle, 26-28 February 1974.14. "Stricken rigs highlight checking weaknesses", Offshore Engineer, March 1975.15 . "Mobile platform, SPM repairs completed for Argyll Field", Ocean Industry, June 1978, p. 63.16. U.S. Coast Guard Marine Casuality Report No. USCG 16732193621, May 1981.17. Moan, T. et al.: "Analysis of the fatigue failure of the Alexander L. Kielland", ASME Winter Annual Meeting, November 1981.18. Burgoyne, J.H. et al.: "Offshore Safety", Report of the Committee, HMSO, March 1980.19. Carlsen, C.A. et al.: "Lessons Learned from Failure and Damage of Offshore Structures", 8th ISSC, Gdansk, 1982.20. Harrison, J.D. : "Partial Failure of a Fixed Offshore Platform", Int. Inst. of Welding, Doc. XIII-708-73, 1973.2 1. Green M.B. : "Experience with Fatigue Analysis and Inspection Results", Paper No. 4524, Proc. Offshore Technology Conference, 1983.22. "Safety and Offshore Oil", Committee on Assessment of Safety of OCS Activities et al., National Research Council, National Academy Press, Washington D.C., 1981.23. Sollie, T.: "Safety and Quality Assurance of Fixed Offshore Installations. In-service Experiences and Prospects after some 10 Years of Involvement", 6th European Maintenance Con- gress, Oslo, June 1982.
    • Chapter 1 . References24. "Repairs to North Sea Offshore Structures - a Review", UEG Report UR 21, London, 1983.25. Petershagen, H.G. et al.: "Report of Committee 111.1",8th ISSC, Gdansk, 1982.26. Kjellander, S. and Persson, B.: - "Hull damages further investigation and significance of weld defect", (in Swedish), STU-report 76-3948 and 77-4205, March 1980.27. Jordan, C.R. and Knight, L.T.: "Further survey of in-service performance of structural details", Ship Structure Committee Report No. 294,1980.28. Harrison, J.D.: "Lessons from Service Fatigue Failures", The Welding Institute Research Bulletin, Vol. 21 .,March 1980.29. Fisher, J.W.: "Fatigue and Fracture in Steel Bridges. Case Studies". John Wiley & Sons, New York, 1984.
    • CHAPTER 2 LOADS ON OCEAN STRUCTURES StAle Fines A.S VERITEC, OsloABSTRACTThe theory of stochastic processes is extensively used for the description ofwaves and the associated structural response, and is briefly summed up.Also some elements of the theory of dynamic systems are discussed, sincedynamic amplification of the structural response of offshore structures may besignificant. The theory of regular and irregular waves and the hydrodynamicforces on offshore structures caused by the waves are described, using thedeterministic as well as the stochastic approach. Finally the different methodsfor arriving at a long time distribution of stress ranges are discussed andillustrated by examples taken from elements of offshore structures.LIST OF SYMBOLS - cross-sectional area - water particle acceleration - amplitude - damping coefficient - drag coefficient - inertia coefficient - added mass coefficient - parameter in Weibull distribution of individual wave heights - diameter - parameter .in Weibull distribution of individual wave heights - water depth
    • List of symbolsDAF - dynamic amplification factor modules of elasticity expected value of x force frequency acceleration of gravity individual wave height parameter in the Weibull distribution of significant wave heights parameter in the Weibull distribution of significant wave heights significant wave height moment of inertia spring stiffness Keulegan-Carpenter number stability parameter surface roughness height wave number wave length member length mass mass per unit length nth order spectral moment cumulative probability distribution of the parameter x probability density distribution of the parameter x autocorrelation function Reynolds number Strouhals number energy spectrum individual wave period peak period zero-upcrossing period transfer function time volume water particle velocity reduced velocity stochastic process stochastic process vertical distance from still water level, positive upwards parameter of the JONSWAP wave spectrum
    • Section 2.1 parameter of the JONSWAP wave spectrum parameter in the Weibull distribution of significant wave heights logarithmic decrement of structural damping spectral width parameter parameter, relating wave heights and stress ranges water surface elevation kinematic viscosity of water damping ratio density of water standard deviation stress stress range time interval phase angle angular frequency peak angular frequency natural angular frequency2.1 GENERALAn offshore structure will be subjected to a number of loads during its life-time. These loads may be categorized as: Permanent loads, which are gravity loads that will not be removed, suchas the weight of the structure, weight of pennanent ballast and equipmentand external hydrostatic pressure of permanent nature. Live loads, which are loads associated with the operation and normal useof the structure, such as stored materials, equipment and liquids, operationof cranes, helicopters and fendering and mooring of vessels. Deformation loads, which are associated with imposed deformation,such as prestressing and temperature. Environmental loads, which are loads due to wind, waves, current, ice,snow, earthquake and other environmental actions. All loads that are varying in magnitude and/or direction will cause stressvariations in the structure and may lead to fatigue damage. The live loadsand the environmental loads are especially important in this connection.The live loads may be the dominating contributors to fatigue damage forequipment like cranes etc ., whereas the environmental loads, and the waveloads in particular, are dominating for the main part of the load carryingstructure.
    • Section 2.1 The aim of this chapter is to present methods that may be used tocalculate the long-term distribution of stresses induced by wave and currentloading. This distribution may then be used to estimate the fatigue life asdiscussed elsewhere in this book. The calculation procedures that are followed in practical cases mayvary in detail. In general the method will depend on the type of structure,the accuracy required, the wave and current data available and the computerfacilities and software at hand. The present chapter aims at presenting thegeneral calculation principles rather than all details of the various methods. The calculation usually includes the following steps:Step 1. Establishment of long-term statistics of waves and currents, i.e. description of how the waves and currents are assumed to vary throughout the lifetime of the structure.Step 2. Representation of these distributions by sets of defined wave and current conditions with associated probabilities of occurence.Step 3. For each of the defined environmental conditions: Calculation of external hydrodynamic loads acting on each member of the structure considered.Step 4. For each of the defined environmental conditions: Calculation of internal cross-sectional forces and stresses due to the external loads established in step 3. This calculation is normally based on elastic theory .Step 5. Etablishrnent of long-term distributions of stresses based on the results of step 4 and the probabilities of occurence of each environ- mental condition. The waves and the associated structural response have a stochastic(non-deterministic) nature. The theory of stochastic processes is thereforeextensively used for their description. A basic knowledge of the theory willbe helpful to anyone dealing with this subject. The theory is therefore brieflydiscussed in Section 2.2. The natural frequencies of many offshore structures are so close to thefrequencies of the environmental loads that the dynamic amplification ofthe structural response can be significant. Some elements of the theory ofdynamic systems are therefore presented in Section 2.3.
    • Section 2.22.2 STOCHASTIC PROCESSESThe theory of stochastic processes is treated in a number of textbooks, seefor instance Refs. / 11, /2/ and 131. Some basic elements of the theory aregiven in the following. Fig. 2.1 Time history of a stochastic process. The basic nature of a stochastic process may be understood by con-sidering the time history of such a process, as shown in Fig. 2.1. The value ofthe process at time t is denoted by x(t). The value of x at any chosen timet = to cannot be precisely predicted, we may, however, be able to find theprobability that x(to) will be within certain limits. As we are unable todescribe the process precisely as a function of time (as we can for a deter-ministic process) we instead describe the process by its statistical properties,e.g. mean value, -standard deviation etc. A process is said to be stationary ifthese statistical properties do not vary with time. Many processes may be con-sidered as stationary provided the time interval in question is short enough.The sea surface elevation, for example, is normally considered to be stationarywithin time intervals of three to six hours. Only stationary stochastic pro-cesses are considered in the following.The probability density function of x, p(x) is given by: p(x) dx = prob(x < x(t) < (x + dx))The cumulative distribution function is given by: X P(x) = 1p(x) dx -00The expected value of the process is given by:
    • Section 2.2 The expected value is equal to the mean value of the process. In somecases, the co-ordinate system can be chosen so that the mean value is zero.The sea surface variation about the mean water level is an example. A zeromean value is assumed in the following.The autocorrelation function is defined as: R,(T) = E[x(t) x(t +r)]where T is a freely chosen time interval. When the mean value is equal to zero,the autocorrelation function for T = 0 is equal t o the variance of the process:ox is the standard deviation of the process.The one-sided spectral density or energy spectrum is related to the auto-correlation by 00 sX(w)= 1 J R ~ ( T )e- i o r , d r (2.6) -00where w is angular frequency. A stationary stochastic process may be con-sidered as being composed of infinitely many harmonic components, eachwith different frequency. The energy of a harmonic wave is proportional tothe square of its amplitude. The energy spectrum shows how this energy isdistributed on the various frequency bands, Fig. 2.2.Fig. 2.2 A stochastic process x(t) and its energy spectrum S(w). The spectrum shows how the energy of the process is distributed on the various frequency bands. The energy within a band Ac;,is equal to that of a sine wave with amplitude ai.
    • Section 2.2The moments of the energy spectrum are defined as:The zero order moment gives the area under the spectral curve. This repre-sents the total energy of the process. The zero order moment is also equalto the variance of the process: 2 mo = ox (2.8)The spectral width parameter is defined by: -IIt varies between zero and one. When E is close to zero, the spectrum is narrowand a time history of the process is relatively smooth and regular, Fig. 2.3.When E is close to one, the spectrum is broad and a time history is moreirregular in shape. Broad bandFig. 2.3 Probability density of maxima. A broad band process has many local maxima and minima. The maxima (amplitudes) are Rice distributed. A narrow band process has no local maxima. All maxima are positive and follow the Rayleigh distribution. Many of the processes encountered in engineering may be assumedto be Gaussian with zero mean. The probability density function is then ,.
    • Section 2.2The amplitudes of this process are distributed according to the Rice distri-bution with the following probability density function:The corresponding cumulative probability function is :where the error function erf(x) is defined asFor E = 0 the density distribution of the amplitudes may be written , ,This is the Rayleigh distribution. It is a good approximation to the Ricedistribution for small values of E and is much used due to its simple formula.The corresponding cumulative distribution function is:The average zero crossing period of a narrow-band process may be approxi-mated byThe most probable highest of N successive peaks is then given by
    • Section 2.2 In many engineering problems we encounter linear systems, i.e. systemswhere the relation between the input or exitation x(t) and the output orresponse y(t) is described by a linear differential equation with constantcoefficients. An example of such a system may be the wave loading on anoffshore structure, where the ocean wave forces may be regarded as theexitation and the stresses in a point of the structure as the response. It was mentioned above that a stochastic process could be consideredas being composed of infinitely many harmonic components. If one suchcomponent of the exitation process is given by (real part understood)then the component of the response process at the same frequency is given byT(u) is the transfer function. From Eq. (2.19) we see that the exitation andresponse components are proportional. If we consider the above examplewith wave forces and stresses, the system will be linear if Hookes law isvalid, but non-linear if plastic effects are significant. It was mentioned above that the value of the energy spectrum at a givenfrequency was proportional to the square of the amplitude of the harmoniccomponent at that frequency. Eq. (2.19) above shows that the amplitudes ofthe exitation and the response are related through the transfer function. Theenergy spectrum of the response process is thus given by (Fig. 2.4) We will often be primarily interested in some specific properties of theresponse process, e.g. the most probably largest value within a given timeinterval or the distribution of response amplitudes. The procedure belowcan then be followed. - Establish the energy spectrum of the exitation process. - Find the transfer function of the system, for example by calculating the response to harmonic exit ation (Eq. (2.1 9)). - Calculate the energy spectrum of the response (Eq. (2.20)). - Calculate the desired properties of the response process by use of Eqs. (2.7)- (2.17).
    • Section 2.3.1 - 2.3.2Fig. 2.4 The transfer function T(w) relates the exitation spectrum S,(o) I I and the response spectrum Sy(w). Sy(w) = T(w) 2 S,(w).2.3 DYNAMIC EFFECTS2.3.1 GeneralDynamic loading is loading which varies appreciably with time, such as waveloading. The response of structures t o dynamic loading is generally dependentnot only on the magnitude of the loading but also on the time history of theloading . Many load-time histories are irregular, i.e. they are stochastic processes.It was mentioned in the preceding section that such processes could be con-sidered as composed of infinitely many harmonic components. Providedthat the relation between the acting loads and the corresponding structuralresponse is linear, the response to each loading component can be consideredseparately. The response of structures subjected to random loading can thus befound by studying the response to harmonic loading. The theory of dynamicanalysis is treated in a number of textbooks, e.g. Refs./3/,/4/and/5/, and is out-side the scope of this book. The basic formulas for a single-degree-of-freedomsystem (SDOF system) are given in the following. Although a detailed analysisof most structures requires a much more complex dynamic model, an SDOFmodel may be used for simplified calculations in many cases.2 -3-2 Single-degree-of-freedom systemA SDOF system consists of a mass, a linear spring and a viscous damper, Fig.2.5. Consider first a system consisting only of a mass and a spring. The springproduces a force
    • Section 2.3.2 ForceFig. 2.5 Single-degree-of-freedom system. K = spring stiffness, M = mass, C = viscous damping.The behaviour of the system when no external forces are acting is describedby M a y = -K.y (2.22)A solution to this equation iswhere C 1 and C2 are constants and WN is the natural angular frequency ofthe systemThe natural period is given byThe viscous damper produces a force which is proportional to the velocityand directed against it: FD = -C 9 (2.26)Incorporating this force in the above equations would have modified thenatural period, but for most offshore structures the damping is so small thatits effect on the natural frequency can be neglected.
    • Section 2.3.3The damping is normally expressed in terms of the demping ratiowhere C , is the critical damping, given by c c =2 , / RAssume that an external force x = a, * c o s o tis acting on the system. The behaviour of the system is then described byThe solution to this equation isThe amplitude (displacement) of the response is given by ay - - DAF - ax Kwhere DAF is the dynamic amplification factor 1 DAF = - J(1 -522)2 + (2.Ewhere a=" ONThe phase angle between the exitation (applied force) and the response(displacement) isEqs. (2.33) and (2.34) are plotted in Figs 2.6 and 2.7.2.3.3 Physical properties used for dynamic analysisMass.In addition to the structural mass one must also consider the added mass forsubmerged or partly submerged bodies. The added mass represent hydro-dynamic forces acting on the body from the surrounding water, and for mostpractical purposes one can model this effect as a certain amount of waterthat is fixed t o the body and thus has to follow its motions. The added massis discussed in more detail in Sec. 2.5.
    • Section 2.3.3Fig. 2.6 The dynamic amplification factor (DAF) as a function of w/wN. WN = natural frequency, = damping ratio.Fig. 2.7 The phase angle @ is the phase lag between the exitation x(t) and the response y(t). O N = natural frequency, 5 = damping ratio.Damping.The damping types of major significance for offshore structures are structuraldamping, hydrodynamic damping and, for bottom-founded structures, soildamping. The structural damping is due to internal damping in the structuralmaterial, and to friction and slippage in structural joints. The hydrodynamic damping is of two types: One is due to the forma-tion of surface waves (radiation damping) and the other to viscous effects. The soil damping is due to the formation of waves in the ground andto internal damping in the soil.
    • Section 2.3.42.3.4 Natural frequencies of common structural elementsThe natural frequency of some common structural elements is given by WN = 2 ~ f N = a~ - * d T rad/s me1 (2.35)where: EI = the bending stiffness of the section 1 = the length of the beam m = the mass per unit lengthof the beam aN = a numerical constant, see Fig. 2.8. Cantilever or "clamped-free" beam a, = 3.52 a Sinlply supported or "hinged-hinged" beam a,= I?= 9.87--- "Free-free" bean1 or floating ship a1 a l = 22.0 a2 = 61.7 a2 a3 = 121.0 a4 = 200.0 a3 as = 298.2$c- a, "Clamped-clamped beam has same frequencies as "free-free" a , = 22.0 "Claniped-hinged" beam may be considered a as half a "clamped-clamped" beam for even Fig. 2.8 The value of the numerical constant a~ in Eq. (2.35) for some common structural elements.
    • Section 2.4.1 - 2.4.22.4 WAVES2.4.1 GeneralTwo different methods are commonly used t o describe ocean waves. The seamay be regarded as composed of discrete o r individual waves, each describedby its height H and period T (Fig. 2.9) (discrete wave method). Alternatively,the sea may be described in terms of the statistical properties of the sea sur-face elevation (stochastic method). In both methods, the calculation of wavekinematics is based on regular wave theory.Fig. 2.9 A time history of the irregular sea surface. TI ,T2,. . ., T5 are indivi- dual wave periods. H I , H z , . . ., H 5 are individual wave heights.2.4.2 Regular wavesFig. 2.10 Regular waves. H = wave height from crest to trough, L = wave length, d = water depth, SWL = still water level, q = free water sur- face profile.Regular waves are a train of two-dimensional periodic waves which may bedivided into individual waves of identical form. The most important para-meters for description of regular waves are given in Fig. 2.10. The simplestdescription of the wave form is given by the linear wave theory (AIRY wavetheory), by which the surface profile is given by a sine function
    • Section 2 -4.2where: ~ c= , 2n/T = angular frequency T = wave period k = 27rlL = wave number The wave kinematics beneath a linear wave are given by Eqs. (2.37)through (2.43) below. Due to the simplicity of these equations, the theoryis well suited for simplified calculations. The linear wave theory is also abuilding stone in the description of irregular waves (Sec. 2.4.3). The waterparticle motion is illustrated in Fig. 2.1 1.Surfuce profileWave lengthWater particle velocity horizontal a) component =H 2 . fl . T=+f. cos(wt) L cosh(2n d/L) 1 (2.39) vertical w=- . g * T H . sinhl2n(zkd)/L1 sin(~t) (2.40) b, component 2 L cosh(2n d/L)Water particle acceleration horizontal - g o n * H . co~h[2n(z+d)/L_I.~~~(,~) a) component ax - L c o s h ( 2 ~ d/L) (2.41) b) vertical az = - x R H . 5inh[?n(z + d)/LI . cos(wt) (2.42) component L cosh(2n d/L)Su bsurjace pressure H = wave height g = acceleration of gravity L = wave length z = distance t o water particle from T = wave period SWL, positive upwards d = water depth w = angular frequency k = wave number p = density of water 7 = water surface elevation
    • Section 2.4.3 SWL I I I d Fig. 2.11 Particle orbits according to linear wave theory. A number of wave theories have been developed in addition to thelinear. The Stoke wave theories, the Cnoidal wave theories, the stream func-tion wave theory and the solitary wave theory are commonly used for designpurposes (Refs./6/,/7/). The range of application of the various theories isshown in Fig. 2.1 2. T I CJY 0.003 depth waves ~ 8 J ~ ~ 0.003 0.03 0.3 d p Fig. 2.12. The area of validity of various wave theories (Ref. 171).2.4.3 Irregular wavesA real sea does not possess the regular characteristics of a regular wave, buthas an irregular form as shown in Fig. 2.9. The wave periods of such a sea-state are defined as the time between successive upcrossings through still
    • Section 2.4.3water level, whereas the wave heights are defined as the difference betweenmaxima and minima values within the wave periods. In a short time interval (hours), the statistical properties of the sea-state may be considered t o be constant, and the sea is termed stationary.The theory of stationary stochastic processes (Sec. 2.2) is used to describesuch a seastate. The following terms are used in the description: - The zero upcrossing period T, (average wave period) is the average value of the wave periods as defined by Fig. 2.9. - The significant wave height Hs is the average of the highest third of the wave heights as defined by Fig. 2.9. - The wave spectrum S(w) is the energy spectrum of the sea surface elevation. Wave spectra can be obtained by analyses of recorded wave-timehistories. For design purposes the model wave spectra are normally used,which are analytical expressions describing the spectral shape. The spectra arethen described by statistical parameters like Hs and T,. A number of suchspectra have been developed. The most commonly used in the North Sea are:The Pierson-Moskowitz (PM) spectrum defined by 2 1 w.TZ -5 1 ueTz-4 (2.44) S(o) = Hs T, - ( - ) exp [- - ( ---) ] 8r2 27~ 7~ 27~The JONSWAP spectrum, defined by (= , - 1 ) 2 W The parameters a, up and 7 are functions of Hs and T,, as shown inTable 2.1. The peak angular frequency up is the frequency at maximum valueof S(o). The PM spectrum is applicable to a fully developed sea, i.e. when thegrowth of waves is not limited by the size of the generation area. This willbe the case for the major part of the time in the North Sea. Thus the PMspectrum may be used for most fatigue analyses. The JONSWAP spectrum applies when the growth of the waves islimited by the size of the generation area. This is the case for extreme waveconditions in the North Sea. The PM and JONSWAP spectra are illustratedin Figs. 2.13 and 2.14.
    • Table 2.1 The parameters of the JONSWAP spectrum as functions of Hs and T (Ref. 181). , Significant wave height (m) HS (m)02. 2.0- 2.5- 3.0- 3.5- 4.0- 4.5- 5.0- 5.5- 6.0- 6.5- 7.0- 7.5- 8.0- 8.5- 9.0- 9.5- 10.0- 10.5- 11.0- 11.5- 12.0- 12.5 130- 13.5 14.0- 145- is/ 2.49 2.99 3.49 3.99 4.49 499 5.49 599 6.49 6.99 7.49 7.99 849 8.99 9.49 9.99 10.49 10.99 11.49 11.99 12.49 12.99 13.49 13.99 14.49 14.99 - - . -- .- - . -.- - . - - - -- - - .. - -4.0- 5.490 5.970 6.330 6.600 6.8904.99 0.0138 0.0201 0.0277 0.0359 0.0485 0.1800 0,1810 0.1820 0.1830 0.1850 . -- . .--- . -. . . . . . -.-- - . .-- -- - --- - - -- . . -- - -- -- --- -- - - - .. - -2 I -5.0- 4.130 4.910 5.400 5.770 6.070 6290 6.490 6.680 6.830 6.9605.99 0.0064 0.0094 0.0129 0.0171 0.0219 0.0267 0.0323 0.0390 0.0455 0.0523 1 0.1440 0.1460 0.1470 0,1480 0.1490 0.1490 0.1490 0.1500 0.1500 0.1500 - .- .. ~~ --- - - . .- - - - -. . . ---6.0- 1.260 3.370 4.280 4 . m 5.210 5.530 5.770 5.840 6.170 6.320 6.490 6.610 6.730 6.870 6.9606.99 0.0036 0.0051 0.0069 0.0092 0.0113 0.0142 0.0170 0.0180 0.0239 0.0274 0.0323 0.0363 0.0410 0.0475 0.0523 0,1110 0.1200 0.1220 0.1240 0.1240 0.1250 0.1250 0.1260 0.1260 0.1260 0.1270 0.1270 0.1270 0.1280 0.1280 . -7.0- 1.090 1.650 3.620 4.240 4.690 5.040 5.280 5.490 5.540 5.870 6.020 6.150 6.300 6.410 6.510 6 . W 6.690 6.770 6.880 6.9607.99 0.0032 0.0042 0.0055 0.0067 0.0083 0.0102 /0.0119 0.0138 0.0143 0.0185 0.0210 0.0235 0.0269 0.0299 0.0329 0.0359 0.0394 0.0427 0 . M O 0.0520 0.0960 0.0980 0.1050 0.1060 0.1070 0.108010.1080 0.1080 0.1090 0.1090 0.1090 0.1090 0.1100 0.1100 0.1100 0.1100 0.1100 0.1100 0.1110 0.11108.0- 1.210 1.960 3.460 4.040 4.460 4.800 5.020 5.220 5.440 5.590 5.730 5.850 5.960 6.110 6.210 6.300 6.380 6.470 6.540 6.610 6.680 6750 68408.99 0.0035 0.0044 0.0052 0.0062 0.0074 0.0088 0.0100 0.0114 0.0133 0.0148 0.0165 0.0182 0.0199 0.0227 0.0248 0.0269 0.0290 0.0316 0.0339 0.0363 0.0390 0.0419 0.0460 0.0850 0.0880 0.0920 0.0930 0.0940 0.0950 0.0950 0.0950 0.0960 0.0960 0.0960 0.0960 0.0960 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0980 --. - -9.0- 1.000 1.230 1.770 3.230 3.810 4.230 4.480 4.770 4.960 5.120 5.330 5.470 5.580 5.690 5.800 5.890 5.980 6.110 6.190 6.270 6.340 6.4109.99 0.0029 0.0036 0.0043 0.0050 0.0058 0.0067 0.0075 0.0087 0.0097 0.0107 0.0123 0.0136 0.0147 0.0160 0.0175 0.0188 0.0202 0.0227 0.0244 0.0261 0.0280 0.029910.0 11 I 0.0750 0.0760 0.0780 0.0820 0.0830 0.0840 0.0840 0.0850 0.0850 0.0850 0.0850 0.0860 0.0860 0.0860 0.0860 0.0860 0.0860 0.0870 0.0870 0.0870 0.0870 0.0870 1.020 1.230 1.560 2.700 3.220 3.650 4.230 4.440 4.710 4.870 5.010 5.150 5.260 5.420 5.540 5.640 5.730 5.810 5880 596010.99 0.0030 0.0036 0.0041 0.0047 0.0050 0.0055 0.0067 0.0074 0.0084 0.0092 0.0100 0.0109 0.0117 0.0132 0.0143 0.0154 0.0165 0.0176 0.0186 0.0199 0.0680 0.0690 0.0700 0.0730 0.0740 0.0750 0.0760 0.0760 0.0770 0.0770 0.0770 0.0770 0.0770 0.0780 0.0780 .00780 0.0780 0.0780 0.0780 0.0780 .. -- - -- -. --- - -- . .11.0- 1.010 1.180 1.450 1.920 2.930 3.500 3.910 4.130 4.380 4.580 4.730 4.870 4.970 5.110 5.230 5.360 5.480 5.54011.99 0.0029 0.0035 0.0040 0.0044 0.0048 0.0053 0.0660 0.0064 0.0070 0.0079 0.0085 0.0092 0.0098 0.0106 0.0114 0.0126 0.0136 0.0143 1 0.0620 0.0630 0.0640 0.0650 0.0670 0.0680 0.0690 0.0690 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0710 0.071012.0. 1.260 1.540 2.050 3.020 3.450 3.760 4.000 4.270 4.420 4.550 4.650 4.810 4.950 5.09012.99 0.0036 0.0041 0.0045 0.0048 0.0052 0.0057 0.0061 0.0068 0.0073 0.0078 0.0082 0.0090 0.0099 0.0105 0.0580 0.0590 0.0600 0.0620 0.0630 0.0830 0.0640 0.0640 0.0640 0.0640 0.0640 0.0650 0.0650 0.0650 - -13.0 1.040 1.140 1.320 1.680 2.150 2.830 3.360 3.710 3.920 4.100 4.250 4.300 444013.99 First number: y 0.0030 0.0034 0.0038 0.0043 0.0045 0.0047 0.0051 0.0056 00060 0.0064 0.0068 0.0070 0.0073 Second number: a 0.0530 0.0540 0.0540 0.0550 0.0560 0.0570 0.0580 0.0580 0.0590 0 . 0 5 ~0.0590 0,0590 0.058014.0- Thud number: fp 1.190 1.290 1.570 2.030 2.670 3.120 3.440 3.650 3.78014.99 0.0035 0.0037 0.0042 0.0045 0.0047 0.0048 0.0052 0.0055 0.0067 0.0500 0.0500 0.0510 0.0520 0.0530 0.0536 0.0540 00540 0.055015.0- 2.90015.99 0 0048 I 1 0 0500
    • Section 2.4.3 Fig. 2.13 Pierson-Moskowitz wave Fig. 2.14 JONSWAP wave spectra. spectra. Hs = 1 0 m , T, = 10s. - - - - - - Hs = 8 m , T z = 9.5 S.The spectral moments are defined as (Eqs. (2.7), (2.8)) 00 m, = J w n *S ( o ) dm (2.46) 0Specifically, the zero order momentrepresents the total wave energy of the seastate. In a stationary seastate, the sea surface is normally taken to be Gaussiandistributed with zero mean and a variance o2 = mo. If the wave spectrum is assumed to be narrow-banded, the wave ampli-tudes will follow the Rayleigh distribution, see Sec. 2.2. It can then be shown
    • Section 2.4.4that also the wave height will follow the Rayleigh distribution The probabi-lity density function of wave heights following the Rayleigh distribution(Eq. (2.14)) is thus given byThe cumulative distribution of wave heights is correspondingly P(H) = 1 - exp [- ( l21 2&Still assuming the wave heights to be Rayleigh distributed, we have: For the significant wave height For the zero upcrossing wave period For the most probable largest value of N wave heights2.4.4 Long-term wave statisticsAs mentioned in 2.4.3, the statistical properties of the sea are assumed to beconstant within a short time interval and the parameters Hs and Tz may beused to describe a seastate. The duration of a seastate is normally taken as3 hours. A long-term observation of the sea may be performed by recordingthe parameters Hs and T,. Typically, the sea surface is observed for 20minutes each third hour, and Hs and T, are estimated for each observationperiod. This may be done from the observed wave record directly using thedefinitions of Hs and Tz given in 2.4.3 (zero crossing analysis) or by calcu-lating the wave spectrum and applying Eqs. (2.50) and (2.5 1). The pairs ofobserved Hs and Tz values thus obtained may be divided into classes and theprobability of each pair written in a matrix as shown by Table 2.2. Thisis called a wave scatter diagram. Also, the cumulative distribution of long-term significant wave heights may be found from the observations. Thisdistribution is normally well described by the Weibull distributionQ ,Hc and y are the parameters of the distribution.
    • Section 2.4.4 Table 2.2 Scatter matrix representative for the Central North Sea. PROBABILITY I N PARTS P E R THOUSAND I, 0 1 2 3 4 5 6 7 8 9 10 11 12 AVERAGE Z E R O UPCROSSING P E R I O D , T (s) , The distribution gives a straight line if plottet on a Weibull probabi- lity paper. The distribution shown by Fig. 2.15 is representative for the dis- tribution of significant wave heights in the Central North Sea. Assuming that the significant wave height is Weibull distributed with Ho = 0 and that the individual wave heights in a seastate are Rayleigh distri- buted, it can be shown that the long-term distribution of individual wave heights also follows a Weibull distribution: where C and D are functions of y, and Hc and y are parameters in the long- term distribution of significant wave heights. The relation between y, C and D is given in Table 2.3.
    • e(+hs>k. 9 ,//- I , Q CtL) - Section 2.4.4 L I 2 t I - b >ti5 I L , - H 10 z 3 ,Fig. 2.15 Long-term distribution of significant wave heights Hs representative for Central North Sea. Weibull parameters:y = 1.49, Hc = 2.7, H, = 0. Table 2.3 Parameters of the Weibull distribution of individual wave heights.
    • Section 2.4.4 The number of waves exceeding a given individual wave height in oneyear is given bywhere No is the total number of waves in one year. The above equation isshown by Fig. 2.16.Fig. 2.16 (left) Wave exceedance diagram showing the number of waves ex- ceeding a given wave height in one year.Fig. 2.1 7 (right) Simplified long-term exceedance diagram distribution of wave heights. Hl is the 100 year wave height. Nl is the num- ber of waves in 100 years. Log Nl Z 8.72 for North Sea conditions. The directional distribution of waves may be represented by a set oflong-term distributions of waves, each representing a sector of wave approachdirections. A useful approximation to the long-term distribution of individualwave heights may be obtained by setting D = 1.0 and H, = H l o O/(ln N1 o )in Eq. (2.55). HI is the most probable largest wave in 100 years and N l o 0is the total number of waves in 100 years. This gives for the number of wavesN exceeding a wave height H (Fig. 2.17) log N H = H, (1 - ) log N10 0
    • Section 2.5.1 - 2.5.22.5 HYDRODYNAMIC FORCES2.5.1 GeneralThree wave force regimes are normally identified. These are termed the drag,the inertia and the diffraction regimes. Flow separation and viscous effects are of major significance in thedrag regime. In the diffraction regime, the incident wave undergoes significantdiffraction or scattering, whereas flow separation is of minor significance.In the inertia regime neither flow separation nor diffraction are dominating.Offshore structures are grouped according to the nature of the acting waveforces. Small-volume bodies are bodies for which drag and inertia forcesare dominating, whereas large-volume bodies are bodies for which diffrac-tion effects are significant. Examples of large-volume bodies are ships and thecaissons of concrete gravity plat forms. Examples of small-volume bodies arejacket structures and the shafts of concrete gravity platforms.2.5.2 Loads on small-volume bodies - Morisons equationThe hydrodynamic forces on structures in the drag and inertia regimes arenormally calculated by Morisons equation. Normally, Morisons equationis applicable when the wave length L is more than five times the diameterof the structural member D. The hydrodynamic force per unit length on a body expressed byMorisons equation is: Froude-Krylov added mass force drag force forcewhere: A - is the cross-sectional area of the body A, - is a reference area a - is the component of the water particle acceleration normal to the member axis C , - is the added mass coefficient a, - is the relative acceleration between water particle and member normal to member axis CD - is the drag coefficient v, - is the water particle velocity relative to the member normal to the member axis D - is the diameter of the member exposed to the sea p - is the density of seawater.
    • Section 2.5.2 The Froude-Krylov force is the sum of the hydrodynamic pressuresacting on the surface of the body, not including the pressure disturbance dueto the presence of the body. This latter effect is included by the added massforce. The term p C, A, is called the added mass. It is often considered asan amount of water that is "fixed" to the member. This is not a correctinterpretation of the phenomenon, although it may serve to give an under-standing of the nature of the acting forces. The added mass force is due t othe relative acceleration between the water and the body. In general it isdependent on the flow conditions and the location of the body. The addedmass is wave-frequency-dependent for bodies at or close to the surface,whereas it is independent of frequency for deeply submerged bodies providedtheir dimensions are small relative to the wave length. The drag force is the viscous force acting o n the body. The sum of the Froude-Krylov force and the added mass force is calledthe inertia force. For a fixed body, a, = a and v, = v. If we set A, = A, wemay writeThe inertia coefficient is defined asFor three-dimensional cases, the equation is writtenwhere F is the force, V is the volume of the body, and A is the cross-sectionalarea of the body. The coefficients CM and CD are generally dependent on theshape of the body, the flow conditions and the body surface roughness.Circular cylinders.For a circular cylinder, CM and CD are found to be functions of the followingnondimensional parameters: v, D Reynolds number Re = - v v, T Keulegan-Carpenter number KC = - D Surface roughness = k/D
    • Section 2.5.2where: v, - is the maximum wave-induced velocity v - is the kinematic viscosity of water, = 1.1 1 x 10-6 m2 /s T - is the wave period k - is the surface roughness height. For North Sea conditions a range of roughnesses from 0.005 m to 0.05 m may be appropri- ate, depending on the precautions taken to reduce the growth. Inertia and drag coefficients should preferably be found by testing infull scale or model scale. Full-scale testing is difficult to perform, expeciallyin waves, and it is difficult to obtain the relevant conditions in a model.Thus, there are still large uncertainties associated with the values of thecoefficients.Fig. 2.18 The drag coefficient CD of circular cylinders in steady flow. Re = Reynolds number, D = cylinder diameter, k = roughness height. Ref. / 191. In steady flow the drag coefficient is a function of Re and k/D only,see Fig. 2.18. Drag coefficients obtained from full-scale tests in waves, areshown in Fig. 2.19. The results show considerable scatter. The mean curveindicated by a dotted line may be used in design. However, the designershould try to consult the latest research work available. The inertia coefficient has a theoretical value of 2.0 based on potentialflow theory. Full scale and model tests have given lower values. However,it is common design practice to use the theoretical value of 2.0.
    • Section 2.5.3 Mean C D KC -- Fig. 2.19 Drag coefficient CD as a function of KC. Full-scale test data, Ref. 11 11.Non-circular shapes.Drag and inertia coefficients of sharp-angeled bodies are normally taken t o beindependent of Re. Drag coefficients for members of various cross-sectionalshapes are given in Fig. 2.20. The added mass per unit length for variousmembers is given in Fig. 2.21, and Fig. 2.22 gives the added mass of somethree-dimensional bodies.2.5.3 Loads on large-volume bodiesWhen the body is not small compared to the wave length, the incident wavegenerally undergoes scattering or diffraction. This effect is normally con-sidered to be significant when the cross-sectional diameter of the body islarger than one fifth of the wave length. The viscous wave forces acting onsuch structures, i.e. the drag forces, are normally of little significance. In this case the calculation of wave forces may be based on the poten-tial flow theory. This theory describes the flow kinematics of an ideal fluid,i.e. a fluid without shear stresses. The pressure at every point of the structureis calculated and the wave force is found by integrating the pressure over thesurface of the structure. This normally requires the use of numerical methodsprogrammed in a computer. An analytical solution, i.e. the McCamy andFuchs theory, is available for vertical cylinders standing on the bottomand penetrating the surface. The inertia force term in Morisons equation iscalculated, using the equivalent inertia coefficient in Fig. 2.23.
    • Section 2.5.3 -[+m-l 01 I Sect~onshape CD 2.0 0 . i - 0 . 1 7 0.6 - -- I. [I = 0.33 0.5 a D 2.0 -0 1.5Fig. 2.20 Drag coefficients of cylinders of infinite length, Ref. 1101. SHAPE -1 ADDED MASS PER U N I T LENGTH MOTION -- - CIRCLE pnc 2 . 1 ll+-2b-i T 2a RECTANGLE a/b 10 1.00pna2 1.14 a/b 1 0.5 1.51pna2 1.70 " 5 1.21 " 0.2 1.98 " b- 2b 4 2 1.36 " 0.1 2.23 " (Wendel 1950) DIAMOND 2 0.85 " ELLIPSE 9ab2 I, 1 0.76 " c . - ) 0.5 0.67 " 0.2 0.61 (Wendel1950) I-BEAM - c PmJ 2 0 ... ... REGULAR P L Y n = 3 4 0.654 qaz 0.787 1.000 M (Wendel 1950) n SIDED Fig. 2.21 Added mass per unit length of cylinder, Ref. / 1 11.
    • SPHERE 4 0nR3ELLIPSOID OF k q pnb3 (Wendel 1950)REVOLUTION(Sarpkaya 1960, Yu 1945) -I -;u-- h FLOATING CYLINDER ( B a i 1977) FLOATING RECTANGLE 4 - 1 .o (Sarpkaya 1960) 1.2 1.6 2.0 2.4 2.8 3.6 ( B a i 1977, Flagg a n d NemMn 1 Fig. 2.22 Added mass of three-dimensional bodies, Ref. / 1 11.
    • Section 2.5.4Fig. 2.23 McCamy and Fuchs theory for a vertical circular cylinder standing on the bottom and penetrating the free surface.2.5.4 Deterministic calculation of response to hydrodynamic loadsIn a deterministic calculation of hydrodynamic loading, the structure isloaded with a regular wave described by the wave height H, the wave period Tand a suitable wave theory. A design current may be included. The directionof the current is normally assumed to be in the direction of wave propagation,and the velocities due to wave and current are added vectorially. The calculation of hydrodynamic forces is performed according to themethods described in 2.5 -2 or 2.5.3, whichever is applicable. Depending on thenature of the relation between wave height and response, various methods maybe used to find the variation of the hydrodynamic force and the associatedresponse throughout the wave cycle. When the relation between the wave height and the response is stronglynon-linear, the response-time history may be defined by calculating theresponse for various positions of the wave relative to the structure (Fig. 2.24).The number of positions chosen depends on the required accuracy. For structures where the relations between wave height and responseare linear, e.g. large volume structures, a simplified method may be used. Theresponse-time history at a given point in the structure may then be assumedto vary as a harmonic function, and the wave surface elevation is expressedby the linear wave theory The response, .y(t), is calculated for two positions in the wave, definedby t = to and t = to + T/4. The response may then be expressed as
    • Section 2.5.5Fig. 2.24 Calculation of the response for various positions of the wave relative to the structure. q(t) = wave surface elevation, y(t) = structural response.where The method may also be used when the relation between the waveheight and response is non-linear, provided a linearization is carried out. Thisis done in the same manner as described for stochastic analysis, cf. Sec. 2.5.5.2.5.5 Spectral method for calculation of response to hydrodynamic loadingThe spectral method applies the theory of stochastic processes for calculationof the response to hydrodynamic loading, see Section 2.2. For a particularseastate, the spectrum of a response variable is found by combining the wavespectrum with the transfer function relating the wave amplitude t o the ampli-tude of the response, Eq. (2.20). By integrating the response spectrum, thevariance of the response and the spectral moments can be calculated. Thesecalculations will normally be performed numerically. Particular care must betaken to ensure that the frequency grid used for the integration of the responsespectrum is appropriate. Furthermore, attention should be given to theselection of integration points in the vicinity of any irregularities in theresponse spectrum to ensure that an accurate integration is achieved. Havingestablished the response spectrum, the various statistical properties of theresponse, such as probability distribution of response amplitudes and maxi-mum probable response, can be calculated using the formulas given in Sec. 2.2.
    • Section 2.5.5 The transfer functions can be found by two different methods: Theregular wave approach and the time history simulation method.Regular wave approach.The value of the transfer function at frequency w may be found by calcula-ting the response due to a simple harmonic wave with height H and periodT = 27rlw. The transfer function value is then the ratio between the responseamplitude and the wave amplitude, see Eq. (2.19). This procedure is repeatedfor a number of frequencies thus yielding a number of points on the transferfunction. The spacing between the points should be sufficiently small toensure that the transfer function is adequately described. The above procedure implies the assumption that there is a linearrelation between the wave height and the response for a given wave period.This is generally not true. Non-linearities can be introduced due to variouseffects, the most significant being the non-linear drag term in Morisonsequation. A linearization must therefore be carried out.The drag term may be written as FD = KD ~ ( t ) ( ~ ( t ()whereWe consider a regular component of the water particle velocity, (Eq. (2.40)): v(t) = vo sin(wt) (2.65)If the drag term is expanded in a Fourier series and higher order terms areneglected, we obtain (Fig. 2.25) Nonlinear forceFig. 2.25 The non-linear drag force in harmonic waves and various lineariza- tion techniques.
    • Section 2.5.5 The above linearization renders the same energy dissipation per wavecycle as the non-linear force. It is recommended when dynamic effects aresignificant. If it is required that the maximum non-linear drag force shall beequal t o the maximum linearized force, we get FD(t) = KD vo ~ ( t ) The stochastic linearization is obtained by assuming that the particlevelocity at a given point is normally distributed and finding the functionthat minimized the mean square approximation error to the non-linear dragforce : FD(t) = KD J$ uv ~(t)where a, is the standard deviation of the water particle velocity. In all the linearization techniques mentioned above, the transfer func-tions obtained will be functions of the wave height used for the calculation.It is thus essential that an appropriate wave height is used when calculatingthe linearized transfer functions.Time history simulation.An alternative method of stochastic analysis is t o calculate the structuralresponse to a time history of the hydrodynamic forces. The distributionof response amplitudes may then be found from statistical analysis of thetime history of the response. Time histories of the wave-induced velocities and accelerations may beconstructed from the wave spectrum by use of linear wave theory and theMontecarlo simulation technique, see e.g. Ref. 1121. The hydrodynamicforces are calculated at discrete time steps and the structural response at eachtime step is calculated by use of a numerical integration procedure, seeRef. /13/ and 1141. A time history of the response is thus obtained. Thedistribution of response amplitudes within the seastate considered may thenbe obtained by a counting of the amplitudes directly from the time history,e.g. by use of the rainflow technique (Ref. / 1 51) or similar procedures. Alter-natively, the response spectrum may be calculated and if found t o be narrow-banded, the distribution of response amplitudes are found by use of Eq. (2.15). The advantage of the time history simulation technique is that allnon-linearities may be taken into account in a proper manner. However, thecalculation of the transfer function by Equation (2.20) also involves a line-arization process which is basically appropriate only for the seastate for whichthe simulation was done.
    • Section 2.5.6 - 2.5.72.5.6 SlammingMembers in the splash zone will be hit by the rising surface when a wavepasses. This will cause an impact force, called slamming,on horizontal mem-bers, as their whole length may be hit by the wave surface simultaneously.The slamming force per unit length may be calculated aswhere : Cs = the slamming coefficient vs = the velocity of the water surface. It is usually taken as the vertical particle velocity at the time of the impact. As the slamming force is impulsive, dynamic amplification must beconsidered when calculating the response. Ref. 1161 recommends the following values for horizontal circularcylinders fixed at both ends: Slamming coefficient : C, = 3.0 Dynamic amplification factor: 1.5 for ends and 2.0 for midspan .The member will respond with a dampened oscillation to each slam.Ref. 1171 recommends that each slam is associated with 20 linearly decayingoscillations. It also states that only waves with propagation directions + l odegrees to the normal of the member axis need be considered.2.5.7 Vor tex-induced oscillationsA structure with a bluff trailing edge sheds vortices in a subsonic flow. Periodicforces are generated in the structure as the vortices are shed alternately fromeach side of the structure. The oscillating forces can cause large amplitudeoscillations and thus high stresses in elastic structures. This phenomenon isa major problem for submerged parts of risers and conductors and also forantennas, stacks, etc. exposed to wind.The vortex shedding frequency is: v f" = s t 5where: St = the Strouhal number v = the flow velocity normal to the member axis D = the member diameter The Strouhal number is in the range of 0.12-0.14 for sharp edgedmembers and approximately 0.2 for circular cylinders.
    • Section 2.5.7 Large amplitude resonant oscillations may occur when the frequencyof vortex shedding is close t o the natural frequency f N . This is expressedby the reduced velocity The nature of the oxcillations is complex and model or full-scale testsare normally needed to determine the response of a particular structuralconfiguration. Vortex induced oscillations occur in several regions of the reducedvelocity. Ref. 1181 recommends the following calculation procedure forcircular members in a uniform current: 1.0 < vR < 3.5 : The cylinder oscillates in the direction of the flow (in-line oscillations). 3.5 < vR < 10: The cylinder oscillates in the direction normal to the flow (cross-flow oscillations).The amplitude of oscillation is a function of the stability parameter Ks :where: m = mass per unit length, including added mass 6 = logarithmic decrement of structural damping = 2 .rr $ , p = fluid density D = cylinder diameter The relation between Ks and the maximum oscillation amplitudeis given by Figs. ( 2 . 2 6 ) and ( 2 . 2 7 ) . The cylinder oscillates with its naturalfrequency. Large amplitude oscillations of sharp-edged members in steady flowhave been observed when vR > 5. The effect of vortex shedding in waves is not well known, and nogenerally recommended design procedure is available at present.EXAMPLE 1:Vortex-induced oscillations of a free span of a pipeline.A submarine pipeline with a 25 m long free span (Fig. (2.28)) may undergovortex-induced oscillations due to the presence of a bottom current. The steelpipeline has a concrete coating and is carrying oil. Calculate the stress range inthe pipe produced by the oscillations.
    • Section 2.5.7 -First instability r e g i o n , V R < 2.2 In-iine motion I Second instability r e g i o n , V R > 2.2 Fig. 2.26 Max. amplitude of in-line motion, Ref. 1181. For a simply supported beam in fitst mode, is equal to 1.16. For a cantilever beam in fist and second mode, the 7-value is equal to 1.31 and 1 .SO respectively. Fig. 2.27 4 Max. amplitude of cross- I I I 1 I I flow motion, Ref. / 181.Fig. 2.28 Free span of a pipeline.
    • Section 2.5.7Characteristics of the pipeline: Steel pipe Outer diameter = 0.273 m Wall thickness = 0.015 m Moment of inertia = 1.02 m4 Concrete coating Thickness = 0.005 m Density = 3000 kg/m3 Oil Density = 800 kg/m3Based on the above data, the following values have been calculated: Total pipeline diameter Df = 0.283 m Mass of steel pipe m, = 96.1 kg/m Mass of concrete coating m, = 12.7 kg/m Mass of internal oil m = 37.0 kg/m , Added mass ma = 64.5 kg/mThe added mass is taken equal to the mass of the water displaced by thepipeline, i.e. the added mass coefficient is 1.O. Total mass:So Eution.The pipeline is assumed t o be simply supported at both ends. The first naturalfrequency is calculated as (Eq. (2.35))Substituting the values above, and taking E = 2.1 10 ~ / mwe get ~ ,The reduced velocity determines the current velocity at which oscillations willoccur: VR = - v f, * DIn-line oscillations, 1 . instability region: 1.0 < vR < 2.2 * 0.23 m/s < v < 0.5 m/sIn-line oscillations, 2. instability region: 2.2 < v, < 3.5 =+ 0.50 m/s < v < 0.79 m/sCross-flow oscillations: 3.5 < vR * 0.79 m/s < v
    • Section 2.5.7The oscillation amplitude is a function of the stability parameter Ks (Eq.(2.72)). Substituting 6 = 0.05 and p = 1025 kg/m3, we getFigs 2.26 and 2.27 give the maximum oscillation amplitudes as functionsof Ks : In-line oscillations. 1. region: A = 0.13 Df In-line oscillations, 2. region: A = 0.16 Df Cross-flow oscillations: A = l.lO*r*DfThe mode-shape parameter y is taken as 1.16 according to Fig. 2.27.The following expression is used for relating the stress amplitude at thecenter of the span and the oscillation amplitude (Fig. 2.29): Fig. 2.29 Moment corresponding to assumed mode-shape.This gives the following maximum stresses: In-line, 1. region: om, = 20 MPa for 0.23 mls < v < 0.50 m/s In-line, 2. region: om, = 25 MPa for 0.5 m/s < v < 0.79 m/s Cross-flow : om, = 200 MPa for 0.79 m/s <vThe stress ranges may be taken as Ao = 2o,,The span will oscillate with its natural frequency for all types of oscillation.The number of oscillations per hour is therefore: N1 hour = 3600 0.80 = 2880.
    • Section 2.6.1 - 2.6.22.6 LONG-TERM STRESS RANGE DISTRIBUTION2.6.1 GeneralThis section outlines three different methods for arriving at a long-termdistribution of stress ranges: - Deterministic analysis - Stochastic analysis - Simplified analysis A deterministic analysis is based on a relatively simple description ofthe environmental data and the associated loads. Non-linear wave height-stress relations are easily taken into account and the calculation procedureis easy to follow. It should be used with great care when dynamic ampli-fication is significant, as this effect is difficult to account for in a propermanner. A stochastic analysis requires a more complex description of theenvironmental data and loads, and a more detailed knowledge of these pheno-mena is required. Non-linear effects are not so easily taken into account asin a deterministic analysis. A time history simulation may be performed,but this may be very expensive for complex structures. Dynamic effectsare taken care of more properly in a stochastic analysis than in a deterrni-nistic analysis. A simplified analysis based on a simple description of both the environ-mental data and the associated response, may be a valuable tool in the earlydesign phase.2.6.2 Deterministic approachA deterministic approach to calculate the long-term stress distribution isbased on the deterministic method of wave force calculation given in Sec.2.5.4. It involves the following steps: i) Selection of major wave directions. A few wave directions, typically 4-8, are selected for analysis. The total number of waves is distributed between these major direc- tions. Major wave propagation directions should be included, as well as directions causing high stresses in major structural elements. Ad- vantage may be taken of structural symmetry, as identical waves propagating in opposite directions may cause equal stress ranges in many structures.
    • Section 2.6.2ii) Establishment of long-term distributions of waves. For each wave direction considered, a long-term distribution of wave heights must be established, such that the total number of waves reach- ing the structure during the time considered is the sum of the waves from the directions considered. For a given direction the long-term distribution of wave heights is represented by a set of regular waves, which adequately describes the directional long-term wave distribution. Special care should be taken to properly describe the range of wave heights which gives the highest contribution to the fatigue damage. The wave period to be associated with a given wave height is normally taken as the most probable period for that wave height.iii) Calculation of stress ranges. For each wave thus identified (direction-height-period), the stress range is calculated, using one of the methods given in Sec. 2.5.4. If the stress range is found by placing the wave at various positions relative to the structure (Fig. 2.24), the positions should be chosen with great care in order to estimate the maximum and minimum stresses and the resulting stress range as accurately as possible.iiii) Establish stress distribution. The long-term stress distribution for each wave direction is established using a methodology as shown in Fig. 2.30. Fig. 2.30 Calculation of a stress range exceedance diagram from a wave height exceedance diagram. Aoi is the stress range induced in a given wave direction by wave height Hi. Log N 79
    • Section 2.6.2EXAMPLE 2 : Long-term distribution of stresses in a riser span, deterministic analysis.Fig. 2.3 1 Jacket platform with riser clamped t o the platform leg. The span between -1 5.0 m and -25.0 m is considered in Example 2.Consider a riser clamped to the leg of a jacket platform (Fig. 2.3 1). The long-term distribution of stress ranges at the center of the span is wanted. As theonly aim of this example is to show the principles of the calculation, weintroduce the following simplifying assumptions: - The span is considered as fixed in both ends. - Wave kinematics are calculated by the linear wave theory. - All waves are assumed t o approach from one direction.The span has the following characteristics : Length 1 = 10m Riser outer diameter D = 0.27 m Riser wall thickness t = 0.0 15 m Moment of inertia I = 9 . 8 . 1 0 ~ m4Solution.According to Eq. (2.35) the first natural period of the span, fN1, is calculatedto 0.17 s, which is low enough t o make dynamic amplification insignificant(cf. Fig. 2.7).
    • Section 2.6.2The wave force intensity is denoted F(z). The moment at the center of thespan (z = -20 m) is given byand the maximum bending stress at the center of the spanThe linear wave theory gives the same maximum wave force in both directions,thus: A a = 20,,- - -.D M IThe wave data are given by the wave diagram in Fig. 2.16 for individual waveheights with Hc = 2.7, Ho = 0 and y = 1.49. Each height used in the analysismust be associated with a wave period. This is taken as the most probablewave period for the given wave height. For North Sea conditions, the followingrelation may be used :The long-term distribution of individual wave heights is given by Eq. (234) - Lnc %!Iwhere Hc = 2.7 and C and D are respectively 0.462 and 0.928 for y = 1.49,cf. Table 2.3. ii AThe number of waves exceeding a wave height H per year is given by N = No[l -PL(H)] > -0 t dwhere No is the total number of waves in one year, taken as NO = 106.72.The following waves are now selected for analysis: H = 3.0m T = 7.2 s log N = 5.74 H = 5.0m T = 8.7s log N = 5.14 H = 7.0m T = 9.8 s log N = 4.57 H = 9.0m T = 10.8 s log N = 4.00 H = 11.0m T = 11.7s log N = 3.45 H = 15.0 m T = 13.1 s log N = 2.35 H = 20.0 m T = 14.6 s log N = 1.OO
    • Section 2.6.2The wave forces are calculated by Morisons equation (Eq. (2.5 7)) , F = -1* p 0 C D * D * $ + p e C M --• a ~ n * ~ 2 4The coefficients CD and CM are taken as 1.0 and 2.0, respectively.As an example, consider the wave: H = 1 1.0 m, T = 11-7 s.The angular frequency isApplying linear wave theory (Fig. 2.1 I), the wave number k is given by(Eq. (2.38))where g = 9.8 1 m/s2 and the water depth d is LOO m. The equation is solvednumerically, giving k = 0.0296 m-Setting x = 0 at the center of the riser, the horizontal wave-induced waterparticle velocity is given by (Eq. (2.39))and the horizontal wave-induced acceleration (Eq. (2.4 1))When linear wave theory is used, one can simplify the calculations by separat-ing drag and inertia forces. The moment due to the drag forces alone is givenyielding MD ( a t ) = MD , sin2 ( a t ) = 4596 sin2( a t ) (Nm) ,The moment due to inertia forces is calculated in the same manner:
    • Section 2.6.2yielding MI(mt)= M, I -cos(wt)= 1306*cos(wt)(Nm)The total moment: M(wt) = MDm, sin2 ( a t ) + M I , cos(wt)Maximum value of M(at) occurs for dM(wf)= 0, whichgives (Fig. 2.32) d ( 4The maximum moment is thus: , M = 4596 sin28 1.BO + 1306 cos 8 1.go = 4689 Nmand the resulting stress range: Ao= M D= 4689 0.27 = 12.9 MPa - 0 I . 9.8 1 o -~ sin* [at) Fig. 2.32 Drag force FD ,inertia force FI and total force F, Example 2.The procedure above is repeated for all waves selected for the analysis.For each wave height analysed, the corresponding number of waves exceedingthat height is found by Eq. (2.56) or Fig. 2.1 6. Since the calculation proce-dure implies a unique relation between wave heights and stress ranges, thenumber of exceeding stress ranges is found in a similar manner. The finalresults are shown in Fig. 2.33.
    • Section 2.6.3 0 2 4 6 LogNFig. 2.33 Deterministic analysis of long-term distribution of stress ranges, Example 2. Left: Number of cycles (N) exceeding given wave heights, forces and stress ranges in one year. Right: Stress range exceedance diagram, one year.2.6.3 Stochastic approachA stochastic approach for calculating the long-term distribution of stressranges is based on the stochastic methods of wave force calculation describedin Sec. 2.5.5. It involves the following steps: i) Selection of major wave directions. The same considerations as dis- cussed for the deterministic analysis should be made. ii) For each direction select a number of seastates which adequately describes the long-term distribution of waves. Associate a duration to each seastate. iii) For each seastate calculate the short-term distribution of stress ranges using the methods described in Sec. 2.5.5. iiii) Combine the results for all seastates in order to find the long-term distribution of stress ranges.EXAMPLE 3: Short-term distribution of stresses in a riser span, stochastic analysis.As explained above, steps iii) and iiii), calculation of the long-term distri-bution of stress ranges is done by combining the short-term distributions fora number of seastates. The calculation below shows how a short-term distri-bution is obtained.
    • Section 2.6.3The same riser span is considered as in Example 2. The short-term distributionof stress ranges within a given seastate is wanted. The same assumptions asused in the above example will be applied.Solution.The seastate is described by: Hs = 5 m, Tz = 7.5 s, duration = 3 hours.A Pierson-Moskowitz wave spectrum is assumed, Eq. (2.44) :The first step in the analysis is to establish the transfer function relatingwave heights and stresses. This is done by calculating the stresses for a set ofregular waves with different periods. The calculation is performed in thesame manner as in the deterministic analysis. The transfer function for a givenwave period is then calculated according to Eq. (2.19). As mentioned inSec. 2.5.5, the relation between wave heights and wave forces is non-lineardue to the drag term, and the calculated transfer function is thus a functionof the wave heights used.We have for the most probable wave period for a given wave height, as ex-plained in Example 2 :For periods higher than 16 seconds, the formula gives wave heights higherthan the 100 year wave height (= 29 m). The wave height 29 m is thus usedfor all periods longer than 16 seconds.The transfer function may be expressed bywhere a,,,(w) is the maximum stress caused by the wave at frequency w .Consider again the wave H = 11 m, T = 11.7 s, w = 0.539. In the deterministicanalysis we found that M, (w = 0.539) = 4698 Nm, a, , (w = 0.539) = 6.9 MPa.
    • Section 2.6.3The transfer function is thusThe procedure is repeated for a set of wave periods within the range 3-25seconds. The result is shown in Fig. 2.34. Fig. 2.34 Transfer function relating stress and wave surface elevation.This transfer function is now combined with the wave spectrum definedpreviously in order to obtain a stress spectrum for each seastate, Eq. (2.20): So(4 = ( T(w) l2 S?)(W)The stress spectral moments are found by numerical integration of Eqs.(2.47) and (2.48) : 00 m2 = J w2 ~ , ( w ) dw = 35.74 1MPa - ( 2 0 SThe average stress cycle period is thus, Eq. (2.1 6)and the number of cycles within the seastateThe stress spectrum obtained is narrow-banded and the Rayleigh distribution
    • Section 2.6.4is used to describe the stress amplitudes. The probability of an arbitraryamplitude exceeding a level o l is thus, Eq. (2.1 5) n2.6.4 Simplified long-term distributionA simplified long-term distribution of stress ranges may be obtained from thesimplified wave height distribution, Fig. 2.17, and a general knowledge ofthe relation between wave height and response for the considered structure.The wave height H is given by Eq. (2.56): log N H = Hloo (1 - 1 log N1ooThe relation between wave height and stress range is assumed to be of theform Aa= C * H ~ (2.73)The long-term distribution of stress ranges may then be expressed as log N )K Aa = Aaloo (1 - log N1oowhere Auloo is the stress range induced by the 100 year wave. The value of the parameter K is dependent on the type of structure andthe environmental conditions (wave height - wave period relation). For NorthSea conditions, the following values may be appropriate: Jacket structures 1.6 < K < 1.8 Concrete gravity structures 1.3 < K < 1.6 Semi-submersibles ~ . O < K < 1.3 The above method should be used with care. The choice of the para-meter K should preferably be based on the. results of a detailed analysisperformed for a similar structure. This may be done by a curve-fitting proce-dure whereby Eq. (2.74) is fitted to the known distribution.EXAMPLE 4: Long-term distribution of stresses in a platform, simplified analysis.Consider a semi-submersible platform as shown in Fig. 2.35. An analysisof the stresses induced by the 100 year wave has been performed and resultedin a stress range Aaloo = 80 MPa. A preliminary estimate of the long-term
    • Section 2.6.4 JOINT Fig. 2.35 Semi-submersible platform.distribution of the stress ranges in the indicated welded joint is wanted for afirst evaluation of fatigue damage.Solution.The platform is intended to operate in the North Sea. The mean wave periodis assumed to be 6 seconds, i.e. the number of waves in 100 years is:The stress ranges are assumed to follow Eq. (2.74): ACJ Aaloo (1 = - log N )K log N1oowhere N is the number of stress cycles exceeding Ao. Previous analyses haveshown that K = 0.9 is a reasonable value. We therefore get for the long-termstress distribution n o = s o - ( 1 ---- N)o9 log 8.72Note that a lower value of the parameter K will result in generally higherstressranges. A
    • Chapter 2. ReferencesREFERENCES1. Newland, D.E. : "Random Vibrations and Spectral Analysis", Longman, London, 1975.2. Bendat, J.S. and Piersol, A.G. : "Random Data: Analysis and Measurement Procedures", Wiley-Interscience, 1971.3. Langen, I. og Sigbjsrnsson, R.: "Dynamisk Analyse av Konstruksjoner", TAPIR, Trondheirn, 1979.4. Clough, R.W. and Penzien, J. : "Dynamics of Structures", McGraw-Hill, 1975.5. Meirowich, L. : "Elements of Vibration Analysis", McGraw-Hill, New York, 1975.6. Skjellbreia, L. and Hendrikson, J.: "Fifth Order Gravity Wave Theory", Proc. Seventh Conference on Coastal Engineering, The Hague, 1961, pp. 184-196.7. Dean, R.G.: "Evaluation and Development of Water Wave Theories for Engineering Application", Vols. I and 11. U.S. Army, Coastal Eng. Research Center, 1974. 8. Houmb, O.G. and Overvik, T.: "Parameterization of wave spectra and long term joint distribution of wave height and period". Proc. Conference on Behaviour of Offshore Structures, Trondheim, 1976.9. Heideman, J .C., Olsen, O.A. and Johansson, P.I. : "Local Wave Force Coefficients", Civil Engineering in the Oceans IV, ASCE, 1979, pp. 684-699.10. "Dynamics of Marine Structures", CIRIA Report UR 8, London, 1977.11. Sarpkaya, T. and Isaacson, M.: "Mechanics of Wave Forces on Offshore Structures", Van Nostrand Reinhold Co., New York, 1981.12. Harnrnersley, J . and Handscomb, P.: "Monte Carlo Methods", Methuen, London, 1964.13. Houbolt, J.C.: "A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft", J. Aeronaut. Science, Vol. 17, 1950.14. Newmark, N.M. : "A Method of Computation for Structural Dynamics", J . Eng. Mechanics Div., Vol. 85, ASCE, 1959.15. Dijk, G.M.: "Statistical Load Data Processing", National Aerospace Laboratory, Amsterdam, 1971.
    • Chapter 2. References16. Det norske Veritas: "Rules for the design, construction and inspection of offshore structures", Appendix B, 1977.17. Det norske Veritas : "Rules for the design, construction and inspection of offshore structures", Appendix C, 1977.18. Det norske Veritas : "Rules for submarine pipeline systems", Appendix A, 1977.19. British Standard CP3. Code of basic data for the design of buildings. British Standard Institution, London 1972.
    • CHAPTER 3 FRACTURE MECHANICS AS A TOOL IN FATIGUE ANALYSIS Knut Engesvik SINTEF,TrondheirnABSTRACTThis chapter deals with the basic theory of fracture mechanics with emphasison its application in fatigue analysis. The fundamentals of fracture mechanicsare presented. The relationship between the stress intensity range and crackgrowth is used to evaluate the development of cracks under variable loading.This approach is related to ordinary SN-curves.NOMENCLATUREGeneral ruleRandom variables are denoted by capital letters, while their realizations aredenoted by the corresponding small letters.Operators and special notationsE( - expectation operatore - within (the interval)SymbolsThe symbols are generally explained where they first appear. The mostfrequent symbols and their meaning are listed below.Roman letters:a - crack depth, minor half axis of semielliptical crack, half crack length of through cracka, - critical a
    • Chapter 3. Nomenclatureaf - final a initial a crack aspect ratio (shape) crack growth rate major half axis of semielliptical crack constant, crack growth coefficient Youngs modulus probability density function (pdf) of X basic crack shape factor stress gradient factor front free surface factors finite thickness factor finite width factor total correction factor energy release rate influence function Rices J-integral stress intensity factor mode I stress intensity factor mode I1 stress intensity factor mode 1 1stress intensity factor 1 critical stress intensity factor elastic stress concentration factor stress intensity factor range threshold stress intensity factor range weld leg length crack growth exponent crack growth exponent, number of cycles number of cycles t o failure initiation part of Nf propagation part of Nf polar coordinate crack tip plastic zone size radius, stress ratio; R = omin/omaX plate thickness plate thickness plate width
    • Chapter 3. NomenclatureGreek letters:P - empirical constantr( - gamma function8 - polar coordinate, weld flank angle, parameter in Weibull distributionv - Poissons ratiog - parameter in Weibull distributionP - radius, notch tip radius, weld toe radius(7 - nominal normal stresso(x) - crack surface stress distributionOc - critical stressamax - maximum stressOmin - minimum stressOX ,OY,OZ- normal stresses referred to a specified coordinate systemOY - monotonic, uniaxial yield stressAo - stress rangeAffeq - equivalent stress range4 - constant amplitude fatigue limit7XY - shear stress in X-Y-planeTXZ - shear stress in X-Z-plane7Y Z - shear stress in Y-Z-plane4 - angleAbbreviations:CA - constant amplitudeCOD - crack opening displacementEPFM - elastic-plastic fracture mechanicsfcg - fatigue crack growthIF - influence functionLEFM - linear-elastic fracture mechanicsSCF - stress concentration factor
    • Section 3.1 .13.1 FUNDAMENTALS OF FRACTURE MECHANICS3.1 .1 IntroductionFracture mechanics seeks to define the local conditions of stress and strainaround a crack, in terms of the global parameters of loads, geometry, etc.,under which the crack will extend (Fig. 3 .I). Local condltlons - magnitude and d i s t r i b u t i o n of stresses/strains G l o b a l conditions - material properties - geometry; - e x t e r n a l - crack (shape, size) - Loading i.e. n o m i n a l s t r e s s -Fig. 3.1 Linear-elastic fracture mechanics linking global conditions with local crack-tip response. Various approaches have been employed in the analysis of fracture problems, leading t o the introduction of various fracture mechanics para-meters, e.g. G, J, COD, K - all being interrelated. The most popular among these parameters has been the stress intensity factor, K . In fact, a fundamentalprinciple of linear-elastic fracture mechanics is that the stress field ahead of a.sharp crack can be characterized in terms of this single parameter, K. Fracture mechanics can be subdivided into two general categories, namely linear-elastic (LEFM) and elastic-plastic (EPFM). This section will be restricted to LEFM, its analytical basis and the practical evaluation of thestress intensity factor.
    • ,1 .. - -4 - , - Icclrrt ~ttr (rlr - Section 3.1.23.1.2 Analytical basis of LEFMCrack tip stress fieldThe basis of LEFM is an analysis of the elastic stress field at the tip of a crack.A crack in a solid can be stressed in three different modes, as illustrated inFig. 3.2. The superposition of the three modes describes the general case ofcracking. Mode I is technically the most important, as it is the most commonmode, particularly in fatigue. I mode I opening mode mode I1 s l i d i n g mode mode111 t e a r i n g mode Fig. 3.2 The three modes of cracking. Now, consider a through thickness sharp crack in a linear elastic iso-tropic body subjected to mode I loading. Such a two-dimensional crack isshown schematically in Fig. 3.3. An arbitrary stress element in the vicinity ofthe crack tip with coordinates r and 8 relative to the crack tip and crack planeis also shown. The stresses and displacements at any point near the crack tip can bederived, using theory of elasticity and complex stress functions. The elasticstresses near the crack tip (r/a -4 1) for the mode I case are as follows: 8 cos - sin - cos3 8 8 r x=f ~ i 2 2 uz = TXZ = TYZ = 0 for plane stress (3.1 d) uz = v[ox + oy] for plane strain Txz = Tyz= 0
    • Section 3.1-.2 dFig. 3.3 Schematic illustration of the elastic stress-field distribution near the tip of a crack (Mode I deformation).where: K = KI = mode I stress intensity factor r, 8 = polar coordinates, as shown in Fig. 3.3 v = Poissons ratio - -Similar expressions exist for the other modes. It is seen that the crack tip stress field is singular, with singularity ofthe type r-12 . This is a common feature of the crack tip stress field, regardlessof mode of deformation. Strictly speaking the stresses are defined by a series of terms involving +r and 8 , but close to the crack tip (i.e. for r a) only the first (i.e. singular)term is significant since the others involve higher-order terms in r.The stress intensity factor conceptFrom Eqs. (4.1 a-c) it is seen that the elastic stresses close t o the crack tipdepend on r, 8 and K only. It is also noted that the distribution of stressesaround the crack tip depends only on the values of r and 8, while their magni-tude at any given position (r, 8) depends only on K. Thus, the distributionsof stresses at the crack tip are invariant with respect t o loading and geometry.The effect of these global parameters are incorporated in K. Hence, the wholestress field at the crack tip is known, when K is known.
    • noCclz. - $OI"~Y. Section 3.1.2 It is important to realize that the value of K is not dependent on the material or on the coordinates r and 8. However, it depends on external load, external geometry, and crack geometry (size and shape). Hence, K provides a link between the very localized crack tip response and the more global con- ditions (Fig. 3.1 ). It also follows that combinations of external load, external geometry and crack geometry resulting in the same K, yield identical stress fields in the crack tip region, i.e. the same local response. This representation of the stress field around a crack tip by the stress intensity factor is a basic concept of fracture mechanics. An obvious advantage of the fracture mechanics approach to fatigue is the ability to incorporate the pertinent external loading variables (alternating stress and loading configuration) and geometry factors (flaw size, -shape, and component geometry) into a single-term parameter, such that data (e.g. for - crack growth) are applicable to a wide variety of loading and geometry configurations other than those from which they were initially obtained. This allows a correlation of test results from different specimen geometries, and also a correlation between e.g. test results and service failures. K should not be confused with the elastic stress concentration factor-I< F Kt, which is the ratio of the maximum stress to the nominal stress at a notch. Hence, Kt is a scaling factor for the nominal stress, while K acts as a scaling factor for the crack tip stress field. For this reason, K is called a stress field parameter. Furthermore, Kt is a descriptive parameter relative to notches (stress concentrations), while K characterizes conditions at cracks (stress singularities). Kt is-incapableof treating cracks, as Kt=-, regardless of external loading and geometry, i.e. it is incapable of discriminating between the various loading and geometry configurations influencing the crack-tip response. The numerical value of Kt depends on the type of loading (i.e. tension, bending) and external geometry (including notch geometry), while the value of K depends on the loading (type and level), external geometry, crack geo- metry (size and shape) and mode of crack displacement. K used without a mode subscript I, I1 or I11 normally refers to mode I. Limitations of LEFM LEFM is based on a linear-elastic analysis of the stresses at the crack tip, and inherently takes no account of plasticity. Hence, LEFM is not strictly correct as r + 0.Since infinite stresses cannot exist in a physical body, and as ductile materials will always show some plasticity at the tip of a crack, the elastic solution (Eq. 3 .l) should be modified to account for crack tip plasticity.
    • Section 3.1.3 In general, crack tip plasticity can be assessed, and the effect taken intoaccount through a correction term. If, however, the plastic zone size (rp)at the crack tip is small relative to local geometry (for example, rp/t andrp/a<O. 1,where t is thickness), little or no modification to the stress intensityfactor K is needed. Thus an important restriction to the use of linear-elasticfracture mechanics is that the plastic zone size at the crack tip must be smallrelative to the geometrical dimensions o f the specimen or part. In the majority of fatigue situations (at least for high-cycle fatigue)cracking will occur under quasi-elastic conditions. In other words, the sizeof any plastic zone at the crack tip will tend to be small compared with thecrack length, and it is possible and adequate to calculate the conditionsaround the crack by linear elastic stress analysis. The reason for this is three-fold. Firstly, the load (i.e. nominal stress) level is low or moderate, and thecrack tip stresses are proportional to the nominal stresses, according to linearelasticity. Secondly, the triaxiality of the crack tip stress field acts to reduceplasticity. Thus, crack tip plastic zones are smaller in plane strain than inplane stress. Thirdly, the cyclic plastic zone size is known to be only aboutone quarter the size of the monotonic plastic zone. Hence, crack tip plasticity usually does not invalidate the practicalapplication of LEFM to problems involving plane strain and cyclic plasticity,as e.g. in high-cycle fatigue.3.1.3 Evaluation of stress intensity factorsIntroductionThe application of fracture mechanics principles bears largely upon the stressintensity factor. An essential part of the solution of a fracture problem inlinear-elastic fracture mechanics is the establishment of the stress intensityfactor for the crack problem under consideration. Since the introduction offracture mechanics, much effort has been put into the derivation of stressintensity factors, and a variety of methods have been developed to approachthe problem. Stress intensity factor solutions are now available for a wide range ofgeometrical configurations, both two- and three-dimensional, and manysolutions have been collected 11, 2, 31. Solutions are also available, for in-stance, in the series of Special Technical Publications by the American Societyfor Testing and Materials (ASTM), in the series entitled Fracture, edited byLiebowitz 141, and in the series entitled Mechanics o f Fracture, edited b ySih 1st. The methods, both theoretical and experimental, of obtaining thesesolutions have been reviewed by Cartwright and Rooke 161, Liebowitz (Vol.
    • Section 3.1.3I1 of Ref. /4/), Sih (Vol. I of Ref. 151) and Kobayashi 171. Numerical methodshave also been reported recently /8/. In practical problems, structural geometries and loadings are often socomplex that the available stress intensity factor solutions are inadequate.Evaluation of the stress intensity factor for the actual problem using standardmethods may be prohibitively expensive in both time and money. Thus thereis a need to develop simpler methods which will be cheap and easy to use evenif less accurate than most standard methods. Many simple methods have beensuggested, and their relative merits are discussed in 191. In the following, some techniques for obtaining approximate engineeringestimates are treated. Tables for the conversion of units related to stress and stress intensityare given in Appendix 3 .A.&perpositton methodsSuperposition is probably the most common and simplest technique in use forobtaining stress intensity factors. Complex (load-geometry) configurations areconsidered to be a combination of a number of separate simpler configurationswith separate boundary conditions and which have known stress intensityfactors. The stress intensity factors for the simple configurations are thenadded to obtain the required solution. Errors from using superposition canarise when the complex configuration being analysed cannot be preciselybuilt up from configurations with known stress intensity factors. An illustration of the use of this technique is shown in Fig. 3.4 191. a b c Fig. 3.4 Superposition of stress intensity factors.
    • Section 3.1.3The stress intensity factor for the configuration shown in Fig. 3.4a, is the sumof the stress intensity factors for the two simpler configurations shown inFigs. 3.4b and 3 . 4 ~ . Another important application of superposition, the analysis of pin-loaded lugs is shown in Fig. 3.5. By using the procedure shown, openingmode stress intensity factors for non-symmetrical loadings can be found byadding the more easily obtainable results for simpler symmetrical loadings. Fig. 3.5 Superposition for a pin-loaded hole with radial cracks. The stress intensity factor for a crack in a loaded body may be deter-mined by considering the crack to be in an unloaded body with appliedtractions on the crack surface only (Fig. 3.6). These surface tractions areequal in magnitude but opposite in sign to those evaluated along the line ofthe crack site in the uncracked configuration. This method of determiningstress intensity factors is important in the use of the influence functionmethod (See later section). Thus, application of the principle of superposition leads to an importantresult about the equivalence o f stress intensity factors resulting from externalloading o n a body and those resulting from internal tractions on the cracksurface. When employing superposition, it is important to be aware of theparticular restrictions pertaining to the superposition of stress intensityfactors. 1) The stress intensity factors to be superposed must correspond to the same mode of crack deformation (I, I1 or 111).
    • Section 3.1.3 Load Stress f r e e crack S t r e s s over Crack surface crock site=cj(x) tractions=-d(x) (a1 (b) (c >Fig. 3.6 Superposition showing the equivalence of K(K, = Kc) for general loading and crack surface tractions; a) initial cracked configuration; b) uncracked configuration; c) initial configuration with applied loading removed. E.g. components that contain cracks may be subjected to one or moredifferent types of mode I loads such as uniform tensile loads, concentratedtensile loads, or bending loads. The stress-field distributions in the vicinity ofthe crack tip that is subjected to these loads are identical and are representedby Eqs. (3.1 a-f). Consequently, the total stress-intensity factor can beobtained by algebraically adding the stress-intensity factors that correspondto each load. However, some components may be subjected to loads thatcorrespond to various modes of deformation. Because the stress-field distri-butions in the vicinity of a crack are different for different modes of deforrna-tion (Section 3.1.2), the stress-intensity factors for different modes of defor-mation cannot be added. Under these loading conditions, the total energy-release rate, G, rather than the stress-intensity factor, can be calculated byalgebraically adding the energy-release rate for the various modes of defor-mation.
    • Section 3.1.3 2) Problems with compressive forces/stresses. Although stresses may be combined linearly, even when the loadingover a portion of the crack length tends to close the crack, the stress intensityfactors cannot without further restrictions. This breakdown of the linearsuperposition occurs since stress singularities, and therefore stress intensityfactors, do not exist for crack closing forces. Stress intensity factors of cracks can be superimposed for loads thateither tend to open or to close the crack along the entire crack front only ifthe combined loading state opens the crack along the entire periphery. Thus,the crack surfaces in the final configuration must be separated along theirentire length, although there may be some overlap of the crack surface, or K1may be negative, in some of the ancillary configurations. If overlap does occurin an ancillary configuration, it must be ignored in evaluating the ancillarystress intensity factor, otherwise the results of the superposition will beinvalid. 3) Boundary problems. A configuration containing a crack may have several boundaries, e.g.holes, other cracks or sheet edges, which influence the stress intensity factor.Using the method of superposition a solution is obtained by separating theconfiguration into a number of ancillary configurations, which have knownsolutions. Each ancillary configuration will often contain only one boundary,which interacts with the crack. The interaction of several boundaries is usuallyneglected in the compounded solution /9, 101, and thus is a source to error.Errors due to neglecting boundary - boundary interactions depend on: - nearness/closeness of boundaries, - boundary shape, - number of boundaries. E.g. consider the configurations shown in Figs. 3.7 - 3.9. These repre-sent widely different boundary effects, namely a pair of boundaries of infinite,finite or zero radius of curvature in the path of the crack. Consider again the configuration shown in Fig. 3.7. Figure 3.10 showsthe appropriate ancillary configurations. Comparison of Figs. 3.7 and 3.1 0shows that we require c = b and d = b, + e. Studies of configurations as the above, show that: - The errors of the compounded solution increases with increasing crack length, i.e. as the crack tip approaches the boundaries. - At a fixed crack length errors tend to increase with increasing boundary radius, i.e. boundaries with large radii of curvature will have an effect over a larger distance than boundaries with small radii of curvature.
    • Section 3.1.3Fig. 3.7 Eccentric crack in a finite width sheet subjected to a uniaxial tensile stress.Fig. 3.8 Crack between two holes in an infinite sheet subjected to a uniaxial tensile stress.Fig. 3.9 Three collinear cracks in an infinite sheet subjected to a uniaxial tensile stress.
    • Section 3.1.3Fig. 3.10 Crack near the edge of a half plane subjected to a uniform tensile stress; ancillary configuration for Fig. 3.7 (d 2 c). - Errors increase with the number of boundaries. E.g. increasing the number of collinear cracks in Fig. 3.9 would increase the solution error. The basic compounding equation for calculating the resultant stressintensity factor K,, neglecting boundary interactions might be expressed as:where K, is the stress intensity factor for a crack in the presence of a singleboundary B,, and K is the stress intensity factor in the absence of all boun-daries. This compounding technique has been extensively used on aerospaceproblems. However, the methodology has general applicability and potentialfor providing engineering estimates of K for complex configurations. Thetechnique has been used in very local as well as more global applications,e.g. to cracks in stiffened sheets /11/. This might be of interest in the assess-ment of residual strength in a structure, and closely related to considerationson inspection and structural reliability.The influence function methodConsiderable effort in analytical fracture mechanics is devoted to the com-putation of K for complex stress/geometry combinations of actual crackedstructures. Traditional approaches have been to use literature solutions orto obtain numerical solutions of K with a finite element or boundary-integralequation model of the cracked structure. There are inadequacies in both ofthese approaches for a large class of problems. Literature solutions lack gene-rality, while repeated two or three-dimensional numerical stress analyses of
    • Section 3.1.3cracked idealizations are costly, time-consuming and subject to errors due topoor program performance or user inexperience. To reduce errors and mini-mize cost, a method involving the use of influence coefficients or influencefunctions (h) to compute K has been shown to provide a viable alternative formany geometries. The influence function (IF) method has also been labeledthe weight function or Greens function method. This method of determiningstress intensity factors is applicable to a wide variety of problems, and hasbeen used for two- as well as three-dimensional elastic crack problems 1121. Fig. 3.1 1 illustrates the elastic superposition principle which is thebasis of the IF method. The superposition reduces the K solution of anarbitrary crack problem to the solution of: 1) the problem without the crack (i.e. uncracked problem), and 2) a crack problem in which only the crack face is pressurized so as to cancel the uncracked stresses ( o(x) in Fig. 3.1 1) that would exist across the crack locus in the absence of the crack. Influence functions are used to solve this second, pressurized crackproblem. To solve the pressurized crack problem, and hence the original problem,consider the differential load o(x)dx (assuming constant thickness), whichcauses a differential increment of K given byso that the stress intensity factor is given by K = LdK(x) = $ h(x,geo.)o(x)dx (3.4) Lawhere La is the straight crack face boundary parallel to the x axis. h( ) is theinfluence function. Equivalent forms can be written for KI, KII and KIII. Thus, the methodology consists of the following steps: 1) The reduction of the actual problem into two (or more) simpler problems, i.e. employing elastic superposition of (loadlgeometry) configurations (See Section on "Superposition methods"). 2) Determination and specification of the uncracked stress field, i.e. the distribution of stress along the crack site in the uncracked body, which is a non-singular elasticity problem. 3) Obtaining the appropriate influence function for the actual (i.e. the pressurized) crack problem.
    • Section 3.1.3 (Compressive L o a d i n g on (Tensile stress a c t u a l crack face) on c r a c k f a c e dFig. 3.1 1 The reduction of a problem into two simpler problems, ( 1) and (2) for computations of stress intensity factor. An influence function h is simply the K value arising from a unit point load at some position, usually on the crack face. Thus h is independent of loading, and depends only on the crack face position and structural geometry. The influence function can be accurately obtained from relatively simple loading conditions and applied t o complex stress fields. Sources of influence functions are found in e.g. 11, 2, 31. Methods of computing influence functions are treated in e.g. 16, 12, 131. Some exact and approximate influence functions are given in / 121.
    • Section 3.1.3 The influence function method is exact providing that the correct influence function is used. However, it is often possible to construct approximate influence functions, so avoiding the need to use more time-consuming and costly methods. 4 ) Integration according to Eq. (3.4). Thus, once the uncracked stress field and the influence function are known, obtaining a stress intensity factor is reduced to a simple summation procedure which can be done numerically, graphically or analytically depending on the form of the influence function. The reader is reminded of the restrictions pertaining to the superpositionof stress intensity factors (See Section on "Superposition methods"). E.g. forcracks in residual stress fields care must be taken to ensure that the cracksurfaces are separated along their entire length. If they are not, crack surfacecontact conditions must be included in the influence function. Thus, one can see that the major advantage of the IF method is themarkedly reduced amount of stress analysis. Once h has been determinedfor a geometry, K can be calculated for any crack size and shape from the"uncracked" stress field. Through the use of elastic superposition, the IFmethod properly accounts for stress redistribution as the crack dimensionsincrease due to propagation through the structure. Thus, there is no needto include the crack explicitly in the stress analysis for each crack size. To illustrate the utility of Eq. (3.4), consider the center-crackedplate under symmetric loading shown in Fig. 3.12. For the case of uniformstress of an infinite plate (a/b + O ) , the stress intensity factor is given bywhere a is the half crack length and uo is the applied uniform stress. It hasbeen shown 1121 that, for any symmetric stress field, o(x) = o(-x), the in-fluence function for the infinite plate is given by 1 0 < x < a defines -La 2Eqs. (3.4) and (3.6) reduce to Eq. (3.5) for the case of constant o(x) = oO. Thus, we see by example that the IF method can correctly quantifythe crack-induced redistribution of the uncracked elastic stress field.
    • Section 3.1.3 Fig. 3.1 2 Center-cracked plate under symmetric stress.A practical hybrid methodIntroductionThis method is basically an influence function - and a superposition method.It employs available solutions for two- and three-dimensional crack problems.From these the influence of different factors affecting K are separated andused to "compose" an estimate of K in an actual case 114-20/.General expression for KK may be conveniently expressed as: K= o 6 . Fwhere : F = FE*FSFT*FW*FG FE = basic crack shape factor FS = front face factor FT = back face or finite thickness factor FW = finite width factor FG = stress gradient factor
    • Section 3.1.3The basic crack shape factor - FE.This factor takes into account the effect of crack front curvature, i.e. crackshape. A good approximation is obtained through the expression:which pertains to point A in Fig. 3.1 6.The front free surface correction factor - FS .This factor accounts for a free surface at the "mouth" of the crack (Fig. 3.13),and depends on: - crack opening stress distribution (Fig. 3.14) - free surface shape (Fig. 3.14,.15) - crack shape - position on crack frontThe influence of crack shape might be approximated as:which pertains to point A in Fig. 3.16. FS might be estimated as: Fs = Fb fSwhere : F i = FS(o(x),B) from Fig. 3.14.The finite thickness correction factor - FT .This factor (also called "the back free surface correction factor") accountsfor the effect of a finite plate thickness, i.e. a free surface ahead of the crackfront (Fig. 3.13b and c). It dependson: - crack geometry (size, shape) - bending conditions (free, restrained) during cracking - crack opening stress distribution - position on crack frontApproximate values of FT are given in Fig. 3.16.The finite width correction factor - FW.This factor accounts for a free surface ahead of the crack front of a throughcrack (Fig. 3.13a). The following expression yields a good approximationof this effect :
    • Section 3.1.3 I a) "Through" crack I b) "Edge" crack I 1 C) "Surfacen crack Fig. 3.13 Plate cross-section with various crack geometries. Free surfaces and related correction factors.
    • Section 3.1.3Fig. 3.1 4 Influence of free surface shape (Fig. 3.15) and crack stress distribution on FS. Fig. 3.1 5 Free surface shape parameters.
    • Section 3.1.3
    • Section 3.2.1The stress gradient correction factor - FG.This factor (also called "the geometry correction factor") accounts for non-uniform crack opening stresses, i.e. stress field gradients at the crack locus.The gradients may be due to e.g. non-uniform applied stress (such as bending)or stress concentration caused by detail geometry. This stress gradient shouldnot be confused with that which occurs at the crack tip. FG represents amore global condition than the crack tip, but may account for a local stressdistribution, which is not acknowledged by a strength of materials analysis. Estimates of the gradient effect on K might be extracted from knownsolutions to crack problems / 14, 151. Some approximate expressions for FG pertaining to welded joints aregiven in Section 3.2.1 .3.2 FRACTURE MECHANICS APPLIED TO FATIGUE PROBLEMS=Ji #Wbm%a ef crack growthIntroductionNumerous relations for predicting the growth rate (da/dN) have been pro-posed. These may be divided in two main categories, i.e. theoretical and semi-empirical "laws". The theoretical laws might be further grouped according to the differentapproaches employed in developing them. Many attempts have been madeto deduce a law of fatigue crack growth (fcg) theoretically, but none of theproposed expressions has a general applicability. It is anticipated that suchan expression will be a complicated one if it is to have general validity. Forthe technical problem of fcg the simple knowledge that da/dN is a functionof AK will often be sufficient. Therefore, the crack propagation relationshipis more often deduced from test data. Semi-empirical laws might be viewed as empirical fitting to availabledata, and each is legitimate insofar as it represents the data. As to the useof such relations, the questions will always be: - are the data on which the relation is based of relevance, i.e. do the material and testing conditions represent reality? - is the precision of fit sufficient for the purpose for which the law will be used? Broek /21/ concludes that there is little basis for arguments about theusefulness of the various empirical expressions proposed. The scatter in
    • Section 3.2.1actual data implies that many empirical expressions may have certain merits,i.e each one may be found reasonably satisfactory in a limited region orfor limited sets of data. Therefore no particular expression for da/dN vs AKwill have significant advantages over another. A best polynomial fit may bethe most suitable in view of computer processing.Crack growth rate relationsFig. 3.17 shows a schematic crack growth rate curve, with three distinctregions indicated, i.e. the well-known threshold-, intermediate-, and failureregions. I I - "TWO-STAGE" MECH. CONT. MECH. I Log aKFig. 3.17 Schematic crack growth rate curve showing sigmoidal variation of fatigue crack propagation rate da/dN with the alternating stress intensity (AK). A&h is the threshold stress intensity for crack growth, and Kc the stress intensity at final failure (terminal K).
    • Section 3.2.1 Some of the most common crack growth relationships are given in thefollowing, together with comments indicating how they adapt to the generalsigmoidal shape of the crack growth rate curve (Fig. 3.17). Region B : -, JJ Regions A and B : = C~AK* - A K ~ ) dN Regions B and C - R-effect explicitly accounted for: Regions A, B and C - R-effect explicitly accounted for:The relationship (3.1 8) is particularly useful in the absence of available crackgrowth data. In the above expressions: da/dN= crack growth rate, i.e. crack growth per cycle AK = stress intensity factor range = 4C ( 3 .F AKth = threshold-value of AK Kc = critical value of K, triggering fast fracture R = stress ratio = omin/omax = Kmin/I<max OY = yield stress E = modulus of elasticity C and m = crack growth parameters
    • Section 3.2.1The Paris equationThe simplest relation, in mathematical terms, is the Paris-equation (Eq.(3.1 3)), where C and m are "constants" for a particular material and particulartesting conditions. This equation provides an adequate description of thebehaviour only for the mid-range (i.e. region B) of growth rates (typically10*-10-~ mmlcycle). The complete variation of da/dN with AK is morecomplicated , being roughly sigrnoidal in form (log-log plot), and boundedat extremes by values of AKth and Kc (Fig. 3.17). Since K incorporates the various geometrical factors (e.g. joint- andcrack-geometry), Eq. (3.13) may be regarded as a law of crack propagationrelevant to any geometry of cracked body provided factors not related to AK,such as material and environment, correspond t o the C and m values applied. For purpose of integration, limits t o the AK regime over which thisequation can operate, must be set at the threshold and final fracture condi-tions, and regions A and C assumed to be vertical (Fig. 3.1 8). Crack growth None I Log A K Fig. 3.1 8 Idealized crack growth rate curve. It is observed that the Paris-equation is conservative in region A, andnon-conservative in region C . Usually, most of the fatigue life is spent propa-gating cracks in regions A and B. Very little fatigue life is left when a crack
    • Section 3.2.1enters region C. Thus, the Paris-relation will in general yield conservativeresults, i.e. computed life < actuallreal fatigue life. In such a simple relation as Eq. (3.13), only the primary parameteraK is explicitly taken into account. All the secondary parameters (e.g. materidproperties, frequency, mean st= and R, environment) enter the computa-tions implicitly through the constants C and m . Fatigue crack growth is in-fluenced by so many uncontrollable factors that a large scatter has to beexpected in practice. This is also observed on plots of da/dN vs AK, as theyexhibit a wide scatter band. Several attempts have been made to find an empirical relationshipbetween C and m. In general, the proposed relations are of the kind:where A and B are constants for the particular type of material. Experimentalresults on steels tested in air at R * 0, confirm that log C and m are linearlyrelated in plane strain fcg. Gurney 1291 analysed several published crackpropagation results and found as a best fit relationship (considering resultsfor structural - and high strength steels together):Stress concentrations and stress intensities for welded joints */Some results are available for calculation of stress concentrations and stressintensities of welded joints. They may be used to obtain: - an approximate solution, where this is sufficient - a first estimate, pending a more elaborate and accurate analysis - a fairly accurate solution, if the actual case resembles closely one of the underlying cases.Some of the published results are given in the following.Transverse butt welds.With the overfill in the shape of a circular arc, and W = T (Fig. 3.19), thecorresponding value of the stress gradient factor FG for a crack initiating atthe weld toe is 1301:where: (next page)
    • Section 3.2.1 Fig. 3.1 9 Transverse butt weld with circular arc overfill. q = log (1 1.584 - 0.0588 $)/log (200) @ = obtuse toe angle (degrees)This equation is reasonably valid over the range 135O < 4 < 180".Transverse load-carrying fillet welds.The value of AK for a crack at the weld root of a cruciform joint may beexpressed as /3 1/ : Ao(A, + A,&)&-= AK = W 2 w (3.22) 1 +-- 22 T +where: w = II T/2 (Fig. 3.20) Ao = nominal stress range in the main (longitudinal) plates 2a = length of internal weld root crackRestrictions : 0.2 < Q/T < 1.2 0 < a/w < 0.7 9F- I Weld t o e c r a c k Weld r o o t c r a c k Fig. 3.20 Transverse load-carrying fillet welds.
    • Section 3.2.1Transverse non-load-carrying fillet welds (Fig. 3.211. Fig. 3.21 Transverse non-load-carrying fillet welds.For alTG0.05 1301:where: Q = weld leg length T = thickness of main plate t = thickness of attachment plate a = crack depth = t/T k = 1 -0- log Pllog 4.49 q = 0.054p + 0.2255 For 0.05 < a < 0.325 it can be assumed that there is a linear relation Tbetween log FG and log (2a/T) passing through FG = 1 .O at a/T = 0.325, andthe value of FG from Eq. (3.25) at a/T = 0.05. An approximate formula for predicting FG automatically is 116,171: where: (next page)
    • Section 3.2.1 FG = stress gradient correction factor (Section 3.1.3) SCF = elastic stress concentration factor at the weld toe a = non-dimensionalized crack length (a/T or a/W) d = stress gradient correction factor decay coefficient q = stress gradient correction factor decay exponent The constants in the decay function (Eq. 3.26) are given in Table 3.1. Table 3.1 Constants for the FG decay function. Weld detail d 9 Typical stiffener geometry ) / 161 0.3602 0.2487 Average cover plate detail ) / 161 0.1473 0.4348 Typical gusset plate geometry 2, / 17/ 1.158 0.6051 1) a = a/Tf (Figs. 3.22,3.23) 2) a = a / W f (Fig.3.24) Another rapid, but more precise method of obtaining FG is treated in116, 171. I I a . Section b.Plan view Fig. 3.22 Detail geometry for transverse stiffener.
    • Section 3.2.1 F i [ l e t weld T Cover p l a t e F Lange I-Fat igu crack a Section d I b . P l a n view Fig. 3.23 Detail geometry for cover plate. Groove weld Point of W,/2 t r a n s i t ion d Flange tangency Symne t r y Web Fig. 3.24 Detail geometry for gusset plate.From Eq. (3.26) it is seen that FG = SCF (= Kt) (3 -27)when: a = a = Oi.e. at the surface. This has general validity. Thus, knowledge of the SCFprovides important information about K close to the surface. Hence, toobtain a first estimate of K, by employing the FGdecay-function in Eq.(3.26), an estimate of the SCF is needed. Ref. 116, 171suggest the followingequations:
    • Section 3.2.1 Stiffeners: (Fig. 3 -22) + SCF = 1.621 log (A) 3.963 Tf Cover Plates: (Fig. 3.23) T SCF = -3.539 log (K) + 1.981 log (A)+ 5.798 1161 (3.29) Tf Tf Gusset plates: (Fig. 3.24) SCF = -1.115 log(&) + 0.5370log(L) + wf wf 0.1384 log (s) (a) w + f + 0.2848 T Tf 0.6801 1171 (3.30)where: Tf = flange thickness TCp = cover plate thickness Tgp = gusset plate thickness Wf = flange width Wgp = gusset plate width Q = weld leg size R = radius of circular transition at end of groove-welded gusset plate L = attachment length In evaluating FG at welded structural details, the crack is usually takento be the through (or edge-) type (a/2c = 0). However, it is worthwhile notingthat FG varies with crack shape, and in welded joints the shape is oftendifferent from that of a straight crack. Hence, Fig. 3.25 has been developedusing through and circular crack Greens functions for a crack in an infinitesolid. This figure shows that the values for FG diverge as the stress decaybecomes more rapid. The limiting ratio, Y, for a concentrated load at thecrack origin is estimated t o be 0.548. This number represents twice thedeviation from 1.0 recorded between the uniform and linear stress cases. Hence, FG related to a straight crack front yields conservative (toohigh) K-values, compared with FG for a curved front. The crack shape significantly influences K (Section 3.1.3), and thusthe fatigue life. Therefore, the fatigue designer employing fracture mechanicstechniques should seek for relevant shape relations. In order to predict cyclicchanges in crack shape, the shape of the surface crack is modelled with afinite number of degrees of freedom. Most often a semi-elliptical shape is
    • Section 3.2.1 Through Embedded Crack crack penny shape shaped Ratio Stress Y distribution 1 1.o a 1 .ooo 1 .ooo 1 .ooo 5. r rn 0.363 0.281 0.774 b 0. 548Fig. 3.25 Comparison of stress gradient correction factors FG for various crack shapes and stress distributions 11 81.assumed, described by the half-axis ratio, or the aspect ratio a/2c. Predictionsof the (a/2c)-evolution during crack growth might be done empirically ortheoretically. Empirical a-c-relations may be based on measurements on thefractured surface of welded joints (without parameterization of the influen-cing factors). Some of the published crack shape relations are given in thefollowing. These are valid only for the specific welded joint considered,i.e. with the actual geometry, loading, material, and welding method. How-ever, lacking relevant data they provide easy-to-use practical information, ifavailable for a case similar to the actual case.Gusset specimens (Fig. 3.26) 4a lower bound 20a a < 1 mm upper bound 20aoe3 a > 1 mmStiffener specimens (Fig. 3.2 1) 2c = 2.59 [mml
    • Section 3.2.2 Fig. 3.26 Gusset specimen. (Stiffener specimens cont .) 2c = -0.27 6.34a+a < 3 mm a/2cxO aZ3mm 2.8a lower bound 12 a upper boundi 3.2.2 Estimation of fatigue life Crack initiation One might generally subdivide the fatigue life in a crack initiation period (Ni) and a crack growth period (Np), ending with failure, i.e. As is further discussed in Chapter 4, the crack initiation period in welded joints, that are not stress relieved, usually occupies a small part of the total life, and is often neglected. In most cases it leads to small errors only, in the conservative direction. Cmck propagation Having the means of determining the crack growth rate (Section 3.2.1), one is able to make various estimates concerning crack growth, e.g. the time or number of cycles required to grow a crack from one size to another:
    • Section 3.2.2 This may be required when the structure is in service. E.g. a crack maybe detected and reported through the in-service inspection programme, anddecisions have to be taken whether this crack should be stopped, or allowedto grow further, with due consideration to the actual material specification,loading conditions, repair possibilities, and costs.The crack propagation part of the fatigue life may be expressed as:where : ai = initial crack length (depth) af = final (critical) crack length (depth) By inserting the relevant expressions for crack growth rate and stressintensity, one is able to obtain an estimate of the fatigue crack propagationlife. Thus, by employing Eqs. (3.7,3.13) : L . *. --- - ----- ---------- --- ----.I &> Constant terms need not be included in the integration, i.e.: For constant amplitude loading, the integrand is further reduced, i.e.: In the case of a very simple F-function the above integral may beevaluated analytically, but generally numerical integration must be employed. In cases where F does not depend on a (which are the exceptions),Eq. (3.41) may be written as:
    • Section 3.2.2This integral is easily evaluated analytically, i.e. : Thus, for this simple case one obtains the following closed-form ex-pression for the constant amplitude fatigue (crack propagation) life:whenm # 2. For structural steels and aluminium alloys 2 < rn < 6. For welded steeljoints 2.5 5 m 54.5. Thus, if ai 4 af, an approximate estimate of the constantamplitude fatigue life is: 1-m/2 Np " - ai (3.45) c Aom rmI2 P (m/2 - 1) - , > ;-r ,. & , - ? . If the failure condition is brittle fracture, the critical crack length maybe estimated from Eq. (3.7): - Kmax - Omax * * Fwhich reads at failure:and hence the critical crack length:Remarks concerning fatigue life computationsSome words of warning to the novice within fatigue calculations, whetherbased on fracture mechanics or not. The "correct" or "exact answers don t "exist. Results from deterministic fatigue calculations, as treated above, aremeaningful in a qualitative and relative sense, but must be used with careand judgement when interpreted in an absolute sense. This is partly due tothe numerous uncertainties involved in a fatigue life computation, i.e. un-certainties/weaknesses in the fatigue model, uncertainties linked with input
    • Section 3.2.2(material, loading and geometry) parameters due to e.g. lack or scarcity ofdata, and - last but not least : the uncertainty incurred when trying topredict - in a deterministic manner - an outcome of highly random nature. One vital question might be: What is the prediction accuracy?Thisnaturally depends on the computational accuracy, the accuracy of the fatiguemodel, and the relevance and quality of input data. (Garbage in - garbage out!)However, even if model - and statistical uncertainties were removed, how totackle randomness in a deterministic calculation? - A "worst case"dpproach might lead to extremely conservative results (with unknown reliability). - A ymean-valuey-approach, i.e. employing mean values of the input parameters, generally yields a fatigue life different from the mean fatigue life. In view of the above, it is of vital importance to bear in mind therandom nature of fatigue, and the many uncertainties involved, when workingwith fatigue life computations.Variable amplitude loading adds complexity to the problem of predictingfatigue life; i.e. the definition of load/stress cycles - through cycle countingmethods (Chapter 4), and sequence or interaction effects (Chapter 4). Themost common approaches to the problem are given in the following.Cy cle-by-cycle approach.Crack length after n cycles: Crack length increment (i.e. crack growth) in cycle "j":where: ai = initial crack length Cj = interaction coefficient, with value pertaining to cycle "j" (a)= constant amplitude crack growth rate. d N ~ ~ Thus, the interaction coefficient modifies the constant amplitudegrowth rate to account for interaction, i.e. acceleration or retardation. Mostexisting interaction models are retardation models. There is no proof that
    • Section 3.2.2these models in general improve a fatigue life prediction. Hence, before takingthe step of including interaction in the computations, one should give closeconsideration t o the stress history (irregularity factor, frequency and sign of"overload" stress peaks, etc.), to decide whether significant interactionsare likely or not. Besides, neglecting retardation gives conservative results,while accounting for retardation but not for acceleration might yield non-conservative results.Equivalent constant amplitude stress range approach.In this approach a variable amplitude stress history is represented by anequivalent constant amplitude stress range (Chapter 4) that causes the sameamount of fatigue damage, i.e. crack growth. This equivalent stress range maybe expressed as (Fig. 3.27a): interval Fig. 3.27 Stress range distribution (a) and histogram (b).
    • Section 3.2.2 (3.5 1)or as (Fig. 3.27b):where: fA2(Ao) = probability density function of stress range (Ao) fi = frequency of occurrence of stress range "i" (Aoi) k = number of histogram class intervals ni = number of cycles within interval "i" NT = total number of cycles Aoi = midpoint of histogram interval "i" p = empirical or calibration constantSpecial cases: p = 3 -+ RMC (root-mean-cube) stress range /3 = 2 -+ RMS (root-meansquare) stress range fi = m = Slope of the crack growth equation a =C(AK)~ dN + no interactionInteraction may be taken into account by adjusting P. It is pointed out (Chapter 4) that: - /3 = m is in effect a Miner-approach, in that crack growth increments are added linearly, with no account of interaction. - the approach has no sound theoretical basis, but is a very practical empirical approach. It is common practice to assume that the stress range Ao is Weibulldistributed, i.e.:where: E= shape parameter of the distribution 0 = scale parameter of the distribution The nth moment of this distribution might be expressed as:
    • Section 3.2.3where: r ( ) = gamma-functionThus, A, U, = {eo r ( i + p/g) = e { r ( i + pig) The r-function may be approximated by simpler functions. Thefollowing expression is a functional fit to the I-function in the argumentrange x c (3 .-6 .) ; r(x) r 0.0076 exp (1.60 x ) + 1.26 (3.5 6)and hence an approximate expression is: Ao,, % 0 (0.0076 exp {1.6 x ) + 1.26)ltP (3.57)where: x = 1 + PI,$. i * , t d 2 " I *3.2.3 Fracture mechanics applied in the calculation of SN-curvesThe Paris-equation for crack growth rate (Eq. 3.1 3) may be transformed tothe equation of an SN-curve through a simple integration. Thus, Eq. (3.41)may be reformulated as:where I is the integral in Eq. (3.4 1). This further yields:and The integral I depends on geometry (i.e. external- and crack-geometry),and is only weakly dependent on stress through the critical crack size. Thisinfluence is insignificant when af >> ai. Further, if initiation is absent or insig-nificant, then Nf = Np and :which is the equation of an SN-curve in the high-cycle region (N 5 lo4).
    • Section 3.2.3 III // Kmar=K c (a) $-curve m / / - / / , log C I log AK Log ad (b) SN-curveLog a 6 I F g 3.28 Relationship between i. a- SN-curves. dN and
    • Section 3.2.3 Equation (3.59) yields the following expressions:where: m, C = exponent and coefficient in Paris equation. The close relationship between crack growth rate curves and SN-curves isshown in Fig. 3.28 and Table 3.2. Table 3.2 Comparison of da/dN- and SN-curves. I Region da/dN-curve SN-curve I Threshold region Fatigue limit region (No - or intermittent (Infinite life) growth) I1 Intermediate region Finite life region (Regular striation (Intermediate - and growth. Paris eq .) high-cycle region) 111 Failure region Lo w-cycle or static (Fast fracture or failure region yielding)
    • Section 3.3 nrc 1T 3.3 EXAMPLES . # b ~of& 3 c f~ 6 # ~SR n stress fleld. Consider a crack extending through a tensile residual stress field (equal to yield stress oy) under uniform tension, as shown in the figure. When a 4 by Eq. (C. 1) in Appendix 3 .C yields: tttt Res i dua 1 stress When a > b, from Eqs. (3.C. 1) and (3 .C.3) : K = 1.122 ofia + $(oy-o) *fla(sin-:)* F () : where F(b/a) is given by Eq. (3.C.3).
    • Section 3.3Example 2 - Estimation o f stress intensity factor related to a crack in a transverse butt welded joint.A crack is detected at the toe of the joint. Estimate K!Data: i) Geometry.. . . - T = 20mm - due t o specified requirement, 8 < 30 = 180- @ - a = 1.0mm - assumed crack shape, a/2c = 0.25 ii) Loading ... . - axial load, amax = 350 N/mm2 K = o*@*FSaFT*FE*FG Eqs. (3.7) and (3.8) a/T= 1/20 = 0.05,+FT = 1.0 Fig. 3.16 FE = { I + 4.5945(0.25)1.65 }*. = 0.82 Eq. (3.9) q = log (1 1.584 - 0.0588 150)/log 200 Eq. (3.2 1) = 0.19 , . / FG = (5120)-*I9 = 1.30 -, Eq. (3.21) fs = 1 - 0.16(0.25) = 0.96 Eq. (3.10) ~k = 1.04 Fig. 3.14 Fs = 1.04 0.96= 1.0 Eq. (3.1 1) KT = 350 4-0 1.0 1.0 0.82 1.30 Eqs. (3.7) and (3.8) -Example 3 Cracking in transverse stiffener weld.Estimate K for a surface crack with depth 3 mm.Data: i) Geometry . . . . - T = 40 mm - assumed weld flank angle, 8 = 45" - weld leg length, II = 20 mm - a = 3mm ii) Loading ... . - axial load, omax = 300 N/mm2
    • Section 3.3 + SCF= 1.62 1 log(20/40) 3.963 = 3.5 Eq. (3.28) FG = 3.5 { 1 + 0.3602- (3/40)OS2 13 r1 Eq. (3.26), Table 3.1 = 1.41 2c = 2.59 (3)OSg4 = 7.32 mm Eq. (3.33) + a/2c = 3/7.32 = 0.41 = + FE = { l 4.5945 (0.41)"~ }.5 = 0.70 Eq.(3.9) fs = 1-0.16*(0.41)= 0.93 Eq. (3.10) F; = 0.98 Fig. 3.14 FS = 0.98 0.93 = 0.91 Eq. (3.1 1) a/T = 3/40, -+ FT = 1.0 Fig. 3.16 KI = a - - * 0 . 9 1 - 1 . 0 - 0 . 7 0 - 1 . 4 1 Eqs.(3.7)and(3.8) = 2.76 a = 829 ~ m m - . ~ 26.2 M P a r m = - VB!Let us assume that a very wide SAE 1020 plate is subjected to a constantamplitude uniaxial cyclic loading that produce nominal stresses varyingfrom omax = 200 MPa to omin = -50 MPa. ,----6t; What fatigue life would be attained if an initial through the thicknessedge crack were no greater than 0.5 mm in length? Kc = 104 MPafi. Before we can solve this problem, several questions must be answered.Namely, - What is the applicable stress intensity factor expression for this com- ponent and loading? - What crack growth rate equation should be used?
    • Section 3.3 - How do we integrate this equation? - What value of AK will cause fracture? - Does corrosion or temperature play an important part? Let us assume that corrosive environment is not involved, and that room temperature prevails. The Paris crack growth rate equation (Eq. 3.13) is often a reasonable expression for region B (Fig. 3.1 7) crack growth behaviour. Integration of the Paris equation involves numerical methods unless F from Eq. (3.7) is independent of crack length. In an infinite plate with a single edge crack loaded in uniform tension, F is constant and equal to 1.12. This is approximately correct for a finite plate as long as the crack length does not exceed about 10% of the width. which is above threshold levels and hence the Paris equation is applicable. The final crack length can be obtained by setting Kmax at fracture equal to Kc, i.e.: Eq. (3.48) Constant amplitude fatigue life:1 1 - 1 I A. A - 0.068)-~.~ (0.0005)-~~ Eq. (3.44) , N~ = (-0.5) :6.9 10-I 2 ) ( 2 0 0 ) ~ (n)1.5 ( I . I 213 = 189 000 cycles i.e. neglecting the negative (m = 3 , C = 6.9 lo- , m / ( ~ ~ a J m ) ~,a = 200 MPa, of the stress cycle, ) Now let us assume that the fracture toughness Kc were incorrect by a factor or divisor of 2, that is, Kc = 208 MPa Tor 52 MPa J . r n m The final fracture length from Eq. (3.48) would result in af = 270 mm and 17 mm, respectively, and the corresponding fatigue life Nf from Eq. (3.44) in 198 000 and 17 1 000 cycles. Thus increasing or decreasing the fracture toughness by a factor of 2 caused an increase or decrease in the final crack length by a factor of 4, respectively. However, the corresponding changes in fatigue crack growth life were less than 10%. If the initial crack length ai were 2.5 mm, the life would be only 7.5 000 cycles, instead of 189 000 cycles for the original problem with ai = 0.5 mm.
    • Section 3.3 These calculations illustrate the importance of minimizing initial flaw -or crack lengths to increase fatigue life, and that appreciable changes infracture toughness wl alter final crack lengths, but produce small effects on ilfatigue lives. Thus, Eq. (3.45) for a very long crack yields:i.e. about 9% longer life than estimated above. High fracture toughness in fatigue design, however, is still very desir-able because larger crack lengths are easier to detect by inspection. s. -Consider a joint of the type in Example 3. How many fatigue loading cyclescan the joint endure without getting a "through crack", i.e. a crack thatcompletely penetrates the main plate?Data: i) Geometry . . . . - plate thickness, T = 20 mm - weld leg length, R = 10 mm - weld flank angle, 8 = 45 degr. - initial crack depth, ai = 0.1 5 mm ii) Material . . . . - Paris eq. parameter, m = 3 iii) Loading . . . . - axia1,Ao = 2 0 0 ~ l m r n ~ C(Pariseq.)= (1.315.10-) = 2 8 . 3 1 ~ ~5.8. 10-l2 Eq. (3.20) B = 45 degr., -+ F = 0.98 : Fig. 3.14 + SCF = 1.62 1 log (10120) 3.963 = 3.5 Eq. (3.28) The computations are tabulated on the next pages. The fatigue lifeintegral I is evaluated numerically (Simpson). This computation is too rough for general use, but shows the method.
    • Section 3.3 a (mm) a/T a/2c fS FS FT FE a/2c from Eq. (3.33) fs >> Eq.(3.10) FT >> Fig. 3.16 FE >> Eq. (3.9) FG >> Eq. (3.26) and Table 3.1
    • ; - a; Chapter 3. References ,-- I-.- -- -L- . ,- -. 7_A- I = 0.5 (240 + 65) lo3 (0.5 - 0.15) lo- + 0.5 (65 + 33) lo3 (1 .O - 0.5) lo- + 0.5 (33 + 8.4)- lo3 (3.0 - 1.0) loe3 Eqs. (3.40) + 0.5 (8.4 + 5.5) lo3 (5.0 - 3.0) and (3.58) + 0.5 (5.5 + 2.5) lo3 (10.0-5.0) + 0.5 (2.5 +0.78)- 10 (20.0-10.0) lo- 169.575 Np = 5.8 10-17 . . (200)3 . .nl.5 = 656 325 cycles Eq. (3.41), REFERENCES 1. Tada, H., Paris, P.C. and Irwin, G.R.: The Stress Analysis of Cracks Handbook, Del Research Corporation Hellertown, ,Pennsylvania,1973. 2. Rooke, D.P. and Cartwright, D.J.: Compendium of Stress Intensity Factors, London, HMSO, 1976. 3. Sih. G.C.: Handbook of Stress Intensity Factors, Bethlehem, Pennsylvania, Lehigh University, 1973. 4. Liebowitz, H. (Ed.): Fracture (in 7 volumes). Academic Press, New York, 1968-70. 5. Sih, G.C. (Ed.): Mechanics of Fracture (in 6 volumes). Noordhoff, Leyden, 1973. 6. Cartwright, D.J. and Rooke, D.P.: "Evaluation of stress intensity factors", J. Strain Analysis, Vol. 10, No. 4, 1975, pp. 217-224. 7. Kobayashi, A.S. : Experimental Techniques in Fracture Mechanics. SESA, Connecticut, 1973.
    • Chapter 3. References8. Luxmore, A.R. and Owen, D.R.J. (Ed.): Proc. Int. Conf. Numer. Methods Frac. Mech., Swansea, 1978. Luxmore, A.R. and Owen, D.R.J. (Ed .): Proc. Second Int. Conf. Numer. Methods Frac. Mech., Swansea, 1980.9. Rooke, DP., Baratta, F.I. and Cartwright, D.J.: "Simple Methods of Determining Stress Intensity Factors", Engng. Fract. Mech., Vol. 14,1981, pp. 397-426.10. Cartwright, D.J. and Rooke, D.P. : "Approximate Stress Intensity Factors Compounded from Known Solutions", Engng. Fract. Mech., Vol6,1974, pp. 563-571.11. Rooke, D.P. and Cartwright, D.J. : "The Compounding Method Applied to Cracks in Stiffened Sheets", Engng. Fract. Mech., Vol. 8,1976, pp. 567-573.12. Besuner ,P.M. : "The Influence Function Method for Fracture Mechanics and Residual Fatigue Life Analysis of Cracked Components under Complex Stress Fields", Nuclear Engng. and Design, Vol. 43, No. 1,1977, pp. 115-154.13. Labbens, R., Pellissier-Tanon, A. and Heliot, J. : "Practical Method for Calculating Stress Intensity Factors through Weight Functions", Mechanics of Crack Growth, ASTM STP 590,1976, pp. 368-384.14. Engesvik, K.M. : Analysis of Uncertainties in The Fatigue Capacity of Welded Joints, Dr. ing. disserta- tion, Division of Marine Structures, The University of Trondheim, The Norwegian Institute of Technology, Trondheim, 1981.15. Albrecht, P. and Yarnada, K. : "Rapid Calculation of Stress Intensity Factors", Journal of the Struct. Div., ASCE, Proc. Paper 12742, Vol. 103, No. ST2,1977, pp. 377-389.16. Zettlemoyer, N. and Fisher, J.W.: "Stress Gradient Correction Factor for Stress Intensity at Welded Stiffeners and Cover Plates", Welding Research Supplement, Vol. 56, No. 12, 1977, pp. 3934 - 398-s.17. Zettlemoyer, N. and Fisher, J.W. : "Stress Gradient Correction Factor for Stress Intensity at Welded Gusset Plates", Welding Research Supplement, Vol. 57, No. 2,1978, pp. 57-s - 62-s.18. Zettlemoyer, N. and Fisher, J.W. : "Stress Gradient and Crack Shape Effects on Stress Intensity at Welded Details", - Welding Research Supplement, Vol. 57, No. 8,1978, pp. 246-s 250-s.19. Maddox, S.J.: "An analysis of fatigue cracks in fillet welded joints", Int. Journ. Fracture, Vol. 11, No. 2, 1975, pp. 221-243.
    • Chapter 3. References20. Newman, Jr. J.C.: "A Review and Assessment of the Stress-Intensity Factors for Surface Cracks", Part-Through Crack Fatigue Life Prediction, ASTM STP 687.1979, pp. 16-42.2 1. Broek, D. : Elementary Engineering Fracture Mechanics, Noordhoff Int. Publ., 1974.22. Paris, P. and Erdogan, F.: "A Critical Analysis of Crack Propagation Lawsy, Journ. Basic Engng., Dec. 1963, pp. 528-534.23. Klesnil, M. and Lukas, P.: "Influence of Strength and Stress History on Growth and Stabilisation of Fatigue Cracks", Engng. Fract. Mech., Vol. 4,1972, pp. 77-92.24. Forman, R.G., Kearney, V.E. and Engle, R.M.: "Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures", J. Basic Engng., 89,1967, pp. 459-464.25. Erdogan, F. and Ratwani, M. : Int. Journ. Fract. Mech., 6,1970, p. 379.26. Hartman, A. and Schijve, J. : Engng. Fract. Mech., 1,1970, p. 615.27. Schiitz, W. : "Procedures for the prediction of fatigue life of tubular joints", Int. Conf. on Steel in Marine Structures, Paris, 1981, pp. 254-308.28. Austen, I.M. and Walker, E.F.: Research Report PT/6795/8/77/A.29. Gurney, T.R.: An Analysis of Some Fatigue Crack Propagation Data for Steel Subjected to Pulsating Tension Loading, Report 5911978/E, The Welding Institute, March, 1978.30. Gurney, T.R.: Fatigue of Welded Structures, 2nd ed., Cambridge Univ. Press, 1979.3 1. Frank, K.H. and Fisher, J .W. : "Fatigue Strength of Fillet Welded Cruciform Joints", Journal of the Structural Division, Vol. 105, No. ST9,1979, pp. 1727- 1740.32. Yarnada, K. and Hirt, M.A.: "Fatigue Crack Propagation from Fillet Weld Toes", Journ. Struct. Div., ASCE, Vol. 108, No. ST7, July 1982, pp. 1526-1540.33. Albrecht,P.: Fatigue Strength of Welded Beams with Stiffeners, Ph.D. dissertation, Lehigh Univ., 1972.
    • Appendix 3 .A34. Rolfe, S.T. and Barsom, J.M.: Fracture and Fatigue Control in Structures. Applications of Fracture Mechanics, Prentice-Hall, Inc., 1977.35. Lawrence, Jr. F.V., Mattos, R.J., Higashida, Y. and Burk, J.D.: "Estimating the Fatigue Crack Initiation Life of Welds, Fatigue Testing of Weldments, ASTM STP 648,1978, pp. 134-158.36. Tada, H. and Irwin, G.R.: "K-value Analysis for Cracks in Bridge Structures", (Rough draft review copy), Fritz Engineering Lab. Rept. No. 399.1, June 1975.APPENDIX 3.A CONVERSION TABLES Stress in tensity factor M P a 6 ksifi ~ m m - ~ kp mm-32 ~ MPa 6 1 0.9101 3 1.623 3.223 5 ksifi 1.0988 1 34.747 3.5420 ~ m r n - ~ " 0.03 1623 0.028780 1 0.10194 kp mm-32 0.3 1022 0.28233 9.8067 1 A Stress MPa ksi N/mm2 kp/mm2 MPa 1 0.1449 1 0.1019 ksi 6.904 1 6.9033 0.7037 N/mm2 1 0.1449 1 0.1019 kp/mm2 9 3067 1.421 1 9 24067 1
    • Appendix 3 .C Fig. 3.C.19. Fig. 3.C.20. The stress intensity factors are given by the following formulasWhere : a. When the local in-plane transverse displacement near the cracked section is not restrained Fig. 3 .C. 1 9.(Better than 2%for any a/w.) b. When the local transverse displacement is also restrained (Fig. 3.C.20). (3.C. 15) 2w(Exact)
    • Appendix 3 .C(Better than 0.5% for any a/w.)(C-3) Concentrated splitting forces (Greens function), Fig. 3 .C. 18. Fig. 3.C.18.(Better than 2% for any b/a and a/w.) It should be noted that the solutions illustrated above are valid onlywhen the displacement of the strip is free from constraint. In actual structures,any connected structural member is under constraints imposed by the connec-tions. When a crack occurs in a certain component, its compliance increasesand load and deformation are redistributed between members. Thus, theboundary condition is not displacement-free but displacement-limited.(C-4) Examples of displacement constrained strip with a single edge crackare given in Figs. 3.C.19, 3.C.20. The inplane transverse displacement atinfinity is restrained.
    • Appendix 3.C(C-I) Uniform tension, Figs. 3 .C. 1 5 , 3 .C. 1 6 . Fig. 3.C.15. - d d - I A C a - - a , W i Fig. 3.C.16. 0.752 + 2.02a + 0.37(1- ~ i n x ) ~ F(a/w) = J2-w tan-aa w 2w (3.C. 1 1) aa 2w COS- na 2w(Better than 0.5%for any alw.)(C-2) Uniform bending, Fig. 3 .C. 1 7. d -6 -6 Fig. 3.C.17.
    • Appendix 3.C (3.C. 10)(Much better than 5%; better than 2% for S 2 0.5.)When b = 0 F(0,S) = 1.10- 0.60s + 0.03S2+ 0.89S3 s3/2(Better than 2% for any S.)C. An edge crack in a long strip, Fig. 3.C.14. Fig. 3.C.14.Stress intensity factor solutions are known for various loading conditions forthis geometry. Only approximate formulas and their accuracies are given forseveral basic cases. For more information se /I/, pp. 2.10-2.2 1 and 2.25-2.29.
    • Appendix 3.C (B-2) Linearly varying stress (in-plane bending), Fig. 3 .C. 1 2. Fig. 3 .C. 1 2.(Better than 1% for any S ) .(B-3) Concentrated splitting forces (Greens function), Fig. 3 .C.13. Fig. 3.C.13.
    • Appendix 3 .C Fig. 3.C.10.is relatively small, the solutions for the configuration shown in Fig. 3.C.10may be of some value for estimating stress intensity factors.(B-1 ) Uniform normal stress, Fig. 3 .C. 1 1. Fig. 3.C.11.(Better than 1% for any S.)
    • Appendix 3.C Fig. 3.C.8. within 4% accuracy. For the example shown in Fig. 3 .C.8, K is estimated at K 1.122 0,6+ 1.255 K, (3 .C.7) and the accuracy improves as o o / o increases. (Even when o0 = 0, accuracy is within 476.) Although this method applies to the case where the stress distribution changes its sign over the crack length, the accuracy is not expected to be as good.B. An edge crack in half-plane (free boundary consists of two straight lines), Fig. 3.C.10.In welded structures or components, surface cracks often initiate in theresidual stress zone near the welding as shown in Fig. 3.C.9. When the crack c Crack Fig. 3.C.9.
    • Appendix 3.C Fig. 3.C.6. entire crack.) A complicated, more rigorous analysis may not be justi- fied.4. When a more accurate value is desirable, K estimate is improved by se- parating non-uniform stress into uniform stress and non-uniform stress as shown in Fig. 3 .C.8. From Equations (3 .C. 1) through (3 .C.4), the ranges of free surface correction factors K / K , for various non-uniform stress distributions are known (Fig. 3.C.7) and the values at the middle of the range are Fig. 3.C.7.
    • Appendix 3 .C(A-4) Concentrated splitting forces (Green s function), Fig. 3 .C.5. Fig. 3 .C.5. 2P K= - 1 F (b3 6 ,hi (better than 2% for any b/a) (3.C.4) b - FG) E 1.30 0.30 (b 3/2 -) -F(b/a) is the free surface correction factor.Note: 1. For any non-uniform stress distributions, stress intensity factors are obtained by integration of Equation (3.C.4). 2. Equation (3.C.4) shows that the correction factor for a single free surface for any normal stress distribution as long as the normal stress has the same sign over the entire crack length. K, is the solution for the infinite plane with geometry and loading configuration reflected across the free boundary, Fig. 3 .C.6. For the infinite plane problem, the exact Greens function is known (in Eq. (3.C.4), F(b/a) = 1) and K, calculations are considerably simpler. 3. In engineering practice, when only the rough idea with acceptable accuracy wl suffice, one can simply estimate K as il without causing substantial error. The error is never beyond 15% and usually much less. (When the normal stress has the same sign over the
    • Appendix 3.C(A-2) Linearly varying stress (in-plane bending), Fig. 3 .C.3. Fig. 3 .C.3. K = 0.439 o f i (accurate) = 1.210 (1 - +) o f i -The factor representing free surface influences is 1.2 10.(A-3) Partially distributed constant pressure, Fig. 3 C.4. Fig. 3.C.4. K= 2 o + (sin- 7T (better than 2% for any b/a) (3.C.3) b b 5/2 F(T) -)" 1.30 -0.18 (T)F(b/a) is the free surface correction factor.
    • APPENDIX 3.C A SMALL COMPENDIUM OF STRESS INTENSITY FACTORS (From "K-value analysis for cracks in bridge structures", by Tada and Irwin 1361.)3 .C.l Two-dimensional edge crack problemsWhen surface cracks have a large surface length-todepth ratio, solutions fortwo-dimensional edge crack problems provide approximate stress intensityfactors for the region near the deepest crack edge.A. An edge crack in half-plane (straight free boundary) (Fig. 3 .C. 1) Fig. 3.C.1.Stress intensity factors for various loading conditions are known for thisgeometry. Only approximate formulas and their estimated accuracies will bepresented for several basic stress distributions. For more information see / 1/pp. 8.1-8.8.(A-1) Uniform tension, Fig. 3 .C.2. Fig. 3 .C.2. K = 1.122-ov7iT (accurate) (3.C.1)The factor representing free surface influence is 1.122.
    • Appendix 3 .BAPPENDIX 3B GENERAL REFERENCESTextbooksKnott, J.F.:Fundamentals of Fracture Mechanics, Butterworth & Co (Publishers) Ltd., 1973.Frost, N.E., Marsh, K.J. and Pook. L.P.:Metal Fatigue, Clarendon Press, Oxford, 1974.Broek, D. :Elementary Engineering Fracture Mechanics, Noordhoff Int. Publ., 1974.Rolfe, S.T. and Barsom, J.M.:Fracture and Fatigue Control in Structures. Applications of Fracture Mechanics,Prentice-Hall, Inc., 1977.Gurney, T.R. :Fatigue of Welded Structures, 2nd ed., Cambridge Univ. Press, 1979Hellan, K. :Bruddmekanikk, Tapir, Trondheirn, 1979 (in Norwegian).Cherepanov, G.P. :Mechanics of Brittle Fracture, McGraw-Hill Inc., 1979.Fuchs, H.O. and Stephens, R.I.:Metal Fatigue in Engineering, John Wiley & Sons, Inc., 1980.Parker, A.P. :The Mechanics of Fracture and Fatigue, W. & F.N. Spon Ltd, 1981.Journals- Engineering Fracture Mechanics- Fatigue of Engineering Materials and Structures- International Journal of Fatigue- International Journal of Fracture- Journal of Applied Mechanics, ASME- Journal of Strain Analysis- Journal of the Structural Division, ASCE- Metal Construction
    • Appendix 3.C Equation (3 .C. 14) is 12 to 30 percent larger than Equation (3.C. 15).When the strip has attachments such as stiffeners, Equation (3.C.15) is ex-pected t o give reasonable estimates for stress intensity factors. An edge crackin the flange plate of a beam is a typical example in practical structures.3.C.2 Elliptical cracksCompletely embedded crackApproximate influence function (i.e. stress intensity at boundary point Acorresponding t o the parametric angle @, due to unit splitting forces appliedat point B (Figs. 3.C.21,3.C.22)): h# = h&,y,afiA) +- .*.R = nw2 , Q2 J a T (3.C.16) (1-k2 - C O S ~ # ) ~ . ~ ~where: $ = angle (Fig. 3 .C.2 1) R,r,R= lengths (Fig. 3 C.22) k2 = 1 - ( a / ~ ) ~ a2 = ( ( ~ / a +~ y / ~ ) ~ ) ( x,y = coordinates for point B itting ces P=l B Fig. 3.C.21. Fig. 3.C.22.When # = 0 and 7r/2, Eq. (3 .C. 16) specializes to: = hj(a,c,x,~) 6 .C nl.s * Q;where: (next page)
    • Appendix 3.C j = 1 , 2 corresponds to Q, = n/2 , O . + r = (x2 y2 )Oa5 + C = la)^ (y/cl2 )- - 1)0-5= { a - 2 - 1 }0-5Thus, approximate stress intensity factors are obtained as:The influences of free surfaces might be taken into account through correc-tion factors. Eq. (3.C.16) is exact for k = 0 (a = c), and the loss of accuracy formoderate increases of k is expected to be relatively small. Numerical inte-gration trials and comparisons with known solutions indicate that Eq. (3 .C. 16)yields an upper bound estimate of K. The accuracy (within +(5-lo)%) is bestwhen q5 is close to ~ / 2 .
    • CHAPTER 4 BASIC FATIGUE PROPERTIES OF WELDED JOINTS Stig Berge Norges tekniske hsgskole, TrondheimABSTRACTThe purpose of this chapter is to give a basic understanding of the fatigueproperties of metals in general and of welded steels specifically. The followingtopics are discussed : - Basic fatigue mechanisms, characteristics of fatigue failures, and metho- dologies for fatigue strength assessment. - Constant amplitude (SN) testing, types of tests, test specimen vs. structural behaviour in fatigue loading. - Cyclic strain and material response, total strain response to fatigue loading. - Variable amplitude loading, cycle counting methods, load spectra. - Cumulative damage, the Miner summation, equivalent stress range. - Fatigue of welded joints, effects of geometry, residual stresses, material properties. - SN data for welded joints, classification of joint types, statistical analysis of SN data, assessment of design curves.LIST OF SYMBOLSUnless otherwise indicated, symbols in this chapter are according to thefollowing standards, cf. Annual Book of ASTM Standards Part 10: E6 -81 Methods of Mechanical Testing E206-72 (1979) Fatigue Testing and the Statistical Analysis of Fatigue Data E5 13-74 (1980) Constant-Amplitude Low-Cycle Fatigue Testing E6 16-8 1 Fracture Testing
    • Chapter 4. List of symbols elongation at fracture (ISO/DIS 82-1 972) cross sectional area of unstressed specimen cross sectional area at fracture crack length fatigue strength exponent crack growth rate parameter fatigue ductility exponent modulus of elasticity engineering strain irregularity factor stress intensity factor fracture toughness plain strain fracture toughness fatigue notch factor stress intensity maximum in one cycle stress intensity minimum in one cycle elastic or theoretical stress concentration factor range of stress intensity in one cycle threshold stress intensity range for crack growth gauge length of unstressed specimen increment of gauge length crack growth exponent fatigue life, number of cycles to failure number of stress cycles endured number of cycles with same stress range load at fracture fatigue notch sensitivity stress ratio = omin/oma = Kmin/Kmax notch root radius nominal stress stress amplitude variable component of stress equivalent stress range fatigue limit mean stress steady component of stress maximum stress in one cycle minimum stress in one cycle
    • Section 4.1 fatigue strength at N cycles yield tensile stress ultimate tensile stress range of stress, stress range maximum stress range in a load history reduction of area at fracture (ISO/DIS 82-1972) true strain, based on actual (strained) cross section elastic strain strain at fracture, fracture ductility in monotonic loading fatigue ductility coefficient plastic strain total strain strain range in one cycle elastic strain range in one cycle plastic strain range in one cycle spectral shape parameter true stress, based on actual (strained) cross section stress at fracture in monotonic loading fatigue strength coefficient maximum stress in one cycle minimum stress in one cycle monotonic yield stress cyclic yield stress stress range in one cycle effective stress range4.1 BASIC FATIGUE MECHANISMS AND CHARACTERISTICSFatigue may be defined as a process of cycle by cycle accumulation of damagein a material undergoing fluctuating stresses and strains. A significant featureof fatigue is that the load is not large enough to cause immediate failure.Instead, failure occurs after a certain number of load fluctuations have beenexperienced, i.e. after the accumulated damage has reached a critical level. In fatigue, the most important load effect parameter is the fluctuatingcomponent of stress or strain, commonly referred to as stress or strain range,defined as the difference between a load peak and the subsequent valley.The mean or peak levels of loading are of relatively minor importance ascompared to the range of stress.
    • Section 4.1.1 A fatigue process will go through several stages, from the initial stateof the material t o final fracture, each stage characterized by the nature ofthe fatigue process. For a smooth or notched (machined) component ofa metallic material, the stages are commonly denoted Stage I: Initiation or crack nucleation Stage 11: Crack growth Stage 111: Final failure A brief discussion of these stages will be given, with emphasis on thephenomenological aspects.4.1.1 Fatigue initiationFatigue initiation is a process of cumulative plastic strain. The developmentof plastic strain is associated with dislocation mobility, which is greater ata free surface than in the bulk of the material. Hence, fatigue initiation isin general a surface phenomenon. Only in rare cases, for example at theinterface between the carburized layer and the core of case hardened steels,have fatigue cracks been observed to initiate in the interior of a material.The term "surface" in the context of fatigue initiation refers to exterior aswell as interior surfaces. An embedded weld defect, for example, representsa free surface where fatigue initiation may take place in the same way as onan exterior surface. Fatigue initiation is linked to microscopic material behaviour. Undercyclic strain, the macroscopic plastic deformation in each cycle will cancelout, cf. Fig. 4.1. Microscopically, however, defects produced in the latticestructure by the cycling will accumulate, leading t o a progressive fatiguedamage. Fig. 4.1 Cyclic stress-strain response in a metallic material (schematic).
    • Section 4.1.2 In crystalline materials, plastic deformation, or slip, takes place inpreferred directions and along preferred crystallographic planes. Microscopicslip may occur in single grains at stresses below the general yield stress of thematerial. Due to oxidation of the newly created free surfaces and hardeningof the strained material, reversed slip tends to take place on neighbouring slipplanes. The cumulative effect of this process is to cause a cyclic weakeningof the material, giving rise to a band of concentrated slip, a so-called per-sistent slip band which develops by localized plastic flow into extrusionsand intrusions on the surface (Fig. 4.2).Fig. 4.2 The development of persistent slip bands, extrusions and intrusions by cyclic slip. An intrusion is clearly a nucleus of a crack, which may develop intowhat is commonly denoted Stage I crack growth. In Stage I, crack growthtakes place on cry~tallographicslip planes, in a shear mode. This implies thatin this stage, cracks are of subgrain size, and oriented 45 to the maximumprincipal stress direction. No rational theory seems to exist for the crack initiation and Stage Icrack growth. Commonly these two stages are denoted "initiation", or "cracknucleation", and characterized through material parameters relating macro-scopic stress and strain to initiation life, cf. Section 4.3.4.1.2 Crack growthAfter initiation and Stage I crack growth, the crack will in general changemode and the growth direction will become perpendicular to the largestprincipal cyclic stress. (There are exceptions, for example torsional fatigueof cylindrical bars, where cracks may grow in shear modes.) In this stage,the maximum principal stress, and not the shear stress, will be the drivingforce.
    • Section 4.1.2 As has been discussed in detail Sec. 3.2.1, the stress and strain fieldsin the vicinity of a sharp crack under essentially elastic conditions is uniquelycharacterized through a single parameter, the stress intensity factor K, whichis a function of the applied load (or nominal stress), crack length and shape,and external geometry. Assuming the crack growth increment in a load cycleto be a function of stresses and strains at the crack tip, then crack growthrates should correlate to the range of the stress intensity factor AK. Thishas indeed proved to be a valid assumption, and the general crack growthrates for Mode I cracks in metals are as shown in Fig. 4.3. / R e g i o n 111 UnstabLe fracture R e g i o n 11 Stable crack Region I Inltlation threshold *Kt h Log A K Fig. 4.3 Crack growth rate curve showing the three regions discussed in the text. The virtue of this discovery is that it allows for fatigue crack growthlife calculations of any geometry, provided a crack growth rate curve forthe particular material has been established by simple specimen tests. Thedetails of such analyses are discussed in Secs. 3.2.2, 3.3, 10.3 and 1 1.5. The sigmoidal shape of the crack growth curve in Fig. 4.3 suggests asubdivision into three regions. In Region I, the crack growth rate goes asymp-totically to zero as AK approaches a threshold value AKth. This means thatfor stress intensities below AKth there is no crack growth, i.e. there is afatigue limit. The threshold effect is believed to be caused by a complicatedsynergism of processes which leads to crack blocking for small stress inten-sities. Corrosion deposits in the crack, surface oxidation, fracture surfacemicroroughness, and residual plastic strains from the crack tip zone arebelieved to be important mechanisms contributing t o the threshold. Thethreshold level depends on stress parameters like mean stress, residual stresses,and stress interaction (stress memory) effects. Environmental effects are alsovery important. Sea water submersion, particularly under cathodic protection
    • Section 4.1.2conditions, tends to increase the threshold level, most probably throughcrack blocking by corrosion products or by calcarious deposits. This is furtherdiscussed in Sec. 7.3 c lo5, c lo9, 10 20 50 100 10 20 50 K)O AMPLITUDE OF STRESS INTENSITY FACTOR AMPLITUDE OF STRESS INTENSITY FACTOR A K / 2 kglmm)i7 AK12 kglrnrf?Fig. 4.4 Crack growth rate as a function of stress ratio for two high tensile steels (Ref. 171). Typical threshold data for a high-tensile steel in constant amplitudeloading are shown in Fig. 4.4. For partly negative stresses, the growth ratesseem to follow the range of the positive part of the cycle AK,ff = K,, - - - AK 1 -Rwhere This indicates that the negative part of the load cycle is nondamaging.It is generally assumed that crack closure is responsible for this effect. ForR > 0,i.e. tensile stresses, the threshold effects cannot be explained by simpleconcepts.
    • Section 4.1 -2 A popular form of the crack growth relation in the threshold region isIn this formula, the threshold value AKth is t o be inserted appropriate to themean stress and other parameters of importance. For welded joints, in whichresidual stresses tend t o prevail over any applied mean stress, this formula hasproved t o be sufficient for many types of analysis. Region I1 crack growth follows a power law, the so-called Paris-Erdogancrack growth law,This part of the curve is the basis of most finite life fatigue analyses of weldedjoints, cf. Secs. 3.2.1, 10.3 and 11.5. As indicated in Fig. 4.4, Region I1 crack growth rates at stress ratiosR > 0.4 are relatively insensitive to mean stress. For R < 0, i.e. partly negativestresses, the growth rates are seen t o follow the range of the positive partof the cycle, cf. Eq. (4.1). This indicates that the negative part of the cycleis non-damaging, as would be anticipated if crack closure occurs for negativestresses. The description of the mean stress independency for R > 0.4 is validonly in non-corrosive environments. In sea water with cathodic protection,particularly with high strength steels, high mean stresses may cause an accele-ration of crack growth rates which is quite significant, cf. Sec. 7.3. Region I1 crack growth rates for steels are remarkably insensitive tomaterial properties. In Fig. 4.5 are shown mean curves for three differentgeneric classes of steels: ferritic-pearlitic, martensitic, and austenitic stainless.The difference between these three mean curves is of the same order ofmagnitude as the inherent scatter in crack growth data (Ref. /8/). In Fig. 4.6 are shown data for different structural steels: plate material,heat-affected zone, and weld metal. No significant difference is seen betweenthe different materials (Ref. 191). A similar trend has been found for aluminium alloys. In fact, crackgrowth data for structural aluminium alloys and steel may be brought on acommon basis by the equation
    • Section 4.1.2 AK, k s l K 1 0 15 I I X) 25 RANGE OF STRESS INTENSITY FACTOR .AK Nmm- fFig. 4.5 Fig. 4.6Crack growth rate curves for three Crack growth rates for various types ofdifferent classes of steels (Ref. 181). weld metal, plate, and heat-affected zones in structural steels (Ref. 191). This means that the stress which gives equal fatigue crack growth ratesin these two materials, is three times larger in steel than in aluminium. Fromthis fact, and from fatigue testing of aluminium weldments, fatigue designrules for welded aluminium structures have been assessed by simply taking thedesign SNsurves for corresponding welds in steel and divide the stresses bythree (Ref. /lo/). This corresponds to the ratio of specific weight betweensteel and aluminium, which indicates that in terms of weight-saving, alumi-nium has no advantage over steel in fatigue design of welded structures. Region I11 crack growth is exhibiting a rapidly increasing growth ratetowards "infinity", i.e. ductile tearing and/or brittle fracture. Using conceptsof linear-elastic fracture mechanics (which for most engineering materialsis strictly not valid in this range), instability occurs when
    • Section 4.1.2This has led to the conception of parametric crack growth laws coveringRegion 111, like the Formans equation, which is much used in aircraft design,The material constants C and m in Eq. (4.8) are not necessarily equal t o thoseof Eqs. (4.3) and (4.4). Crack growth in Region I11 is of minor importance for marine structuresdesign. The reason for this is that if Region I11 crack growth becomes impor-tant, the cycle rate and the load spectra for most marine structures is suchthat final fracture will be imminent. Exceptions to this would be structureswith a low natural frequency, causing large peak loads with a very low proba-bility of occurrence. Functional loads may also have the same characteristics. The sigmoidal shape of the crack growth curves leads to considerablecomplications in fracture mechanics calculations, even if simplified parametricequations are used in order to describe the different regions. A commonlyused engineering approximation is shown in Fig. 4.7. Region I1 crack growthby the Paris-Erdogan formula (Eq. (4.4)) is assumed, and the threshold isapproximated by a cut-off. The cut-off model is conservative in the thres-hold region, and the deviation from a more accurate model is in many casesnegligible in relation to the uncertainty associated with an assessment of thethreshold. In many cases this uncertainty is so great that practical calculationsare performed with a straight-line extrapolation of the Region I1 crack growthcurve as shown in Fig. 4.7. With this "engineering crack growth curve",fracture mechanics calculations become much simplified. log A KFig. 4.7 Actual da/dN curve (solid) and two approximations for the threshold region commonly applied in engineering calculations.
    • Section 4.1.2 In summary, for most engineering purposes, a crack growth law of theParis-Erdogan type (Eq. (4.4)) is appropriate. Fatigue crack growth ratesof structural steels in air seem to fall within a common scatterband. Thresholdeffects need to be considered for each case, taking into account residualstresses and mean stresses in particular. Typical values of C, m, and AKthare given in Table 4.la-b. The influence of sea water environments and ofcathodic protection is discussed in detail in Chapter 7.Table 4.la Fatigue crack parameters C and m (Eq. (4.4)) for C-Mn structural steels BS 4360 Grade 50 or similar, in air. C ( 2 - ) m Validity Comments Ref. (MPa flm)m 7.1 10-l2 3.0 R>0.0 Mean values 42 5.32 1 0 " ~ 2.53 R > 0.0 Upper bound 42 5.9 lo-* 3.15 RZO.O Mean values 43 AK < 22 M P a 6 2.8 10-l1 2.65 R Z 0.0 Mean values 43 AK > 22 M P a d E 3.9 10-l2 3.1 R > 0.0 Mean values 44 5.2 1012 3.0 R=O Mean values 9 9.5 lo-* 3.0 R=O Upper bound 9Table 4 . l b Fatigue crack growth thresholds compiled in Ref. 1451. Air data. AKth (MPaJm) Sy (MPa) Material R = 0.0 R = 0.8 8.2 3 .O 309 Mild steel 7.8 12.3 7.7 12.5 3 .O 3.7 3.3 2.5 232 :ii 399 1 Mild steel Medium carbon steels 8.2 2.6 479 ASTM A 533 B
    • Section 4.1.3 - 4.1.44.1.3 Final failureIf a fatigue failure in a load-carrying member is allowed to progress, finalfailure will inevitably take place at some stage of crack growth (disregardingother types of limit states which may have been reached before final failure).Final failure may occur by basically three mechanisms: brittle fracture,ductile fracture, and plastic collapse, depending on the toughness of thematerial, temperature, loading rate, plate thickness, and constraint. A dis-cussion of these topics is given in Chapter 9. In a fatigue life assessment,final failure represents the end of the fatigue life, commonly defined by SNtests or by a maximum tolerable defect size in crack growth calculations.4.1.4 Characteristics of fatigue failuresIn this section, characteristics of fatigue failures will be discussed with refe-rence to typical details of welded offshore structures. In Fig. 4.8 are shown the fracture surfaces from fatigue failure ofan offshore structure (Ref. 11 11). Two features are to be noted, typical ofhigh cycle fatigue of offshore structures: - The material has undergone only minor plastic strain, i.e. the strains have been essentially elastic. - The fracture surface is smooth, with characteristic beachmarks reflect- ing the variations in load intensity through interchanging periods of storms and calmer weather. By microscopic examination, striations representing single cycle ad-vancements of the crack tip may also be observed. In high-cycle fatigue,however, it is not possible to associate these striations with cycle-by-cyclecrack growth, due to the fact that crack growth does not occur simultaneouslyalong the crack front. On a certain location, the crack may advance in onecycle, and then be arrested during the subsequent cycle(s) while the crackgrows in other locations along the crack front. The da/dN rate measuredexperimentally is thus a measure of an average crack growth rate along thecrack front. Only in special cases, generally with large growth rates in ductileand very homogeneous materials, may growth rates be inferred from cycle-by-cycle striations. In engineering steels, the crack advances partly by ductilemechanisms, partly by cleavage of individual grains, and striations are ingeneral difficult t o observe except in areas of large crack growth rates (Fig.4.9).
    • Section 4.1.4Fig. 4.8 Fig. 4.9Fracture surfaces showing beachmarks Striations on the fracture surfaceresulting from a variable amplitude shown in Fig. 4.8 (Ref. / I I/).load history. Crack growth directionfrom bottom to top (Ref. / 1 11).
    • Section 4.1.4 For a design engineer, the development of crack length vs. time in afatigue failure is an important aspect, with bearing on defect significance,quality control, inspection strategy, and redundancy requirements. Featuresof fatigue failures may be illustrated by examples. Crack growth through the plate thickness in a plane weld is illustratedin Fig. 4.10. An initial toe defect of 0.05 mm has been assumed, typical ofmanual welds. The feature to be noted is the extremely rapid accelerationof growth after the crack has reached a length of some few millimeters. Thisis typical for crack growth in plane unstiffened structures, where crackswill tend to advance with a straight crack front (small aspect ratio). Theacceleration of crack growth is then reflecting the power-law growth ofEq. (4.4).Fig. 4.10 Fatigue crack growth from the toe of a cruciform joint, as obtained by computer simulation. A similar behaviour is seen for cracks growing from cut-outs in un-stiffened structures. A special case are cut-outs in tubular braces, Figs. 4.1 1and 4.12. Even though the crack is growing away from a stress concentrator,the growth rate accelerates rapidly after the crack has reached a length ofsome few millimeters. The reason for this is that the cut-out itself may beregarded as part of the crack when a > d/ 10. In fracture mechanics terms:
    • Section 4.1 -4Fig. 4.1 1 (left): Crack growth from a cut-out. A short crack will sense the hot spot stress at the cut-out as a homogeneous field. A long crack will sense the average stress, but with the cut+ut as a part of the crack, leading to an accelerated crack growth rate, cf. Fig. 4.12.Fig. 4.1 2 (right): Crack growth from a circular cut-out in a tubular brace (Ref. 1111). K 1 K~ s (n a)/* for a/d 0.1 K1S*[n-(a+d/2)]"~ foralds0.1leading to a crack growth behaviour as shown. A consequence of this is that for the geometries in Figs. 4.10 and 4.1 1,any engineering size weld defect will have a very detrimental effect on fatiguelife. Moreover, the time to failure after the crack has reached a detectablesize may be too short for inspection routines to be reliable. Therefore, asudden loss of load-carrying capacity of single members should be consideredin the design of fatigue loaded structures. For stiffened members the progress of crack growth is somewhat diffe-rent. In Fig. 4.13, a crack growing in a stiffened plate is shown. In this case,redistribution of stresses to the stiffeners will take place during crack growth.The net effect is a reduction in stress intensity, and a retardation of growth
    • Section 4.1.4Fig. 4.13 Fatigue loaded stiffened plate (a) and stress intensity factor for a crack growing perpendicular to the stringers (b). Crack growth rate (c) and crack length (d). Also shown in Fig. (d) is crack growth for an unstiffened plate.rate when the crack tip approaches a stiffener. This general effect of stiffeningand load shedding is one reason why fatigue cracks may be tolerated in shipstructures to an extent which is not allowed in tubular offshore structures. Tubular joints are a category of welded joints which warrant a closerconsideration. Unstiffened tubular joints feature large stress concentrationsand a very complicated stress distribution with large gradients, Fig. 4.14.In this case, contrary to the case of a cut-out, the stress intensity of a crackgrowing out of the hot spot region will not increase. The crack growth ratewill therefore be fairly constant throughout a large part of the fatigue life. A typical crack length vs. time history for a tubular joint is shown inFig. 4.15. From initial microscopic defects along the weld at the weld toe or
    • Section 4.1.4 Fig. 4.14 Circumferential stress in a tubular T-joint in axial loading. I I I I Region 111 I I (circum- I I ferentlal I I growth) I I I I I I I I I I I I I 1 I I I I I 0 0.2 0.4 0.6 0.8 1.0 Fraction of tubular joint life Fig. 4.15 Fatigue crack growth in a tubular joint (schematic).interpass locations, the crack will initially tend to grow in a circumferentialdirection under the influence of the very local stress concentration created bythe weld profile. In this stage, the through-thickness growth will be limited.In the next stage, the crack will grow in a through-thickness direction, witha nearly constant growth rate, reflecting the gradual decrease in effectivestress as the crack grows out of the hot spot region. The last stage is thecircumferential growth of a through-thickness crack. In this stage, the crackwill be intolerably large from an ultimate strength point of view. Crackgrowth in tubular joints are further discussed in Sec. 8.3.5.
    • Section 4.1.5 The purpose of these examples is to demonstrate that damage accumu-lation over time in a fatigue failure is strongly dependent on the type ofstructure or the structural element. This fact has implications on defecttolerance criteria, inspection strategy, and design philosophy for differentstructures and different parts of a given structure. The essential parameterto be monitored is crack length, and for a refined study the appropriatedesign method should be based on the principles of fracture mechanics.4.1.5 Fatigue capacity assessmentThe assessment of fatigue capacity in design of structures may follow severalroutes, depending on the type of structure, type of loading, etc. In general,a distinction can be made between four different methodologies: i) Prototype or component testing ii) SN-curves iii) Crack growth rate curves and fracture mechanics iv) Cyclic strainThese methodologies will be discussed briefly in relation to marine structures.Prototype testing.Prototype or component testing is the most direct way of assessing fatiguestrength for a particular structure or structural component. The methodis in common use in the automotive industry, in the design of for examplecrankshafts, bearing pins, etc. Also in the aircraft industry, pro totype testingis a standard technique, even in full scale testing of entire aircraft structures. Prototype testing is very expensive, and is cost-effective only forfatigue critical structures, and/or structures which are produced in large series.Moreover, the fabrication procedure and load conditions need to be welldefined, otherwise the inherent uncertainties in the test conditions mayinvalidate the findings of the testing. Obviously, prototype testing is not feasible for welded offshore struc-tures, except for selected components of novel design or in new applications.Examples are cast tubular joints and tendons for tension-leg platforms. Evenin these cases, the test programs have generated data more of a comparativenature, with reference to standard components or materials tested underthe same (simplified) conditions, rather than prototype lives under realisticloading and environmental conditions.SN-curves.An SN-curve is a plot of fatigue life versus stress. The stress parameter, which
    • Section 4.1.5for welded joints is the stress range, is normally plotted as the ordinate.Fatigue life is generally defined as the number of cycles to failure. Most SN plots are based on constant amplitude loading, in which casethe parameters of stress and fatigue life are easily defined. Variable amplitudedata may also be plotted on an SN format. As will be discussed in Sections 4.4and 4.5, stress and fatigue life in variable amplitude loading may be definedin various ways. Fatigue cracks in welded structures will be confined to the weldedjoints or to flame cut edges. Only in very rare cases will fatigue cracks beinitiated in plain rolled material. The reason for this should be obvious:The welds provide notches and initial defects which even in the most opti-mized designs will give a much lower fatigue strength than the adjacent plainmaterial. The appropriate SN-curves for welded structures are thereforeSN-curves for welded joints, including flame cut edges. Exceptions to this rule are cast or forged components which are weldedinto the structure. In such cases, stress raisers in the cast or forged part maybe such that cracks will initiate from plain material surface rather than fromthe adjacent weld, e.g. cast tubular joints. The design will then be based onan SN-curve for the plain material, with an (elastic) stress concentrationfactor for the detail in question. In some codes, generally not of the latest developments, this lastapproach is applied to welded joints as well. The fatigue strength of eachjoint is based on a fatigue notch factor relative to plain material. This notchfactor is empirical, and takes into account the geometric, metallurgical, andother factors which may have an influence on the fatigue strength of welds.The method has several weaknesses, and is not applied in recent codes.Crack growth rate curves and fracture mechanics.Fatigue of welded joints is mainly a crack growth phenomenon. Fracturemechanics may thus be used in order to calculate the growth, and therebyto give assessments of fatigue lives, cf. Sec. 3.2.1. A direct design calculation by fracture mechanics for a given weld is,however, not feasible. The reason for this is that there are many uncertaintiesin the calculation procedure, particularly linked to the initial stages of crackgrowth, like size of initial defects, crack growth for short cracks, and thres-hold effects. Due to this, absolute calculations of endurance can rarely betrusted as such. In comparative studies, however, the initiation problem maybe eliminated. One is then limited to a study of cases in which the initiationconditions are identical. By choosing suitable values for the initial crack
    • Section 4.2.1length, the calculated endurances can be brought into accord with experimen-tal values by calibration. Provided the initiation conditions remain unchanged,fracture mechanics can then be used for calculating the influence of differentparameters (geometrical, environmental, etc.) on the endurance. In this sense,fracture mechanics has been used extensively as a research tool, employedin order to generalize experimental data. For assessment of the significance of defects, the situation is morein favour of fracture mechanics analysis. Engineering defects, i.e. defectswhich can be found by non-destructive testing techniques, are generally solarge that linear-elastic fracture mechanics with a crack growth power lawworks reasonably well.Cyclic strain.The cyclic strain approach was originally developed for machined smoothor lightly notched components in which fatigue life is dominated by a crackinitiation period. The method is of limited use in the design of welded struc-tures, in which fatigue life is dominated by crack growth. It may be usedin low cycle fatigue assessments of structures where functional loads maycause plastic strains (ship structures, crane pedestals, pipelines during layingoperations, etc.).4.2 CONSTANT AMPLITUDE SN TESTING4.2.1 SN testing versus crack growth testingSN testing and crack growth testing may be viewed as two different ap-proaches t o fatigue. In crack growth testing, material parameters are obtained,characterizing fatigue crack growth as a material property in a given environ-ment. In SN testing, fatigue life of a specimen, a component, or a structureis determined under given conditions of stress and environment. In manycases, particularly with machined (non-welded) specimens, the outcome ofan SN test is taken as life to crack initiation. However, crack growth is an important, sometimes dominating phaseof fatigue life. This is particularly true for welded joints, where crackgrowth in fact occupies a major part of the fatigue life. SN testing and crackgrowth testing may thus be viewed as complimentary methods, which canbe brought on a common basis by fracture mechanics analysis. In this sec-tion, the SN test approach will be discussed, leaving fracture mechanics toChapter 3 .
    • Section 4.2.24.2.2 Basic conceptsAll practical fatigue theories contain empirical parameters which may accountfor qualities like material properties, surface condition, geometry, stressstate, effect of environment, etc. This means that in order to apply a certaintheory to a specific design case, experimental calibration is a prerequisite. The basic fatigue test is the constant amplitude SN test. In this test,a specimen is subjected t o cyclic constant amplitude loading till failure. Inthis respect loading may be force, strain, or displacement controlled. Formost applications of interest t o structural engineers, the loading is a constantamplitude stress. Fig. 4.16 Definition of terms relating to SN testing. The prime parameter of the loading is the stress amplitude S,, or stressrange S, (cf. Fig. 4.16). Besides, the mean level of stress Sm is of interest,often denoted by the stress ratioR, S, and S, are interrelated through Typical load histories in SN testing are shown in Fig. 4.17. Note thesingularity in the stress ratio for pulsating compression stresses. In certaincodes, stress ratio is defined differently in order to avoid this problem. In an SN test, several identical specimens are usually tested at differentstress or strain ranges, in order to obtain an SN-curve as shown in Fig. 4.18.Usually, either the mean level or the stress ratio is kept constant in one testseries. The general effect of the stress ratio is shown in Fig. 4.19. High ratiostend to reduce the fatigue life at a given stress range. It is t o be noted thattesting with Sm = const. or R = const. will in general give different SN-curves.
    • Section 4.2.2 1 I Pulsating P u l s a t i ng compression tension I Compression- compression Alternating Tension- tension Fig. 4.1 7 Different types of loading applied in SN testing.Fig. 4.18 SN-curves for sharply notched specimens of mild steel and alumi- nium (Ref. / 121).As indicated in Fig. 4.20, testing at S, = const. and tensile (which is a normaltest condition), will give an increased stress ratio as the stress range is lowered.This will tend to reduce the fatigue life, and the comparative SN-curves willbe as indicated in Fig. 4.20. Offshore structures in general will experience a constant mean load.Most fatigue experiments, however, are traditionally performed at a constantstress ratio, with 0 < R < 0.5. (R = 0.0-0.1 is a particularly popular test
    • Section 4.2.2 10 log NFig. 4 .19 SN-curves for a notched high tensile stainless steel (18 Cr - 9 Ni) at varying stress ratios (Ref. / 131).condition). Hence, SN data from such tests may be unconservative at lowstresses when applied to offshore structures. The difference is disregardedin most applications. Several models have been proposed for the effect of mean stress, basedon the limiting stress concept. The limiting stress for any material is of, thetrue fracture stress in monotonic tension. SN testing is normally monitoredin terms of a nominal or engineering stress. Hence, the ultimate stress S, orthe yield stress Sy is used as the limiting stress. Adding the mean stress S ,and an alternating stress S,, this sum cannot exceed the limiting stress In the Haigh type diagram of Fig. 4.21, this amounts to a straight line,which limits the allowable combinations of S, and S,. Outside the allowableregion, the material would break during the first one quarter of a cycle, andcyclic stresses are of course not possible. This idealized description of the combined effect of S, and , is valid Sonly under monotonic loading. In fatigue, Eq. (4.12) will be distorted bythe cumulative effects of cyclic loading, which in general will cause a changein material properties. Empirical formulas have been established, based on
    • Section 4.2.2 Log NFig. 4.20 The difference between R = const. and S, = const. testing, and the influence on the SN-curve (schematic).Fig. 4.21 The Haigh diagram showing allowable combinations of stress ampli- tude and mean stress.
    • Section 4.2.2Fig. 4.22 The Modified Goodman, Gerber, and Soderberg relations for the effect of mean stress on fatigue strength for N = lo7 cycles, with data for a high tensile stainless steel (Ref. 1131).the same simple idea as displayed in Fig. 4.2 1. In Fig. 4.22 are shown threecommonly used expressions in the Haigh diagram. The limiting point on thealternating stress axis is the stress Sa,N at a given fatigue life under reversedloading (S, = 0 or R = -1). The lines are drawn for a given fatigue life andexhibit empirical combinations of stresses S and S, which will give that ,life. Modified Goodman relation: S, = S a , ~ (- - l ) srn su Gerber relation : Soderberg relation: None of the models are generally valid, as they are based on experi-mental data obtained under different conditions. Moreover, the concept ofusing monotonic tensile properties in defining fatigue strength is fundarnen-tally wrong. As will be discussed in Section 4.3, the stress-strain relation ofmaterials may be very different under cyclic loading as compared to monoto-nic strain, thus invalidating the concept of S, and S, as material parameters ,in fatigue.
    • Section 4.2.3 Fig. 4.23 The data shown in Fig. 21 plotted in a Smith diagram for N = 1o7 cycles. A more practical version of the same diagram is obtained through theSmith diagram (Fig. 4.23). Here, S,, and Smi, for a certain fatigue life areshown in the same diagram, giving a pictorial impression of the allowablecyclic stress range for a given fatigue life.4.2.3 Types of SN testsIn this section, various types of SN tests are described, and the relation ofsuch data to fatigue design is discussed.SN testing of plain materials.A basic fatigue test for material characterization is the SN test of plain mate-rial. Specimens are usually smooth cylindrical or hour-glass shaped as shownin Fig. 4.24, and loaded axially or in bending. The influence of the surfacefinish on the fatigue properties is minimized through standardized machiningprocedures. The test is thus a test of the basic fatigue strength of the materialin terms of engineering stress. In applications of the data, any effects of sur-face treatment like residual stresses, work-hardening, heat cycling, surfaceroughness etc. different from the conditions of the test, must be accountedfor.
    • Section 4.2.3Fig. 4.24 Typical specimens for fatigue testing of plain material in predomi- nantly elastic loading (ASTM E 466-82 Constant Amplitude Axial Fatigue Tests of Metallic Materials). In this type of test, most of the fatigue life is spent in the crack initia-tion stage. After crack initiation, the remaining fatigue life is relatively short.An SN plot will have a general form as shown in Fig. 4.1 8. SN data of this form are not very useful in design. One reason is thesensitivity to surface conditions as mentioned above. Another fact t o bearin mind is that fatigue cracks usually are initiated in areas of local stressconcentrations, and that stress gradients and stress concentrations are impor-tant parameters in fatigue. Stress gradients define the volume of stressedmaterial, which will be different in bending as compared to tension. Stressconcentrations raise the stress level, usually by a geometry dependent factorwhich may be non-linear due to local yielding as shown in Fig. 4.25.SN testing of welded joints.In a welded structure, the welds will constitute weak links with regard tofatigue strength. Plain material data of fatigue strength are not very useful
    • Section 4.2.3 Axia1,elastic Notched,axial, elastic Bending,elast ic Notched,axial,Local yieldingFig. 4.25 Specimens loaded to the same nominal stress but with different geometries and loading conditions will in general give different fatigue response, due to effects of stress gradients and of local yielding.for this problem. Fatigue design of welded structures is therefore based onSN data obtained with realistic welded specimens. Typical test configurationsand data are shown in Fig. 4.26. The statistical analysis and conversion ofsuch data into design criteria is described and discussed in Sec. 4.7. o Fracture I I I I 1 o5 1 o6 1 o7 Io 8 log N Fig. 4.26 Typical specimens and SN data for welded joints (Ref. 1141).
    • Section 4.2.4SN testing of structural components.The type of specimens shown in Fig. 4.26 may be taken as a part of a struc-tural member. In many cases, the stress distribution of members is so com-plicated that the fatigue strength cannot be reliably assessed from singlespecimen data. Typical cases are tubular joints and built-up beams (Fig. 4.27).Tests of these types of models are in principle similar to small-scale specimentesting, but requires extensive test equipment, and are in general more closelymonitored with regard to crack initiation and growth.Fig. 4.27 Structural components which have been subject of large-scale fatigue testing, tubular joint (a) and welded beam (b).4.2.4 Fatigue failure criteriaFatigue life in an SN test is usually taken as life till complete fracture hasoccured, or till displacements become so large that the load cannot be main-tained. In the last stage of a test, the crack size may therefore be larger thanwhat can be tolerated in structures. Two main reasons for this situation are: a) Fatigue tests are normally constant amplitude tests with relatively small loads. A crack can thus grow to a much larger length before becoming critical than in the case of realistic loading with occurrent peak loads. b) Fatigue tests are normally performed at room temperature and with scaled down plate thicknesses, leading to an unconservative fracture toughness. For most types of small scale specimens, the difference between thefatigue life at "end of test" and at a more realistic assessment of tolerablecrack size is negligible, as shown in Fig. 4.10. In large scale structural testing,however, the situation is more complicated. Considering crack growth in atubular joint, F&. 4.15, there is a significant amount of fatigue life from a half
    • Section 4.2.5through thickness to a through thickness crack, and the choice of fatigue lifecriterion may become important in the evaluation of fatigue data. A rational basis for assessing critical crack length is given in Chapter 9.4.2.5 Fatigue limitIn the past, much attention has been given to the fatigue limit and to experi-mental methods for determining the region of what has been termed non-damaging stresses. In offshore design, the concept of a fatigue limit has lostmuch of its significance, for three main reasons: i) The stress range at the fatigue limit found in constant amplitude testing of welded specimens is very low, typically in the range 50-1 00 MPa depending on type of joint and test conditions. It would be very uneconomical to design offshore structures with design loads below the initial threshold level, since in practical design, there will always be some stress cycles above the threshold which will cause crack growth. Also, with growing crack lengths, the stress level correspond- ing to the crack growth threshold will be gradually lowered, thus allowing a greater part of the load spectrum to lie above the threshold level. ii) The fatigue limit determined in small-scale testing is not representative of fatigue limits in large scale structures, since the limit is strongly linked to the size and occurrence of initial defects. In large-scale structures, the probability of exceeding a certain size of defect will be much greater than in a test series with small scale specimens. More- over, localized corrosion may create pits and crevaces in the region of welds, causing a time-dependent growth of initial defects. iii) The fatigue limit, or crack growth threshold, is strongly dependent on various factors like mean stress, load history, and environment. Environmental effects are in particular difficult to handle, due to a general lack of data. Assessment of the fatigue limit of real structures is therefore subject to large uncertainties. From the discussion above, it should be clear that the question of afatigue limit or a fatigue threshold for offshore structures is very complicated.Because of the uncertainties involved, the fatigue limit is therefore set verylow in design codes. A specific discussion on this topic is found in Secs. 11.1and 11.2.
    • Section 4.2.64.2.6 Real structures versus test specimensIn the previous sub-sections, frequent references have been made to diffe-rences between test specimens and real structures with regard to fatiguebehaviour. Design criteria are mainly based on statistical analyses of SN dataobtained with small scale specimens, and lack of similitude between testsand real structures in fatigue loading is an important point.Fabrication effects.Most laboratory specimens are purpose-made, and are not production-linewelds. The specimens are invariably produced in the most favourable con-ditions for welding, in a dry, clean, indoor environment, and with carefullycontrolled welding procedures. The liability of most experimentalists todiscard "rare events" from their collection of data should also be mentioned.The test specimens should therefore be expected to display a much smallerscatter and a larger mean fatigue strength than production-line structuralwelds.Size effect - defect probability.Fatigue is a weakest link process, the fatigue crack will start growing from themost severe notch or defect along the weld. Thus, the fatigue strength ofspecimens will tend to decrease as the weld length per specimen increases.The effect is shown in Fig. 4.28. In fatigue testing, the weld length is typicallysome centimeters, whereas in a structure, each welded joint will have dimen-sions of order meters. One should thus expect that structural joints will havea mean strength, in the lower part of the scatter band found in traditionaltesting. t 1 & - - - - - F u l l scale Log N Fig. 4.28 The effect of increasing the weld length tested per specimen.
    • Section 4.2.6 Structural redundancy. Considered as load-carrying members, test specimens either carry the full load or no load at all. Structural welded joints, however, will in most cases be part of a redundant structure. If a fatigue crack starts growing, the com- pliance of the joint will increase and the load will decrease. For part-through- thickness cracks, this effect is of little importance, because a main part of the fatigue life is spent in the growth of very short cracks with negligible influence on the compliance. For other failure modes, where a certain amount of cracking is allowed, the effect of redundancy may become significant. Residual stresses. Residual stresses in structures may be separated into two types (Fig. 4.29): Fig. 4.29 Residual stresses (schematic). (a) Long range stresses. (b) Short range stresses.. 1 . Short-range stresses exist only in and close to a weld, and are self- balanced over the cross section of one member. The cause of these stresses is the thermal contraction of parts of the cross section, under restraint from the cooler portions. Stresses will generally be large, at or above yield magnitude, and with large through-thickness gradients. Due to the short range, the stresses will be associated with small end displacements. Hence, they may fairly easily be reduced by heat treat- ment, or by local yielding caused by peak loads.
    • Section 4.3.1 - 4.3.2 Long-range stresses are uniform throughout a structural member, and are self-balanced within the structure. Their origin is from the proce- dure of assembling a monolithic structure from pre-fabricated com- ponents, whereby welding shrinkage and the use of local heating, mechanical restraints, brute force, etc., in the process of fitting the pieces together, may cause significant locked-in stresses. Long-range stresses are generally small compared with the yield stress, with small gradients. However, the associated end displacements, and hence the stored strain energy, may be large. As a consequence, these stresses are not easily relaxed by local heat-treatment procedures, nor are they much affected by peak load conditions and local yielding. Very little is known about residual stresses in marine structures, theirmagnitude, through-thickness variation, and variations through service life.In one particular investigation on welds in a ships deck, the residual stresseswere found to be far in excess of stresses from applied loads. Long-rangestresses were approximately 25 per cent of the short-range stresses (Ref. 1151). In small scale specimens typical of SN testing, short range residualstresses only will be present. In many types of specimens residual stresseswill be unrealistically low, an effect which needs to be accounted for in theanalysis of SN data, Sec. 4.7.3. The effect of residual stresses is particularlypronounced in the threshold region. In sea water with cathodic protection,residual stress effects are important also at higher load levels, see Sec. 7.3.4.3 CYCLIC STRAIN AND MATERIAL RESPONSE4.3.1 IntroductionThe main purpose of this section is to present the basic principles of cyclicstress and strain response in engineering materials, and the derivation offatigue strength criteria from this. Methods will be reviewed for the assess-ment of fatigue strength of structural components on the basis of materialflow properties. The methods are well established for machined, notchedcomponents typical of automotive structures, aircraft structures, machinecomponents, etc. They have also been applied in the analysis of the fatiguestrength of welded structures but have not as yet found general acceptanceexcept in low cycle fatigue.4.3.2 Monotonic stress and strainThe stress-strain relation for a steel in monotonic loading (tensile test) is
    • Section 4.3.2 Fig. 4.30 Tensile test, typical specimen and stress-strain relation in monoto- nic loading.shown in Fig. 4.30. The data provided by such a test are well-known to allengineers, and constitute the most basic characterization of the strengthof a material. Sy - yield strength Strength S, - ultimate strength parameters A - elongation at fracture Ductility Z - reduction of area at fracture parametersIn a tensile test, engineering definitions of stress and strain are applied. S = P/Ao - engineering stress (4.16) e = AL/Lo - engineering strain (4.17)True stress and strain may be derived by o = S(l +e) e = Qn(1t e )For small strains, the difference between engineering values and true valuesis small and is neglected in most instances.In fatigue analysis, the state of stress and strain at fracture in monotonicloading is of some importance. Of = Pfbf (4.20) - true fracture strengthq - true fracture ductility
    • Section 4.3.34.3.3 Cyclic stress and strain Fig. 4.31 The effect of strain hardening when unload- ing and reloading a plastically deformed material (schematic).When a material is stressed beyond the elasticity limit, the unloading curvewill follow Hookes law (Fig. 4.3 1). After yielding, there will be a permanentoffset in strain and an increase in the yield strength due to strain hardening.After unloading, the next load cycle will therefore follow the previous un-loading curve. The significant feature is the memory effect -the stress-straincurve in one load cycle depends on the previous stress-strain history. If the material is cycled further, a gradual change in the stress-strainrelation will take place, generally along two possible courses - cyclic harden-ing or cyclic softening, Fig. 4.32. For most engineering materials, a fairlystable state is reached after some few hundred cycles, or at a number ofcycles which is small compared to the fatigue life. This means that for amajor part of the fatigue life, a proper description of the flow properties of t I Controlled functton, stress Controlled function, strain 0 0 t -Cycle dependent hardening; Cycle dependent hardening; t 0 Cycle dependent softening; Cycle dependent soften~ng;Fig. 4.32 Material response under cyclic loading in stress control (left) and strain control (right).
    • Section 4.3.4the material must be based on the cyclic stress strain relations, and not onthe monotonic stress-strain curve shown in Fig. 4.30. E Fig. 4.33 Stabilized cyclic stress-strain hysteresis loop for a mild steel. A stable stress-strain hysteresis loop for a steel is shown in Fig. 4.33.All the stress and strain data needed for the fatigue characterization of a mate-rial are taken from the collection of stable hysteresis loops at different strainlevels. The basic equation is that total strain equals plastic plus elastic strain:For completely reversed testing (zero mean stress) the amplitude is equalto one half the rangeApplying Hookes lawthe plastic strain amplitude is given by4.3.4 Cyclic stress and strain resistanceThe response of a material to cyclic stress and strain may be summarized asfollows: i) The flow properties of metals are in general different in cyclic loading than in monotonic loading. This in particular refers to yield stress and fracture stress. ii) Metals respond in a different manner in stress cycling than in strain cycling.
    • Section 4.3.4 As a consequence it is necessary to distinguish between stress and strainfatigue resistance. Moreover, a relation between fatigue strength and materialproperties should be based on the cyclically stabilized properties of thematerial.Stress resistance.A plot of the fatigue life vs. true stress amplitude for a metal gives in generala curve of the Basquin form (Ref. 1161)N - cycles to failure2N - load reversals to failureoi - fatigue strength coefficientb - fatigue strength exponent - the sign of b is negative The fatigue strength coefficient is the stress intercept at one loadreversal (2N = I), hence it is related to of,the true fracture strength in mono-tonic loading. For most materials it turns out that # of 2 of (4.27)Plastic strain resistance.The plastic strain resistance is best described by the Manson-Coffin relation-ship (Ref. / 171, / 181)E; - fatigue ductiiity coefficientc - fatigue ductility exponent - the sign of c is negative The fatigue ductility coefficient is the plastic strain intercept at oneload reversal (2N = 1). The relationship between the e; and the monotonictrue fracture ductility ~f is not as simple as noted for the case of oi and of.For a majority of the materials which have been investigated,is a good approximation. But many steels fall far below this prediction, anda range of values has been found (Ref. / 19/),
    • Section 4.3.5TotaE strain resistance.In most practical cases of fatigue design, the critical location will be a notchin which plastic strains are imposed by surrounding elastic material. Thus,the situation will be strain controlled with a total strain range composedof an elastic and a plastic part. Manson proposed that a metals resistance tototal strain cycling can be considered as a superposition of its elastic and plas-tic strain resistance (Ref. 1171). By combining Eqs. (4.25), (4.26), and (4.28) The total strain life curve approaches the plastic strain life curve in thelow cycle region, and the stress life curve in the high cycle region as shownin Fig. 4.34. Data for a high-strength steel are shown in Fig. 4.35 t o followthis trend (Ref. / 191). The significance of the cyclic strain properties in fatigue is illustratedin Fig. 4.36. In the high cycle region, strong materials will have a greaterfatigue life. In the low cycle region, ductile materials will be superior. A toughmaterial with an optimum combination of strength and ductility will give thebest overall fatigue resistance. It appears that the crossover point in Fig. 4.34 is nearly the samefor many materials and is found at a strain amplitude of 0.01 and a life ofabout 2000 reversals. Therefore, at this strain range, the fatigue life is quiteinsensitive to material properties.4.3.5 Fatigue of notched membersMost fatigue failures are initiated from notches, thus fatigue design needto take into account the effect of notches on fatigue strength. The basic idea of notch theory of fatigue is that fatigue life is life tocrack initiation. Thus, if a local measure of the cyclic stress and strain atthe notch can be obtained, the fatigue life of the notched member can beassessed by comparison with an unnotched specimen undergoing the samestress and strain, cf. Fig. 4.36. As a first, and often quite useful approximation, local stress at thenotch is related to the nominal stress through the theoretical elastic stressconcentration factor Kt Related t o the fatigue strength of an unnotched specimen, for whichdata are generally available for most engineering materials, Eq. (4.3 2 ) states
    • Section 4.3.5 1 Log (2N) IFig. 4.34 Representation of elastic, plastic, and total strain resistance fatigue loading. 18ZNi Maraging ( 3 0 0 ) w v Load control Fig. 4.35 Test data and strain resistance curves for a high tensile steel (Ref. / 171). Fig. 4.36 Fatigue of notched members. Fatigue life is assumed to be equal to the life of an unnotched specimen undergoing the same stress-strain loading as the most highly strained material.
    • Section 4.4.1that the fatigue strength is reduced in inverse proportion to Kt. In mostcases Kt can be assessed by relatively simple analytical or experimental means. For more detailed analyses, this method is inadequate, due to the factthat Kt is not directly related to the fatigue notch factor Kf. Experimentally,Kf is measured as Kf = fatigue strength of a smooth specimen - - fatigue strength of a notched specimenat the same fatigue life. Kf will in general vary with stress level and with notch acuity. At lowstresses, where the material response at the notch is essentially elastic, Kf isapproximately equal to Kt. There is still under elastic conditions a size effect in Kf, related t o thevolume of material which undergoes large cyclic stresses. A practical formulafor the size effect of Kf is the Peterson formulawhere A is a material constant and r is the radius of curvature of the notch.As shown by Eq. (4.34), small notches have less effect in fatigue than pre-dicted by Kt. At high stresses, or in specimens with sharp notches, the response atthe notch will become plastic and non-linear. The elastic stress concentrationfactor Kt will then give a very inadequate description of the stresses andstrains at the notch. In general, Kf will tend to decrease by increasing stress.As a consequence, a direct measurement of Kf for a given notch case willrequire testing at several stress and strain levels, and becomes expensive andtime-consuming.4.4 VARIABLE AMPLITUDE LOADINGMethods for calculating the stress response of a structure t o various formsof fatigue loading by waves are discussed in Sec. 2.6. The purpose of thissection is to discuss the effect of irregular stress histories on the fatigue capa-city of steel structural components.4.4.1 Characterization of fatigue loadingAs stated frequently throughout this volume, fatigue is a cumulative effectof an irregular load history which for typical offshore structures spans aperiod of 20 years, or the order of 10%cycles assuming an average frequency
    • Section 4.4.1of 116 6. In order to be manageable in design procedures, this time historymust be reduced to some convenient format, representing the characteristicsof the loading.Variable amplitude loading, spectrum loading, and irregular loading arefrequently used synonyms for any loading which has not constant arnpli-tude. Various types of variable amplitude loading are defined below.Block loading is composed of blocks of constant amplitude cycles.Random loading or stochastic loading is a variable amplitude loading gene-rated by a random process. With digital test systems, the load signal genera-tion is often performed by an algorithm giving a fixed sequence of peaks andvalleys. The term pseudorandom is often attached to this procedure. If agiven sequence is repeated, it is termed random-ordered.In variable amplitude loading, certain events may be identified, cf. Fig. 4.37: -- Time Fig. 4.37 Definition of terrns related to irregular load histories.Reversal is the occurrence where the first derivative of the load-time historychanges sign.Peak is the occurrence where the first derivative of the load-time historychanges from positive to negative sign.Valley is the occurrence where the first derivative of the load-time historychanges from negative to positive sign.Range is the algebraic difference between successive valley and peak loads(positive range) or between successive peak and valley loads (negative range).Note that range may have different definitions, depending on the countingmethod used. "Overall range" is defined by the algebraic difference betweenthe largest peak and the smallest valley of a given load-time history.
    • Section 4.4.1Mean crossings (or zero crossings) is the number of times that the load-timehistory crosses the mean load level during a given length of the history. Nor-mally, only crossings with positive slopes are counted.Irregularity factor is a measure of the irregularity, or the bandwidth of thesignal, defined as the ratio of mean crossings with positive slope to the num-ber of peaks or valleys in a given load history. In fatigue analysis of welds,mean stresses are generally neglected, and mean-crossings are commonlyreferred to as zero-crossings. The irregularity factor I is linked t o the spectralbandwidth factor e (Eq. (2.9)) byFor narrow band loading, the irregularity factor will be close to unity (c % 0).Typical load histories for fixed offshore structures have an irregularity factorin the range 0.6 < I < 0.8.Root-mean-square (RMS) may be defined in two ways, either by a weightedaverage of the fluctuating stress itselfor by the stress rangesIn the latter case, will depend on the specific counting procedureapplied for the definition of individual cycles (see below). Whereas RMS has a defined physical meaning related t o energy in manyapplications of signal analysis, it does not necessarily have so in fatigueanalysis. As will be shown later, the power of two in Eq. (4.36) has no physi-cal significance in fatigue. In cumulative damage calculations, it can be shown(cf. Sec. 4.5.2) that the effect of variable amplitude loading may be taken intoaccount on an SN format by defining an equivalent stress rangewhere m is the slope of the crack growth curve (cf. Sec. 4.1.2 and Table 4.1).For welded joints the value of m is commonly taken as m = 3.The equivalent stress defined in Eq. (4.38) is often referred to as RMC oryroot-mean-cube"of stress. This stress entered into an SN diagram gives thenumber of cycles to failure for the corresponding irregular load history.
    • Section 4.4.2Crest factor is a measure of the "peakedness" of the stress spectrum, definedas the ratio of maximum stress in a load history to SRMs.The crest factor mayalso be defined by the stress ranges, i.e. the maximum stress range dividedby Sr,RMS The latter defmition is again subject to a choice of countingprocedure.Clipping level is sometimes introduced in test procedures, due to limitedload capacity of the test equipment or for more technical reasons, e.g. toavoid buckling, excessive yielding, etc. A clipping level may be a fact inreal structural loading as well, e.g. by safety-valve limitation of pressure inpressure vessels, automatic load limitations on cranes, one-sided (non-rever-sible) loading (both of the above), etc. Clipping of a load-time history isshown in Fig. 4.38. U n c l i p p e d random Loading; ---Clipping level ----Clipping level Fig. 4.38 Clipping of a random load signal.4.4.2For cumulative damage analysis, the stress-time history is broken down intoindividual cycles which are summed up to a distribution of stress ranges.Various procedures commonly referred to as cycle counting methods havebeen devised. The problem of cycle counting is illustrated in Fig. 4.39. Theload history may be broken down into individual cycles in several ways,leading to different assessments of fatigue damage. In many cases it is there-fore important to apply a counting method which gives the physically mostcorrect representation of the fatigue process. Several such methods will bediscussed. - Cycle counts are normally represented by spectra:Occurrences spectrum is a representation of variable amplitude loading bythe number of times a particular loading parameter (peak, range, level, etc.)
    • Section 4.4.2 1 Narrow bond Ln 1 Broad bandFig. 4.39 With narrow band loading, individual stress cycles are easily identi- fied and counted, and most counting methods yield similar results. In broad band loading, large cycles are interrupted by small cycles with varying mean level, and the resulting cycle count may depend significantly on the counting procedure.occurs within each specified interval of the parameter. In statistical termsan occurrences spectrum is the frequency function or probability densityfunction of the given parameter (Eq. (2.1)).Exceedances spectrum is a representation of spectrum loading contents bythe number of times specified values of a particular loading parameter (peak,range, level, etc.) are equalled or exceeded. t - I - Occurrences of Level crossings Exceedances of peaks/valleysFig. 4.40 An irregular load-time history (left) converted into an occurrences spectrum of level crossings (right). The difference in counts between two adjacent stress levels is equal to the number of peaks (above S, ) or valleys (below S,) in that interval of stress. Thus an occur- rence spectrum of level crossings is equivalent to an exceedances spectrum of peaks and valleys.
    • Section 4.4.2Level crossing counting.The method is shown in Fig. 4.40. In order to reduce the counting eventsby a factor of two, positive going level-crossings are recorded at and abovethe mean load, and negative-going crossings below the mean load. The difference between the counts on two neighbouring levels on thepositive side of the mean level is equal to the number of peaks in the corre-sponding interval of stress. Thus, an occurrences spectrum of stress levels is thesame as an exceedances spectrum of peak levels. An exceedances spectrum ofvalleys is obtained in a similar manner on the negative side of the mean level. The main problem with the level-counting method is that no informa-tion is obtained about the irregularity of the load. The normal method ofcycle count is to construct the largest possible cycle followed by the secondlargest, etc., until all level crossings are used as demonstrated in Fig. 4.4 1. d m Time- - ---- a ) L e v e l crossing coun t i n g ---- --- Time- - ( b ) L e v e l crossin counting w i t h 1 l e v e l leeadband ( l e v e l s counts d -0-1 ----- 4 0 1 1 2 ( c ) Cycles derived from level c r o s s i n g count o f ( a )Fig. 4.41 Level crossing counting of a broad-banded load history (a). The resulting distribution of ranges is shown in (c). In many cases, small stresses may be assumed to be non-damaging, and are there- fore disregarded. In level crossing counting, this may be achieved by introducing a dead band, as shown in (b).
    • Section 4.4.2 B C I O c c u r r e n c e s of Time Cycle count level crossingsFig. 4.42 By level crossing counting, stress cycles with a mean level different from the overall mean level (a) will be accounted for in an unrealis- tic way (c).Reversal points are assumed to occur halfway between levels. By this method,narrow-band processes are represented in a realistic way. For broad bandloading, stress ranges with mean values different from the mean level of theloading, are combined in an unrealistic way, cf. Fig. 4.42. For broad bandload histories, the level count method therefore tends to be conservative.Peak counting.Peak counting is illustrated in Fig. 4.43. Peaks are counted above, and valleys I Peak I~ounts] ( a ) Peak counting u n ? e Cycle s Ran s c o u n t 3 15 ( b ) Cycles derived from peak c o u n t o f ( a )Fig. 4.43 Peak count of a broad banded load history (a). The resulting cycles are shown in (b).
    • Section 4.4.2 ( b ) Mean crossing peak countingFig. 4.44 Peak count of the same load history as shown in Fig. 4.55, but counting only extreme peaks and valleys between reference (mean) level crossings.are counted below the mean level. Results for peaks and valleys are usuallyreported separately. A variation of this method is to count all peaks andvalleys without regard to the mean level. In some cases it may be justified to disregard small variations in stress("ripples"). One practical way in which to do that is to count as peaks andvalleys only the extreme values between successive mean level crossings,cf. Fig. 4.44. Similar to level counting, peak counts are combined by constructingthe largest possible cycle, then the second largest, and so on. In this way, aconservative count is obtained. An alternative method is to combine pairsof peaks and valleys in a random way.Simple range counting.For this method, a range is defined as the stress difference between tworeversals, Fig. 4.45. The method distinguishes between positive and negative I Ranges counted Method 2 1-4Fig. 4.45 Part of an irregular load history and two methods of counting ranges. With Method 1, each range between reversals is counted. With Method 2, small reversals are ignored. The difference in terms of cumulative damage may be significant.
    • Section 4.4.2ranges. If the mean of each range is also counted, the method is called range-mean counting. If only positive ranges are counted, each range is countedas a cycle. If both positive and negative ranges are counted, each range iscounted as one half-cycle. One problem with range counting is how to take care of small cycleswithin large cycles. The sequence shown in Fig. 4.45 may be counted as threeindividual and small half cycles, or as one large half cycle. The resultingdamage summation will depend significantly on the choice of thresholdlevel for counting small cycles.Rainflow counting.Rainflow counting is often used as a common name of a large class of count-ing methods: range-pair counting, the Hayes method, the original rainflowmethod, range-pair-range counting, ordered overall range counting, racetrackcounting, and hysteresis loop counting. The various methods are summarizedin Ref. /20/. If the load history begins and ends with its maximum peak, orwith its minimum valley, all these methods give identical counts. In othercases, the counts are similar, but not generally identical. Only one methodof this class will be reviewed here, rainflow counting (Ref. 1211). This counting procedure is designed to count reversals in accordancewith the materials stress-strain response, cf. Sec. 4.3. The principle may beillustrated by the strain history shown in Fig. 4.46 and the correspondingstress-strain path. The individual cycle 2-3-2 does not effect the remainderFig. 4.46 Part of a strain history (a) and the stress-strain response (b) of a material being subjected to this history. Note that the small cycle 2-3-2 forms a closed hysteresis loop within the large range 1-4, the latter being undisturbed by the interruption.
    • Section 4.4.2of the stress-strain history. Each time the hysteresis loop is closed, a cyclecount is made. The method is illustrated for a more complicated strain historyin Fig. 4.47. 2-3-2 Cycles 8-9-8 5-6-5 Half 1-2-4 cycles 4-5-7 7-8-1 0Fig. 4.47 A more complicated strain history (a) and the corresponding stress- strain response (b). The rainflow counting method counts small cycles within large cycles similar to the way closed hysteresis loops are formed. The cycle count is thus reflecting the way in which the material is responding. Rainflow counting has obtained its name from an analogy of rain fallingdown a pagoda roof, Fig. 4.48. The strain history in Fig. 4.48 is the same asin Fig. 4.47. The rules of rainflow counting are as follows, 1. Rain will flow down the roof initiating at the inside of each peak or valley. When it reaches the edge it will drip down. 2. The rain is considered to stop, and a cycle is completed, when it meets another flow from above. 3. Starting from a peak, the flow also stops when it comes opposite a more positive peak than that from which it started. Starting from a valley, the flow stops when it comes opposite a more negative valley than that from which it started.
    • Section 4.4.2 Strain Counting t TimeFig. 4.48 The same load history as in Fig. 4.47 (a) illustrating the pagoda roof rainflow analogy. By inspection, it may be verified that this counting procedure repro-duces the cyclic stress-strain loops of the material undergoing the same load-ing history. For wide-band loading, rainflow or similar counting proceduresis therefore recommended. For narrow-band loading all the counting proce-dures reviewed above will yield similar results. Unless the load history isrearranged to start with its most positive peak or its most negative valley,a rainflow count will give a number of unpaired half cycles which are difficultto handle in cumulative damage analysis. Moreover, rain flow counting loses itsphysical significance when applied to cracked specimens where crack closuremay occur under compressive loading.Symmary of cycle counting.The problems of cycle counting and choice of method arise only if the designis to be based on an actual load-time history. Such histories can berecorded as loads or stresses from an actual structure, simulated load historiesfrom model experiments, or computer simulated time histories. Moreover,if the structural response is narrow-banded, all counting methods converge.Even for moderately wide band load histories, the different counting proce-dures give only minor differences when applied in fatigue analysis. Only forvery wide band load histories with irregularity factor less than about 0.5 doesthe counting procedure become important.
    • Section 4.4.3/23/), although experimental verification is scarce. A detailed discussion ofvarious aspects of cycle counting is found in Ref. /22/.4.4.3: w=*The most common way of representing irregular load histories for fatigueanalysis is by an exceedances diagram of stress ranges, Fig. 4.40. This diagramis often called the stress spectrum. Note that for a given load history, thestress spectrum may depend on the counting method applied. Typical stress spectra are given in Fig. 4.49. l o g ( E x c e e d a n c e s of s t r e s s ranges)Fig. 4.49 Typical forms of exceedances spectra of stress ranges, cf. text for discussion. a) Constant amplitude loading. . b) Maximum stress (range) is limited, stresses below this level are random (cranes, pressure vessels, etc.). c) Minimum load is above a certain level. d) Gaussian stationary (statistical properties do not vary with time) loading. e, f)Typical long term spectra for environmentally loaded offshore struc- tures as discussed in Secs. 2.6 and 10.5. In many cases, the load spectrum can be approximated by a two-para-meter Weibull distribution, which can be written on the following form: S, = S,,, [l -(- 1% n )]K log no
    • Section 4.5.1where: Sr,0 - stress range which is exceeded once out of no stress cycles no - total number of stress cycles n - number of stress cycles equal to or exceeding S, K - shape parameter This spectrum is shown for various shape parameters in Fig. 4.50.Eq. (4.39) is a convenient formula for cumulative damage calculations, inparticular for simplified analyses at the early design stage as explained inSecs. 10.2.2 and 1 1.4. Fig. 4.50 Exceedances of stress ranges repre- sented by the Weibull distribution with different shape parameters. I 2 3 4 5 6 7 8 log n (Eq. (4.39))4.5 CUMULATIVE DAMAGE4.5.1 The Miner summationFatigue design of welded structures is based on constant amplitude SN data.A marine structure, however, will experience a load history of a stochasticnature. The development of fatigue damage under stochastic or random loadingis in general termed cumulative damage. Numerous theories for calculatingcumulative damage from SN data may be found in the literature. However,the Miner summation has proved to be no worse than any other method,and much simpler. Hence, virtually all fatigue design of steel structures(bridges, cranes, offshore structures, etc.) is based on this procedure. It will beshown below that the Miner summation conforms with a fracture mechanicsapproach. The basic assumption in the Miner summation method is that the"damage" on the structure per load cycle is constant at a given stress rangeand equal t o
    • Section 4.5.1where N is the constant amplitude endurance at the given stress range. In aconstant amplitude test, this leads to the following failure criterion In a stress history of several stress ranges SrYi,each with a number ofcycles ni, the damage sum follows fromwith the failure criterion still given by Eq. (4.4 1). The procedure is shown inFig. 4.5 1. Jl el log NFig. 4.51 The Miner summation procedure for one particular stress block with stress range exceedances diagram (a) and SN-curve (b). asumrnatian and the tractwe mechanics monstrated by assuming a block stresshistory as shown in Fig. 4.52. In a block of stress range Sr,i there are ni cycles.The fatigue life at stress range Sr,i is Ni. Assuming the Paris-Erdogan crackgrowth law (Eq. (4.4))the number of cycles in each block may be expressed as (Sec. 3.2.2, Eqs.(3.38-3.42))
    • Section 4.5.2Fig. 4.52 Block loading program in a fracture mechanics derivation of the Miner sum.The constant amplitude fatigue life at a stress range Sr,iis given by Ni = 1 laf da C (S, ,i)m a(] [(na)Om5 * F ] ~andAssuming a total of k blocks, the damage sum isIf this load history causes failure, the right hand of Eq. (4.46) will equalunity which it also should according to the Miner rule.4.5.2 Equivalent stress rangeThe Miner sum may be expressed in terms of an equivalent stress rangeS, , q. Inserting for the SN-curve N (s,,~)* = a (= const .) (4.47)
    • Section 4.5.3the Miner sum at fracture isThe total number of cycles to fracture isConstructing from Eq. (4.48)Eq. (4.50) now has the form of Eq. (4.47) for the SN-curve with an equivalentstress range given byand the fatigue life given by the total number of cycles N. Thus, the Minersum at fracture may be represented by an equivalent stress SN-curve, whichfor a weld detail with a given constant amplitude SN-curve will depend onthe shape of the load spectrum. The Weibull distribution function has been shown to fit many stressspectra for marine structures. For this particular distribution, a closed formexpression for Eq. (4.5 1) may be calculated, giving a simple method for com-puting Miner sums (Ref. /24/), cf. Sec. 10.2.2. With this procedure, no accountis taken of any fatigue limit, leading to conservative estimates of fatigue life. e of cycle-by-cycle plastic strains at a notch or at afatigue crack tip. The state of stress and strain in the damage area is a resultof the preceding stress-strain history. Hence, the damage in one cycle is nota function of that stress cycle only, but also of the preceding cycles, leadingto interaction or stress memory effects. * wt *&I $$m into account.For that reason, the Miner summation may in many applications be biased,quite often in an unpredictable manner (Ref. /25/), leading to large uncertain-ties in the fatigue strength calculations. Stress interaction effects are closely linked to the characteristics of theload history. Thus, certain types of load histories are found to introduce a bias
    • Section 4.6.1in the Miner sum, which may be accounted for by the so-called relative Minersum. This quantity may be established by testing, and used as a referencewhich is valid as long as certain conditions of similitude are complied with. The load history of offshore structures is characterized by a randomlyvarying stress around a constant mean level, with a cumulative stress spectrumas shown in Fig. 4.50. For this type of loading, the interaction effects tend togive Miner sums less than unity. A mean value of 0.5 has been assessed from alarge collection of data (Ref. 1261). This value has therefore been suggestedas a relative Miner sum to be applied in design. However, all current designcodes seem t o be based on a Miner sum of unity as a failure criterion, whichmeans an overestimation with a factor 2 on cumulative fatigue life. The Miner sum is an assessment of cumulative damage. The uncertaintyassociated with the relative Miner sum seems to be no larger than the inherentuncertainty in SN data. In fact, test series have shown a reduced scatter in theMiner sums as compared to the basic constant amplitude data (Ref. 1271).Calculated against a design SN-curve, the Miner sum procedure based on therelative sum should thus give the same probability of failure as the SN-curve. In design codes, the required Miner sum is often set much lower thanunity. The reasons are not effects of cumulative damage, but the need for anadditional factor of safety. For example, the Miner sum for submerged partsof the structure may be set to 0.1, whereas identical weld details above thewater may be set much higher (Ref. /28/). The rationale for this is accessibilityfor inspection and repair. For similar reasons, redundant and non-redundantparts of the structure may be designed to different Miner sums. In this waythe Miner sum is not only used as a measure of cumulative damage, but alsoas a general safety factor in order t o optimize structural reliability.4.6 FATIGUE OF WELDED JOINTS4.6.1 Crack initiation versus crack growthThere has been - and still seems to be - a certain amount of controversy overwhether fatigue of welded joints is predominantly a crack initiation or acrack growth phenomenon. The current consensus, at least among Europeanresearches, is that the crack growth stage is dominating the fatigue life ofwelded joints. Only with certain post-weld improvement methods may anappreciable fatigue initiation life be introduced (Ref. 1291). This chapter iswritten in support of those views. The application of cyclic strain conceptsto fatigue of welded joints is described in Ref. 1301.
    • Section 4 6 1 .. Poor weld Undercut prof l le I ~ a c kof f u t l o n Root d e f e c t Hydrogen cracking I Lamellar Lack of Solidlf ication tearing penetration crackingFig. 4.53 Various types of weld defects which significantly affect fatigue life. IM mason why a crack initiation stam is urrimpt.jlaptantin welded j h t s ,b that weld defects are always found, In this context, not only the normalengineering size defects are to be considered (Fig. 4.53). Even a nominallyperfect weld contains defects along the weld toe or at interpass locations.In all arc welding processes, slag intrusions are found at the fusion line (Fig.4 5 ) For manual metal arc methods, defect sizes are typically 0.1 mm deep. .4.For tungsten inert gas or metal inert gas methods, the defect size has beenshown to be significantly smaller, but defects of similar type are still found.Besides, undercuts and microcracks are common, depending on weldingprocess and material quality (Ref. /3 11). These defects are to be taken asintrinsic features of any production type weld, and act as nucleating sites for Stag intrusionsFig. 4.54 Even in sound welds, microscopic defects are present, acting as crack nucleation sites. The fatigue notch factor of a weld is there- fore much greater than what can be predicted from the external geometry.
    • Section 5.2.1Lamellar tearing (Fig. 5.3).Lamellar type cracks may appear when the plate material is subjected tostresses in the thickness direction during welding. The lamellar pattern iscaused by separation of weak planes of rolled inclusions.Solidification cracks (Fig. 5.4). Fig. 5.4 Solidification crack in butt weld.Solidification cracks may appear in the centre-plane of the weld. They areoften caused by a high sulphur content in the weld (generally supplied bymelted base material). High carbon content also increases the tendencytowards solidification cracking, while basic electrodes remove sulphur fromthe pool and are beneficial.Hydrogen induced cracking.Cracks which develop due to the presence of hydrogen. They occur when thewelding results in a hardened HAZ structure and the stresses in the jointreach a certain level. Low carbon equivalent, high heat-input, preheat andlow-hydrogen electrodes are common counteracting measures.Undercuts (Fig. 5.5).Undercuts are irregular grooves in the parent metal at the toe of a weld,or in previously deposited weld metal. The toe groove may be continuousand it may be wide and open or narrow and shut. The groove increases signifi-cantly the local stress, and in addition small slag inclusions at or below thebottom of the groove may add t o its severity. Undercuts are likely initiationpoints for fatigue cracks. The occurrence of undercuts may be minimized
    • Section 4.6.3 s (eklc4hy-h t I s M+yde fatigue, the m @ e stm@h and the ductility of thematerial are important p d ~ t e r in dedding the f a w e strength. T i is s hsin contrast to the high cycke w , where tensile pmyjerties have no signifi-cant influence o n am - drcngth weld geomeiry and initial defectsbehg the most imports The high-cycle range of fatigue is the range which is applicable t o mostoffshore design problems. The reason is that this is the range of the mostdamaging fatigue stresses for a majority of environmentally loaded structures. me finite Ilfe m@on is the region where fatigue data may be fittedto a log-linear curve (a. 4.26). This is consisteht 4 t h a fracture rnechaniosanalysis using the Pasis-Erdogan crack growth law. In constant amplitude testing, there will be a fatigue limit in the rangeof 2.1 o6-1 o7 cycles, depending mainly on the residual stress state. With smallresidual stresses, the fatigue limit will be in the lower range. Small residualstresses in the as-welded condition is generally obtained with small-scalespecimens, particularly with welds transverse to the loading axis where thewhole cross-section is heated and allowed to cool simultaneously. Thishappens t o be a typical specimen for SN testing, and has led t o the miscon-seption that a life of 2 - lo6 cycles is a fatigue limit for welded joints. Withmore realistic residual stresses, the constant amplitude fatigue limit is foundin the range 0.8-1.0.10~ cycles (Ref. 1321). This can be read from the crackgrowth curves shown in Fig. 4.4. The shift in crack growth threshold fromR r 0 (no residual stresses) to R > 0.5 (large residual stresses) comes to a fac-tor of two or more on the stress intensity range, corresponding to a factoreight or more in fatigue life.4.6.3 %&% & # c of geometry k# rnttry.Consider a stressed member as shown in Fig. 4.55 with a uniform axial stressor nominal stress. If a hole is made, the stress distribution will be distorted.The cross section at the hole will be decreased, leading to a larger averagestress, Snet = net section stress. Furthermore, the hole is a stress concentrator,leading to a magnification of the net section stress by a factor Kt - the (elas-tic) stress concentration factor. In complicated geometries the net section stress may not be easilydefined, and the stress concentration factor is calculated on the basis of thenominal stress. Stress concentrations are not only caused by cross sectional decrease.
    • Section 4.6.3Fig. 4.55 Stresses in an unnotched plate (left) and a plate with a circular cut-out (right).Also by increasing cross sections, the stress is locally raised as shown inFig. 4.56. Stress concentration factors may be calculated from theory of elasticityby various methods. Analytical methods tend t o become mathematically com-plicated, and are applicable to simple geometries only. Finite element methodsare more versatile, and can easily cope with two-dimensional problems. Forthree-dimensional cases, the finite element method is still practical, but isvery expensive in many cases. Welded joints will often lead to cross sectional changes. Typical casesare reinforcements of beam flanges, reinforcement and stiffening of plates,etc. Stress concentrations caused by structural shapes are often called structu-ral stress concentrations. For many structural details, the structural stressconcentration factor may be difficult to assess, not only because of a com-Fig. 4.56 Stress distribution across the plate at a weld showing the nominal stress (B - B) and the stress distribution across the weld toe (A - A).
    • Section 4.6.3plicated geometry, but also because of a complicated stress pattern. Typicalexamples are cross girders where axial, bending, and shear stresses may actsimultaneously (Fig. 4.27). Tubular joints are another example (Fig. 4.14).wwIn addition to the structural stress concentration, the weld reinforcementalso is a stress concentrator in most cases, Fig. 4.56. Even welds which arelongitudinal to the loading direction act as stress concentrators, due to therippled surface of a weld layer. Only by careful machining of the weld surfacemay this local stress concentration be eliminated. Using welds transverse to the loading direction as an example, weldshape may be defined by the following parameters, Fig. 4.57, 8 - weld toe angle p - notch root radius at the weld toe s - throat thickness, overfill L - leg length, an alternative parameter to s tl - thickness of load-carrying plate t2 - attachment thickness Fig. 4.57 Parameters defining the nominal geometry of welds. nite element analysis it may be shown that theiatr the stmm conmritration factor at the weld toeis some influence from leg length (or throat thickness) and attachment thick-ness, but relatively minor. Stress concentration factors of welds may be calculated by finite ele-ment methods. Parametric formulas are also available (Ref. 1331). It shouldbe noted, however, that stress concentration factors calculated by thesemethods refer to idealized shapes of welds. Real welds exhibit an irregulargeometry, and even more important, there will always be defects of the
    • Section 4.6.3 types described in Fig. 4.54. For this reason, the fatigue notch factor Kf of a weld (Eq. 4.33) is significantly greater than the theoretical (ideal) stress concentration factor Kt which can be calculated from elastic theory. The role of Kt is t o give trends with regard to fatigue strength of various welded geometries. The actual fatigue strength can only be found by fatigue testing.I , , Local nominal stress. Fatigue design is based on the local nomi~zalstress approach. The term nomi- nal means that the stress concentration created by the shape of the weldment is to be disregarded. For example, the stress in Section A - A (Fig. 4.56) is assumed to be the same as it would be in the absence of the weld, and the relevant stress for design purposes would be S. The effect of the stress con- centration caused by the weldment is included in the SN-curve as an implicit fatigue notch factor. The effects of stress concentrations due t o the overall geometry must, however, be taken into account. Thus, in Fig. 4.55, the fatigue design stress will be the nominal stress magnified by the stress concentration factor caused by the hole, hence the term "local". It is to be noted that the local nominal stress approach has been adopted also in fatigue design of tubular joints. The stress concentration effect of the overall shape of the joint is taken into account, but the notch effect of the weldment is disregarded by an extrapolation procedure of the stresses close to the weld, cf. Sec. 8.3.2. The one exception to the local nominal stress approach is cases when design is based on the stress in load-carrying transverse fillet welded joints. Then the design stress is the nominal shear stress on the minimum weld throat area, unless this requirement is overruled by the design stress for the plate, cf. Fig. 4.58. Stresses to be considered when SN-curves are used for fatigue life calculations are also discussed in Sec. 10.2.4. Secondary effects of geometry. So far, idealized or nominal geometries have been considered. In welding fabrication, production tolerances may have an effect on stresses. For transverse load-carrying welds, misalignment has been proved to have a strong effect on fatigue strength (Ref. 1341). Misalignments may be characterized by parallel and angular misalignment, as shown in Fig. 4.59. A special problem with longitudinal seam welds of pressure vessels is the "roof-topping" caused by angular misalignment, Fig. 4.60.
    • Section 4.6.3Fig. 4.58 In load-carrying transverse fillet welds, fatigue cracks may develop from the weld toe (design stress S) or through the fillet (design stress r1).Fig. 4.59 Misalignment of unrestrained load-carrying welds, parallel (a) and angular misalignment (b) with respective formulas for stress con- centration factors. In misaligned joints subjected to a nominal axial stress, secondarybending stresses will arise. In general the secondary stress will be proportionalto the nominal stress. Applying the concept of local nominal stress, capl be faken into account by a s t m w ~ concentration factor( & % ) . ~ ~ ~ i c SCF formulas are given in Figs. 4.59 and 4.60. The formulas alin Fig. 4.59 are valid for unrestrained joints, e.g. butt welds. For cruciform
    • Section 4.6.3Fig. 4.60 Roof-topping of seam-welded tubulars with a formula for the stress concentration factor.joints, or butt welds in stiffened plates, lateral or rotational restraint mayreduce the secondary bending quite significantly (Ref. 1351). It is to be noted that a parallel misalignment of 20% of the platethickness reduces the fatigue strength of an unrestrained joint by about 40%,which for instance is in excess of the effect of sea water observed in weldedjoints. In other words, the misalignment effect is significant.Size effect - plate thickness.Increasing the size of a given type of fatigue specimen while maintainingall the other parameters, will in general cause a decrease in fatigue strength.This size effect in fatigue may be given several interpretations. The so-calledstatistical effect stems from the fact that fatigue is a weakest link process,nucleating at the location where stresses, geometry, defects, and materialproperties combine to form optimum conditions for fatigue crack initiationand growth. Increasing the size of a specimen will statistically produce loca-tions which are more vulnerable to fatigue failures. For welded joints, thissize effect will essentially be a function of weld length. Very little is, however,known about the statistical effect in fatigue of welds. As indicated in Fig.4.28, the effect will tend t o lower the fatigue strength of large size weldsfrom the mean value to the lower bound region found in small scale testing. Independent of the statistical effect of size, there is also an effect ofplate thickness in welded joints. It has been noted experimentally as a de-crease in fatigue strength by increasing plate thickness. Possible reasons forthe influence of thickness are weld technology and residual stresses, whichtend to be more adverse for heavy section welds. However, it has been shownthat plate thickness primarily influences the fatigue strength of welds througheffects of geometry, which act independently of any other effects of platethickness.220
    • Section 4.6.3 A useful model for describing the thickness effect in weld toe fatiguefailures is obtained by the following assumptions (Ref. 1361): a) Welded joints of the same type in various plate thicknesses are geo- metrically similar (typical for load-carrying welds). b) Initial conditions of fatigue crack growth is independent of plate thickness (ai = const .). for andFig. 4.61 Geometric model for the effect of plate thickness in fatigue of welded joints. @q taltial d e b t in the thicker joint will experience a larger stma than a corresponding defect irr the thinner joint. From these assumptions, the effect of plate thickness may be under-stood from a simple geometric model as shown in Fig. 4.6 1. From assumption(a), the stress distributions across the load-carrying plates in the plane ofcrack growth are geometrically similar, leading to a steeper stress gradient inthe thinner joint. Hence, from assumption (b) the initial crack in the thinnerplate will experience a smaller stress than the initial crack of the same lengthin the thicker plate, causing a smaller initial crack growth rate i the former ncase. The difference in initial crack growth rate overmatches the differencein crack length to cause fracture, hence the thinner joint will have a longerfatigue life. In fracture mechanics terms, the stress gradient through the platethickness enters into a calculation of the stress intensity factor, leading tonumerical assessment of what has been described in qualitative terms above. The thickness effect is thus caused by the following parameters: i) The magnitude of the stress concentration at the weld toe (mainly determined by the local weld geometry).
    • Section 4.6.3 ii) The gradient of the stress in the plane of crack growth (mainly deter- mined by the plate thickness). iii) The number of cycles in crack growth through the region of a steep stress gradient, relative to the total number of cycles t o failure (mainly determined by the size of the initial crack and the crack ellipticity). Using this model, it has been shown that the effect of plate thicknesscan be assessed by the following correction formulas (Ref. 1371): to N = No (-) 314 (4.52) twhere No and SN,o refer to fatigue life and strength for a reference platethickness to. The corrections expressed by Eqs. (4.52) and (4.53) have been includedas mandatory clauses in current design codes (Ref. 1381). The reference platethickness t o , assumed to be a mean plate thickness in the tests from whichthe design SN-curves have been derived, is 22 mm for plane joints and 3 2 mmfor tubular joints. In Fig. 4.62 are shown a collection of SN data on the thickness effectof welded joints, and the correction curves for two arbitrary stress levels. 200 -,Fig. 4.62 Data showing the effect of thickness on fatigue strength for various types of welds (Ref. 1361).
    • Section 4.6.4 - 4.6.5In Sec. 4.2.6 residual stresses in welded structures were discussed. The mainconclusion was that in large welded structures, tensile residual stresses mustbe accounted for, even in parts of the structure which have been subjectedto stress relief. On this basis, the so-called stress range approach has been adopted infatigue design of welded structures. In the design SN-curves, endurance isgiven in terms of stress range S,. The mean stress, or stress ratio, does notappear explicitly. However, the SN-curves are assessed on the basis of largetensile mean stresses being present, hence the effect of residual stresses aretaken into account implicitly. The procedure applied in including the effectis described in Sec. 4.7.3.Fatigue of welded joints is essentially a process of fatigue crack growth.Only in post weld treated welds (grinding, peening, etc.) may the crackinitiation or nucleation period be of significance. Crack growth data for steels are remarkably insensitive to materialproperties. In Fig. 4.6 are shown crack growth data for various structuralsteels, for parent plate, heat affected zone (HAZ), and weld metal respective-ly. As shown, all the data fall within the same scatter band. Even with largevariations in material properties as in Fig. 4.5, the crack growth curves fallwithin the same band. Crack growth rates are in particular insensitive to the yield strengthof steels. This means that provided fatigue is a process of crack growth,fatigue strength should be independent of parent or weld metal yield strength.This has proved to hold true in SN testing. In Fig. 4.63 are shown fatigueendurance data for steels as a function of yield strength. For machined plate,the effect of yield strength is large, as predicted by the cyclic strain modelsof fatigue initiation, cf. Sec. 4.3. For as-rolled plate, the initiation period isdecreased, and a larger part of the fatigue life is occupied by the crack growthstage. The effect of yield strength is comparatively smaller. For welded joints,the fatigue strength is nearly independent of the yield strength as predictedby crack growth data. It is to be noted that the data and the conclusions referred above arefor as-welded joints tested in air. For post weld improved joints and forsteel in sea water environments, the effect of material properties in generaland of yield strength in particular may be quite pronounced. These topicsare discussed in Chapters 6 and 7.
    • Section 4.7.1 Machined p l a t e As rolled plate Butt welds 200 400 600 BO O 1000 S, Fig. 4.63 Fatigue strength of machined steel plate, as-rolled steel plate, and steel butt welds, as functions of yield stress. The invariance of fatigue strength to the yield strength has some severe implications on design. The rationale for using high strength steels is to be able to increase the allowable stresses. In design against an ultimate load, this may well be acceptable. A consequence of an increased stress level is, however, a reduced fatigue life. Therefore, the use of high strength steels may lead to fatigue problems. For structural components which are fatigue critical, there is no advantage in using high strength steel. Particular fatigue problems in a structure may be solved by lowering of the stress level, by improvement of the fatigue strength by post weldL 1, ,, I,, ,, treatment (Chapter 6), or by inserting cast components in the critical areas. If lowering of the stress level is mandatory, this may be achieved by improved design of the weld details, or by increasing the plate thickness. In many cases the latter is the only method viable. 4.7 SN DATA FOR WELDED JOINTS 4.7.1 Introduction In this section, a short review will be given of the data and the analyses and interpretations underlying present codes for fatigue design of welded steel structures. The discussion will be based on the fatigue clauses of the British code for design and construction of bridges (BS 5400), as it has evolved from the re-analysis work (Ref. /39/). The codes as such and their use in fatigue design are discussed in Chapter 1 1. The reason for the choice of BS 5400, apart from the work being well documented, is the fact that BS 5400 is the leading fatigue design code in
    • Section 4.7.2Great Britain, and has formed the basis for several fatigue design codes foroffshore structures. Other design codes may differ in certain respects. How-ever, as revisions are being made, different codes should be expected to con-verge towards the same design criteria, as they indeed should - test data andmethods of analyses being generally the same.4.7.2 Classification of SN dataThe core of any fatigue design code of welded joints is i) An allocation of the different joint designs into joint or strength "Classes" according to their comparative fatigue strength. ii) A set of design SN-curves, defining the fatigue capacity for each class of joints. Welded joints are classified with regard to fatigue strength on the basisof three charactbriStics, a) The geometry of the weld detail b) The direction of the fluctuating stress relative to the detail c) The method of manufacture and inspection of the detail The terms relating to this classification should be self-explanatory.However, some details will be discussed below.Weld geometry.Weld geometry may be described on a nominal level, a local level, and a"microscopic" level. Considering for example butt joint of two plates, thismay be accomplished in several ways, cf. Fig. 4.64. On a nominal level, allthese joints are butt joints. In terms of fatigue strength, the various jointdesigns may vary considerably, depending on the local geometry. On a "mic-roscopic" level, the same local geometry may again be given various geome-tries, cf. Fig. 4.57, leading to a considerable variability in fatigue strength. LFig. 4.64 Various forms of butt joining of plates and the different flows of stress.
    • Section 4.7.2 In the fatigue classification of welded joints, only the local weld geo-metry is specified. The "microscopic" geometry is assumed to follow fromthe weld method and is not defined explicitly.Loading direction.The design rules are in general based on test data obtained with uniaxially tistressed specimens with welds either traniverse or longitudinal to the loadingdirection. Hence the terms "longitudinal" and "transverse" welds. The load-ing to consider in fatigue design is the fluctuating component of stress.In plated structures, nominal stresses are in general bi-axial. A basic problemis then t o define which component of stress to use, and the direction of thisstress relative to the weld. As shown by Fischer (Ref. 1401) in his experiments on welded beamswith attached stiffeners, fatigue cracks tend to grow in a direction normal tothe largest principal stress. Principal stress may thus be taken as the "drivingforce" in fatigue, and not e.g. the von Mises equivalent stress. For design,the differences are in many cases negligible, but in some cases a detailedanalysis may be required. The maximum principal stress range may not always be normal orparallel to the weld direction, but at some other angle. With the commontype of classification of welds (Chapter 11, Appendix A) it may be difficultto decide which class is applicable. It has been proposed that if the maximumprincipal stress direction deviates more than 25 from the direction of theweld, the classification is "transverse" (Ref. 1411). A particular problem arises if the direction of the principal stresschanges during each load cycle. If the fluctuations are periodic, design shouldbe based on the direction of the peak value of the principal stress (Ref. /41/).If, however, the stress components are not correlated in phase, as is oftenthe case for offshore structures (superposition of local and global loads,multidirectional waves), no recipe seems t o exist. In general, design rules describe the maximum principal stress rangeas the appropriate stress component. This is in accord with the reference(uniaxial) stress in fatigue testing, and corresponds to Mode I crack growth.The von Mises equivalent stress may be used, according t o some rules (Ref.1411). The directionality of stress with regard to the weld is obviously subjectto engineering judgement.Manufacturing factors.The main effect of manufacturing methods is due to geometry. Different weldprocesses may lead to different "microgeometry" for nominally identical
    • Section 4.7.3welds, cf. Fig. 4.57, and a subsequent effect on fatigue strength. The initialdefects from which fatigue cracks are nucleated may also be a factor of pro-duction methods. A typical geometrical effect is the irregularity in weld pro-file caused by interruptions in a weld pass, often called stoplstart positions.In manual welding these interruptions are unavoidable whereas automaticwelding may be performed without them. The stoplstart positions tend tolower the fatigue strength, particularly in longitudinal loading, and this isreflected in the classification of welded joints with regard to welding methods.4.7.3 Assessment of design SN-curvesSelection of SN data.Design SN-curves are based on experimental data. In the development ofBS 5400, data from various sources were scrutinized for their applicabilityand reliability. Applicability criteria were a minimum of correspondance tostructural welding in terms of material quality, welding procedure, plate thick-ness e t ~ As a general policy, data obtained earlier than 1950 were discarded, .as they were believed to be unrepresentative of current welding technology. The test data were obtained mainly in the high cycle region of fatigueendurance, i.e. at fatigue lives in excess of lo4 cycles. The analysis wasrestricted to data emanating from specimens tested under uniaxial tensileloading or from tests on beams in bending, where the stress conditions in theflange are similar to those in an axially loaded specimen.Statistical analysis.The SN data were analysed on the basis of a linear SN-curve on log-log scale,using standard methods of statistics. A mean line was fitted by regressionanalysis, and confidence intervals for individual test results were calculated. The confidence interval is a measure of the scatter of the individualresults. The regression line is defined by two parameters, which may be takento represent the slope and the abscissa intercept of the line respectively.Both these parameters are identified with an uncertainty, leading to a totaluncertainty which increases at an increasing distance from the centre ofgravity of the experimental data. The resulting confidence limits are hyper-bolae, cf. Fig. 4.65. The shape of the confidence limits is reflecting the fact that SN datatend to be concentrated in an interval of fatigue life which is relatively smallas compared to the scatter. The increased width of the confidence intervalis therefore not reflecting the physical behaviour of welded joints in fatigue,but is rather a result of the particular statistical method employed.
    • Section 4.7.3 log N log N log NFig. 4.65 A collection of SN data with regression line showing uncertainty in slope (a), uncertainty in abscissa intercept (b), and total uncer- tainty (c) (schematic). In fact SN-curves at low lives tend to become more horizontal, leavingthe upper confidence level in this region over-optimistic, In the long liferegion there will be a fatigue limit, which leaves the lower confidence limitover-pessimistic. For these reasons, the confidence limits were approximatedwith straight lines, parallel t o the regression line and tangent to the hyperbolaeas shown in Fig. 4.65 (b). The confidence interval defines the probability that similar SN testresults will be within the given limits. E-g., a 95% confidence interval definesthe limits within which there is a 95% probability that further test resultswill be falling, provided the results belong to the same statistical population.The lower limit thus defines a 97.5% probability of survival. The lower 95% confidence limit is often taken as a design curve infatigue. This line corresponds to a lowering of the mean line approximatelytwo standard deviations of individual test results. In this way the mean lineand the standard deviation of fatigue life for a given class of welds may beused to define design curves representing different levels of safety, as shownin Fig. 4.66 and Table 4.2. Based on physical reasoning, three different adjustments to the re-gression analysis were found necessary as outlined below.Consistency of data.In some data collections it was found that the individual test series weresystematically different from the trend shown by the joint regression ana-lysis. The cause for this was believed to be differences in weld procedures,specimen geometry, etc., in combination with differences in mean fatiguelife for the different series. This would give a bias in the regression line whichwas adjusted for by analysing the data using a fixed slope taken to be themean slope for the individual test series.
    • Section 4.7.3Fig. 4.66 Regression line giving the mean fatigue life (a), mean minus one standard deviation (b), and minus two standard deviations (c) (schematic). Table 4.2 The relation between standard deviations, confidence levels, and probability of survival. Number of standard deviations 1 2 3 below mean line Confidence level 63.2 94.5 99.0 (per cent) Probability of survival 84.1 97.7 99.5 (per cent)Residual stresses.In welded structures, residual stresses are found to be large. Even in structureswith post weld heat treated welds, the residual stresses are significant in rela-tion to fatigue stresses due to assembly welding and various other effects.For this reason, design criteria must take into account that the mean stressesare large and tensile. The specimens used in ordinary SN testing are in many cases too smallto contain residual stresses representative of full scale structures. This isparticularly true for welds which are transverse to the loading axis, in whichthe whole cross section is heated simultaneously in the welding process, withlittle restraint on the subsequent thermal contraction. For longitudinal welds,residual stresses are in general much larger, due to greater constraint. Localresidual stresses will in general be relaxed by cyclic loading if the total stress- applied plus residual - exceeds yield. Residual stresses are therefore insigni-
    • Section 4.7.3 Mean S-N curve determined 07 9 I I I I 1 o5 2A06 Log NFig. 4.67 Correction procedure for stress-relieved specimens in order to include the effect of large residual stresses.ficant in the low life range of SN-curves. Based on experimental evidencea correction procedure was designed in order t o correct SN-curves for lack ofresidual stresses. The procedure, leading to a rotation of the SN-curve, isshown in Fig. 4.67. An important consequence of the effect of residual stresses is that themean applied stress is an insignificant parameter - effective stresses acting inthe welded joint regions are assumed t o fluctuate from yield and downwards,cf. Fig. 4.68. This has led to the stress range philosophy of fatigue design,which has been adopted in all codes relevant to offshore structures. ----- - Local stress history a t weld Nominal stress historyFig. 4.68 Nominal stress history and local stress history at a weld with large residual stresses (schematic).
    • Section 4.7.3 It has been argued that in variable amplitude loading, local yieldingduring peak loads will lead to a shake-down of residual stresses, leaving thestress range philosophy over-conservative. For short-range stresses this mayhold true, as has been demonstated in fatigue testing (Ref. 1231). The effectof peak stresses on long-range residual stresses, however, has not been inves-tigated. It may be assumed that the effect will be small, due to the long rangeand the associated large end displacements of these stresses. On this basis,the stress range philosophy is applied in current design codes regardless ofapplied mean stress.The slope of SN-curves.With the two corrections discussed above, the statistical analysis gave regres-sion lines for the different classes of joints of the form N - s ~ : =a N*(AG-)~ = z (4.54)with the slope parameter m in the range between 2.74 and 2.79. The actualslope of the SN-curve is -l/m. a is constant for each joint class. From fracture mechanics theory of fatigue it is known that if thecrack initiation phase is negligible, the slope parameter m of the SN-curveis identical to the exponent of the crack growth power law. This parameterdepends mainly on the material property, hence all SN-curves for a givenmaterial should be parallel. Most experimental data for crack growth instructural steels give an exponent m = 3 . For this reason, and because thescatter in the slope of the corrected regression lines after all was rather small,a common slope parameter m = 3 was assumed for all SN-curves pertaining towelded joints. For plain plate, machined welds, etc., in which the initiationperiod is significant, shallower slopes as given by the SN data were adopted. In Fig. 4.69 an actual set of SN data is shown, with the correction tothe regression line indicated.Design SN-curves.Based on corrected SN-curves, various types of welded joints for which SNdata have been compiled, have been allocated to classes with regard to fatiguestrength. For plane joints, the classes are termed ByC, D, E, F, ~ 2G, and W, :and a joint regression line and standard deviation have been calculated foreach class. Details of the various types of welds are given in Chapter 11,Appendix A. The design SN-curves are assessed on the basis of a consideration ofthe probability of failure. Thus, in BS 5400, the mean minus two standarddeviations is applied for safe life design, whereas for fail safe design the mean
    • Section 4.7.3 2 3 4 5 2 3 4 5 105 106 Endurance, cyclesFig. 4.69 SN data for non-load carrying transverse butt welds, showing regression line corrected for slope (Ref. 1391).minus one standard deviation is assumed to be sufficiently conservative.The corresponding probabilities of failure are approximately 2.5% (safe life)and 15% (fail safe). Mean minus three standard deviations have also beenproposed as design curve, for very critical components, corresponding to a0.5% probability of failure. It should be noted that the confidence limits and survival rates men-tioned, refer t o laboratory SN tests, and should not be taken as a measureof the reliability of structural components without a much closer considera-tion. The reason for this is that there is a certain lack of similitude betweenthe laboratory tests and real life behaviour of full scale components.
    • Chapter 4. References The safe life design SN-curves generally applied for bridges and off-shore structures and based on the mean minus two standard deviations areshown in Fig. 11.4. As can be seen a higher value of m has been adoptedfor structures in air when N > lo7 cycles. Numerical data for a and m aregiven in Tables 11.1 and 11.2.REFERENCESMost of Chapter 4 is of general nature, and specific references are kept to a minimum.Suggestions for further reading on topics related to basic fatigue properties of materialsare given as references 1-6 below. 1. Dieter, G.E. : Mechanical Metallurgy, McGraw-Hill, 1977. 2. Hertzberg, R.W. : Deformation and Fracture Mechanics of Engineering Materials, John Wiey & Sons, 1976. 3. Sandor, B.I.: Cyclic Stress and Strain, The University of Wisconsin Press, 1972. 4. Fatigue under Complex Loading: Analyses and Experiments, Wetzel, R.M., ed., Society of Automotive Engineers, 1977. 5 . Frost, N.E., Marsh, K.J., Pook, L.P.: Metal Fatigue, Clarendon Press, 1974. 6. Gurney, T.R.: Fatigue of Welded Structures, Cambridge University Press, 1979. 7. Ohta, A., and Sasaki, E.: Influence of Stress Ratio on the Threshold Level for Fatigue Crack Propagation in High Strength Steels, Engn. Fract. Mech., Vol. 9, 1977, pp. 307-315. 8. Rolfe, S.T. and Barsom, J.M.: Fracture and Fatigue Control in Structures, Prentice-Hall, 1977. 9. Maddox, S.J.: "Assessing the Significance of Flaws in Welds Subject to Fatigue", Welding Journal, 53, No. 9, Sept. 1974.10. CP 118, Proposed fatigue design rules for welded aluminium structures, British Stan- dards Institution.
    • Chapter 4. References11. Moan, T. et al.: "The Alexander L. Kielland Accident", report of the investigation commission, NOU 1981 :11, Universitetsforlaget, 1981 (In Norwegian).12. Frost, N.E. and Greenan, A.F. : Environ. Eng. 25, 11 (1967).13. Bell, W.J. Benharn,P.P.: and "The effect of mean stress on fatigue strength of plain and notched stainless steel sheet in the range from 10 to lo7 cycles", STP 338, pp. 25-46, 1963, American Society for Testing and Materials.14. Gurney, T.R.: Some recent work relating to the influence of residual stresses on fatigue strength, Weld. Inst. Autumn Conf. 1977, pp. 151-164.15. Leide, N.: "The significance of residual stresses - some experimental results and practical experi- ence in a shipyard", Residual Stresses in Welded Construction and their Effects, The Welding Inst., 1977.16. Basquin, O.H.: Yroc., ASTM 10, Part 11, 1910, p. 625.17. Manson, S.S. and Hirschberg, M.H. : Fatigue : An Interdisciplinary Approach, Syracuse University Press, Syracuse, N.Y., 1964, p. 133.18. Coffin, L.F., and Tavernelli, J.F. : "The Cyclic Straining and Fatigue of Metals", Trans. of the Metallurgical Society of AIME, Vol. 215, Oct. 1959, p. 794.19. Landgraf, R.W.: "Cyclic Deformation and Fatigue Behaviour of Hardened Steels", Report No. 320, Department of Theoretical and Applied Mechanics, Univ. of Illinois, Urbana, 11I., Nov. 1968.20. Symposium on Statistical Aspects of Fatigue Testing, Warwick University, 1975.Chapter 4. References36. Berge, S.: "Effect of plate thickness in fatigue design of welded structures", Offshore Tech- nology Conference, OTC 4829, 1984.37. Gurney, T.R.: The influence of thickness on the fatigue strength of welded joints, Behaviour of Offshore Structures, London (1979).38. Offshore Installations: Guidance on design and construction, Department of Energy, United Kingdom, 1984.39. Gurney, T.R., and Maddox, S.J. :
    • Chapter 4. References24. Nolte, K.G. and Hansford, J.E. : "Closed-form expressions for determining the fatigue damage of structures due to ocean waves," Offshore Technology Conference, OTC 2606,1976.25. Brose, W.R., Dowling, N.E., and Morrow, J.D.: "Effect of Periodic Large Strain Cycles on the Fatigue Behaviour of Steels", Paper 74022 1, SAE Automotive Engineering Congress, Detroit, Mi., Feb. 1974.26. Schiitz, W. : "Procedures for the prediction of fatigue life of tubular joints", Rapporteurs report PS5, ECSC Conference on Steel in Marine Structures, Institut de Recherches de la Paris, 1981. Siderurgie Fran~aise,27. Schilling, C.G., Klippstein, K.H., Barsom, J.B., Blake, G.T. : "Fatigue of welded steel bridge members under variable-amplitude loadings", NCHRP - Project 12-12, Transportation Research Board, National Research Council, Wash- ington D.C., 1975.28. Rules for the Design, Construction and Inspection of Offshore Structures, Det norske Veritas, 1977.29. Haagensen, P.J.: "Improvement of the Fatigue Strength of Welded Joints", Rapporteurs Report PS6, ECSC Conference on Steel in Marine Structures, Institut de Recherches de la SidCrurgie Frangaise, 1981.30. Mattos, R.J. and Lawrence, F.U. : "Estimation of the Fatigue Crack Inititation Life in Welds Using Low Cycle Fatigue Concepts", Society of Automotive Engineers, SP-424,1977.31. Fatigue Performance of Welded High Strength Steels, The Welding Institute Report Series, 1974.32. Gurney, T.R.: "Cumulative Damage Calculations Taking Account of Low Stresses in the Spectrum", The Welding Institute Report 211976/E.33. Nishida,M.: "Stress Concentrations", Morikita Publidung, 1973.34. Wylde, J.G. : "The effect of axial misalignment on the fatigue strength of transverse butt welded joints", The Welding Institute Research Report 9911979.3 5. Berge, S. and Myhre, H.: "Fatigue strength of misaligned cruciform and butt joints", Norwegian Maritime Research, No. 1,1977.
    • Chapter 4. References36. Berge, S . : "Effect of plate thickness in fatigue design of welded structures", Offshore Tech- nology Conference, OTC 4829, 1984.37. Gurney, T.R.: The influence of thickness on the fatigue strength of welded joints, Behaviour of Offshore Structures, London (1979).38. Offshore Installations: Guidance on design and construction, Department of Energy, United Kingdom, 1984.39. Gurney, T.R., and Maddox, S.J.: "A Re-Analysis of Fatigue Data for Welded Joints in Steel", Welding Institute Report No. E/44/72, 1972.40. Fisher, J .W., Albrecht, P.A., Yen, B.T., Klingerman, D.J., McNarnee, B.M. : "Fatigue strength of steel beams with transverse stiffeners and attachments", NCHRP Rep. 147, Highway Research Board, National Research Council, Washington DC, 1974.41. Regulations for the structural design of fixed structures on the Norwegian Continental Shelf, Norwegian Petroleum Directorate, 1977.42. Austen, I.M.: "Factors affecting corrosion fatigue crack growth in steels," update paper, European Offshore Steels Research Seminar, Cambridge, 1978.43. Scott, P.M., et al. : "The effect of sea water corrosion in fatigue crack propagation in structural steel", ibid .44. Lohne, P. : "A fracture mechanics approach to fatigue analysis of welded joints in offshore struc- tures", Det norske Veritas Report 79-0060, 1979.45. Lindley ,T .C ., and Richards, C.E. : "Near-threshold fatigue crack growth in materials used in the electricity supply indu- stry", Proc. Second Int. Conf. on Fatigue and Fatigue Thresholds, Engineering Mate- rials Advisory Services Ltd., England, 1982.
    • CHAPTER 5 SIGNIFICANCE OF DEFECTS Stig Wastberg and Agnar Karlsen A.S VERITEC, OsloABSTRACTThe first two sections describe common defects and other undesirable featuresthat reduce the fatigue life of welded structures. Section 5.4 explains howweld quality may be described in statistical terms. Section 5.5 describesnondestructive inspection for detecting and sizing defects, and discussesthe reliability of these methods. The final section gives a general view of thefitness-for-purpose approach to deciding whether disclosed defects shouldbe repaired or not, and discusses the relative severity of defects of varioussize and shape.5.1 INTRODUCTIONDefects in structures and components may act as initiation sites for fatiguecracks. Because a fatigue crack grows slowly initially, and then acceleratesas the crack length and the stress intensity range increase, the initial size andshape of the defect have a much larger influence on the total fatigue life thanthe final crack size at which failure occurs. If a defect is large and/or thematerial is brittle, the defect itself may be capable of initiating unstable frac-ture without preceeding fatigue crack growth.5.2 CLASSIFICATION OF DEFECTS ACCORDING TO ORIGINAs far as assessing the significance of a defect, it is necessary to know theshape, size and location (with respect to the stresses) of the defect. However,it can also be desirable to know the possible reasons for the occurence of adefect. If one knows why defects occur, one knows where they are likely
    • Section 5.2.1to occur and also how to prevent their occurrence. Also it is importantto know the likely sites of defects because it makes them easier to disclose,and because sites likely t o contain defects should not be designed to carryhigh stresses. For example, a quick glance at the subjects in the rest of thischapter indicates that defects are likely to occur in welds. From the point ofview of fatigue design it is therefore important to choose the correct weldingconsumables and welding procedures and to inspect welds for defects. Ifpossible, welds should be kept away from stress concentrators. Defects may be divided into two types; those introduced during fabrica-tion, and those arising after a period in service.5.2.1 Fabrication defectsLack of fusion (Fig.5.1). 0 Fig. 5.1 Lack of fusion defect in MMA-weld (x7.5).A two-dimensional defect located on the line between weld metal and basematerial or between individual weld passes. This type of defect may occurwhen using gas shielded metal arc welding (MIG, TIG), and is generally causedby too low heat input or by oxidation of weld metal in the arc.Incomplete penetration.Incomplete filling of the weld root, generally caused by inappropriate weldingparameters such as low heat input or by faulty groove preparation.Slag inclusions (Fig.5.2).Welds may contain porosities and slag inclusions of nearly spherical form.They produce only minor notch effects and have usually little or no influence
    • Section 5.2.1 6 Fig. 5.2 Slag inclusion in MMA-weld (x4).on the fatigue behaviour. However, if located at the surface, they may signifi-cantly reduce the fatigue strength. Elongated slag inclusions may be of a two-dimensional form and are considered more dangerous than the sphericaltypes. Fig. 5.3 Lamellar tearing in MMA-weld (x2).
    • Section 5.2.1Lamellar tearing (Fig. 5.3).Lamellar type cracks may appear when the plate material is subjected tostresses in the thickness direction during welding. The lamellar pattern iscaused by separation of weak planes of rolled inclusions.Solidification cracks (Fig. 5.4). Fig. 5.4 Solidification crack in butt weld.Solidification cracks may appear in the centre-plane of the weld. They areoften caused by a high sulphur content in the weld (generally supplied bymelted base material). High carbon content also increases the tendencytowards solidification cracking, while basic electrodes remove sulphur fromthe pool and are beneficial.Hydrogen induced cracking.Cracks which develop due to the presence of hydrogen. They occur when thewelding results in a hardened HAZ structure and the stresses in the jointreach a certain level. Low carbon equivalent, high heat-input, preheat andlow-hydrogen electrodes are common counteracting measures.Undercuts (Fig. 5.5).Undercuts are irregular grooves in the parent metal at the toe of a weld,or in previously deposited weld metal. The toe groove may be continuousand it may be wide and open or narrow and shut. The groove increases signifi-cantly the local stress, and in addition small slag inclusions at or below thebottom of the groove may add t o its severity. Undercuts are likely initiationpoints for fatigue cracks. The occurrence of undercuts may be minimized
    • Section 5.2.2 Fig. 5.5 Undercuts in MMA-weld (x2.5).by keeping a correct position of the electrode during welding, and by a suit-able choice of welding procedure and electrodes.Casting defects.The defects mentioned so far were welding defects. Also castings may exhibitdefects which can affect the fatigue performance. During solidification, mode-rate stresses can create cracks due to segregations, non-metallic films, etc.During the cooling period shrinkage stresses may cause cracks, for example infillets. Castings may also contain small internal cracks induced by hydrogen.Pores and inclusions located at the surface may have a significant influenceon the fatigue strength especially if located at sites with high stresses. Suchdefects can be caused by segregation of non-metallic inclusions, by moistureor by high gas content in the melt.5.2.2 In-service defectsIf a component or structure is examined after a period in service, the follow-ing defects may appear:Corrosion pits (Fig.5.6).Corrosion pits tend to spread either irregularly over a surface or concentrateto areas adjacent to welds. They may be rounded at the bottom, but theremay also be sharp root-like extensions. These corrosion pits may act asinitiation sites for fatigue cracks and therefore reduce the fatigue life. How-ever, in the case of welds there are usually other, more severe, crack initiatorspresent, so that the fatigue life of weldments is not significantly affected bycorrosion pits.
    • Section 5.3 Fig. 5.6 Corrosion pit in weld metal. A fatigue crack has developed at the bottom (x4.5).Stress corrosion cracks.If a stressed surface is exposed to certain corrosive environments, stress corro-sion cracking may occur. The stress corrosion cracks can lead to unstablefracture or they may act as initiators for fatigue cracks. Note that residualstresses, due to e.g. a weld, are often enough to induce stress corrosion crack-ing in the presence of certain corrosives.Fatigue cracks.Common in-service defects, and the subject of this handbook. Once dis-covered, they should be treated like any other sharp defect.5.3 OTHER FAULTS IN FUSION WELDSWelded joints often deviate from the geometry intended by the designer.Inaccuracy in matching leads to a misalignment of the joining plates. Themisalignment may be axial and/or angular (Fig. 5.7). Both irregularitiesintroduce an additional bending stress in the joint and thus influence thefatigue strength (Fig. 5.8). Misalignment may therefore be a factor to deter-mine the initiation point of a fatigue crack. Thus in a straight plate, the crackmay initiate from an internal defect, whereas the increase in surface bendingstresses due t o misalignment may shift the initiation point to the weld toe. At the weld toe there is also a considerable stress concentration pro-duced by the weld profile. A heavy weld reinforcement will lead to a highstress concentration at the toe and consequently lower the fatigue strength(Fig. 5.9). Undercuts further increase the stress concentration at the toe.
    • Section 5.3 Fig. 5.7 Axial (a) and angular (b) misalignment.Fig. 5.8 The relation between misalignment and fatigue strength (Ref. / 11). 2 E Z 300 Plain plate - cn (machined), , - - N C 0 @ , . a , s L -c, 100 5 Plain plate YOOL * .- L ul ( w l th m i 1 l s c a l e ) 0 - Reinforcement angle,@ (deg.) Fig. 5.9 The relation between reinforcement angle and fatigue strength (Ref. /I/).
    • Section 5 -45.4 STATISTICAL DESCRIPTION O F WELD QUALITYWelded connections will inevitably contain some defects even if great careis taken to avoid them. The quality of a manual metal arc weld depends to agreat extent upon the welder and his skill. However, even skilled welders whohave passed qualification tests, will produce defects. The size and location ofwelding defects will show a considerable scatter which may be expressed instatistical terms. Also the fracture toughness of welds shows great scatter,which reflects the heterogenity of the weld metal. This scatter may be ex-pressed statistically, as in the case of welding defects. A convenient way to present the statistical variation of a variable isby probability density functions, such as the normal or Gaussian distribution.All probability density functions have the following characteristic properties(Fig. 5.10): The total area under the curves is equal t o unity and the areaunder the curve between lines X = a and X = b represents the probability thatX lies between a and b, and is denoted P ( a < X < b ) . Some examples ofmeasured distributions of weld defects are discussed below. X X=a X=b XFig. 5.10 Illustrating the characteristic properties of a probability density distribution f(x). The first example is based on approximately 180 misalignment measure-ments of full penetration cruciform welded joints in semi-submersible drillingrigs (Ref. 121). The histogram given in Fig. 5.1 1 shows the results and is fairlywell approximated by the one-sided normal distribution. The second example shows the distribution of the depth of undercutsobtained from 827 randomly selected point measurements on productionwelds at various shipyards (Ref. 131). The depth values were reproduced onreplicas of liquid silicone rubber allowed to harden on the toe region of thewelds. Of 827 measurements, 502 revealed no undercuts, and the histogramin Fig. 5.12 was obtained from the remaining 325 locations. The histogramwas represented by the exponential probability density function:
    • Section 5.4 Fig. 5.1 1 Misalignment sample and fitted density function, f(e/t). n = number of measurements (approximately 180) (Ref. 131) 0.5 1.0 D e p t h of undercuts a (mm)Fig. 5.12 Relative frequency of measured depths of undercuts and the applied density function (Ref. 131). Probability density functions for internal defects are difficult to obtain.Some examples based on ultrasonic testing reports exist, but the uncertaintyof the testing method must be considered when the reports are evaluated.Distributions based on direct observations hardly exist. However, it is reason-able to expect that there will be a large number of small defects and a de-creasing number of larger ones. Such distributions may be half-normal, log-
    • Section 5.4 5 10 Height of internal defects, (mm)Fig. 5.13 Calculated relative frequency of the depth of internal defects (histogram) and the applied density function, f(a) (Ref. 131).normal, exponential, etc. Fig. 5.1 3 shows a probability distribution basedon results from ultrasonic testing (Ref. 131). About 3200 m of productionbutt welds were tested. The test locations were randomly selected from a totalweld length of 40000 rn and were assumed to give a fairly good picture of theworkmanship. About 6400 lengths of 0.5 m each were inspected, and in450 test lengths 327 defects were detected. Some of the defects extendedover two test lengths, and some test lengths also contained more than onedefect. The given numbers refer to defects which gave ultrasonic echoesabove a certain reference level. Numerous small defects, giving echoes belowthe reference level, may have been present but were not detected or reported.It is also possible that some larger defects for one reason or another did notgive an echo above the reference level and consequently were not disclosed. Taking account of the uncertainties in the ultrasonic detection method,the half normal probability density function given as the dotted line in Fig.5.13 was established for the height of the internal weld defects. The examinedwelds were made between plates with thicknesses from 10 t o 25 mm. In Fig. 5.13 no attempt was made to divide the defects into variousgroups (e.g. crack-like and non-planar). A collection of ultrasonic test datais presented in Fig. 5.14 (Ref. 141). The data were divided into crack-like andnon-planar defects. It is noted that the two types have different probability
    • Section 5.5.1 ----- Planar d e f e c t ------ Non-planar defect 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 D e f e c t height ( m m ) Fig. 5.14 Weld defect height distributions (Ref. 141).density functions. The data were obtained from inspection work on anoffshore structure and consist of results from 12 vertical and 6 horizontalnode joints with a total weld length of the order of 1000 m. All defectsreported were embedded and the average defect rate was 0.7/m. After repairand final NDT the defect rate was reduced to 0.2/m.5.5 NON-DESTRUCTIVE INSPECTION 5.5.1 Non-destructive inspection methodsLiquid penetrant.This technique is used to reveal the presence of surface flaws, but can providelittle information on the depth of the flaws. The surface must first be thoroughly cleaned. Then a brightly colouredor fluorescent dye is applied. After allowing the dye to penetrate possiblecracks, the surface is wiped and a fine white absorbent powder is applied.The powder draws remaining dye out of the defects, enabling them to belocated.Magnetic particles.This is another technique suited for revealing surface flaws, and it will alsoindicate flaws just below the surface. Only ferro-magnetic materials can beinspected. Magnetic particle inspection does not require a clean surface,which gives it a practical advantage over liquid penetrant techniques as surfaceflaws often contain grease.
    • Section 5.5.1 A magnetic field is induced in the body to be examined, either bypassing a large electric current through it or by attaching magnets. Iron filingsin a light oil or water suspension is applied to the surface. The iron filingswill gather around the defects and make them visible.Eddy currents.Eddy current techniques are most commonly used for automatic qualitycontrol of sheet, tube and wire. They primarily detect surface flaws, and aremost simply applied t o non-ferrous metals. The method is based on the factthat eddy currents will be induced in a specimen subjected to an alternatingmagnetic field produced by a coil. The eddy currents produce a magneticfield which tends t o reduce the current in the coil. The degree of reductiondepends on the magnitude of the induced currents which in turn depends onthe electric resistance in their path. This resistance is a function of the con-ductivity of the material and the length and cross section of the currentpath. A defect which changes the current path will thus affect the inducedmagnetic field and consequently the current in the coil. The current is themeasured quantity during testing. For various reasons the method is difficultto apply t o welds.Radiography.Radiography is a method of detecting internal defects. Radiation (x or y) ispassed through the region to be inspected, and some of it is absorbed. Raystraversing a defect is less absorbed than those passing through homogeneousmaterial. The intensity variations due to defects are generally recorded onphotographic film. Thus, the image on the film is a "shadow picture" of thedefects (Fig. 5.15). To obtain a uniform assessment of welds, the Interna- X-ray source r:, Defect Dark oreb on photographic f i l m Fig. 5.15 The principle of radiography for the detection of defects.
    • Section 5.5.2tional Institute of Welding (IIW) has published a collection of referenceradiographs of welds. The quality range is divided into five degrees and charac-terized either by a colour or by a number where 5 is the best degree and 1is the poorest.Ultrasonics.Ultrasonic inspection is the most flexible and convenient way of detectingand sizing internal defects. The main disadvantage as compared with radio-graphy is that a permanent record of the inspection is not easily obtained. Ultrasonic signals are generated by piezo-electric crystals contained inprobes that can be moved over the surface in the region to be inspected.The waves are reflected by the surfaces of the examined body, and also byany defects that might come in their way. These echoes are usually detectedby the same probe that generates the signal. By measuring the time delaybetween the emission signal and the reception of each reflection, the sourceof reflection can be located, and the position of defects identified. Thesignals are usually registered on a cathode-ray tube (Fig. 5.16). @ Cathode-ray tube Reflected signal Fig. 5.16 Ultrasonic testing of welds, principle.5.5.2 Nondestructive inspection reliabilityA non-destructive testing method is often characterized by its ability todetect small defects with a specified confidence level. When the defects arelater to be assessed by for instance fracture mechanics methods, it is neces-sary to determine both the type of defect and its dimensions, of which theheight in the direction of the plate thickness is the most interesting. The reliability of ultrasonic inspection in determining the height ofweld defects was examined in a Nordic research project, where 70 m of butt
    • Section 5.5.2welds were inspected by several operators (Ref. 151). After inspection thewelds were broken up and the real size of the defects was measured. Itappeared that the ultrasonic echo amplitude was the only parameter whichcould be correlated with defect height and which was recorded during con-ventional ultrasonic examination. In Fig. 5.17 the average ultrasonic echoamplitude is plotted versus defect height. The uncertainty in predicting thedefect height is seen t o be rather great. 1 10 D e f e c t height, (mm)Fig. 5.1 7 Average ultrasonic amplitude for twelve ultrasonic operators versus defect height for lack of root penetration and lack of fusion defects. The broken curves indicate the 95% confidence limits for the regression line (Ref. 151). The individual operators evaluated the defects differently. Each one ofthe 12 operators investigated the same 70 m length of butt welds, and eachone compared the ultrasonic echo amplitudes of the different defects with an"acceptance level echo" equal for all operators. Fig. 5.1 8 shows the proba-bility of acceptance for the different defect heights, measured as the ratiobetween the number of accepted defects and the total number of defectsof a particular size. It would be expected that defects of heights between8-12 mm would show low acceptance by all operators. That is, however,not so, 6 operators are seen to accept 40% or more of rather large defects. In a radiograph there is no obvious parameter to correlate with defectheight. In the Nordic reseach project there seemed to be a certain correlationbetween IIW degrees and defect height for lack of root penetration (Fig.5.19).
    • Section 5.5.2 0 2 4 6 8 10 12 Defect height, mmFig. 5.18 Acceptance curves obtained by twelve ultrasonic operators. "Probability of acceptance" was obtained as follows: Assume that the inspected weldment contained eight defects of height approx. 5 mm. One of the operators detected six defects. Five of them gave an echo which exceeded 50% of the reference curve and were consequently "not accepted" by the operator. Therefore the ope- rator "accepted" three out of eight defects with height equal to 5 mm, i.e. the probability of acceptance was 318 = 0.38. IIW degree 0Lack ( 5 ) - 00 Blue ( 4 ) -00 Green ( 3 ) - p 080 o Brown ( 2)-- a h 0 0 o Red (1)- 000000000 # 00 000000 I 1 1 1 1 1 ~ ~ 1 1 ~ 1 0 2 4 6 8 10 12 D e f e c t height (mm) Fig. 5.19 IIW degree versus defect height for lack of root penetration (Ref. 151). The rather poor capability of the conventional non-destructive testingmethods in estimating correctly the defect sizes, should be born in mindwhen a defect is being assessed.
    • Section 5.6.15.6 ASSESSMENT OF DEFECTS5.6.1 Fitness-for-purpose approachWhen a defect is found, a decision must be made as to whether it shouldbe repaired or not. The decision may be based on an arbitrary standard ofgood workmanship, but consideration should also be given to the loads thatthe structure is likely to encounter, the environment in which it will be usedand the consequences of a failure. An approach that evaluates these factorsis often called a fitness-for-purpose approach and should be preferred to thearbitrary standards because: - Repairs can be very expensive, particularly if the structure must be taken out of service or if the installation of a structure is being delayed. - The fatigue life of a "repair" may actually be lower than that of the original execution. This is so because repairs are often made by grinding out the defect and subsequent rewelding. The repair weld itself may contain defects, the toughness may be low, and the welding may intro- duce additional residual stresses. Stress relief heat treatment is generally inconvenient and expensive to apply. The fitness-for-purpose approach to defect assessment is summarizedbriefly below in a five step procedure. More detailed descriptions of thevarious aspects are given in the design codes, e.g. PD6493: 1980 (Ref. 161): - The defect is characterized with respect to size and location. This involves measuring the size of the defect or defects by NDI, and then making appropriate simplifying assumptions. As stress intensity factors are readily available for straight, elliptical and semi-elliptical cracks, the defects are often idealized to one of these geometries. - The local stress spectrum is determined. - A fatigue crack propagation calculation is performed. The possibility of non-propagation should be considered. - The critical size to which the defect can grow before fracture occurs, is determined (Chapter 9). - If the calculations show that the critical size is reached within the next inspection period, (which frequently may be the total expected service life), a repair will be necessary.
    • Section 5.6.1 The following example demonstrates the procedure: A surface flaw was detected at the toe of the butt weld of a pipe withoutside diameter D = 965 mm and wall thickness WT = 25 mm. Allowing forthe uncertainty of the NDI method, the maximum depth of the flaw wasestimated to 3.0 mm and the maximum length to 25 mm. Based on thesedata the flaw was idealized by a semi-elliptic crack with half axes a = 3 mmand c = 12.5 mm, with its plane vertical to the pipe axis. The maximum applied axial stress oaPp was estimated to 250 MPaand the effective dynamic stress range Ao to 40 MPa. A rough estimationof the stress intensity factor at the bottom of the crack was obtained (Section3.1.3): In a weld the stress ratio is high, and 4 MPa 6 was assumed to beabove the threshold value for non-propagating cracks. The crack growth wastherefore calculated using a cycle by cycle integration of Paris equationin the direction of the two semi-axes (Chapter 3):AK, and AK, are the stress intensity factors in the thickness direction, respec-tively along the surface, and dependent on a/2c and the ratio between a andthe plate thickness b. The results are shown in Table 5.1 for C = 2 10- l 3 mm andm=3. (MPam)m Table 5.1. N a c
    • Section 5.6.2 The fracture toughness in terms of critical CTOD value 6, at operatingtemperature was estimated to minimum 0.5 mm. The pipe had not been heattreated after welding, and residual stresses of magnitude equal to the yieldstrength Re = 420 MPa would prevail in and close t o the weld. Based on theseassumptions the allowable through-thickness crack size, a , was calculated,using the CTOD design curve (Chapter 9): It is seen in Table 1 that an unstable fracture may be expected afterapproximately 1.2 lo7 load cycles. At that stage the crack has developedalmost through the plate thickness, and for such crack depths the ima-value is equivalent to the half length of the crack. Consequently it wasdecided t o carry out a repair within approximately lo7 load cycles which inthis case corresponded to two years.5.6.2 Defect severity5.6.2.1 Sharp defectsThe service loads must be considered in a fitness-for-purpose analysis. How-ever, it can be useful to compare the severity of defects under equal loadingconditions as this can lead to a better feeling for what might represent adangerous defect. It should be pointed out that the sharper a defect, the more severeit is. Thus, a planar fatigue crack of 10 mm radius is more severe than aspherical defect of radius 10 mm, assuming that the maximum tensile stressacts perpendicular to the crack plane and is the same in both cases. In predict-ing design lives, defects are usually assumed to be as sharp as a fatigue crack.Apparently this is a lconservative approach, but is justified since roundeddefects often have sharp edges. The elastic stress field near the tip of a sharp crack subjected to Mode Ideformation is described in Chapter 3 by Eqs. (3.1 a - 3.1 0. These equationsshow that the distribution of the elastic stresses at the crack tip are invariantin. all components, and that the magnitude can be described by the stressintensity factor KI.
    • Section 5.6.2 The severity of planar defects can be compared by comparing the stressintensity factors for the different defects under equal loading conditions.A few examples are given below (Fig. 5.20). Embedded d e f e c t Surface defect Fig. 5.20 Usual defect size convention. 1. For embedded elliptical cracks, the stress intensity factor is given by: where @ = 1 + 4.595 -) (2ac It is seen that equal severities exist for constant stress when the ratio a/@ is kept constant. Thus the following embedded cracks have equal severities : 2. If c is greater than 5 a, the severity of the crack is nearly independent of c. For example, a slag line or lack of penetration defect which is 2 mm high and 10 mm long would not be significantly more severe if its length were increased to 100 mm or more. 3. For the same a and c values, surface defects are about 12%more severe than embedded defects. In some cases, large defects need not be repaired or considered in adetailed fracture mechanics analysis because more severe defects may limitthe life of the structure. Consider the cruciform joint loaded in tension inFig. 5.21, Ref. / 7 / . There will always be small surface defects of depth about0.1-0.5 mm at the weld toes. Due to the stress concentrating effect of the
    • Section 5.6.2 I Weid t o e d e f e c t depth assumed to be 0.1 mm - pFig. 5.21 Diagram showing whether fatigue cracks will develop from the toe or root defects (Ref. 171).weld geometry, these small cracks experience high local cyclic stresses andmay therefore grow by fatigue at lower applied cyclic loads than needed toextend substantially larger root defects. In that case the root defect neednot be repaired. In Fig. 5.2 1 it is not expected that fatigue failure will occurfrom root defects of size less than 0.5 5 P if a/P is around 0.7.5.6.2.2 Rounded defectsThe elastic stress field in the vicinity of narrow rounded notches subjectedto tensile stresses normal to the notch plane may be described by adding aterm to the set of equations for sharp cracks (Fig. 5.22). (~y)notch = (xy )crack - KI . -- 38 sin - (27rr)l2 2r 2
    • Section 5.6.2 Fig. 5.22 Coordinate system for notch tip stress field. KI is the stress intensity factor for a sharp crack of length equal to thatof the notch and subjected to the same loading. The second term representsthe influence of the blunt notch with radius p. From these equations it is seenthat the maximum stress at the bottom of the notch is:This equation indicates that the severity of blunt notches and other roundeddefects may be compared by the ratio K I / f i . It is expected that the parameter K I f l will lose its significance whenthe plasticity at the notch is extensive. However, if the plastic zone is small,the sourrounding elastic stress field will govern the strains of the localizedplastic zone. And it is as a characterizing parameter for non-propagatingcracks that K I / f i can be used. The following threshold values for the K I / f iratio have been found experimentally from testing of ferritic-pearlitic, mar-tensitic and austenitic steels (Ref 181). ferritic-pearlitic steels martensitic steels austenitic steels n : strain hardening exponent. For a 5 mm deep surface notch in a ferritic-pearlitic steel of yieldstress Re = 360 MPa subjected to a stress range Aa = 50 MPa, no initiation offatigue cracks should thus be expected if:
    • Chapter 5. References These relationships have been obtained from testing of specimens withmachined blunt notches and should not be applied t o real defects such asslag inclusions which may have sharp edges. Also their range of validity is -limited. For tests with ferritic-pearlitic HY-130 steel (Re 900 MPa) it wasfound that the fatigue crack initiation behaviour was independent of thenotch tip radius p for p < 0.2 mm and p > 6.4 mm.REFERENCES 1. Gurney, T.R. : Fatigue of welded structures. Cambridge University Press. Second Ed. 1979. 2. Berge,S. andMyhre,H.: Fatigue strength of misaligned cruciform and butt joints. Norwegian Maritime Re- search, April 1977. 3. Bokalrud, T. and Karlsen, A. : Control of fatigue failure in ship hulls by ultrasonic inspection. Norwegian Maritime Res. No. 1. Vol. 10. 1982. 4. Wong, W.K. Rogerson, J.H.: and Weld defect distributions in offshore structures and their influence on structural reliability. OTC, Houston, 3-6 May 1982. 5. Fsrli,O.: Reliability of ultrasonic and radiographic testing. Conference on Fitness for Purpose Validation of Welded Constructions. The Welding Institute. London, 17-19 Nov. 1981. 6. British Standards Institution: "Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints." PD 6493: 1980. 7. Bokalrud, T. : Finite element analysis of butt weld and cruciform joints to determine the significance of internal crack-like defects. Norwegian Maritime Research. No. 31 1978. 8. Rolfe, S.T. and Barsom, J.M.: Fracture and fatigue control in structures. Application of fracture mechanics. Prentice- H l ,Englewood Cliffs, New Jersey, USA, 1977. al
    • CHAPTER 6 IMPROVING THE FATIGUE STRENGTH OF WELDED JOINTS Per J . Haagensen SINTEF, Trondheimq- ABSTRACT In this chapter several methods for improving the fatigue strength of welded joints are reviewed. An evaluation of existing test results shows that improved weldments made from high strength steels have consistently higher fatigue strengths than mild steel connections having been treated with the same methods. In a comparison of improvement methods it is shown that each method has its strength and weakness when considering service loading, cost, case of application and quality control. Thus the most effective method depends on the type of structure and type of welded joint. 6.1 INTRODUCTION 6.1 .1 General Any weld in a structure usually represents a weakness both with regard to brittle fracture and fatigue strength. The low fatigue strength of welded joints is a limiting factor for the design of more efficient structures, in particular since the fatigue strength normally does not increase with static strength. 1. dsrtdl , fbr example by subtitu- a lower class jaint &th one having s higher iil#igue strength. 2. k p h g the fatigue -q$h of the jobt g an improvement ~ t h d .
    • Section 6.1.2 Improvement methods are usually employed as remedial measurest o extend the fatigue life of welds that have failed prematurely and have beenrepaired, or to extend the life of welds that through service load monitoringhave been shown to be more severely loaded than assumed during the designphase. A strong incentive for applying improvement methods to new structuresis the potential for increasing the fatigue strength in some relation to thestatic strength, i.e. to make an improved welded joint behave like a mildlynotched component as shown in Fig. 6.1. m Cn C 0 too- VI VI 0 I G sa- R=O Steel to BS 4360 I Grade SOB CyclesFig. 6.1 Relationship between endurance limit and ultimate tensile strength for some components (Ref. / 11). The use of higher allowable stresses for welded joints in higher strengthsteels entails other benefits as well: The thickness effect in fatigue is reduced,bringing about a further reduction in weight as compared with a lower strengthsteel joint with the same load bearing capacity. A reduced section size ingeneral also improves the brittle fracture properties of the joint. The lowerwelding, handling and erection costs may partially offset the higher fabrica-tion expenses incurred by the improvement methods. In this survey the emphasis is on the degree of improvement in fatiguestrength that is possible to obtain using the various improvement techniques.However, from a practical point of view other consideration such as costs andreliability of the treatment (quality assurance) may be important. Variousaspects of quality control and costs are discussed briefly at the end of thechapter.6.1.2 The potential for improving fatigue strengthIn order to exploit the full potential of fatigue life improvement methods
    • Section 6.1.2 l n 400 600 800 ? 3; ULtlmate tensile strength o f steel, MPaFig. 6.2 Typical fatigue strengths at R = -1 of unnotched, mildly notched and welded components, dependent on the tensile strengths of the steels.it is useful to look at the reasons for the poor fatigue performance of weldedjoints. The low fatigue strength of welded joints as compared with othernotched components is illustrated in Fig. 6.2. Welded joints differ from othernotched components in several ways even if the elastic stress concentrationfactors Kt are similar. It is important to identify the main factors that tendto reduce fatigue life in order to choose efficacious methods for improvingthe fatigue performance mmnm beCw^mbatBed and wnwelded,notched cornpanents are : 1. Mo&h s e e curd defem l!/k % a ; ~ ~ ~ f M c n l of the weld toe region notoh which ~Od;laflYis the m&t fatigue critical are* is generally less uni- form than notches in a machined component, see Fig 6.3. Moreover, welded joints contain an assortement of defects, most of which are so sharp that they start growing as fatigue cracks when the structure is subjected to dynamic loads, thus reducing or bhinating the crack a&atksnstage of the fatigue life;. 2. MetafIurgical chaages in the base material. The material in the heat effected zone (HAZ), in which the fatigue crack is likely to initiate and propagate, undergoes metallurgical changes that may affect the local fatigue properties. Thus the softened material in the HAZ of a higher grade steel whose high strength has been obtained by thermo- mechanical treatment, may limit the fatigue strength that is possible to obtain by improvement techniques. 3. RddtasC #tI"esesare set up in and near the weld due to the contraction of the weld metal as it cools to ambient temperature. These local
    • Section 6.1.3 c ac l, E mT f: CONCENTRATION CRACK-LIKE / /HYDROGEN CRACK FUSION L I N E , - LACK OF FUSION LACK OF PENETRATIONFig. 6.3 Factors affecting fatigue life of welded joints: a) 1 - cracklike defect; 2 - undercut; 3 - hydrogen crack; 4 - lack of fusion; 5 - lack of pene- tration, b) residual transverse stress field across the weld. residual stresses due to welding which may attain yield stress magni- tude, affect the fatigue properties in a similar manner as externally imposed mean loads, i.e. a tensile residual stress reduces fatigue life while a compressive stress increases life. The distribution of transverse residual stresses in a welded plate of simple shape is shown in Fig.6.3 b). Residual stresses do not arise only from the thermal strains associated with the welding process and subsequent cooling. Global or long range residual stresses are introduced in a structure whenever members are forced together due to misfit, uneven thermal expansion or when restraint is being used. Long range stresses act over large areas and are therefore not relaxed by peak loads at stress concentration or by local treatment. They are generally of smaller magnitude than welding stresses. 4 . Environmental effects. A corrosive environment may have a strong adverse effect on fatigue life as discussed in Chapter 7. The fatigue life of common welded joints are typically reduced by a factor of two to four under free corrosion in seawater. However, the prevention of corrosion by either cathodic protection or protection coatings, which may restore the air fatigue properties of a welded joint, are not re- garded as improvement methods per se because corrosion protection is part of normal practice for the construction and operation of off- shore structures.6.1.3 Improvement methodsIn the preceding discussion the three factors that most strongly affect the
    • Section 6.1.3 We of welded joint w r identified as: 1. Slesg concentration due to eejoint and weld geometry; 2. Defects, shape and di-stsibution; 3. Residuald&s. According t o the main principle on which the improvement is based, for i n c d g the fatigue strength of weiMed structures can begrouped in two basic categories: 1. Weld geometry modification and defect removal methods. 2. Residual stress methods.The various workshop techniques within the two groups are shown in Fig. 6.4. 1A - GRINDING ) MACHINING METHODS 5L.y ;n9 REMELTING w DRESSING DRESSING SPECIAL WELDING I (AWS) 1 TECHNIQUES SPECIAL ELECTRODES - SHOT PEENING - PEENING METHODS - HAMMER OR - WIRE BUNDLE PEENING - MECHANICAL - METHODS I INITIAL OVERLOADING - OVERLOADING METHOOS - LOCAL COMPRESSION - STRESS RELIEF THERMAL + THERMAL METHODS HEATING GUNNERTS METHOD Fig. 6.4 Classification of some weld improvement methods.
    • Section 6.2.1A brief discription of each method and the degree of improvement whichhas been achieved in laboratory tests are given in the following sections.6.2 WELD GEOMETRY MODIFICATION AND DEFECT REMOVAL METHODS6.2.1 Grinding techniquesBy full profile burr grinding the entire weld face is machined and given afavourable shape to reduce the stress concentration and t o remove harmfuldefects at the toe, see Fig. 6.5. For all types of grinding it is of vital importancethat material is removed to a depth of 0.5 to 1-0mm t o remove defects suchas intrusions and undercuts, Fig. 6.3 b). Toe burr grinding usually results ina somewhat lower increase in fatigue strength compared with full profileburr grinding. For example in Ref. /3/, full burr grinding gave 100% increasein fatigue strength, while toe grinding gave 60%. The cost for toe grinding is,however, substantially lower. Disc grinder R o t a r y burr grinder L 1 Full profile grinding ~ o e g r i nding 0.5-1.0 mmFig. 6.5 a) Two grinding methods: 1 - rotary burr grinding; 2 - disc grinding. b) 3 - full profile grinding; 4 - toe grinding. Disc grinding is the least time-consuming grinding process, but thefatigue strength of disc ground joints is usually found to be somewhat lowerthan for joints subjected to toe burr grinding because of the score marksthat are transverse to the applied stress. However, test results do not showa clear trend as exemplified in Fig. 6.6, where toe burr grinding gives higherfatigue strength than disc grinding for a high strength steel, while the situationis the reverse for a lower strength steel. The effect of free corrosion in sea water was investigated by Booth,Ref. 151, and deBack et al, Ref. 161. In Ref. /6/ the fatigue lives of as-weldedand ground joints were reduced by similar amounts by corrosion. In Ref. / 5 /however, only the lives of improved (ground) joints were reduced significantly,
    • Section 6.2.1 500 Heavy d l r c ground 400- Toe burr ground 0 I , J 5 L 300- ul 240- -C Ln 200- K.y 1 8 0 - B S 4360 (+ 43A ( 2 4 5 MPa yleLd 160- strength) 140- -- SuporeLso 7 0 ( 6 8 5 MPa yield strength) 120- 100 I I I I r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1o 4 1 o5 lo6 1o7 Endurance, c y c l e sFig. 6.6 Fatigue strength improvements due to burr toe grinding and disc grinding, data from Ref. 131. air r e s u l t s - Number o f c y c l e s t o f a i l u r e , NfFig. 6.7 he effect of free corrosion in sea water on the fatigue strength of as-welded and ground specimens (Ref. 151).
    • Section 6.2.2see Fig. 6.7. This was attributed to the formation of corrosion pits. The pitswould act as stress raisers and thus shorten the fatigue life considerably,whereas the more sharply notched as-welded specimens would be less affectedby corrosion. The variation of improvement with base material strength for groundspecimens is shown in Fig. 6.8. The data show that high fatigue strengths areobtained consistently for the higher strength steels. For medium and highstrength steels the increase is always greater than two classes in the designcurve system of BS-5400. Symbol Ref. Typeof weldmen t O O A V 3 Cruclform Fillet welded do l n t s @ B 7 B u t t welds Polish - ---- ----- BS 5400 ---- cycles 50 1- 0 200 400 600 800 1 0 0 0 200 400 600 800 1 0 0 0 Ultimate tensile strength, R,(NPa) Ultimate tensile s t r e n g t h , R,(MPa)Fig. 6.8 Variation of improvement in fatigue strength due to grinding, depen- dent on base material strength. Data from Refs. 131, /4/, and 171.6.2.2 Weld toe remelting methodsRemelting the weld toe region using either a tungsten inert gas (TIG) or aplasma torch generally gives large improvements in fatigue strength for tworeasons: Remelting gives a smooth transition between the plate and the weldmetal, and secondly, non-metallic contarninents such as slag intrusions aremelted and removed. While both methods are somewhat time consuming, theyshare one advantage in that they are suitable for mechanization.TIG dressing.TIG dressing is performed with standard equipment for thin plate TIG weld-ing. The material in the toe region is melted to a shallow depth without theaddition of filler material, Fig. 6.9a). Slag particles are brought to the surfaceand the remelted zone is essentially defectfree. Optimum conditions have
    • Section 6.2.2Fig. 6.9 $&g: a) single run; b) double run. 1- tungsten electrode; 2 - nozzle; 3 - shielding gas; 4 - HAZ; 5 - remelted metal; 6 - remelted metal from second TIG run; 7 - HAZ from second run, Ref. / 121.been proposed by Kado (Ref. 191) and Millington (Ref. /lo/). The heat inputshould exceed 1.0 kJ/mm (Ref. 171) to obtain a good profile. A high heatinput should also be maintained to obtain a low hardness in the heat-affectedzone (HAZ) of C-Mn steels. Argon is the most commonly used shielding gas,but results by Fisher (Ref. / 1 11) indicate that helium would be a better choiceas higher heat input (about 14%) and greater depth of penetration (about 40%)were obtained with helium. Fisher (Ref. 1111) found the deep penetrationof the helium-shielded TIG arc particularly useful for the repair of weldedjoints containing small fatigue cracks. Using a penetration depth of about6 mm, he found that 3 mm deep fatigue cracks could be removed successfully. Reduced hardness in the HAZ can also be achieved by a double-runTIG dressing technique, Fig. 6.9 b). The heat from the second TIG pass madeon the weld metal tempers the HAZ from the first and brings the hardnesslevel down to an acceptable level of about 300HV10 for C-Mn steels, (Ref.1121). The weld and plate should be clean in order to avoid pores and irregu-larities in the remelted metal; this can be achieved preferably by sandblastingor light grinding. A particular problem with the TIG and plasma remeltingtechniques is that of stopping and restarting the remelting run which tendsto give very irregular bead profiles. Stopping and reinitiating the arc on theweld surface is one solution to this problem, see Fig. 6.10.
    • Section 6.2.2Fig. 6.10 Restarting technique for TIG remelting run after accidental stop (Ref. /lo/). Typical results from tests on TIG-dressed specimens (Ref. / 121) areshown in Fig. 6.1 1. Large improvements were also obtained in other test pro-grammes (Refs. 161, /7/, 113-1 81). The summary of air results in Fig. 6.12indicates that the improvements due to TIG dressing increase with increasingstatic strength of the base material. Bateriak F 47 CT G Loading; const. amplitude Environment; lab. air Frequenc. 5 Hz Load r a k ; R=0.1 TIG dressed welded 8= 0-0- Number o f c y c l e sFig. 6.1 1 Effect of TIG dressing on the fatigue strength of a medium strength steel (Ref. / 171). Fig. 6.13 shows results from tests in sea water (Ref 1171) indicating astrong influence of free corrosion on the fatigue lives of TIG-dressed speci-mens; however, significant improvements were still evident. Similar resultswere found in Japanese (Ref. 1151, / 16) and Dutch (Ref. 161) tests, but not inthe British (Ref. 151) which showed no improvement in sea water.
    • Section 6.2.2 50 1 200 400 600 800 I 0 0 0 O zbo 460 d o d o lob0 Ultimate tensile s t r e n g t h , Rm(MPa) Ultimate tensile strength , Rm(MPa)Fig. 6.12 Variation in fatigue strength improvement due to TIG dressing dependent on base material strength. Material; OX602 Loading; constant ampli tude Environment; sea water Frequency; 1Hz Load ratio; 0.1 50 1 I 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 t I 1 1 1 1 1 1 1 lo4 2 3 4 5 lo5 2 3 4 5 to6 2 3 4 5 10 Number o f cycles t o failure, NFig. 6.13 Influence of sea water corrosion on the fatigue strength of as- welded and TIG-dressed specimens (Ref. 1171). similar to TiG dressing, the main cNfYerena? being higher put, and a wider weld pool. In Ref. 1201 a minimum heatinput of 2.1 kJ/mm is recommended. The wider weld pool tends to makeplasma dressing less sensitive to electrode position relative to the weld toe,
    • Section 6.2.3and the resulting improvement in fatigue life is generally larger than for TIGdressing (Ref. 171). Test results from several investigations (Ref. 161, 171, and119-2 1/) are summarized in Fig. 6.14. The data in Fig. 6.14 indicate that theimprovements in the fatigue strength of plasma dressed specimens increase withstatic strength, i.e. the same trend as for TIG dressed specimens (Fig. 6.1 2). 0 Ref. 6 R e f . 21 A Ref. 20 v " " " X Ref. 19 +- 0 a 200 400 600 800 1 0 0 0 O 200 400 600 800 1 0 0 0 U l t i m a t e t e n s i l e s t r e n g t h . R.(MPa) U l t i m a t e t e n s i l e s t r e n g t h , R,(MPa)Fig. 6.14 Variation in fatigue strength improvements due to plasma dressing dependent on base material strength. In one investigation (Ref. 1211) weld metal was added to the toe duringplasma dressing, this gave an increase similar to those obtained by conven-tional plasma dressing.6.2.3 Improved welding techniquesInstead of employing costly post weld improvement methods, the philosophyof the American Welding Society (AWS) has been to attempt to control theshape of multipass welds to obtain, firstly, a favourable overall geometryand secondly, a smooth transition at the weld toe (Ref. /22/). In Japansimilar ideas have led to the development of special electrodes for use in thecapping pass in high strength steel joints. The first approach has met with onlylimited success as described below.A WS improved profile welds.In the AWS Structural Welding Code (Ref. /22/) a reduction in the large-scale stress concentration factor due to weld shape as well as a lowering ofthe local stress at the toe is sought by specifying an overall concave weld
    • Section 6.2.3profile and a smooth transition at the toe, see Fig. 6.1 5. In the latest modifi-cation to API RP2 (Ref. /23/), the use of non-profiled welds is discouragedthrough use of a lower SN-curve. Dime test to be applied to weld toes (A) and weld face irre ularltles (interpass notcfes) Coin or disc yith radius R 1 mm wire shallFig. 6.15 The American Welding Society (AWS) improved profile weld and "dime test" (Ref. 1221). Tests on specimens with various weld geometries showed no particulartrends for nominal weld angles of 70 and 45; this may stem from the factthat the local geometry at the toe (weld contact angle and radius of curva-ture) was not closely controlled (Ref. 161). Tests on tubular joints (Ref. 1241)fabricated to AWS improved profile specifications were also inconclusive asno difference in fatigue life could be found between specimens which hadpassed the dime test and those which failed, see Fig.6.16. Gurney (Ref. 1251)has shown that welds with improved profiles obtained by grinding the weldmetal alone to a concave shape without grinding the toe region gave nosignificant increase in fatigue life. This may explain the results inFig. 6.16.Thus the AWS improved profile can only be expected to give consistentimprovements in fatigue life if the toe region is carefutly ground as indicatedin Fig. 6.5 b). electrodes.Systematic investigations of the effect on fatigue strength of special MMAelectrodes designed to give a smooth transition profile at the toe have beencarried out only in Japan (Refs. 171, /8/ and 126-281). These electrodes weredeveloped specifically for use in the final weld pass at the toe of joints madefrom high strength steels in the 500 to 800 MPa yield strength range to avoid
    • Section 6.2.3 0 Pass e l ? . Endurance, cyclesFig. 6.16 Results from fatigue tests on tubular joints with improved weld profiles according t o AWS (Ref. 1241).costly weld improvement treatments. Good wetting and flow characteristicsare obtained by the use of a suitable flux composition. The improvementin fatigue strength as a function of base material strength is shown in Fig.6.17. A .. . V R e f . 15 . , 0 Ref. 2 8 .. n n n 0 . , - 3 - 4 200 400 600 800 1000 O 200 400 600 800 1000 Ultimate t e n s i l e s t r e n g t h , Rm(MP.) Ultimate t e n s i l e s t r e n g t h , Rm(tlPa)Fig. 6.17 Variation of improvements in fatigue strength with base material strength as a result of using special electrodes.
    • Section 6.3.1 - 6.3.26.3 RESIDUAL STRESS METHODS6.3.1 GeneralDue to the presence of high tensile stresses in as-welded joints, applied stressesbecome wholly tensile in the weld area, even if the applied stress cycles arepartly compressive. Thus as-welded components are insensitive to the stressratio of the applied stresses. Stress relief can therefore be used to improvefatigue strength, but the degree of improvement is strongly dependent on themean stress of the applied load cycles. Significant improvements due to stressrelief are possible only if the applied stress cycles are at least partly com-pressive. Since long range reaction stresses will always be present in a largewelded structure, stress relief itself cannot be regarded as a life improvementmethod. For this reason stress relief is not at present incorporated in anydesign codes that apply to offshore structures. To obtain significant improvements in fatigue strength, it is necessarynot only to remove tensile stresses but also to introduce compressive stressesof sufficient magnitude in fatigue critical areas, to make even completelytensile applied stress cycles partly compressive. An important limitation tothis principle is that the peak service loads, particularly those in compression,should be so low that yielding does not occur, as this would relax the residualstresses. Several methods have been developed to introduce compressiveresidual stresses (Fig. 6.4), the more important are described below.6.3.2 Hammer peeningPeening is a surface cold working process which produces a layer of heavilydeformed material containing high compressive residual stresses. Hammerpeening is performed with a pneumatic hammer fitted with a solid tool witha rounded tip of 6-14 mm radius, the air operating pressure is typically inthe 5-10 bar range. Alternatively the tool consists of a wire bundle, each wireof approximately 2 mm diameter and the tip rounded. It has been found(Ref. /3/) that four passes along the weld toe with a solid hammer tool pro-ducing an indentation approximately 0.6 mm deep, represent an optimumtreatment for mild steel. This type of hammer peening gives much higherfatigue strengths than either shot peening or wire bundle (multiple point)peening, the probable reason being the large amount of cold working and thebeneficial effect of reducing the stress concentration by the severe deforma-tion of the toe region. Most of the work on hammer peening has been carried out at TheWelding Institute (Refs. 131, /4/, /29/), but some tests have been performed
    • Section 6.3.2 A s welded Hammer peened PLate f a i l u r e away Plate failure from No failure 60 0 1 I I 1 1 1 1 I I 1 1 1 1 1 1 ~ 1 o4 1 o5 1 o6 1 0 Cycles Fig. 6.18 Improvement in fatigue strength due t o hammer peening (Ref. 1291). in the US on cover-plated beams (Ref. 1111) and in Belgium on cruciform joints (Ref. 1301). Typical UK tests results on fillet welds are shown in Fig. 6.18. The effect of base material strength on the increase in fatigue strength is shown in Fig. 6.19. 0 0 0 200 400 600 800 1 0 0 0 200 400 600 800 1000 Ultimate tensile s t r e n g t h , R,(MPa) Ultimate t e n s i l e s t r e n g t h , R,(mPa) Fig. 6.19 Variation of fatigue strength improvement with base material strength due to hammer peening.
    • Section 6.3.36.3.3 Shot peeningAs an improvement method for welded joints shot peening has attracted a lotof attention in recent years, possibly because it can be applied to large areasat relative low costs. It gives large increases in fatigue strengths and, becausepractical experience in its use has been gained over a long time in otherindustries, there is a fairly well developed system for defining optimum condi-tions and for quality control of the process. The shot -peening process is similar to sand blasting. However, insteadof sand, small diameter cast iron balls or small pieces of high tensile steelwire are fed into a high velocity air stream. Specification of all shot peeningvariables is cumbersome and therefore impractical. Two parameters, theAlmen intensity and the coverage are used instead. The intensity of the peen-ing (the degree of surface plastic defonnation) is determined by Almen strips,which are small steel strips attached to the component. The strip developsa curvature due to the surface deformation on the exposed side. The curva-ture (the height of the arc) in a strip of a given material and thickness thendefines the Almen intensity. The coverage is related to the amount of areacovered by the dimples produced by the shot. Complete or 100% coverageis obtained when visual examination at 10X magnification reveals that thedimples just overlap. The commonly used specification of "200%coverage"then implies that the object is peened for twice the time required for 100%coverage. 0 1 200 400 600 800 1000 O zoo 460 6i0 860 l o b 0 Ultimate tensile strength, Rm(MPa) Ultimate tensile strength , R,(MPa)Fig. 6.20 Variation of fatigue strength improvement due to shot peening dependent on base material strength.
    • Section 6.4 - 6.5 The size of shot is also important. In order to reach the bottom of allnotches the shot should be small, but the peening intensity decreases withdecreasing shot size. Typical shot size is in the range of 0.2 to 1.0 mm, typicalvelocities are 4 0 to 60 m/s. Test results from three separate investigations (Refs. / 181, 1301, 13 1/)are summarized in Fig. 6.20, which shows that shot peening produces largeimprovements in fatigue strength, particularly for high strength steel joints.6.4 COMBINATION OF IMPROVEMENT METHODSCompounding two or more improvement techniques can give very largeimprovements in fatigue strength. This can be used in situations where costsare of minor importance, for instance when extra fatigue strength is neededto avoid extensive redesign when a damaged structure is to be repaired.Combinations of methods from each of the two main improvement groupsare likely to give best results. Thus Gurney (Ref. 1341) found that combiningfull profile grinding with hammer peening gave a fatigue strength for filletwelded specimens in mild steel equivalent to that of the base material. Simi-larly, Bignonnet et a1 (Ref. 1321) observed a large improvement when com-bining a controlled profile weld technique with shot peening (Fig. 6.2 1). It may be possible to offset partially the higher costs of combinedmethods by incorporating one of the techniques as part of the normal fabri-cating procedure. Shot peening for instance, could possibly be used insteadof sand blasting to clean parts before applying surface protection systems.6.5 TEST ON LARGE SCALE COMPONENTSThe only European tests on improved welds on large scale structures arethose previously mentioned on tubular joints (Ref. 1241) with welds con-forming to the AWS improved profile. Although these tests were inconclusivewith respect to life increase, tests made by Fisher (Ref. 11 11) on cover-plated beams with hammer peened and TIG-dressed welds gave improvementsof at least one design category in the A A S H T O % ~ ~ ~ ~ ~ specifications. Grindinggave smaller improvements. However, the full potential of the improvementtechniques was not realised because of premature failures originating at theweld root. German tests (Ref. 1141) on beams similar to Fishers (350 mmweb depth, 24 mm flange thickness) also gave very modest increases in fatiguestrength because of premature failures originating at hydrogen-inducedcracks in the web-to-flange welds. Swedish tests (Ref. 1341) on beams thatwere almost identical to Fishers also resulted in small but significant increases* American ) Association of State Highway and Transportation Officials276
    • Section 6.5 2;:. Scat ter band for speci&n In the as-welded condl tion A Welds f u l l y ground Welds f u l l y round,then hamrnw poene8 Endurance, cycles Improved profile E 460 30 mn Air, R=0.1 10-20 Hz inlt. failure As welded o Shot peened 50 ! l l l l I I , 1 1 1 1 1 I I l l l l l r l 1 o5 1 o6 10 Number o f c y c l e sFig. 6.21 Fatigue strength improvements obtained by compounding; a) grinding and hammer peening (Ref. 1341); b) improved prome and shot peening (Ref. 1321).
    • Section 6.6in fatigue strength. The small increase was, as in Fishers test, attributed tofailures starting at the roots of the cover plate fillet welds.6.6 COMPARISON OF IMPROVEMENT METHODSTypical results from various improvement methods are shown for a mildsteel, Fig. 6.22, and a high strength steel (HT60), Fig. 6.23. In all cases largeincreases in fatigue strength were obtained , particularly at low stress ranges.The shallow slopes of the SN-curves indicate that the improvements arisemainly from the addition of a crack initiation stage. Endurance, cyclesFig. 6.22 Effect of some improvement techniques applied to mild steel transverse fillet welded joints (Refs. / 2 / , /19/). A statistical analysis has been carried out on a large number of testresults to compare the improvements obtained by various methods (Ref. /36/).The main results are shown in Fig. 6.24. Although two weld classes (butt andfillet welds) are mixed and the scatter therefore is large, the trends are similarto those observed in the test series surveyed here with 49, 83, and 57%average increase in fatigue strength for machined, remelted, and peened spe-cimens, respectively. The strengths and weaknesses of some of the more important improve-ment methods are listed in Table 6.1.
    • Section 6.6 Plasma dressed . -c ---------- TIG dressed .-Ground ---- As welded HT 60 steel R , = 589 MPa 50 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 o4 2 4 6 lo5 2 4 6 lo6 2 4 6107 Number of cycles t o failure, NFig. 6.23 Effect of some improvement methods applied t o high strength steels (Ref. 1351); data from Ref. 1211. Table 6.1 Evaluation of improvement methods.GROUP. METHOD ADVANTAGE DISADVANTAGE GRINDING Relatively simple and Applicable mainly to planar joints w METHODS easy to perform. that can be expected to fail from 8 General Give large improvement. the toe. All grinding techniques E give a poor working environment regarding noise and dust. Access to weld may be a limiting factor. H Relatively simple to per- Marginal increase can be expected Zi form, inexpensive. for large size welds tubular joints @ 0 Simple insection criterium (depth min. 0.5 r r below nn plate surface or undercut). due to stress concentration effect of groove. Full profie Very slow. Expensive Large improvements to be ex- b u n grinding due to h a labor costs pected for all types of welds. and high tool wear rate. C n ;gding 8 Very fast compared with burr grinding. Can cover Score marks give lower improve- ments than burr grinding. C3 large areas Improper use may introduce serious defects.
    • Section 6.6Table 6.1 (Continued) - -GROUP METHODS ADVANTAGE DISADVANTAGE REMELTING Large improvements are Operator needs special METHODS possible. Suitable for training. General mechanization. TIG Small physical effort Careful cleaning of weld and dressing required. plate necessary. Inexpensive. High hardness may result in C-Mn steels due to low heat input. Plasma Easy to perform due to Lower hardness than TIG dressing large weld pool. dressing. Somewhat larger improve- Heavy, cumbersome equipment. ment than TIG dressing Accessibility may limit use. WELD The improvement is intro- Defects at weld toe not PROFILING duced in the welding pro- removed. METHODS cess itself General AWS Well defined inspection Very large scatter in test results improved criterion (the "dime test") due to variations in microgeome- I profile try at weld toe. Consistent im- Suitable for large welds provements only possible if and tubular joints method is combined with others, e.g. toe grinding, hammer peening or shot peening. Special Easy to perform. Suitable Improvement smaller than e.g. electrodes for smalljoints. Inexpensive grinding or TIG dressing. - General 1 Large improvements Not suitable for low cycle fatigue possible. applications. ~eneficial effects may disappear under variable amplitude loading involving peak compressive loads. Hammer Very large improvements Limited to toe treatment only. peening possible for poor quality welds. Simple inspection criterion Excessive peening may cause (depth of groove > 0.6 mm) cracking. Shot Well developed procedures Practicable application to large peening for small parts. Covers scale structures not demon- large areas. strated. Simple methods for Best suited for mild notches. quality control. Improves resistance to Very thin surface layer stress corrosion cracking. deformed; corrosion may quickly remove beneficial effects.
    • Type of joint Type of joint Fatl ue improvement by AG a piasma arc dressing Fatigue improvement by shot-or hammer-peening1 2 0.8 1 2 4 Ratio 6i/%,50z R a t i o 6; /6A,S0x Type of joint Probability onaly s i s of characteristic fatigue strength UA Fatigue improvement by machining 0.011 2 30 50 100 150 R a t i o 6 /d,,50x ; Characteristic f a t i g u e strength (MPa)
    • Section 6.76.7 COST OF IMPROVEMENT METHODSMost techniques for improving the fatigue strength are time consuming andconsiderable costs are therefore involved. Obviously costs and increase infatigue strength are equally important factors when evaluating improvementmethods, particularly when the treatment is to be included in the fabricationprocess of a new structure. Little information about the costs of improvementmethods is available; some data are listed in Table 6.2. Table 6.2 Comparison of costs of improvement methods. RELATIVE COSTS METHOD Ref. /38/ Ref. 1371 Ref. 1301 Ref. /3/ . Butt w. T-joint TIG dressing 1 1 1 1 Hammer peening 113 3 1 Toe burr 3 3-4 grinding Full profile 37 15 12 burr grinding Heavy disc 2 0.7-1 -1 0.4-1.7 grinding Large uncertainties are associated with the figures in Table 6.2. It is notclear, for instance, if the costs of checking that the treatment has been cor-rectly performed are included. However,Table 6.2 indicates that the costs ofTIG dressing, hammer peening and disc grinding are of similar magnitude,while full profile burr grinding is extremely expensive. In a Swedish studyon the economics of disc grinding and TIG dressing (Ref. 1381) it was foundthat the type of joint had a strong bearing on the costs. Thus disc grindingwhich was found to be generally faster and cheaper than TIC dressing whenapplied to butt welds, was the more expensive method when access to theweld was limited.
    • Section 6.8.1 - 6.8.26.8 APPLYING IMPROVEMENT METHODS TO OFFSHORE STRUC- TURES6.8.1 GeneralAlmost all current knowledge about improvement techniques has been gainedfrom tests on small planar joints. The question of the relevance of these datato large scale structures then has to be addressed. The fatigue properties oflarge components of complex shape differ from those of small scale planarspecimen in the following ways: 1. Higher levels of residual stresses exist in larger components. Long range reaction stresses are not relaxed at stress connections by occasio- nal large peak loads. 2. Plate thicknesses are larger. 3. Stress distributions are more complex; the peak stress may not occur at the weld toe, but somewhere on the weld reinforcement. The higher levels of residual stresses in larger components may to someextent be simulated in tests on small specimens by applying high stress ratiosor correcting the results for the influence of mean stress. However, the sizeeffect in thick plate improved joints and the implications of stress distribu-tions differing from those found in simple planar joints should be consideredin more detail.6.8.2 Effects of size and stress distribution in improved joints.The effect of plate thickness on fatigue strength of welded joints is mainlydue to two factors: a) Severity of the stress concentration and b) Stressgradient in the thickness direction at the notch root. Other influencing fac-tors are the size and distribution of defects and the static strength of the basematerial. Due to the reduction of the stress concentration factors of jointsthat have been improved by modification of the weld profile, it can be shownboth by considering crack initiation at notches and by fracture mechanicscalculations of crack growth that size effects are much less dominant in geo-metry improved joints than in untreated ones. In contrast to small joints where the peak stress occurs at the weld toe,the area of highly stressed material in a large scale joint encompasses severalweld runs and fatigue cracks may initiate anywhere in this area, see Fig. 6.25 a) - b). For welds in tubular joints this effect is even more pronounced,especially for joints with large ratios of brace to chord diameters as illustratedin Fig. 6.26.
    • Section 6.8.2 v ( aI (b)Fig. 6.25 Stress distribution in a) small joint with peak stress in toe region affecting material in one weld pass only; b) large scale weld with peak stresses including several weld passes. Chord wall Peak stress i n Fig. 6.26 veld fillet Typical stress distribution across Stress a t weld toe weld in a tubular joint. The stress distributions in Figs. 6.25 and 6.26 have important impli-cations for the choice of improvement methods for large scale joints. Firstly,removing material by grinding the toe region of a weld in a tubular jointmeans that the leg length is reduced and the stress distribution is altered asshown in Fig. 6.27. The resulting peak stress may well be higher at the toe ofthe ground weld and the improvement in fatigue life marginal. Thus a weldwhich is to be improved by toe grinding must have a sufficient large leg lengthto avoid moving the new toe into a higher stress field. Stress prior to grinding , yk, from original material removed by grindingFig. 6.27 Stress distribution in the weld of a tubular joint prior to and after toe grinding.
    • Section 6.8.3 The second aspect of highly stressed welds is that an effective improve-ment involves treating the entire weld, not only the toe region. Thus im-provement methods that cover large areas such as shot peening or disc grind-ing are likely to be preferred. Alternatively, if choosing a method which isnormally used for local (toe) treatment, e.g. burr grinding or TIG remelting,the treatment should be extended to cover all interpass notches.6 3 . 3 Inspection criteriaAlthough the many test programmes surveyed here have verified that it ispossible to obtain large increases in fatigue strength by various improvementtechniques, it is still necessary to establish procedures and inspection criteriato ensure consistent results. The depth of grinding, Fig. 6.2, at the weld toe isa simple inspection criterion. However, cracks at the bottom of deep under-cuts could possibly remain after grinding, and such cracks would be difficultto detect because of the heavily deformed surface, particularly after heavydisc grinding. To ensure consistent improvements following a remelting treatment,it would probably be necessary to establish remelting procedure qualificationtests for welders, similar to the procedure tests used for welding, to ensuresufficient heat input and low hardness in the HAZ. Visual inspection wouldprobably be sufficient to detect pores and defects that tend to result fromimproperly deslagged welds or contaminated electrodes. For hammer peening the indentation depth is a simple and reliableinspection criterion. Shot peening, however, presents a more difficult problembecause recent work (Ref. 1301) has shown that there is a poor correlationbetween Almen strip intensity and the resulting fatigue strength followingshot peening. To ensure adequate coverage the erosion of an ultravioletsensitive coating may have to be used (Ref. 1301).6.9 CONCLUSIONSOn the basis of a large number of results from many test programmes, thefollowing conclusions are drawn: 1. All techniques gave improvements in air corresponding to a shift of at least two design classes in the BS 5400-SN-curves. 2. In free corrosion most improvement techniques gave small but signifi- cant increases of fatigue strength. 3. The full potential of the weld toe improvement techniques can be realised only if premature failure from other sites, e.g. the weld root, can be avoided. 4. The amount in increase in fatigue strength due to post weld improve- ment is larger for higher strength steels than for mild steel. 285
    • Chapter 6. ReferencesREFERENCES 1. Maddox, S.J. : "Avoiding fatigue failure by good design and construction practice." Welding Institute, Seminar, Bradford, April 1980. 2. Gurney, T.R.: "Fatigue of welded structures." 2nd ed., Cambridge University Press, 1979. 3. Knight, J.W.: "Improving the fatigue strength of fillet welded joints by grinding and peening." Welding Research Intl, 8 ( 6 ) , 1978. 4. Booth, G.S.: "Constant amplitude fatigue tests performed on welded steel joints in air." Select Seminar "European Offshore Steels Research", Abington, 27-29 November 1978, Paper 4. 5. Booth, G.S.: "Constant amplitude fatigue tests performed on welded steel joints in sea water." Select Seminar "European Offshore Steels Research", Abington, 27-29 November 1978, Paper 9. 6. deBack, J. et al.: "Fatigue and corrosion fatigue behaviour of offshore steel structures." 72 10-KB/6/602 (5.7.1 f/76) Final report, April 1981. 7. Hanzawa, M. et al.: "Improvement of fatigue strength in welded high tensile strength steels by toe treat- ment." IIW Doc. XIII-829-77. 8. Ikeda, K. et al.: "Improvement of fatigue strength of fdlet welded joint for 80 kg/mm2 high strength steel." IIW Doc. XIII-835-77. 9. Kado, S. et al.: "Influence of the conditions in TIG dressing on fatigue strength in welded high tensile strength steels." IIW Doc. XIII-77 1-75.10. Millington, D.: "TIG dressing for the improvement of fatigue properties in welded high strength steels." Weld. Inst. Rep. C215/22/71, July 1971.11. Fisher, J.W. et al.: "Improving fatigue strength and repairing fatigue damage." Fritz Engineering Lab. Report No. 385.3, Lehigh University, Dec. 1974.12. Haagensen, P.J.: "Effect of TIG dressing on fatigue performance and hardness of steel weldments." ASTM Symposium "Fatigue Testing of Weldments", Toronto, May 1977. ASTM STF 648,1978.286
    • Chapter 6 . References13. Minner, H.H. and Seeger, T.: "Investigation on the fatigue strength of welded and TIG dressed high strength steels." IIW DOC.XIII-9 12-79.14. Minner, H.H. and Seeger, T.: "Fatigue strength of welded beams of high strength steels. Interim report." IIW DOC. XIII-95 1-80.15. Todoroki, R. et al.: "Effect of toe profile improvement on corrosion fatigue properties of welded joints." IIW Doc. 875-78.16. Todoroki, R. et al. : "Problems on improvement of corrosion fatigue strength of steel in sea water." 8th Congress "Metalic Corrosion", Mainz, 6-1 1 September 1981.17. Haagensen, P.J.: "Fatigue strength of TIC dressed welded steel joints." ECSC Conference "Steels in Marine Structures", Paris, 5-8 October 1981.18. Simon, P. and Bragard, A,: "Am6lioration des proprietks de fatigue des joints soud6s." Commission du Com- munaut6s Europ6en.e~. no. 6210-45//202, Report Final. Con.19. Booth, G.S. and Baxter, C.F.G. : "Fatigue tests on plasma dressed fillet welded joints." Welding Institute Report 8711979.20. Kado, S. et al.: "Fatigue strength improvement of welded joints by plasma arc dressing." IIW DOC. XIII-774-75.2 1. Shimada, W. et al. : "Improvement of fatigue strength in fillet welded joint by C02 soft plasma arc dressing on weld toe." IIW Doc. XIII-830-77.22. AWS D1.l: "Structural welding code." American Welding Society, 1980.23. API RP2 : "Recommended practice for planning, designing, and constructing faed offshore plat- forms." American Petroleum Institute, January 1980.24. Tornkins, B. : "Fatigue design rules for steel welded joints in offshore structures." OTC Paper 4403,1982.25. Gurney, T.R.: "The basis for the revised fatigue design rules in the Department of Energy Offshore Guidance notes. Paper 55 Second Int. Conf. on Offshore Welded Structures, The Welding Institute, London 16-1 8 Nov. 1982.
    • Chapter 6. References26. Kanazawa, S. et al. : "Improvement of fatigue strength in welded high tensile strength steels." IIW DOC.XIII-735-74.27. Kado, S. et al.: "The improvement of fatigue strength in welded high tensile strength steels by addi- tional weld run with coated electrodes." IIW Doc. XIII-772-75.28. Kobayashi, K. et al. : "Improvement in the fatigue strength of fillet welded joint by use of the new welding electrode." IIW Doc. XIII-828-77.29. Booth, G.S. : "The effect of mean stress on the fatigue lives of ground or peened fillet welded steel joints." Welding Institute Report 34/1977/E.30. Maddox, S.J.: "Improving the fatigue lives of fillet welds by shot peening." IABSE Colloquium, Lausanne, 1982.31. Miisgen, B.: "Verbesserung der Schwingfestigkeit von Schweissverbindungen hochfester wasser- vergiiteter Feinkornbaustahle durch therrnische und mechanische Nachbehandlung der Nahte", Stahl und Eisen 103, 1983, p. 225.32. Bignonnet, A. et al.: "Improvement of the fatigue life for offshore welded connections." IIW Conference "Welding of Tubular Structures", Boston.33. Bergquist, L. and Sperle, J-0. : "Influence of TIG dressing on the fatigue strength of coverplated beams." IIW DOC. XII1.-826-77.34. Gurney, T.R. : "Effect of peening and grinding on the fatigue strength of fillet welded joints." British Welding Journal, Dec. 1968.35. Haagensen, P.J. : "Improving the fatigue performance of welded joints." Paper 36, Second Int. Conf. of Welded Structures, The Welding Institute, London 16-18 Nov. 1982.36. Olivier, R. and Ritter, W.: "Improvements of fatigue strength of welded joints by different treatments - sta- tistical analysis of literature date. Int. Conf. on Steel in Marine Structures, Paris 5-8 Oct. 1981.
    • Chapter 6 . References37. Watkinson, F. et al.: "The fatigue strength of welded joints in hlgh strength steels and methods for its improvement." Welding Institute Report C215/16/70, 1970.38. Lindskog, G. "TIG dressing. A technical and economical assessment of a method to increase the fatigue properties of welded joints." IVF-RESULTAT 7864 1, Sveriges Mekanforbund 1978 (in Swedish).
    • CHAPTER 7 EFFECTS OF MARINE ENVIRONMENT AND CATHODIC PROTECTION ON FATIGUE OF STRUCTURAL STEELS Einar Bardal SINTEF,TrondheimABSTRACTThis chapter deals with various effects of marine environment and cathodicprotection on fatigue of structural steels. The mechanisms of different effectsare reviewed. Environmental effects and influence of cathodic protection onSN-curves and crack growth data are quantitatively treated in separate sec-tions. The significance of weld type and quality, materials properties, loadvariables, environmental factors and corrosion protection measures are re-viewed. Based on crack growth data the effects of corrosion and cathodicprotection on fatigue life have been shown by calculation examples for typicalcrack-load conditions. The main trends of the results are discussed andcompared with British design guidelines.7.1 QUALITATIVE PRESENTATION OF EFFECTS, MECHANISMS AND IMPORTANT FACTORSThe effects of marine environment and cathodic protection (CP) on SN- andcrack growth diagrams are schematically shown in Fig. 7.1 a and b. The SN-curves show that free corrosion in marine environment reduces markedly thefatigue life of plain specimens, whereas the reduction is less for welded joints.The fatigue limit is eliminated or at least drastically reduced by corrosion.A normal degree of cathodic protection usually restores the air fatigue life.In the high cycle region, fatigue life and fatigue limit may even be increasedby CP. At high load levels, however, cathodic protection may reduce fatiguelife. This is particularly the case for high degrees of CP (overprotection)and for high strength steels. 29 1
    • Section 7.1 k Sea water+CP P l a ~ n specimen Sea water+CP Specimen <.:, : A ir w ~ t hw e l d or n o t c h x ? ~ P l a ~ ns p e c ~ m e n S e a watey?%- / free corrosion < ,: With or weld notch log (number of cycles failure Nf ) Fig. 7.1 Effects of sea water corrosion and cathodic protection on a) SN-curves d and b) crack growth rate curves. aKth Log nK log ( s t r e s s i n t e n s ~ t y r a n g e A K) For corrosion fatigue and fatigue of welded joints it has been shownthat the crack growth period represents the major part of fatigue life (Sec-tion 7.2). Much attention is therefore given to crack growth data. Comparedwith the growth in air, free corrosion in sea water accelerates the crack growthrate to a higher or lower degree (Fig. 7.1 b). Cathodic protection reducescrack growth at lower AK-levels and increases it at higher levels. Both corrosion and cathodic protection influence fatigue by differenteffects and mechanisms (Refs. / 1, 2, 3 /) . Some of the effects are counter-acting, and the total effect on fatigue data depends on the prevailing condi-tions. The main mechanisms acting on structural steels in sea water, and thetypical conditions favouring each mechanism are briefly reviewed below.
    • Section 7.1a) Corrosion pits and grooves act as stress raisers and thus contribute t o crack initiation at an earlier stage and at a lower nominal stress than initiation in air (Fig. 7.1 a). For ordinary welded joints this mechanism is probably less important because weld defects may be more effective stress raisers than corrosion defects. In the case of improved welds, however, corrosion defects o n the surface are more significant. For low carbon steels in chloride solutions, the significance of pitting corrosion as the initial stage of corrosion fatigue has been questioned (Refs. 11, 21). Pits are often found near fatigue cracks but they might have been formed after the cracks had started.b) Corrosion fatigue is governed by a synergistic mechanism : Local plastic flow and the creation of new, active surfaces at the initiation site or at the crack front accelerate anodic dissolution, and vice versa, local anodic dissolution promotes plastic flow. This mechanism is responsible for easier and accelerated initiation as compared with fatigue in air, with marked effect on the SN-curves for plain specimens (Fig. 7.1 a). It also favours the conditions for crack growth. The reduced threshold value AKth in corrosive environment (Fig. 7.1 b) may be explained by this mechanism.c) Particularly during stressfree periods, corrosion may blunt the crack front and retard crack growth for some time after the stressfree period, and thus counteract mechanism b. Under variable load amplitudes the resulting effect of mechanisms b and c are difficult to assess.d) Sea water corrosion at or near the crack front may make the crack envi- ronment acid. This allows hydrogen development to take place inside the crack, and the development is further stimulated by the enhanced anodic dissolution mentioned under item b. At medium to high load levels the crack growth may therefore increase by hydrogen embrittle- ment (Fig. 7.1 b).e) Full cathodic protection eliminates the mechanisms a, b and c. In deep cracks, however, the effects under items b and c and the cathodic polarization to prevent them, may not be 100% effective (Ref. 141). Also compare mechanism h.f) At medium to high load levels hydrogen embrittlement due to cathodic protection may increase crack growth (Fig. 7.1 b).g) Under cathodic protection, calcareous deposits may be produced on the
    • Section 7.2.1 crack surfaces and lead to crack closure. Subsequently lower crack growth rates and a higher threshold value AKth will result (Fig. 7.1 b). h) Mass and charge transport within the crack affect both corrosion and cathodic protection at the crack front. Supply of reactants t o and removal of products from the crack tip region are restricted, and there will be a potential drop between the crack front and the free surface. Several factors are important for the environmental effects on corro-sion. When test data are applied for practical purposes such as design, evalua-tion of damage tolerances etc., it is essential that these factors and theireffects are known. Load frequency, type of environment, e.g. that 3% NaCl-solution does not simulate sea water properly, stress level and electrochemicalpotential are among the most important factors. The effect of environmentalso depends on temperature, stress ratio, material strength and weld quality.High pressure and low rates of water flow may have some significance. Quanti-tative effects of the majority of these factors are shown in the followingsections. For some factors, the available information is incomplete.7.2 EFFECTS OF CORROSION AND CATHODIC PROTECTION ON EXPERIMENTALLY DETERMINED SN DATA7.2.1 Plain specimens and different types and qualities of welded joints.In dry fatigue of structural parts and specimens with plain surfaces, theinitiation period may be the dominant part of fatigue life. In a corrosiveenvironment, however, the initiation period is greatly reduced. E.g. in a lowcarbon steel in 3% NaCl solution, 0.1 mm deep cracks may be producedduring the first 10% of fatigue life (Ref 121). Welds of ordinary quality with sharp notches may reduce the initia-tion period to about the same extent as does corrosion. There is also anadditive effect of geometrical stress concentration and corrosion which isreflected in the fatigue life (Ref. /I/). This is illustrated in Fig. 7.2, whichshows SN-curves for cruciform joints in air and synthetic sea water, as weldedand as ground (Ref. 151). Ground and other improved welds have smallerweld defects, hence the fatigue initiation period is longer. When such weldsare exposed to sea water, the reduction of fatigue life due to corrosion isgreater than in the as welded condition. In other words, the improvementof welds is less effective in sea water than in air (Ref. 161).
    • Section 7.2.1 air results - Number o f c y c l e s t o f a i l u r e , NfFig. 7.2 SN-curves for transverse welded joints of BS4360-50D steel in as welded and ground condition, tested in air and sea water at t = 5-8OC. Stress ratio R = 0 and frequency f = 0.167 Hz (Ref. 151). The effect of corrosion is also strong on full penetration butt welds.This is shown in Fig. 7.3, where synthetic sea water gives a life reductionfactor varying from 3 to 6, with the highest reduction at the lowest stress I o4 1 o5 1 o6 I o7 Number of cycles t o failure NfFig. 7.3 Effects of corrosion on SN-curves for butt welded joints in steel BS4360-50D, exposed in synthetic sea water, compared to air data. t = 10-12"C, f = 1 Hz (Ref. 171).
    • Section 7.2.2 1 o4 1 o5 1 o6 1 o7 Number of cycles to failure NfFig. 7.4 As Fig. 7.3, but with saline atmosphere instead of synthetic sea water (Ref. 171).(Ref. 171). A saline atmosphere has a smaller effect (Fig. 7.4). Cathodicprotection at -780 and -1 100 mV vs SCE (approx. -800 and -1 120 mV vsAg/AgCl/sea water) gives fatigue lives similar to those in air (Ref. 171). For other types o f welded joiuzts which have generally larger defects,the corrosive effect is smaller, mostly with a life reduction factor from 2 to 3(Refs. 18, 91). Examples are shown for different ioints and stress ratios inFigs. 7.5 and 7.7 for 20°C and in Fig. 7.6 for 5 " ~ These results are from .small scale tests, but a similar reduction factor has been found for tubularjoints (Ref. /lo/).7.2.2 Significance of environmental factors and corrosion protection measuresMost corrosion fatigue tests referred to in the present chapter have beenconducted in synthetic sea water and some in naturul sea water. When theresults from the different laboratories are compared, it seems as if syntheticsea water is a satisfactory substitute for natural sea water. This was alsoconfirmed by a few tests run at Norges tekniske hsgskole and designed sothat a direct comparison was possible. 3% NaCl solution on the other handcan not replace natural sea water in all cases. The life reduction factors given in Section 7.2.1 refer to free corrosionunder continuous immersion in sea water (Figs. 7.3, 7.5 and 7.7). Fig. 7.6also shows the effects of intermittent immersion which seems to give aboutthe same fatigue life reduction as does continuous immersion. Other testsindicate, however, that the intermittent immersion results are closer toair results (Ref. 181) and similar to those observed in saline atmosphere
    • Section 7.2.2 Cruciform non-load ) c a r r y i n g f u l l penetration weld , B - t y p e s a s welded Air Sea water------ T-form, non-load c a r r y i n g f u l l p e n e t r a t i o n we.Ld, A-type,as welded Air Base series - Sea water Cruciform load )carrying full penetration -.--- weld, C-type, as welded A ........... 50 1 I 1 0 Air 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I I I 1 1 1 1 1 I I I I I I I I ~ 16 1 o6 1 o7 I o0 Number o f c y c l e s t o failure, N fFig. 7.5 Fatigue results for different joints in air and sea water. t = 20°C, R = 0.1 ,f = 0.2 Hz in sea water tests. Steel Euronorm 1 13-72, Grade FeE 355 KT (Refs. /8,9/). - 400 0 a 200 - 0 S e a water ( f r e e corrosion) Mean Line C .- E 2 50 a Sea water 0 Sea water I i n t e r m i t t e n t immersion) cathodic protection) f o r air data I I 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 1 o4 1 o5 1 o6 1 o7 Number of cycles t o failure, NfFig. 7.6 SN-data for welded joints of B4360-50D steel in air and sea water under free corrosion, intermittent immersion and cathodic protec- tion. t = 5" C, R = -1, f = 0.167 Hz (Refs. /5,8/).
    • Section 7.2.2 F u l l p e n e t r a t on w e l d , as w e l d e d 1 sea w a t e r air sea w a t e r Air Sea w a t e r Number o f c y c l e s t o f a i l u r e , NfFig. 7.7 Fatigue behaviour of T-shaped specimens in air and sea water at stress ratios R = 0.1 and -1. t = 20°C, f = 0.2 Hz in sea water tests. Steel Euronorm 113-72, Grade FeE 355 KT. As welded (Ref. 191).(Fig. 7.4). Under sea water drip at t = 20°C and f = 0.125-1 Hz, an averagelife reduction factor of about 2 compared with air was found for the aswelded condition, but with a larger scatter than usually observed under freecorrosion (Ref. / 1 11). Temperature is an important variable to consider. Som British SN testsof welded joints at 5OC have shown very little effect from sea water comparedwith air, while similar Dutch tests at 20°C have resulted in the typical reduc-tion factor 2-3 mentioned earlier (Ref. 181). Hydrostatic pressure in the range of 70-140 bar gives a significant butnot very large reduction of corrosion fatigue strength, as compared withusual values under atmospheric pressure (Ref. / 11). Variation of oxygen content and pH over wide ranges affects corrosionfatigue. However, the real variations of these properties are small in marineenvironments and their effects are not significant (Ref. / I/). Water velocitymay be of some importance when the specimen is under cathodic protection.(Section 7.3 -3) As seen in Fig. 7.6, cathodic protection restores the air fatigue life,and may even give longer lives than in air at the lower stress levels. This is aresult obtained in several investigations, but less benificial effects of cathodicprotection have also been observed. E.g. in one case, cathodic protection of atubular joint gave the same life as free corrosion, but with slower initiation
    • Section 7.2.3and faster crack growth (Ref. /lo/). (Compare Section 7.4) Paint coatings will prevent corrosion fatigue as long as they remainintact and are not scratched or cracked.7.2.3 Significance of loading variables and materials proper ties.In the as welded condition the applied stress ratio R has only a small effectboth in air and under free cprrosion (Fig. 7.7) (Ref. /9/), or no significanteffect at all (Ref. / 1/). If the joint is stress relieved, however, there is a signi-ficant effect of R on the SN-curve as shown in Fig. 7.8 (Ref. 191). It willalso be seen that the effect of R is greater in a corrosive environment, inother words the effect of corrosion is greater at R = 0.1 than at R = -1. - F u l l p e n e t r a t i o n w e l d , PWHT 0.1. a i r 0. water 0 . 1 sea water -1 air -1 sea water Air Number o f c y c l e s t o f a i l u r e , N f Fig. 7.8 As Fig. 7.7, but with stress relieved specimens (Ref. /9/). The frequency effect on corrosion fatigue depends on the conditions.The contribution of corrosion to corrosion fatigue is greatest in the initiationperiod, and lowering the loading frequency, markedly reduces initiation life.During crack growth, the frequency effect is more pronounced at mediumand high stress intensity ranges than at low ones (Section 7.3.2). Corrosionfatigue SN data should be determined with a frequency of the right orderof magnitude to ensure their validity in design. High cycle corrosion fatigue strength does not increase with increasingtensile strength of the material. High strength steels are usually the most sensi-tive to hydrogen embrittlement, and this may reduce fatigue life, particularlyat low potentials. The quantitative effects of hydrogen embrittlement areinsufficiently investigated.
    • Section 7.3.1 The effect of sea water under variable amplitude loading is also insuffi-ciently studied. However, a similar fatigue life reduction factor as reportedfor constant amplitude seems to exist. An average factor of 2.2 was foundwith a narrow band spectrum and with Raleigh and Gaussian peak distribu-tions (Ref. 181). Ref. 1121 reported a factor of less than 2 under realisticstress sequences. In this work it was interesting to observe that the loadingfrequency did not significantly influence fatigue life in the range between 0.2and 10 Hz, and that appropriate cathodic protection completely eliminatedthe damaging effect of sea water (small specimens, f = 1-10 Hz, R = -1).7.3 EFFECTS OF CORROSION AND CATHODIC PROTECTION ON CRACK GROWTH7.3.1 Different effects at different levels of crack growth 3 4 6 10 20 40 60 90 3 4 6 10 20 406090 Stress ~ntensity Stress intensity r a n g e n K (MPaCrn) r a n g e A K (MPaTrn)Fig. 7.9 Fig. 7.10Mean crack growth curves showing Crack growth data. Free corrosiontests in air, under free corrosion in in sea water. R = 0.5 (Ref. 1141)sea water and with cathodic protec-tion at two potentials. R = 0.5.(Refs. 113, 14, 151)
    • Section 7.3.2Mean crack growth curves at R = 0,5,based on results from Ref. /13/ withhigh crack growth rates and from Refs. /14,15/ with low growth rates, areshown in Fig. 7.9. The effects of sea water and cathodic protection at diffe-rent growth rate levels were also discussed in Section 7.1. Fig. 7.10 showsgrowth rates under free corrosion, supplying background data for Fig. 7.9.7.3.2 Significance of loading variables and materials propertiesThe effects of environment and cathodic protection at different AK-levelsare shown in Fig. 7.9. It can be seen in Fig. 7.1 1 (Ref. / 131) that the growth rate under freecorrosion increases with increasing stress ratio R up to R = 0.7. A similardependence is found for growth under cathodic protection. In air, however,the same authors found little or no effect of R in the actual high crack growthregion. In other words, the crack growth accelerating effects of corrosion andcathodic protection in this region, as compared with air, are stronger at ahigher than at a lower R. For free corrosion this is in agreement with theSN-curves in Figs. 7.7 and 7.8. A similar trend was found at lower AK-levelsat SINTEF (Ref. / 151). 1 A r Free c a r r 1 2 d . 3 mY .4 .v i CP I - Garwood 2 - Br siol 3 - Bardal 4 - Booth Scatterband (Lfndley and R ~ c h a r d s ) 0 2 0.4 0 6 0.8 1.0 . . AK (MPaCrn) Stress rat 10, RFig. 7.1 1 Fig. 7.12Effect of stress ratio R on crack Effect of stress ratio R on thegrowth under free corrosion in sea threshold stress intensity rangewater (Refs. / 13, 81). AKth (Ref. / 161, revised).
    • Section 7.3.3 At lower growth rates, there is a clear effect of R both in air, underfree corrosion and with cathodic protection, as is indicated by the effect onthe threshold value AKth in Fig. 7.1 2 (Ref. / 161). In Ref. 1171, the R-influence under free corrosion has been taken intoaccount by replacing AK in the crack growth equation by AK + 4R. Thus, thecrack growth curve moves to the left by an amount of 4R when R is increasedabove zero. These results were obtained in 3.5% NaCl solution, but tests insynthetic sea water show a similar dependence (Refs. 113, 15, 191). For growth rates below mmjcycle, loading frequencies between 1 and 0.1 67 Hz are giving the same growth rates, under free corrosion as wellas under cathodic protection (Refs. 14,201). However, at higher growth rates,corresponding to AK = 10 - 40 M P a f i , a decrease of frequency produces amarked increase of the growth rate. The effect is largest for specimens undercathodic protection where a reduction of frequency by one decade may causea 4-8 times increase of da/dN (Refs. 121, 22, 231). This shows that many ofthe earlier corrosion fatigue growth data which were conducted at increasedfrequencies are in fact invalid. Only for low growth rates can some accelera-tion be accepted (up to 1 Hz). Corrosion fatigue crack growth under variable amplitude loading isnot sufficiently studied. Several investigations (Refs. 11, 24, 251) indicatethat corrosion has approximately the same effect on crack growth underspectrum loading as under constant amplitude loading (Fig. 7.1 3). Onedifference may be that the corrosive effect is clear also at rather high fre-quencies (e.g. 6.5 Hz) for variable amplitude loading (Ref. 1241) (cf. the lastcomment on SN-results in Section 7.2.3). Crack growth rates of welded specimens are similar to those of thebase metal (Ref. 1271). Within the class of low and medium strength structural steels (R, <700 MPa) there seems to be no significant effect of strength and microstruc-ture on the crack growth behaviour (Ref. / I / ) However, this is sparselyinvestigated, and one might expect that cathodic protection at low poten-tials would increase the growth rate in high strength steels.7.3-3 Significance of environmental factorsA raise in temperature from a range of -1 - +5"C to a range of 20 - 24°C hasbeen found to increase the crack growth rate by a factor of 2 (Refs. / 1, 131).In Ref. /27/ a factor of 5 was found for AK = 10 - 50 M P a f i , and the sametemperature raise. At lowerAK values, however, the effect is smaller (Ref. /I/).In Ref. /28/ a temperature raise from 30 ti1 8S°C produced a threefold increaseof the growth rate.
    • Section 7.3.3 66 i7 -8 0 0 Const.rnean/Stat.rms 6" -- S e a water t e s t s ; Gauss Const.rnin./Stat.rrns Const.rnin./Stat.rrns Linear Const.mean/Stat.rrns 0 L - inear L Const.mean/Var.rrns I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 10 30 90 Stress i n t e n s ~ t yf a c t o r aKrms(~PalTm)Fig. 7.13 Comparison of different crack growth curves for variable amplitude loading of BS4360-SOD steel in air and sea water. Constant mean or constant minimum load, and stationary o r variable root-mean- square values. Gaussian spectrum with an irregularity factor of 1 and a crest factor of 4.5. Omission level 15% of maximum load. Log linear spectrum composed of four Gaussian spectra. f = 1 Hz, t = 12OC (Ref. 1251) Water flow may prevent the unfavourable effect of strong cathodicpolarization as compared with free corrosion (Ref. /I/). This is illustratedin Fig. 7.9 for AK = 10 - 40 MPaTm. As far as Ref. 1291 can be understood,the applied water velocity has been lower than 0.1 m/s. A similar trend hasbeen found at SINTEF (Ref. /1 St), for water velocities of 0.2-0.4 m/s. According to Ref. 1131, a reduction of the oxygen concentration insea water from 7 mg/l (air saturated) t o 1 mg/l causes a reduction of thefree corrosion crack growth rate by a factor of 4. There is no similar effectwhen the specimen is under cathodic protection. In some hydrocarbons and possibly in sea bed sediments, a considerableconcentration of H , S may be present. It is shown in Fig. 7.9 that a strongdegree of cathodic polarization produces a large increase in crack growth rateat AK % 15 MPa fi (K,, == 30 MPaKm). H2Sin the water produces asimilar but much stronger effect under free corrosion as well as under catho-
    • Section 7.4dic protection (Ref. 1301). In sea water saturated with H2S, the crack growthis accelerated by a factor varying from 9 to 570 compared with growth inair at AK = 30 M P a f i for R = 0 . 0 5 , and at AK = 12.5 M P a r m for R = 0.7.The effect of H, S decreases with decreasing concentration (Ref. /31/). How-ever, no information has been found on the effect of low H qS concentrations.7.4 PREDICTION OF EFFECTS OF CORROSION AND CATHODIC PROTECTION ON FATIGUE LIFE BY MEANS OF CRACK GROWTH DATAIt has been shown (Ref. 1141) that the effects of cathodic protection com-pared with free corrosion can be completely different for conditions resultingin fatigue lives of 40 -300 years, as compared to conditions producing lives of1 -- 10 years. Such differences can not be disclosed by SN tests, where thewhole life is spent in the test. However, long time effects of environmentalconditions can be shown by fatigue life calculations based on fracture mecha-nics and crack growth data, assuming that reliable data are available at lowstress intensity ranges near to the threshold value AKth. That procedure isbased on the knowledge that the major part of the fatigue life of joints inplates and tubulars is spent on crack growth under conditions that can bedescribed by linear elastic fracture mechanics. Some results of fatigue life calculations are shown in the followingpages (Refs. 114, 151). Appropriate data for tests conducted with variableamplitude loading are scarce. Therefore a linear load distribution is assumed,and the crack growth is calculated based on the constant amplitude growthrate curves in Fig. 7.9. It should be observed that by using this approach,possible sequence effects escape attention. A stress ratio of R = 0.5 is assumed, simulating high residual stresses.The calculation is based on a numerical integration of Klesnil-Lukas equation:where the values of A, m and AKth are taken from Fig. 7.9. The following environmental conditions are considered: Air, freecorrosion, and cathodic protection with two different polarization levels,viz. -800 to -850 mV and -1 I00 rnV (Ag;Agcl/sea water). The latter poten-tial is considered the most unfavourable possible when sacrificial anodesare being used. The load spectrum constitutes a linear plot of AolAcr,, versus logN
    • Section 7.4and is divided into 73 blocks at 30 different load levels. The block successionused in the integration process is drawn randomly and independently foreach return period of 1.6 15.604 cycles. Incremental crack growth Aa for eachindividual block is calculated, and AK is updated for the new crack length +ai+l = ai Aa. Crack growth lives have been calculated for three different defect-loadconditions: A. A small initial defect, a ,constant nominal stress spectrum as the crack propagates, and load levels giving life times of 20 - 200 years corre- sponding to 1o8- 1o9 cycles. Such conditions apply to fixed platform elements, where large defects have been disclosed by inspection and repaired. The calculation has been carried out for an edge crack propa- gating from a plane surface, and from a semi-circular stress raiser as shown in Fig. 7.14. Initial and final crack lengths are respectively ai = 1 mm and af = 10 mm, notch radius r = 2 mm. Fig. 7.1 4 Model geometries applied in the calculations (Ref. / 141). ai = initial crack length, af = final crack length. B. A somewhat larger initial defect, assumed to have escaped detection by the inspection after fabrication, a constant nominal stress spectrum, and load levels leading to fracture after a period of 1 - 10 years. Geome- trical conditions as shown in Fig. 7.14 with ai = 10 mm, af = 100 mm and r = 50 mm. Unstable fracture may occur for a <af if AK >K,(l- R) = 80(1 - 0.5) 40 M P a f i . = C. Geometrical conditions as in case B. Redistribution of stresses during crack growth so that AK is constant during crack growth. Constant nr( is being approached when cracks propagate in tubular joints, Refs. 133, 341 and Chapter 8 in this book.
    • Section 7.4Results.Figs. 7.15 to 7.17 show the calculation results when the crack grows from aplane surface. Similar results are obtained in the case of growth from thesemi-circular stress raiser. For case A with long life conditions (Fig. 7.1 S ) ,corrosion decreases the life by a factor of three while a normal and highdegree of cathodic protection increase life by the same factor. Both compari-sons refer to air life. For case B with short life conditions (Fig. 7.16), the relative effect offree corrosion is the same as in case A, that is a life reduction factor of three.However, a moderate degree of cathodic protection does not increase thelife above that of free corrosion, and overprotection reduces it to two thirdof the free corrosion life. In case C with a stress redistribution during crack propagation, therelative effect of free corrosion and normal cathodic protection is the sameas in case B, in that they both reduce life by a factor of three with respectto air. However, overprotection is even more serious in this case since itlowers the life by a further factor of two compared with free corrosion.In case C the effect of overprotection is extreme: High stress ratio R, stressintensities nearly as high as possible for variable amplitude loading, and avery low protection potential. - Q Q N=16.4~10~.*..:.~ - ~=1.86x10~ . ~ = 5 . 6 5 x 1 0 ~ ~=16.7x10~.. - 4 - 2 1 3/ - - 1 1 50 1 1 100 1 1 1 150 1 1 1 200 1 1 Years a t 10 cpm) 250 1 1 1 300 1 1 2 4 6 8 10 12 14 16x10~ N (cycles)Fig. 7.1 5 a-N curves for a crack of initial length 1 mm under long life condi- tions. Crack from a plane surface in air (1), under free corrosion in sea water ( 2 ) , and with cathodic protection at -850 mV (3) and -1 100 mV (4) (Ag/AgCl/sea water). Ao,,, = 28.4 MPa.
    • Section 7.4 50 1 End o f c u r v e s ; F r a c t u r e at AK,, =40MPa T m - . - - - -~ = 0 . 0 7 3 ~ 1 0 ~ . 5 30- ...... N=o.(~s~(oB m i ir ~ = 0 . 1 2 3 x l 0 ~ ..- ~ = 0 . 3 2 9 x 1 0 ~ c ( Y e a r s at I O c p m ) 2 4 6 8 10 0 1 I I I 1 I I I I I I 0 0.2 0.4 0.6~o8 1Fig. 7.1 6 a-N curves for a crack of initial length 10 mm under short life conditions. crack from a plane surface in air (I), under free corro- sion in sea water (2), and with cathodic protection at -850 mV (3) and at -1 100 mV (4). Ao,, = 23.2 MPa. ZO O mV / // 250 / ( Y e a r s at 10 c p m ) 20 40 60 80 100 120 140 160 I I I I I I I 1 I I I I I I I IFig. 7.1 7 a-N curves for a crack of initial length 10 mm, grown from a plane surface. Constant AK-spectrum with AK,, % 37.5 MPacm. These results tally with SN test results concerning the effect of freecorrosion. As for cathodic protection they clearly show some features whichhave also been revealed in a few SN tests: Normal cathodic protection is nobetter than free corrosion at short lives (Ref. / lo/), but better than air at longlives (Fig. 7.6). The calculation results may also explain the often contra-
    • Section 7.5 - 7.6dictory conclusions on effects of cathodic protection drawn from SN tests. The applied geometrical model is simplified. The calculation of therelative effects of corrosion and cathodic protection is, however, thought tobe relevant for other geometries as well (Ref. 1141). The possible sequenceeffects not considered may be an uncertainty. The main trends in the calcula-tion result are, however, in agreement with SN tests with variable amplitudeloading (Ref. 1351). As mentioned earlier, the effects of corrosion and catho-dic protection under variable amplitude loading are little different from thoseunder constant loading.7.5 DESIGN GUIDE-LINES, BRITISH PROPOSALIn "Offshore Installations: Guidance on Design and Construction" (Ref. /36/),corrosion is accounted for in the SN-curves for unprotected welded joints bya life reduction factor of 2 on air data. A slope of -3 is adopted for all lives.The air curves are recommended for cathodically protected joints, as wellas for joints protected by paint coatings, provided that the coating remainsimpervious to sea water. The recommendations are limited to steels withRe < 400 MPa (Ref. 1371). The justification of the recommendations hasbeen questioned (Ref. /38/), but they are continuously under revision, andwill be adjusted when more reliable experimental results are available.7.6 CONCLUDING REMARKSThe results reported in Sections 7.2 and 7.4 indicate that free corrosion insea water is fairly well taken care of in the British guide-lines. What is mostcorrect, a life reduction factor of 2 or 3 , is open for discussion. The design basis for cathodically protected structures is less clear.One trend should be noted (Ref. 1351):Cathodic protection gives fatigue dataas good as or better than air at long lives, while at short lives, moderate CPand free corrosion may give about the same fatigue life. The change from onebehaviour to the other occurs at a lower N-region for small scale specimensthan for large scale joints. On the background of the results of the calculationsin Section 7.4 and Refs. 110, 391, it seems reasonable to use the same designcurves for cathodic protection as for free corrosion at least up to N = lo7cycles, provided that overprotection is avoided. If there exists any risk forinsufficient cathodic protection at some sites, the free corrosion designcurves should be applied.
    • Chapter 7. ReferencesREFERENCES 1. Jaske, C.E., Payer, J H and Balint, V.S.: .. Corrosion fatigue of metals in marine environments, Springer Verlag and Batelle Press, 1981.2. Laird, C. and Duquette, D.J.: "Mechanisms of Fatigue Crack Nucleationy,in Corrosion Fatigue Chemistry, Mechanics and Microstructure, NACE-2, pp. 88-1 17 (1972).3. Duquette, D.M.: "Environmental Effect 1 : General Fatigue Resistance and Crack Nucleation in Metals and Alloys", Fatigue and Microstructure, American Society for Metals, Metals Park, Ohio (1979), pp. 335-363.4. Bardal, E., Ssndenfor, J.M. and Gartland, P.O. : "Slow Corrosion Fatigue Crack Growth in a Structural Steel in Artificial Sea Water at Different Potentials, Crack Depths and Loading Frequencies", Proceedings of European Offshore Steels Research Seminar,Welding Institute, Cambridge, UK, Nov. 1978, pp. VIIP16-1 - VI/P16-12. 5. Booth, G.S.: "Constant amplitude fatigue tests on welded steel joints performed in sea water", Ibid, pp. IV/P9-1 - IVIP9-14.6. Haagensen, P.J.: "PS6 - Improvement of the fatigue strength of welded joints: International conference on steel in marine structures, Paris 1981, Institut de Recherches de la SidErurgie Franqaise, Special and plenary sessions pp. 309-364. 7. Solli, 0 . : "Corrosion fatigue of weldments of C-Mn steel and the effect of cathodic protection, stress relieving treatment and saline atmosphere", Ibid., paper 2.2. 8. Walker, E.F.: "PS4 - Effect of marine environment: Ibid., Special and plenary sessions,pp. 195-252.9. Van Leeuwen, J.L., de Back, J. and Vaessen, G.H.G. : "Constant amplitude fatigue tests on welded steel joints performed in air and sea water", Ibid., paper 2.1.10. Dijkstra, O.D. and de Back, J.: "Fatigue strength of tubular X- and T-joints (Dutch tests)", Ibid, paper 8.4.11. Berge, S.: "Constant Amplitude Fatigue Strength of Welds in Sea Water Drip", Proceedings of European Offshore Steels Research Seminar,Welding Institute, Cambridge, UK,Nov. 1978, pp. IVIP12- 1 - IVIP12-5.
    • Chapter 7. References12. Schiitz, W.: "PS5 - Procedures for the prediction of fatigue life of tubular joints", International conference on steel in marine structures, Paris 1981, Institut de Recherches de la Sid6rurgie Fran~aise, Special and plenary sessions, pp. 253-308.13. Morgan, H.G., Thorpe, T.W., Rance, A., Sylvester, D.R.V. and Scott, P.M.: "An investigation of the corrosion fatigue crack growth behaviour of structural steels in sea water", Ibid., paper 5.1.14. Bardal, E., Haagensen, P.J., Grovlen, M. and Szther, F. : "Effects of cathodic protection on corrosion fatigue crack growth in a platform steel in sea water", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1541-1552.15. Grsvlen, M., Bardal, E. and Eggen, T.G.: "Fatigue crack growth in structural steels in air and in sea water with and without cathodic protection", SINTEF Report, Trondheirn 1985.16. Booth, G.S., Wylde, J.G. and Iwasaki, T.: "Corrosion fatigue crack propagation and threshold determinations in structural steel: Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS, 1984, pp. 1471-1484.17. Vosikovsky, 0.: "Effects of Stress Ratio on Fatigue Crack Growth Rates in X70 Pipeline Steel in Air and Saltwater", J. Testing and Eva., 8(2), 68-73 (March, 1980).18. Havn, T.: "Korrosjonsutmatting av st31 i sjsvann", Dr-ing. thesis, Institutt for rnaterialer og bearbeiding, NTH, Trondheim, 1983 (In Norwegian).19. Scholte, H.G. and Wildschut, H.: "Fatigue crack propagation tests on welded specimens in air and sea water", Confe- rence on steel in marine structures, Paris 1981, Institut de Recherches de la Sid6rurgie Franqaise, paper 5.2.20. Vosikovsky, 0 . : "Effects of mechanical and environmental variables on fatigue crack growth rates in steel. A summary of work done at Canmet", Canadian Metallurgical Quarterly, - 19 (1980), pp. 87-107.21. Austen, I.M.: "Factors affecting corrosion fatigue crack growth in steels", Proceedings of European Offshore Steels Research Seminar, Welding Institute, Cambridge, UK, Nov. 1978, pp. 364-386.22. Vosikovsky, 0 .: "Fatigue-Crack Growth in an X-65 Line-Pipe Steel at Low Cyclic Frequencies in Aqueous Environments", Trans. ASME, J. Eng. Mater. and Technol., Series H, 97(4), 298-304 (October, 1975).
    • Chapter 7. References23. Scott, P.M. and Silvester, D.R.V.: "The Influence of Seawater on Fatigue Crack Propagation Rates in Structural Steel", Department of Energy, UK Offshore Steels Research Project, Interim Technical Report UKOSRP 3/03, (December 19,1975).24. Haagensen, P.J.: "Fatigue Crack Growth of Steel in Air and Sea Water under Constant Amplitude and Random Loading", Paper presented at The Fourth International Conference on Fracture, University of Waterloo, Ontario, Canada, June 1977.25. Brjasaeter, 0. and DrAgen, A.: "Fatigue crack growth in sea water under random loading", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1553-1564.26. Jaske, C .E., Broek, D., Slater ,J .E., Utah, D .A. and Martin, C.J. : "Corrosion Fatigue of Cathodically Protected Welded Carbon Steel in Cold Seawater", Final Report to American Petroleum Institute, Committee on Offshore Safety and Antipollution Research, Dallas, Texas (February 1 1, 1977).27. Socie, D.F. and Antolovich, S.D. : "Subcritical Crack Growth Characteristics in Welded ASTM A537 Steel", Welding J., 53(6), pp. 267-s-271 -s (June, 1974).28. Telseren, A. and Doruk, M.: "Temperature Dependence of Water-Enhanced Fatigue Crack Growth in Mild Steel", Engineering Fracture Mechanics, 6(2), pp. 283-286 (September, 1974).29. Sullivan, A.M. and Crooker, T.W.: "Fatigue Crack Growth in A516-60 Steel - Effects of Specimen Thickness, Saline Environment, and Electrochemical Potential", Proceedings of International Confe- rence on Fracture Mechanics and Technology, Hong Kong, March 21-25, 1977, Vol. 1, pp. 687-698.30. Austen, I .M. and Walker, E.F. : "Corrosion fatigue crack propagation in steels under simulated offshore conditions", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1457-1470.31. Edwards, J.D.A.: A study of the sulphide stress corrosion cracking behaviour of high strength low alloy steels, Dr.ing. thesis, Institutt for materialer og bearbeiding, NTH, Trondheim, Norway, 1984.32. Maddox, S.J.: "A fracture mechanics analysis of fatigue cracks in fillet welded joints", Int. J. Frac- ture, - (1975), No. 2, p. 221. 1133. Gibstein, M.B. : "Fatigue strength of welded tubular joints tested at Det Norske Veritas Laboratories",
    • Chapter 7. References International conference on steel in marine structures, Paris 1981. Institut de Re- cherche~ la Sid6rurgie Fran~aise, de paper 8.5.34. Wilson, T.J. and Dover, W.D. : "Corrosion fatigue of tubular welded joints", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1495-1 504.35. Bignonnet, A.: Resistance i la fatigue corrosion des aciers utilisgs dans les structures soudies marines, Report RE1003 Institut de Recherches de la Sidirurgie Franqaise (IRSID) June 1983.36. Offshore Installations: Guidance on design and construction, Dept. of Energy, Lon- don, 3. Ed. (1984).37. Background to new fatigue design guidance for steel welded joints in offshore struc- tures, Dept. of Energy, London 1984.38. Dower, W.D. and Dharmavasan, S.: "Fatigue of offshore structures - a review", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1417-1434.39. Holrnes, R. and Booth, G.S.: "Fatigue and corrosion fatigue of welded joints under narrow band random loading", International conference on steel in marine structures, Paris 1981, Institut de Re- cherche~ la SidCrurgie Fran~aise, de paper 7.2.
    • CHAPTER 8 FATIGUE OF TUBULAR JOINTS M.B.Gibstein and Einar T. Moe A .S VERITEC, Osloy- ABSTRACT Special aspects of fatigue life evaluation of tubular joints are treated in this chapter. Procedures far the determination of stress concentration factors and hot spot stresses are described. SN-curves for welded tubular joints are presented, and a design procedure for the fatigue life verification of tubular joints is outlined. In-service experience with welded tubular joints is discussed. Furthermore some considerations have been given on the design of heavy duty joints. NOMENCLATURE Ab - cross section area of brace D - chord outside diameter d - brace outside diameter E - Youngs modulus e - eccentricity g - gap p - gap-parameter for gap between individual braces L - length between supports of chord 11, l2 - length of weld, overlap joints Mb - bending moment P - axial load R - chord radius r - brace radius N - number of cycles to failure SCF - stress concentration factor SCFb - brace SCF
    • Section 8.1SCF, - chord SCFSNCF - strain concentration factorSNCFN- strain concentration factor perpendicular to weld frontT - chord wall thicknesst - brace wall thicknessW - cross section modulusX - leg length of fillet welda - L/DP - d/DY - R/TeHS - hot spot strain (maximum numerical value of the principal strain)e HSN - hot spot strain perpendicular to weld frontEN - nominal strain in the braceON - nominal stress in the bracev - Poissons ratio0 - brace angle with the chord7 - thickness parameter t/T8.1 INTRODUCTIONOffshore steel platforms are usually constructed as truss frameworks inwhich tubular members constitute the structural elements (Fig. 8.1). Tubes are well suited as structural members for offshore steel plat-forms. Waves and currents generate comparatively small forces on tubularmembers because of their low drag coefficient. Due to their uniform andsymmetrical cross section, tubular members exhibit minimal stress concen-trations, outstanding buckling strength, and no sensitivity to lateral loaddirection. The latter is especially important in the offshore environment,where wind and wave forces can come from any direction. However, inter-connections and joints, which in the case of offshore platforms usually arewelded, represent structural discontinuities which give rise to very high stressconcentrations in the intersection area (Fig. 8.2). Lowered fatigue strength due to high stress concentrations at theweld toes of the connecting welds is a major problem in welded tubularjoints. Proper design of tubular joints against fatigue failures must thereforebe based upon detailed knowledge of the magnitudes of the stress concen-tration factors (SCF) and the corresponding values of the peak stresses at theweld toes of the connections, and on empirical data obtained from fatiguetests on tubular joints.
    • Section 8.2 Fig. 8.1 Offshore platform constructed with tubular joints. In principle terms, the design procedure to verify that tubular jointshave adequate fatigue strength, is one in which the sum of fatigue damagearising from the expected magnitude and number of dynamic peak stressesare compared with the fatigue lives of similar joints in laboratory tests.See Section 8.3 and Chapters 4, 10 and 1 1 for more information. Tubular joints must also be designed to sustain the ultimate staticdesign loads (i.e. 100-year storm conditions). Furthermore, the joints musthave adequate weldability and toughness to prevent brittle fractures. _4FIT;n G ~ I - c L c * ~.8.2 TYPES OF TUBULAR JOINTSTubular joints appear in a great variety of shapes and design types. Since suchjoints are not regulated by standards, their configurations and dimensionscan be freely chosen to suit structural needs. Tubular joints consist ordinarily of joints between main and secondary
    • Section 8.2 P NUMBERS DENOTE S C F VALUES G / G N , GN = ~ ~ d f ..... INDICATES PHOTOELASTIC ANALYSIS . .. INDICATES FINITE ELEMENT ANALYSIS Fig. 8.2 Stress analysis of a cross joint under axial brace load.member tubes. The former, which are larger in diameter, are denoted aschords, and the latter, which consist of smaller sized tubes, are denoted asbraces (Fig. 8.3). Tubular nodes may be classified and grouped in accordance with theirgeometrical configuration, the action and transfer of loads, and the designtypes. The design types fall into the following categories: - simple welded joints - overlapping joints - complex joints - cast steel nodes 1 heavy duty joints Simple welded joints may appear as uniplane or multiplane designsformed by welding of tubular members without overlap of the brace tubesand without stiffeners or reinforcements. Fig. 8.3 shows some typical simpleuniplane joint types. An overlapping joint is defined both by its geometry and its forcetransfer. Such joints are designed with braces, which are partially joinedtogether at their connection with the chord. At least part of the loads aretransferred between the braces through their common weld. This results
    • Section 8.2 A X- j o i n t -- .+, .- t Fig. 8.3 Simple (ordinary) welded joints.in reduced shear force and smaller ovalization of the chord, and consequentlysmaller stress concentrations and improved fatigue life. Complex joints include : - joints with internal stifferners - joints with external stiffeners - grout reinforced tubular joints - less readily categorized joints of complex geometry and load transfer modeComplex joints are often "heavy duty" type nodes which possess substantialimprovements in fatigue and static strength performance, see Section 8.4.
    • ,.I)( A .Section 8.3.1 Cast steel joints are nodes which have been fabricated by casting. Theconnection weld bracelchord is thereby eliminated and replaced by fillettransitions. Cast steel nodes (CSN) can be designed to exceptional efficiencesin terms of fatigue strength performance, see Section 8.4.3.8.3 SIMPLE WELDED TUBULAR JOINTS8.3.1 Definitions and symbolsThe nodes in the main structure of offshore steel jackets are often multiplanejoints. Uniplane joints are found in the bracings between main legs in horizon- tal planes and in secondary structural elements. In the present state of the art the joints are normally classified and evaluated in tenns of the simpler uni- plane joints such as T-, Y-, K-joints etc., disregarding the effect of braces which are not lying in the considered planes (Fig. 8.3). It should be emphasized that the classification should not be basedonly on the geometry of the nodes, but also on the load transfer mode.Thus for example, a joint of X-configuration may only be evaluated as anX-joint if the vertical axial loads in the braces are equal and of opposite signs.Similarly, a joint of K-configuration may only be evaluated as a K-joint if the components of the axial forces in the braces perpendicular to the chord are in equilibrium. For further illustration, a joint of X-configuration, in which an axial brace load is applied to only one of the braces must be eva- luated as a T-joint, despite its geometry (Fig. 8.1 9). Fig. 8.4 Tubular joint symbols. Fig. 8.4 shows the geometrical parameters which define simple weldedjoints. They are : - chord outside diameter D - brace outside diameter d (cont. next page)
    • Section 8.3.1 - chord wall thickness T - brace wall thickness t - brace inclination angle 8 - gap between braces g - chord total length L - eccentricity eThe non-dimensional geometrical parameters are: - diameter ratio P = d/D k. - cord stiffness r = R/T = C 1c - < ~ i r , A = * ..- d .The y ratio gives an indication of the chord radial stiffness, and it playsa dominant role in the SCF formulas and the ultimate strength of tubularjoints. - wall thickness ratio T = t/T - gap parameter P g/DThe degree of overlapping braces is indicated by negative values of the gapparameter. Other definitions are often found in the literature, such as g/d org sinold. - chord length parameter a = L/D For the fatigue analysis of tubular joints it is convenient to separatethe loads in multiples of three basic load cases, viz. axial load, in-planebending load and out-of-plane bending load (Fig. 8.5). Each load case hasits particular distribution of stresses along the intersection line and therebyits particular influence on the fatigue life. The combined effect of the loadcases is discussed in Section 8.3.7. kwrrl load l* plane bend i n one AL I PB OPB Fig. 8.5 w c twbulau joint load cases.
    • Section 8.3.2 i 1 >8.3.2 Definition of the hot spot stress, and stress and strain concentration factors Global stress/SCF - distribution along the intersection line of an axially loaded Y-joint Hot Spot L o c a t i o n Strain A Local strain distrilJ ~ t l O n ~ t r a ~ n .-t h ~ n n r m a l tn ..s.A.*".* W P M tne 4 at the hot Fig. 8.6 Example of global and local distribution of stresses/strains in axially loaded Y-j oints.The stress distributions at the intersection of tubular joints are very complex.Fig. 8.6 shows the strains along the brace and chords of a Y-joint as wellas the stresses along the intersection line of the same joint. The locations, or
    • Section 8.3.2points at which the highest stresses occur, are called hot In weldedjoints two diffemnt hot spots are found, one at the weld toe on the brace side,the other on the chord side. The maximum stress value may be on the chordside or brace side dependent on the design and geometry of the joint. The stress concentration factor (SCF) is defined as the ratio of the hotspot stress om, to the nominal stress in the brace: Unless otherwise specified, the stresses considered in analysis of tubular hour4joints are the principal stresses. In the process of design evaluation, the hotspot stresses on the chord and brace side of the weld must be consideredindividually. SCF, and SCFb denote the SCF on the chord and brace siderespectively. They are both multiples of the same nominal brace stress. The mod influential factor deciding the fatigue strength of tubularjoints, are the values of the SCF and the companding magnitudes of thehot spot stresses. Reliable and accurate knowledge of the SCF and hot spotstresses are therefore an absolute necessity in order to ensure adequate fatiguestrength. The sensitivity of the fatigue strength to the values of the SCF isillustrated by the fact that an underestimation of 18% of the value of theSCF may cause a 100% overestimation of the fatigue life prediction. In order to be a useful tool in design, the definition of the hot spotstress and the SCF must be compatible with the presently available SN-curves. Some confusion exists in the literature regarding the definition of the hot spot stress which also affects the definition and values of the SCF. The fatigue life depends on the true peak stresses where the fatiguecracks are expected to develop. In welded tubular joints, these locations arethe weld toes at the hot spots. Thus, theoretically, the hot spot stress shouldbe based upon the values of the maximum true stresses at the weld toe.However, in welded joints the maximum true stresses are influenced by weldshape irregularities such as unavoidable notches, and discontinuities. These arehighly localized and difficult to quantify and are therefore not suitable for systematic stress analysis. Instead, the hot spot stress is defmed as the stressat the weld toe localitions due to all geometrical influences except for the!ocal weld notch effects at the weld toe; experimental determination of the hot spot stress value requires Itherefore the extrapolation of the stress distribution curve to the weld toefrom a point which is located just outside the limit of the influence of thenotch on the stress distribution. For this purpose, strain gages are placedin strips close to the weld, and the stress curve is extrapolated based upon
    • Section 8.3.2 the measurements -from gages placed at- end of- the notch influence--zone. - -- - - -- --- - the - - This requires a knowledge of the limit of influence of the notch on the stress distribution close to the weld toe. At present the manner and distance of stress extrapolation to the weld toe are handled somewhat differently by different research institutions resulting in slight differences in the values of experimentally determined hot spot stresses. Extensive research indicates that the hot spot stress definition should be based upon extrapolation from a point located 0.25 T from the weld toe on the chord side, and 0.25 t on the brace side. Furthermore, this distance should not be less than 4 mm (Fig. 8.7). b.) ,: : - y 1 . f Strain , 1 >,, , t , , ,- 1 7 1 I i a- , ,( r ; , 7 , # C x I d , e. -; Chord Fig. 8.7 Determination of the hot spot strain value eHs at the weld toe by linear extrapolation from the end of the notch affected zone. The hot spot stress measured in this manner provides SCF values which are in very good agreement with the values, obtained from finite element (FE) calculations. Furthermore, and most important, it provides consistent fatigue life results independent of the type and complexity of the tubular joint design tested, see Ref. 1181 and Fig. 8.8. The conditions at the weld toe, although not quantified by SCF defini- tion, have a significant influence on the fatigue life. They can be graded as follows (Ref. / 181) :
    • Section 8.3.2 T-JOINTS T - JOINTS, SEA WATER D=508 T=l6mm 0=300 T=lOmm 2000- - .. 1000- -- --- AW S - X 197 5 % SURVIVAL 500 A 200 -- 100 , 10 10 lo6 1 o7 lo8 CYCLESFig. 8.8 VERITAS fatigue test results based on VERITASs SCF - and hot spot definition. Note consistency and small scatter. - Nafch fie, i.e. continuous stress distribution extending into the weld toe (Fig. 8.9). Such conditions are found in ground welds, or quite often on the brace side of the weld where smooth weld toe transitions are more readily obtained in fabrication. - Notch effect, weld toe discontinuity. The welds should be provided with regular and smooth transitions. However, discontinuities at the toe are to be expected. Fig. 8.10 shows the strain distribution resulting from different notch effects. The majority of the welded tubular joints tested at VERITAS showed an average notch No of about 1.2. (For definition of notch No see Fig. 8.10.) - Micro cracks. Micro cracks at the weld toe may be too small to be detected by ordinary NDT-methods. Their presence is discernible from their typical influence on the adjacent stress pat tern (Fig. 8.1 1). Micro cracks or severe notches reduce the fatigue crack initiation period of the fatigue life of the joint. Grinding of the weld toe may be a preven- tive action. G,a x ( -f-,>,o ; - y Hot spot location (l@U is the location of the very ma-urn stress at the weld toe of the brace or chord members of the joint. In one and the same joint the location is different for different loads. The locations may also vary, to a lesser extent, depending on the geometrical para- meters of the joint. - Hot spot stress OH denotes the maximum value of the stress at the weld toe at the hot spot obtained in the case of notch free weld conditions.
    • t (1, j lrJ~c- : Y / - ?? {2(dT+-, ;/*f,? ; "-Section 8.3.2 e -i r fi :, n . d * 1 i , - t 4 CHORD CHORD 5s AXIAL LOAD = 7 TON AXIAL LOAD = 7.5 TON 500- 500- NOTCH NO = 1.00 450 EHS =440 LIMIT O F NOTCH ZONE 400 - 400 - 300 - 300 [ NOTCH NO. * 440 = 1.02 200- . 2 . 4 . - 6 8 - 10 , 12 2 0 0 - I 2 4 I I . 6 3 8 10 . 12 - mm FROM WELD TOE mm FROM WELD TOE I BRACE BRACE AXIAL LOAD = 10 TON OOP LOAD, M = 0.88 TON M E SCF I SCF = 8 6 1 L 0 1.6 3.6 5.6 7.6 9.6 0 1.6 3.6 5.6 7.6 9.6 mm FROM WELD TOE mm FROM WELD TOEFig. 8.9 Notch free stress and strain distribution at the weld toe of tubular T- joints with D=508mrn, d=244.5 mm, T = 16mm, t = 10 and 12mm. The strain concentration factor SNCF is defined as the ratio of the hotspot strain eHs divided by the nominal brace strain eN . That is: SNCF = eH s , (8.2) 1The corresponding concentration factor for the hot spot strain perpeGdicularto the weld front, SNCFN,is defined as:
    • Section 8.3.2 CHORD CHORD AXlAL10AD=15T(*1 AXIAL LOAD = ISTON Y- JOINT300 , ,I , , , , - 300J , , , , ,, 7 4 6 8 10 12 2 I b 8 1 0 1 2 mrn FROM WELD TOE rnm FROM WELD TOE rnrn FROM W E L D TOEFig. 8.10 Effect of notch on the strain distribution at the weld toe of tubular joints. D = 508 mm, T = 16 mm, d=244.5 mm, t = 10 mm, a=4S0. Most design calculations are based on the SCF values although thefatigue tests and SN-curves are based on the SNCFN values. Even whereSN-curves are given in terms of stress range, the latter are based on uniaxialstrain, i.e. o = E H S E. Assuming that the hot spot strain, which is perpendi-cular to the weld front direction, coincides with the direction of the prin-cipal stress at the hot spot, the following conversion formula between SCFand SNCF can be used: 1+ e2 /eHSN SCF = SNCF 1 -v2where: e2 = hot spot strain normal to eHsN v = Poissons ratio In a similar manner, the conversion between the biaxial hot spot stres.:and the uniaxial stress E E H s ~used in SN-curves reads : In the majority of hot spot locations in ordinary tubular joints, theratio between e2 and eHSis found to be about 0.24-0.28 from which follows: SCF r 1.2 SNCF Therefore, when entering SN-curves with calculated hot spot stresses,the designer should be aware that the results may include a conservative factorof about 1.2 in terms of stress value, corresponding to a factor of about2.0 in the fatigue life. 325
    • Section 8.3.3 STRIP GAUGE ( 1 ) STRIP GAUGE ( 2 ) 400 - I 30,- I I NOTCH ZONE , I I I Fig.8.11b) I I , ! . , , , - MICRO 2 6 0 O 2 L 6 0 1 0 1 2 CRACK DISTANCE FROM TOE mm DISTANCE FROM TOE mm 1 E I v= I HS 440 Axial load 2.5 ton t = 12mm llmm DZSOII 400- T = 16 )) 1 I I L-J -- NOTCH ZONF 300- I I 1 I Fig. 8.1 1 a) and 8.11 b) S U P E R IMPOSED FIG. 8.1 1~ 20 0 2 4 6 8 1 0 1 2 DISTANCE F R O M TOE mmFig. 8.1 1 Determination of the notch zone by superposition of strain readings taken 11 mm apart. Note that VERITAS definition provides the same value independent of notch.8 -3.3 Methods for stress analysis of tubular jointsThe most common techniques for stress analysis of tubular joints are:8.3.3.1 Finite element analysisStress analysis with the finite element method (FEM) is by far the most
    • Section 8.3.3.1common approach to determine the stress distribution and hot spot stressin tubular joints. r Brace w a l l mi dd l e sur face ml dd l e sur face Node a t middle surface IntersectionFig. 8.12 Model representation based on thin-shell elements. Note that the weld cannot be accounted for with this element type. The shell elements have traditionally been ones with mid-plane nodesonly (Fig. 8.12). This allowed no possibility of modelling the geometry inthe weld region which in this case is idealized to the intersection line. Fig.8.13 shows a typical thin-shell element mesh for a T-joint. - BRACE PLUG 7 CHORD 7 Fig. 8.13 Typical thin-shell finite element mesh for T-joints.
    • Section 8.3.3.1 Gibstein, Ref. /15/, compared steel model tests and thin-shell FEMcalculations and found that the experimental chord SCFs were well approxi-mated by the values in the integration points immediately adjacent to themid-plane intersection line. On the brace side he found that the FEM stressesat the corresponding points exceeded experimental values by 20%. FEM analyses of tubular joints have previously been very expensive,mainly due to the man hours involved in generating the finite element mesh.Since the beginning of 1980, finite element analysis of tubular joints hasundergone a spectacular and rapid development. It is currently the mostefficient, reliable and economical tool for detailed stress analysis of tubularjoints. The main reasons are: - The increased efficiency of equation solvers, requiring less CPU-time. - The very large reduction of the cost of computers. - The introduction of programs featuring automatic (and semiautomatic) meshing of tubular joints, thus eliminating very time consuming manual work. - The possibility of weld modelling and the inclusion of 3-D solid ele- ments at the intersection. Stress analysis by FEM remains the work of specialists which must befully aquainted with the analysis programs as well as with the special problemsrelated to modelling and interpretation of results. When properly carried out,FEM-results are accurate, reliable and compatible with the experimental re-sults and corresponding SN4ata. There are at present ( 1984) two program packages which are of princi-pal interest:PMBSHELLPMBSHELL is a FEM program designed for effective stress analysis of tubularjoints. PMBSHELL was developed by PMB SYSTEMS ENGINEERING INC.,and features automatic mesh generation of simple joints with or without over-laps. Complex joints, such as stiffened joints and multiplane joints, can beeffectively modelled semiautomatically. Fig. 8.14 shows the element con-figuration used in PMBSHELL. Chord and brace are modelled with 16 nodeshell elements, each having two nodal planes. The weld is modelled witheither eight or twelve node solid elements according to AWS specifications,Ref. /2/. The program has efficient post processors, which facilitate the easeand efficiency of representation of analysis results, such as:
    • Section 8.3.3.1 Fig. 8.14 Element configuration used in PMBSHELL. Ref. 1341 - nodal displacements - surface stresses (principal and von Mises) - strain at the integration points - principal stresses extrapolated into the weld toe - summary of stresses along the intersection lines, and indication of maximum and minimum stresses and their location. PMBSHELL is a linear elastic finite element program and operates inbatch mode only. In addition to the testing undertaken during development, MPBSHELLhas been independently calibrated at VERITAS. It has been found that byextrapolating stresses to the weld toe, reliable SCF values are obtained with-out further adjustment.WAJ PTUJAP is an interactive semiautomatic mesh generator developed by SINTEFand VERITAS, and is the latest and most efficient dedicated program fortubular joint analysis. Being interactive, TUJAP represents a further enhance-ment over PMBSHELL. The semiautomatic approach is more efficient thanthe automatic mesh generation featured in PMBSHELL, and furthermoreextends to all types of joints. TUJAP also models grouted joints and includesalso fracture mechanics applications. The finite element scheme, utilized in TUJAP, is shown in Fig. 8.15.It consists of eight node mid-plane shell elements for the tubular members,twenty node solid elements in the weld, and transition elements adjacent
    • Section 8-3.3.2 Number of Group Illustration Name and description nodes pr.node d.0.f. S H SCQS, Subparametric 8 6 E curved quadrilateral L thick shell L TRSI, Transition element between T R A I HEXIIPRI elements N may be coupled with S the SCQSISCTS I elements. Three T versions of the I transition element 0 are needed: N TRSI 18 316 TRS2 15 316 TRS3 12 316 TRS3 S IHEX, Isopararnetric 20 3 0 hexahedron L I D Fig. 8.15 Element configurations used in TUJAP. Ref. 1351to the weld. The modelling of the chordlbrace intersection is highly efficient,and allows different weld shapes, and even transition fillets. TUJAP utilizes SESAM 80 interface files and is compatible with thissystem. The system has also non-linear analysis capabilities.8.3.3.2 Strain gage measurements on scaled steel modelsA full stress analysis of a tubular joint is usually carried out in two steps: 1. Instrumentation in order to determine the stress distribution along the line of intersection on the chord and brace side, and thereby find the hot spot locations. 2. Detailed instrumentation of the hot spots in order to determine SCF and SNCF at the weld toe. An example of the instrumentation of a tubular joint with strain gagesis shown in Figs. 8.16 and 8.17.
    • Section 8.3.3.3 - 8.3.4.1 Because the strain at the weld toe may vary significantly over just afew millimeters and because it is difficult to measure the strain at the weldtoe due to the physical size of the gage, an extrapolation procedure is re-quired. The hot spot stress or strain has to be determined by extrapolationfrom measurements taken some distance away from the weld toe. The stress gradient close to the weld toe may be very steep. Thereforethe value of the extrapolated hot spot stress may be very sensitive to theposition of the strain gages, which should be located just outside the notchaffected zone as indicated in Figs. 8.9, 8.10 and 8.1 1. It follows that dueattention should be paid to the extrapolation methods as well as t o thestress calculations when reviewing tubular joint fgtigue test results or com-paring results from different investigators. Testing of steel models is a highly specialized undertaking which alsorequires complex and costly test rigs and instrumentations.8.3.3.3 ikbrntory methodsPkroto ehtleityi Three-dimensional photo elasticity is a highly efficientexperimental approach for analysis of complex joints, or for analysis of verylocal stress peaks of geometrical details. Photo elasticity is also most efficientin systematic studies related to optimalization of weld profiles, grind repairs orspecialized items of the design (Ref. 1201). It is a highly specialized discipline.A c ~ l i cmodels: The method utilizes models of acrylic plastics fitted withstrain gages. It is recommendable for stress analysis where rough approxima-tions are adequate.8.3.4 concentrationfactors8.3.4.1 *m @f IiPfiemntpmmetde f o m l a dIn Appendix A four tables with parametric formulas for stress concentrationfactors developed at different institutions are presented.Table No. A1 (Kuangs formulas) Refi / I 4 / .The formulas in Ref. / 14/ are based on thin-shell FEM-analysis of the differentjoint<onfigurations and are listed in Table No. Al. The hot spot stress con-centration factor is taken at the intersection of the brace- and chord-wallmidplanes. The stress evaluated is the maximum principal stress at the hotspot. Kuangs formulas provide incorrect representation of the influence ofthe parameter /3 on the SCF. This is so for all load cases except for out-of-plane bending load. Because of this, the SCF values are too conservative when
    • Section 8.3.4.26 < 0.5. The Kuang formulas also tend to be overconservative for the SCF inthe braces independent of 6. Therefore in the recommended design formulas inTable A4 the SCF on the brace side is reduced according to Marshall, Ref. 171.Table No. A2 (Smedley and Wordsworths formulas) Refs. 126, 271.The formulas in Ref. /26/ are based on measurements with strain-gages onscaled-down acrylic models and are listed in Table No. A2. The models werefabricated as straight pipes without including the weld. The authors proposea correction factor to account for the influence of the weld leg length asfollows:where: SCF = stress concentration factor at the weld toe X = weld leg length It is recommended to use X = T in the calculation, i.e. K = 0.794.That weld leg length and that correction factor are also used for X-joints inthe recommended design formulas listed in Table A4.Table No. A 3 (Gibstein s formulas) Re5 11.51.The formulas in Ref. /15/ are based on thin-shell FEM-analysis of T-jointsand are listed in Table No. A3. The indicated hot spot stress is taken at theintegration point nearest to the intersection of the brace- and chord-wallmidplanes.8.3.4.2 Comments on the parametric formulasAs can be seen above, the basis and the evaluation procedures have differedbetween the various sets of parametric formulas, and the computed SCFsmay differ. Hence care should be taken when selecting parametric equationsfor a specific design purpose. An important limitation of the formulas is that they have been de-veloped for uniplane nodes only. An actual joint will often have braces adjoin-ing in two or more planes. The incorporation of a second-plane brace mayalter considerably the state of stress in a joint. An example is given in Fig.8.18, Ref. 1261. Here, a simple T-joint with a loadfree brace perpendicularto the loaded vertical brace has been analysed. The full lines show the strain-distribution along the circumference of the chord. Broken lines show corre-sponding strain-distribution for a simple T-joint, i.e. with the horizontal braceremoved. By loading axially brace B, the strain concentration may be greatlyincreased beyond that shown in this figure.
    • Section 8.3.4.2 . - STRAIN DISTRIBUTION WITH BRACE B REMOVEDFig. 8.18 Strain distribution in joint with axial load on brace A. Broken lines indicate strain distribution with brace B removed. Ref. 1261 Formulas for stress concentration factors are referred to the geometryof the joint, and a prescribed load condition. For the X-joint in Fig. 8.19 athe joint is acting as assumed in the parametric formulas. The joint in Fig.8.19 b, although it appears to be an X-joint , behaves more like a T-joint andshould be evaluated by the parametric formulas for T-joints when values ofPZ are small. In Fig. 8.19 c a K-joint with balanced forces in the braces is shown. Thisis the configuration used for derivation of parametric formulas. Fig. 8.19 dshows the same geometry but with another load configuration, leading toquite different stress concentration factors depending on the relative magni-tudes of the forces. Therefore, when parametric formulas are used for fatigue design, itmust be verified that they represent the physical behaviour of the jointunder consideration. Furthermore, the formulas should not be used outsidethe validity range they have been developed for. In cases in which the loadconditions, or limit of validity, significantly depart from those representable
    • Section 8.3.4.3 p2 -PI =2P+P2 P sine, =-P s l n 0 2 - 2 P I X-joint for s m a l l v a l u e s of P K - j o i n t f o r r m a f l v a l u e s of P T - j o i n t for s m a l l v a l u e s of P 2 Y - j o i n t for s m a l l v a l u e s of P2Fig. 8.19 The effect of load configurations on the joint type evaluation.by the parametric equations, an ad. hoc. analysis of the joint in question mustbe carried out.8.3.4.3 Genenrl considemtiom concerning stress concentrations in tubular joints. Cross sectional ovalization.The designer should be aware of certain basic principles related to the SCFvalues of tubular joints. The SCF values are basically related to the degree of ovalization of thechord section under the action of the brace loads. In X-joints the verticalforces acting at each side of the cross section, produce a greater ovalizationthan the single load in a T-joint. Therefore SCFx is greater than SCFT.In a Y-joint only the vertical component of the force contributes to theovalization, consequently SCFT is greater than SCFy . In the case of a K-joint, the load transfer occurs through the braces, and the chord is onlyslightly affected. This is even more accentuated in overlap Ktjoints, in whichdirect force transfer takes place through the braces.
    • Section 8.3.4.4Thus, when the geometrical parameters are equal : SCFx > SCF, > SCF, > SCF, SCFs for different joint types with the same geometrical parametersare shown in Table 8.1. SCFx follows from the corrected Wordsworth/Smedleyformulas, SCFT and SCFY from Gibsteins formulas, whereas SCFK is ob-tained from FEM analysis. The values for the overlap K-joint are calculatedby a parametric formula developed at VERITAS. Table 8.1 SCF values with braces under axial loads. Joint type X-joint T-joint Y-joint K-joint Overlap K-joint SCF, 2 1.9 13.6 10.6 5.9 4.8 SCFb 14.8 9.6 7.5 4.3 4 .O p=0.6,y= 15.88,~=0.831,0 6 0 ° , e = 0 =8.3.4.4 of geometrical pruvrrneters y, P and r on the SCF in tubular jointsWithin each group of joints, the influence of the geometrical parametersmay be evaluated from the parametric equations for SCF. However, to givethe designer some general guidance on the influences of the geometry, thefollowing observations can be made:The influence of 4 The SCF increases with increasing 7 , see for exampleFig. 8.20. These results were derived for a T-joint with an axial load in theFig. 8.20 The influence of y on the principal stress distribution at the chord side of a T-joint. Ref. / 151
    • Section 8.3.4.5brace, Ref. 1151. According to Kuang, Gibstein and Marshall, Refs. /7,14,15/,the SCF is a power function of y, while Smedley has assumed a linear relation-ship.Fig. 8.21 Influence of P on the SCF at the chord side of a T-joint for axial load in the brace. Ref. 1151The influence of 0. The influence on the SCF is parabolic (Fig. 8.21), Ref./ I S / . This figure shows the SCF at the chord side and has been derived forT-joints with axial loads in the brace. Similar shapes are obtained at thebrace side and for the other loading conditions. Maximum SCF is measuredfor p in the region around 0.5, and SCF approaches a minimum as 0 approaches 1.O. These observations are generally valid for all tubular joint types.The influence of T . The SCF increases with increasing T (Fig. 8.22). In thisfigure the SCF is a power function of r. The Kuang formulas show corre-sponding relations, while Smedley has assumed a linear relationship.The infltlence of boundary conditions. During FEM-analysis or experimentsit is difficult to simulate the actual behaviour of the joint in an offshorestructure with the true boundary conditions. For example, the real lifeboundary for the chord in a T-joint is neither fixed nor free to move. InFEM-analysis it is advisable to use pin supports because this is somewhatmore conservative than using fixed supports.8.3.4.5 Design SCF,the relative magnitudes of SCFc versus SCFbBoth SCF, and SCFb must be considered in fatigue evaluation. Which of theSCF is most critical and relevant for the fatigue strength will depend ontheir relative magnitudes.
    • Section 8.3.5 CfiORD Y :20 I AXIAL LOAD IN BRACE i Fig. 8.22 The influence of T on the SCF in a T-joint. Gibstein has shown that the value of the SCFb may become equal to,or even larger than the SCF, when the thickness ratio T is about 0.4-0.5 orsmaller. Furthermore, SCFb may become larger than SCFc when SCFc isless than 3 .O-3.5. m pwthah attention must be given to the SCFb when: m8.3.5 Fa#guc testing, expimental results and establishment of SN-curvesBased on experimental results, SN-curves for design against fatigue failure oftubular joints are presented in different rules and regulations, Refs. / 1,4 and 51and Chapter 11 in this book. The curves are relationships between the hot spot stress range Aoand the allowable number of stress cycles at a stress range Ao:where: log Z = intercept of the curve of the logN axis -l/m = the slope of the curve
    • Section 8.3.5 The basic values of log Z and m for the different curves are given inTable 8.2 for structures in air and in sea water with cathodic protection. Table 8.2. Curve log a m Remarks MIX 15.06 4.38 cut off level at N = 2 x 10 VERITAS X 14.57 4.10 cutofflevelatN=2x10 DEn T 12.16 3.00 f0rN>10~:10~Z=15.62,m=5,00 The AWS X-, API X-, VERITAS X- and DEn T-curves are shown in Fig.8.23. The AWS- and API-curves are lower envelopes of fatigue test results,while the VERITAS- and DEn-curves are determined through statisticalanalysis of fatigue test results, and represent a 97.6% probability of survival. DEn, NPD and VERITAS intend to incorporate a size effect in theirnext revision of the fatigue design rules. This size effect, or wall thicknesseffect, can be justified theoretically as explained in Chapters 4 and 10, andhas also been observed in some fatigue tests on plate specimens. lo5 lo6 lo7 cycles - lo8 Fig. 8.23 SN design curves for tubular joints according to AWS, API, 10 VERITAS and DEn. Refs. 12, 1 , 4 , 5 /
    • Section 8.3.5 The number of cycles to failure is given versus the hot spot stress range,although generally in experimental results, the strain range is reported. Thestress range has been obtained on the basis of uniaxial stress, i.e. by rnulti-plying the strain range with the Youngs modulus, i.e. The true stress at the intersection, or the stress obtained by calculations,is a biaxial stress (Section 8.3.2), defined as: It was shown in Section 8.3.2 that the biaxial stress is about 1.2 timesthe uniaxial stress at the hot spots of ordinary tubular joints. Thus, when ENDURANCE (CYCLES)Fig. 8.24 Experimental results expressed i terms of the number of cycles to through-wall cracking, N2 . Ref. / 121
    • Section 8.3.5entering SN-curves with calculated hot spot stress ranges, the results containan inherent underestimation of the fatigue life of about factor 2. The fatigue crack growth in tubular joints shows a rather differentbehaviour from that of less complex welded connections. In the latter, afatigue crack grows rather slowly in the beginning, but accelerates rapidlytowards the end of the fatigue life. In tubular joints, the growth rate is nearlyconstant throughout the fatigue life, even when the crack depth represents aconsiderable fraction of the chord wall thickness. This means that even if alarge crack is found in a tubular joint, a significant part of the fatigue life maystill remain. Thus the presence of a sizable crack may not be immediatelycritical provided no significant load shedding to adjacent members has takenplace and that the remaining static capacity is still sufficient to sustain theforces occurring during the design storm. In brittle materials, however, evenshallow cracks may be critical. 10 10 10 ENDURANCE ( CYCLES)Fig. 8.25 Experimental results expressed in terms of number of cycles to end of test, Ng . Ref. / 12/
    • Section 8.3.5 Figs. 8.24 and 8.25 are taken from Ref. 1121 and deal with simplenon-overlapping unstiffened joints. Fig. 8.24 shows the number of cycles g. 8.25 the number of cycles to end of test. which may be partially explained as follows: - A consistent method to measure the hot spot stress has not always been used by the experimental workers. Furthermore, inappropriate definition and approach to the measurements may lead to serious misrepresentation of the results, and to "fabrication" of undue in- fluences. Thus, if the manner of measuring the hot spot stresses is inappropriately related to the joint dimensions, the results will "intro- duce" an undue fatigue size effect. Indeed, for this same reason, serious doubts have been expressed concerning the validity of the "size effect" which some of the fatigue test results seem to indicate. Side B 1 Side A Side B I Side A T= chord thickness T= chord thickness N= 282 220 N= 400 000 Side 6 1 Side A Side B I Side A T= chord thickness T= chord thickness N= 488 000 N= 1 005 450Fig. 8.26 Development of a fatigue crack in an axially loaded K-joint. The depth of the crack is drawn in a scale ca. 2.6 times larger than the scale of the outer section line. Ref. 1231
    • Section 8.3.5 - The influence of the notch, i.e. the stress peaks due to local discon- tinuities at the weld toe are not included in the hot spot stress. This local stress concentration will vary from specimen to specimen due to differences in welding process, weld shape etc., as explained in Section 8.3.2. - Different workers have used different failure criteria, such as through- thickness crack, crack branching into the chord wall, length of crack, specimen becoming too flexible, etc. Side A I Side B SideA I SldeB T= chord t 4 ickness T= chord tAlckness N= 506 070 N= 616 110 Side A I Side B SideA I SldeB 1 I T= c h o r d t h i c k n e s s Tzchord t h i c k n e s s N= 696 420 N= 796 220Fig. 8.27 Development of a fatigue crack in an axially loaded Y-joint. The depth of the crack is drawn in a scale ca. 2 -3 times larger than the scale of the outer section line. Ref. /3 1 /
    • Section 8.3.6 In spite of the presence of a sizable crack, the global joint stiffnessremains unchanged until rather late in the fatigue life. Therefore, in a jacketstructure, significant changes in the global load transfer due to early fatiguecracks are not to be expected. Fig. 8.26 shows a typical example of the fatigue crack development ina K-joint. Fig. 8.27 shows the fatigue crack development in an Y-joint, Ref. /3 11,and Fig. 8.28 shows the surface crack development in an axially loadedT-joint, Ref. 1171. The linear, non-accelerating character of crack develop-ment in tubular joints is very beneficial from a point of view of safety. Itfacilitates early detection and repair of cracks. I I 500.000 1 .000.000 1.500.000 Number o f c y c l e sFig. 8.28 Surface crack development in percentage of the intersection circum- ference in an axiallly loaded constant amplitude fatigue tested T-joint, Ref. / 171.8.3.6 n and fabricationWith respect to joint design and fabrication the following recommendationsare given to improve fatigue properties: - Design for joint-configurations with low SCF. - The angle between brace and chord axes should not be less than 30" in order to enable good access for welding. - Due regard should be paid to local stress raising if external or the inter- nal stiffeners are used in the design.
    • Section 8.3.7 - Measures should be taken t o avoid the intersection of welding seams. Any girth- or longitudinal weld should be positioned away from in- coming braces by at least twice the chord wall thickness. Otherwise post weld heat treatment and grinding of weld seams should be per- formed. - Attention should be paid to the preparation of weld grooves and the contour of the finished weld (Ref. 141). The finish of the weld toe may be improved by grinding, as explained in Chapter 6 . - Generally, welding of secondary members, such as brackets, fittings etc., should be avoided closer to the bracelchord connection than twice the chord- or brace-wall thickness. - If the stress concentration is too high, it may be considered to reinforce the chord, and hence reduce local chord ovalization.8.3.7 Procedure for fatigue evaluation of tubular jointsFor the prediction of fatigue life of tubular joints, a procedure based on thehot spot stress, SN-design curves and the linear cumulative damage summationis most appropriate. The hot spot stress range and stress distribution along the chordlbraceintersection should preferably be determined through FEM-calculationsor tests. However, estimates of SCF can also be derived from parametricformulas, Section 8.3.4, but due regard should be paid to validity restrictionsand the uncertainties of the results. It is recommended that the fatigue life is checked at 8 points along thebracelchord intersection (Fig. 8.29). In each point and for each load-caseconsidered, the stresses due to the elementary load-cases, i.e. axial load, in-plane bending and out-of-plane bending should be superimposed. A commonpractice is to use a linear superposition: 0, = a1SCFx ox -PISCFy omy 02 = a2SCFx ox - P2 SCFy omy + 7 2 SCFz om, o3 = a3SCFx ox -I-7 3 SCFz Omz o4 = a4SCFx ox + P4SCFy omy + 7 4 SCF, om, + o, = a, SCF, ox P5 SCFy omy o6 = a6SCFx Ox + P6SCFy omy -y,SCFz om, o, = a7SCFx ox - 7 SCFZ 7 O ~ Z
    • Section 8.3.7 A x i a l load Moment Loading a,, SCF, I n plane qy, SCF, Fig. 8.29 Superposition of stresses in fatigue analysis of tubular joints. ox, any and a , are maximum nominal stresses due to axial load andbending loads respecti-l ss shown in Fig. 8.2**& 106 yi m y be under-st& as variabla reflecting that the hot spot stresses may occur at differentplaces along the periphery dependent on the loading situa ig. 8.30). b b b 3.27 AXIAL LOAD OUT - OF - P L A N E IN - PLANE - BENDING BENDINGFig. 8.30 Distribution of principal stress in chord in a T-joint for the three basic load cases. a = 5.3,P = 0.65, = 30,T = 0.71. y
    • Section 8.3.8As the SCF is only given as a maximum value without specifying the location,it is recommended that all the ai,Pi and Ti factors be set equal t o 1.0 whenusing the equations for design purpose. In that case maximum stresses willoccur at point Nos. 2, 4, 6 and 8 , and therefore a Miner analysis should beperformed with respect to these points. The calculation procedure for the Miner-analysis is described in Chap-ters 10 and 1 1, and the corresponding SN data for tubular joints (T-curve)are shown in Tables 1 1.1, 1 1.2 and 8.2. For unprotected joints in corrosiveenvironment, Table 1 1.1 may be used when the resulting number of cyclesis reduced with a divisor of 2. No cut off level is allowed. The thickness effectshould be accounted for as described in Chapter 1 1.8.3.8 In-service experience. Repair.In 198 1 a systematic investigation was carried out in order to prepare a reviewof repairs to offshore installations located on the North Western Europeancontinental shelf, Ref. 1321. The investigation included the early 1960 platforms located in 20-30 mdepths as well as the typical North Sea platforms at depths of 100-1 50 m,yielding a valuable compilation of damage types and the most probable reasonsfor their occurrence. The investigation showed that 35% of all major repairs tooffshore installations were performed t o correct metal fatigue damage. How-ever, the reanalysis and subsequent fatigue evaluation of all the cases reportedhave indicated that the actual joints were underdimensioned. Fatigue damagecould have been avoided if the joints had been properly designed. The reasons for the occurrence of the fatigue problems appear to be: - Fatigue analysis of secondary structural elements, such as conductor frames, caisson manifolds, riser clamps etc., had been inadequate. 70% of all fatigue cracks occurred at such elements. - In cases where the main structure had cracked, the main reasons appear to be increased environmental forces due to marine growth, i.e. the maintenance of the structure had been insufficient, or the value of SCF had been underestimated at the design stage. There is presently (1 984) no evidence based on cases of fatigue damageon offshore structures located on the North Western continental shelf whichindicate inadequacy of present fatigue design data and procedures. However,the need for repair of tubular joints is already very substantial due to damagecaused by collisions, dropped objects etc., and it is expected that this needwill increase as platforms get older.
    • Section 8.3.9 - 8.4 Substantial research is currently being undertaken by VERITAS on proper repair procedures and data over the remaining fatigue life of repaired tubular joints. Additional research projects sponsored by the industry will begin at VERITAS in the near future: - Grind repairs of welded structures 1984 - Grind repairs of tubular joints 1984-1985 - Improved design of grouted clamps 1984-1 985 - Weld repairs of tubular joints 1985-1986 The fracture mechanics approach to predict fatigue crack propagation in tubular joints is receiving increasing interest, but is still at an early stage of development. The theory and methodology is at hand, but the tools available are not yet sufficiently powerful to deal with such complex structures as tubular joints in a systematic manner. There is a general need for more effi- cient FEM computer-programs to determine stress intensity factors and in particularZTor pre-processors for automatic mesh-generation that can deal with cracks of variable geometries in the model. This will reduce the high costs of element-generation by hand. A problem with the fracture mechanics approach is the paucity of relevant experimental data for the calibration of the calculation procedures. Unfortunately, in many experimental series, numerous parameters regarding the fatigue crack growth have been recorded, but there are few reported results detailing the step by step development of fatigue cracks. Nevertheless, it is anticipated, that fracture mechanics will give a significant contribution to the science of predicting fatigue crack growth in tubular joints in the future. 8.4 HEAVY DUTY JOINTS4 With the development of offshore exploration into progressively deeper waters and arctic conditions, structures will become correspondingly larger and more demanding. In order to avoid extreme wall thicknesses with the associated heavy costs and severe problems related to fabrication and welding, designers will make increasing use of heavy duty nodes. They represent somewhat more complex node designs, but provide significant improvements in t e m s of fatigue and static strength performance. Heavy duty joints include over- lapping joints, complex joints and cast steel nodes. Each type will be discussed in turn.
    • Section 8.4.18.4.1 Overlapping jointsFig. 8.31 Photograph showing details of the intersection in an overlap K-joint tested in VERITAS laboratories. The continuous brace is to the right. Overlapping joints are such in which part of the brace forces are directlytransferred between the overlapping braces through their common weld (Fig.8.3 1). They can be designed as uniplane - or multiplane joints. K-joints withequal brace diameters are the most common types. The geometric parameters defining an overlapping K-joint are given inFig. 8.32 and Fig. 8.4. The joint consists of a through-brace and an over-lapping brace. The gap g between the braces is negative. In the literature P = g/D, gld or *the nondimensional gap parameter is defined variously as: sin 8 The dimensions l1 and l2 are often used to define the weld length asshown in Fig. 8.3 2.
    • Section 8.4.1 1 Through brace Over l a p p i n g brace I W l d concea l e d e by the o v e r l a p N e g a t i v e gap "g" Definition of parameters applicable to overlap joints: 1, : Circumference of the portion of the considered brace which con- tacts the chord. 1, : The projected length of the overlapping weld (one side) measured perpendicular to the chord. 8 , : Angle between chord and through-brace. O 2 : Angle between chord and overlapping brace. g : Overlap (see sketch above).Other parameters are as for simple welded joints, see Section 8.3.1 and Fig. 8.4. Fig. 8.32 Definition of geometrical parameters for overlappingjoints. Overlapping K-joints represent an improved design in terms of obtain-able fatigue and static strength compared to ordinary K-joints, as discussedin Section 8.3.4.3. When the braces are under axial loads, SCF reductions upto 50% may be achieved. Overlapping IS-joints are being increasingly used injack-up rigs, in which favourable strengthlweigth-ratio is an important aspect,as well as in jacket structures.
    • Section 8.4.1 Parametric formulas for the SCF in overlapping joints are presently not available in the literature (1984). To obtain the most benefits of the design, it is recommended that numerical stress analysis by FEM is carried out. Com- puter programs in which the weld is included and modelled by 3-D solid ele- ments should be preferred. Where FEM results are not available, it has been common practice to substitute the gap parameter p = g/D in the ordinary K-joint formulas (see Kuangs formulas in Table A l ) by the value p = 0.0 1 which will give a conservative estimate of the SCF in overlapping K-joints. Systematic research into the fatigue behaviour of overlapping K-joints were carried out at VERITAS in the years 1982-1 984. Stress analysiswas carried out with the object of deriving parametric formulas for SCF.Fatigue tests were conducted in order to verify the validity of the hot spotdefinition and the applicability of the SN-curves to overlapping joints. Parti-cular attention was given to the study of crack propagation rates and mode offailure of such joints. The following general comments and recommendationsare based on the investigation : - Overlapping K-joints represent a heavy duty joint type and can be designed to provide improved fatigue strength properties compared to ordinary joints. - Overlapping joints do not seem to represent a superior alternative to ordinary K-joints when the /3 ratio is greater than 0.85. - A gap parameter, p = g sine Id, greater than 0.8 should be avoided. - The stress level of the "concealed" part of the joint, i.e. the throug- brace chord intersection which is covered by the overlapping brace, is generally quite moderate and does not seem to represent an hazard to the safety of the connection. - Overlapping K-joints tend to have the maximum SCF at the brace. And, the joints tested failed due to cracks developing on the brace side. - The mode of failure was typical for brace failures in as much as the joint failed shortly after the cracks had passed the through-thickness stage. - The application of overlapping joints can provide considerable bene- fits, provided that the design is undertaken with the necessary exper- tise.
    • Section 8.4.2.18.4.2 Complex joints8.4.2.1 GeneralComplex joints are joints in which the chord has been reinforced by varioussystems of welded plates or by grouting. Figs. 8.33, 8.34,8.35 and 8.36 show a number of methods of stiffeningby welded reinforcement. They include: - internal ring stiffeners - external ring stiffeners - internal longitudinal stiffening ribs - internal diaphragms - through gussets - external gussets - external wing plates Generally, welded reinforcement influences the joint behaviour iri twoways: - The reinforcement increases the joint stiffness, reduces ovalization and reduces the general stress level. - The reinforcement, if not properly designed, can produce high local stiffness. This can attract force, and give rise to high local stresses. The efficiency of welded reinforcements is quite dependent on thenode type and the nodes design as well as the load type. Thus, as was thecase with overlapping joints, the efficiency of the reinforcement dependson the nodes initial stiffness against ovalization. Reinforcements are mosteffective in flexible joints such as X-, T-, and Y-joints with high y-ratiosand small P-ratios. Reinforcements are less effective in stiff joints. For in-stance, the incorporation of stiffeners and reinforcements in an overlappingK-joint of p = 1 has shown to be counter productive except in the case ofout~f-plane bending loads. Fig. 8.33 Tubular joints with internal ring stiffeners. 353
    • Section 8.4.2.1 Fig. 8.34 Tubular joints with external ring stiffener. Fig. 8.35 Tubular joint with through gusset plate. r d l agona 1 Fig. 8.36 Tubular joint stiffened by wing plates.
    • Section 8.4.2.2 Internal ring stiffeners are the most frequent forms of welded stiffeners.Longitudinal stiffeners are often used in conjunction with internal ring stiffe-ners in large complex joints as, for instance, in semi-submersible rigs. External ring stiffeners may be used in cases where access for internalwelding is difficult, or in situations when post fabrication upgrading is carriedout. Through gusset plates are occassionally used at lifting points. Externalgussets and wing plates have been used to strengthen tubular joints whenstatic strength upgrading was deemed necessary. Gusset plates are not re-commended when fatigue strength is important, because high stress concen-trations may be generated at the gusset plate welds. Further research on thispoint is needed. r)8.4.2.2 Ring stiffenedjointsThe following general recommendations concerning the positioning of ringstiffeners are based on literature review and studies at VERITAS in 1983-1984.AXIAL LOADS:One stiffener : Place stiffener at the saddle position.Two stiffeners : Locate the stiffeners at a distance of 0.7 d/sine symmetri- cally about the brace axis intersection with the chord.Three stiffeners : Place one stiffener at the saddle position and the other two at, or near, the ends of the intersection line bracelchord. Analysis shows that a single ring stiffener can be quite effective inreducing SCF. Two stiffeners provide only a modest additional improvement,and three stiffeners provide very little further improvement.MOMENT LOADS :One stiffener : One stiffener is quite efficient for out-of-plane bending loads. However, one stiffener is not recommended in the case of in-plane bending loads.Two stiffeners : Locate the stiffeners as for axial loads.Three stiffeners : Locate the stiffeners as for axial loads. Parametric formulas for ring stiffened joints are not available. Finiteelement analysis or tests are required in order to determine the SCF andstress distributions. A number of "equivalent thickness" - and "smear out"
    • Section 8.4.2.3approaches have been proposed for approximate evaluations of the SCF inring stiffened joints, see Ref. 1331. However, these approaches lack numerical,or experimental substantiation. When designing ring stiffened joints, careful attention should also begiven to ensure adequate strength of the weld between the chord and thestiffener. When adequatly designed stiffened joints are tested to failure underfatigue loads, they ordinarily fail by cracks developing at the hot spots at thechordlbrace intersection. The tests indicate that the hot spot stress approachand SN-curves for ordinary joints are applicable to ring stiffened joints.8.4.2.3 Grout reinforced tubular jointsA double skin Bout reinforced tubular joint and the parameters definingthe joint are shown in Fig. 8.37. Double skin grout reinforced (DSGR) jointsrepresent an efficient alternative design to joints with welded stiffeners.In both designs, the reinforcement stiffens the chord against ovalization.However, contrary to the case of local stiffeners, in DSGR joints the rein-forcement is continuous and provides smooth and low peaked stress distri-bution. Fig. 8.37 Double skin grout reinforced tubular joints. In new platform designs, DSGR joints can be used to very great ad-vantage whenever a combination of superior ultimate strength and fatiguestrength is required, and where added weight is not a serious detriment. Many existing structures have tubular piles driven through and groutedinto the legs of the structure, thus creating a large number of DSGR jointsalong the legs as shown in Fig. 8.38, where the circled locations representDSGR joints.
    • Section 8.4.2.3Fig. 8.38 Locations circled represent double skin grout reinforced tubular joints in a jacket stmcture due to grouted piles throughout the leg.
    • Section 8.4.2.3 DSGR joints provide a number of important practical advantageswhich greatly enhance their use in offshore applications: - Grouting is a straight forward operation, which can be carried out expediently on location. - Grouting can be carried out on short notice and does not require long fabrication time. - The costs involved in fabrication of grout reinforced tubular joints are considerably lower than the corresponding costs for joints rein- forced by welded stiffeners. Substantial research and development work into DSGR joints hasbeen going on in VERITAS since 1978 with the object of gaining detailedknowledge of DSGR-joints ultimate strength and fatigue strength behaviour,Ref. /21/. A large number of stress analyses and fatigue tests were carriedout on X-, T-, Y-, K- and overlapping K-joints. Furthermore, the FEMapproach has been applied with considerable success for the numerical ana-lysis of the tested joints. DSGR tubular joints have also been investigatedin the U.K. The results of VERITAS research are at present (1984) unavailable forpublication. However, the following general comments can be made: - The grout reinforcement provides remarkable increases in the static strength of the connections, which may amount t o four fold or higher, even under tensile axial brace loads. Under compressive axial loads the DSGR-chords are virtually undestructible. - Remarkable SCF reductions (versus ungrouted joints) are obtainable. SCF reductions to the order of 1/3 are readily obtainable. Even larger reductions can be obtained. - The stress concentration factor of grouted joints is load dependent. The dependency is non-linear. - The SCF reductions (versus ungrouted state) under compressive loads are larger than those under tensile loads. - The SCF and general behaviour of DSGR joints are stable under fatigue load conditions. - Grouted joints can be evaluated for fatigue strength using SN-curves applicable t o ungrouted joints.
    • Section 8.4.3 - DSGR joints can be numerically stress analyzed. This requires the use of non-linear FEM calculations. Otherwise the SCF must be determined by laboratory tests. - The use of "equivalent thickness" approach to analyze DSGR joints is unsafe and should be avoided.8.4.3 Cast steel nodes (CSN)The advantages of cast steel nodes over ordinary welded tubular joints aresubstantial. Cast steel nodes can be designed and fabricated to virtuallyarbitrary configurations and can be optimized to provide very low SCFvalues. Furthermore, the designs are provided with regular and smooth filletsat the bracelchord transition, a fact which further reduces the SCF andimproves fatigue strength. Most important, cast steel nodes do away withwelds at the locations of high SCFs, which is a major problem with ordinarytubular joints. Cast steel nodes are suitable for multi-unit - or mass production, andthis is one of the reasons why they have already made their debut in jack-uprigs. Even in the case of single-unit production, CSN may be a viable and costeffective solution for joints of complex geometries and large wall thicknesses.In order to make full use of CSN, the designers should develop structureswith high repeatability of nodal configurations. High quality cast steel nodes can at present be delivered by BritishSteel Corporation in the U.K. and Hoesch Huttenwerke in Germany. KobeSteel in Japan has commenced development of CSN and is expected toreceive certificate of approval of its concept shortly. VERITAS has carried out numerous stress analyses, photoelasticinvestigations and fatigue tests on prototype cast steel nodes, see Refs./ 19, 20, 221. The results of fatigue tests on 5 cast steel overlapping K-jointprototypes manufactured by Hoesch Huttenwerke can be summarized asfollows: - The SCF in the CSN was about half the value in the comparable welded overlapping K-joint . - The fatigue life of the CSN was about 100 times greater than the fatigue life of comparable welded joints. - Local weld repairs did not seem to influence the fatigue life of the CSN. - Severe defects in one CSN of rejectquality influenced the fatigue life only by factor 2 compared with that of bestquality nodes.
    • Chapter 8. References - During the fatigue tests, the crack growth was found to be stable, slow and non-accelerating during the major part of the life. Due to the variations of shapes and dimensions, no parametric equa-tions for SCF are available. The SCF values must be determined by FEManalysis or model tests. The SN-curves for welded tubular joints are not applicable to CSNdesigns. SN-curves for the particular base material must be utilized. The design of CSN requires specialized expertise, and should be under-taken by, or in close cooperation with the respective foundry.REFERENCES 1. American Petroleum Institute : "Recommended Practice for Planning, Designin