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- 1. Utmattingsberegninger for stålkonstruksjoner ihht NORSOK og Eurokode 3 Fatigue life assessment Tirsdag 13 desember 2011 Professor P J Haagensen Norges teknisk-naturvitenskapelige universitet Fakultet for ingeniørvitenskap og teknologi Institutt for konstruksjonsteknikk Trondheim per.haagensen@ntnu.no 1 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Fatigue life assessment • Topics Approaches to fatigue life estimation 1. Nominal stress 2. Hot spot stress 3. Notch stress 4. Fracture mechanichs Loads and stress calculations Damage accumulation Comparisons of standards 2 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 1
- 2. Fatigue life assessment. Fatigue life predictions analysis should be performed according to standards in order to avoid uncertainties regarding assumptions for loads and component capacity. 3 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Fatigue life assessment approaches - S-N curves, nominal stress - S-N curves, hot spot stress - S-N curves, notch stress - Crack growth curves (da/dN - K diagram 4 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 2
- 3. Loading data – load spectra Cumulative load spectra obtained by stress range counting (rainflow) is converted to histogram to give stress ranges Sr vs. number of cycles ni per stress interval 5 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Narrow band vs. broad band load time histories: Narrow band PSD Stress Time Frequency Stress PSD Broad band Time Frequency PSD = Power Spectrum Density 6 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 3
- 4. Stress range bin # Fatigue damage accumulation k Number of stress range occurrences, ni Number of cycles to failure, Nfi Experimental Design S-N curve i Damage at stress level Sri : di ni Ni Log n, Log N Cumulative damage at fracture (Miner-Palmgren rule: k D i 1 ni 1.0 Ni If damage due to loads in spectrum = DT (during time T ) then: Fatigue life L = T/DT 7 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Uncertainties in calculated fatigue life are caused by: 1. Uncertainties in load spectra 2. Uncertainties in S-N curves - extrapolation 3. Uncertainties in Miner-Palmgren damage summation rule (sequence effects) Fatigue tests with representative load–time histories show k that the damage sum D = ni i=1 Ni at failure varies typically in the range 0.1 < D < 10 Some tests indicate that D decreases with increasing irregularity, i.e. more than one peak in the power density spectrum (PSD) IIW design guidance recommends D ≤ 0.5 instead of 1.0 at failure DNV: D ≤ where is the usage factor. 0.5 < <0.1 depending on inspectability and consequences of failure. 8 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 4
- 5. Sequence effects gives variations in MinerPalmgren damage sum Crack length Overloads in tension blunt the crack tip and introduce compressive stresses that slow down crack growth Cycles 9 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Uncertainties in extrapolation of S-N curves A major source of uncertainty is related to the extrapolation of the S-N curve below the constant amplitude fatigue limit. In most current codes, e.g. Norsok, DNV and IIW the knee point is now at N =107 cycles. However, an increasing amount of test data indicate that the knee point should be at N =108, or a straight line extrapolation should be used. Dahle, 1994 10 Fatigue design of welded structures - Norsok and Eurocode 3 Fisher, 1993 2011 P J Haagensen 5
- 6. Extrapolation of S-N curves New test data indicate that the knee point should be at N =108, or a straight line extrapolation should be used. 107 108 107 EXXON data, OMAE 2003 Sonsino, Maddox & Haagensen IIW 2004 11 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Fatigue life calculation – nominal stress method 1. 2. 3. 3. 4. 12 Choose weld class Calculate nominal stress range Correct stress range for thickness effect and misalignment ? Determine cycles to failure from S-N curve Use Miner rule to calculate damage and life Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 6
- 7. Fatigue life calculation – nominal stress method What loads and stresses to consider? All types of fluctuating load acting on the component and the resulting stresses at potential sites for fatigue have to be considered. Stresses or stress intensity factors then have to be determined according to the fatigue assessment procedure applied. The actions originate from live loads, dead weights, snow, wind, waves, pressure, accelerations, dynamic response etc. Actions due to transient temperature changes should be considered. Improper knowledge of fatigue actions is one of the major sources of fatigue problems. Tensile residual stresses due to welding decrease the fatigue resistance, however, the influence of residual weld stresses is already included in the fatigue resistance data given in S-N curves 13 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Separation of stress components The membrane stress mem is equal to the average stress calculated through the thickness of the plate. It is constant through the thickness. The shell bending stress bend is linearly distributed through the thickness of the plate. It is found by drawing a straight line through the point O where the membrane stress intersects the mid-plane of the plate. The gradient of the shell bending stress is chosen such that the remaining non-linearly distributed component is in equilibrium. The non-linear stress peak nlp is the remaining component of the stress. 14 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 7
- 8. Nominal stress calculations Nominal stress is the stress calculated in the sectional area under consideration, disregarding the local stress raising effects of the welded joint, but including the stress raising effects of the macro-geometric shape of the component in the vicinity of the joint, such as e.g. large cut-outs. Overall elastic behaviour is assumed. 15 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Nominal stress calculations Effects of macrogeometric features of the component as well as stress fields in the vicinity of concentrated loads must be included in the nominal stress: 16 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 8
- 9. Local effects occur in the vicinity of concentrated loads or reaction forces. Significant shell bending stress may also be generated, as in curling of a flange, or distortion of a box section. 17 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Effects of misalignment (eccentricity The secondary bending stress caused by axial or angular misalignment must be considered if the misalignment exceeds the amount which is already covered by fatigue resistance S-N curves for the structural detail. This is done by the application of an additional stress concentration factor (SCF). Intentional misalignment (e.g. allowable misalignment specified in the design stage) is considered when assessing the stress by multiplying by SCF. 18 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 9
- 10. Calculation of nominal stress In simple components the nominal stress can be determined using elementary theories of structural mechanics based on linear-elastic behaviour. In other cases, finite element method (FEM) modelling may be used. This is primarily the case in: a) complicated statically over-determined (redundant) structures b) structural components incorporating macro-geometric discontinuities, for which no analytical solutions are available Using FEM, meshing can be simple and coarse. However, care must be taken to ensure that all stress raising effects of the structural detail of the welded joint are excluded when calculating the modified (local) nominal stress. 19 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Modification of basic S-N curves The basic S-N curves may need to be modified for the following influencing factors: • Misalignment, axial and angular • Effects of stress relief • Plate thickness, for t > 25 mm • Effects of corrosion • Temperature • Effects of high and low stresses in the spectrum Material: Different S-N curves for steel, aluminium, titanium 20 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 10
- 11. Effects of misalignment (DNV & Norsok 004) In the test data on which the design cures are based, some axial misaligment (eccentricity) 0 is included as follows: Butt welds: 0 = 0.1t (10% of plate thickness) The effect of axial misaligment for butt welds e0 is accounted for by applying a stress concentration factor SCF: SCF = 1- 3 δm - δ 0 t where m is the measured eccentricity 21 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Cruciform joints Axial misalignment included in S-N curves: e0 = 0.5t (15% of plate thickness) where δ = (δm + δt) is the total eccentricity. δ0 = 0.3t is misalignment inherent in the S-N data for cruciform joints ti = thickness of the considered plate (i = 1, 2) li = length of considered plate (i = 1, 2) 22 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 11
- 12. Effect of thickness (DNV & Norsok) For plate thickness t > 25 mm the thickness correction is included in the equation for the S-N curve The thickness exponent k is listed as follows: 23 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Thickness effects in welded connections: S / S0 (t / t0 ) k Exponent k depends on weld class: 0.1< n <0.4 (IIW design guidance) 0 < n <0.25 (0.3 for tubular joints with high SCF’s 0.25 for bolts) (DNV-RP-C203) 24 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 12
- 13. Biaxial loading IIW recommendations: 1. Use the equivalent normal stress range is less than 10% of the equivalent shear stress range, or if the damage sum due to shear stress range is lower than 10% of that due to normal stress range, the effect of shear stress may be neclected. 2. If the normal and shear stress vary simultaneously in phase, or if the plane of maximum principal stress is not changed significantly, the maximum principal stress range should be used. 25 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen IIW verification procedures for combined normal and shear stress using S-N curves 26 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 13
- 14. Norsok 004, NS 3472 and DNV RP-C203 Weld classes - 1 unwelded components 27 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen DNV RP-C203 Weld classes – example welded components 28 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 14
- 15. DNV RP-C203- Aug. 2005 S-N curves – welded structures in air 29 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen DNV RP-C203- Aug. 2005 S-N curves – welded structures in air -details 30 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 15
- 16. Fatigue life calculation – nominal stress method 1. 2. 3. 3. 4. 31 Choose weld class Calculate nominal stress range Correct stress range for thickness effect and ?misalignment Determine cycles to failure from S-N curve Use Miner rule to calculate damage and life Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen DNV RP-C203 S-N curve for high strength steel – unwelded material YS > 500 Mpa, machined surface with R a < 3.2 m FAT 235 MPa S-N curve 32 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 16
- 17. DNV RP-C203- Aug. 2010 New S-N curve – small diameter umbilical pipes in super duplex steel Equations for S-N curve: 33 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen The hot spot stress method The hot spot stress is a local stress at the weld toe, taking into account the overall geometry of the joint, except the shape of the weld. It is therefore sometimes called the structural or geometrical stress. It is used when it is difficult to define a nominal stress, e.g. in complicated plate structures. Originally (in the 60’s), the stress was measured at a single spot. In the AWS/API at a distance of 1/8” (3.2mm) from the weld toe, while Haibach recommended 2mm. In recent versions the stress at the weld toe is extrapolated from two or three points near the weld toe. The method is included in DNV’s RP-C203, also and IIW (International Institute of Welding) 34 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 17
- 18. Definition of the hot spot stress (DNV) The hot spot stress is a linear extrapolation at distances 0.5t an 1.5t from the weld toe. In the IIW guidance the to points are at 0.4 and 1.0t. The stress at these two points are obtained from FE analysis or from strain gauge measurements. 35 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Failure locations in welded joints The structural hot spot stress method is normally applicable to surface cracks only, but it is also possible to define a stress in a weld, e.g. by stress linearisation over the weld throat or weld leg. Examples: Fillet weld subjected to local bending, e.g. one-sided welds or welds around cover plates subjected to lateral loads (Fricke et al.,2006) 36 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 18
- 19. Types of hot spot stress The stresses obtained in FE analyses must include any misalignments or by an appropriate stress concentration factor, SCF. Two or three types of hot spot stress are usully defined: 37 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen FE modeling - hot spot stress The stresses obtained in FE analyses must include any misalignments or an appropriate stress concentration factor, SCF. Shell or solid elements are used in the FE meshing depending on the shape and size of the structure 38 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 19
- 20. FE stress analysis – ship structure 39 39 Utmatting - grunnlag Oslo, - Norsok and Fatigue design of welded structures 8. nov. 2010Eurocode 3 P J Haagensen 2011 P J Haagensen Meshing rules and determination of hot spot stress The IIW and DNV fatigue design rules give detailed advice regarding meshing and determination of the hot spot stress Recommended meshing and extrapolation Reference points for different types of meshing At the extrapolation procedures for structural hot spot stress of type “b”, a wall thickness correction exponent of n=0.1 shall be applied. 40 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 20
- 21. Calculation of hot spot stress Since the stresses obtained in FE analyses depend strongly on the type of element and the mesh that are used, detailed guidance is given in the design rules. The degree of bending influences life. The DNV RP C-203 correction: A single hot spot S-N curve is used by DNV (in air). This is the Tcurve = the D-curve = the FAT 90 curve. This is the S-N curve for a “good” butt weld, welded from both sides. In IIW the FAT 90 curve is used for load carrying welds and FAT 100 for non-load carrying welds. 41 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen The hot spot stress method – tubular joints The hot spot stress method is used for tubular structures, and parametric equations are given for stress concentration factors (SCFs) for simple joint configurations. The hot spot stress to be used when entering the S-N curve is given by: HS SCF nom An example of SCFs for a simple tubular joint: 42 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 21
- 22. Example of FE analysis - out of plane loading of brace 43 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen S-N curves to use with the hot spot stress In air: Use the T-curve (= the D-curve) 44 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 22
- 23. Effective notch stress method The effective notch stress is the total stress at the root of a notch, obtained assuming linear-elastic material behaviour. For structural steels an effective notch root radius of r = 1 mm in the FE analysis gives consistent results. For fatigue assessment, the effective notch stress is compared with a common fatigue resistance curve.)The method is valid for plate thickness t> 5 mm The FAT 225 (m=3) S-N curve is to be used in this method. For t < 5 mm a radius o The method is included in DNV’s revised RP-C203, April 2010 For t < 5 mm a radius of 0.05 has been proposed (Sonsino 2002) with an S-N curve with FAT 630 45 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Effective notch stress method An effective notch radius of 1 mm is assumed in the FE analysis Main advantages: Only one S-N curve is required, the FAT 225 curve. Can be used to assess fatigue life for root cracks 46 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 23
- 24. Example of stress analysis of cover plate which can fail from the weld toe or the root 47 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Example from 2D FE analysis 50 mm long plate 142 MPa 225 MPa 50 mm Ref. Stress = 100 MPa Small risk of root cracking 48 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 24
- 25. Comparison with nominal stress method Effective notch stress S-N curve FAT 225 225 51 mm long plate gives the F curve L = 51 mm 49 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Alternative local stress methods In recent years several local stress based methods have been proposed as follows: Battelle/Dong “mesh insensitive” method (Dong, et al. 2000) Xiao and Yamada 1 mm method (2004) Notch stress intensity factor approach (Lazzarin et al. 2006) 50 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 25
- 26. The Battelle/Dong method In this method the through-thickness stress distribution is used to obtain an equivalent stress surface stress SS based on equilibrium of nodal forces and moments. A large number of test data can from many types of test specimens be correlated on the basis of SS in a single master curve. 51 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Master S-N curve according to Dong (2003) 52 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 26
- 27. The Xiao-Yamada method Xiao and Yamada found that the influence of various sharpness of the notch practically disapears at at dept of 1 mm, and proposed to use this as a structural stress SS . A large number of test data can from many types of test specimens be correlated on the basis of SS in a single master curve. 53 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Stress distribution at the surface and in the depth direction (Xiao and Yamada) 54 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 27
- 28. Test data correlated on the stress at 1 mm below the surface The data indicate that the FAT100 curve can be used for design. 55 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen The fracture mechanics method - describing the behaviour of cracked components Useful for: Calculating residual strength Calculting remaining life spent in crack growth under cyclic loading 56 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 28
- 29. Stresses at the crack tip 57 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Stresses at the crack tip X K cos 1 sin sin 3 2 2 2 2r Y K cos 1 sin sin 3 2 2 2 2r XY K cos sin cos 3 2 2 2 2r for = 0 i.e. in the plane directly ahead of the crack the trigonometric function = 1 When r 0 all stresses infinity Use K as a loading parameter 58 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 29
- 30. The Stress Intensity Factor K (SIF) The stress intensity factor K is a scaling factor for the stress field at the crack tip, i.e. all stresses are proportional to K K Y a = global stress Y = geometry factor a = crack depth, or crack half length for interior crack 59 2a a Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen The critical value of the stress intensity factor is the fracture toughness of the material, i.e. fracture occurs when K KIC The fracture toughness KIC can be used to: a) determine failure stress, when the crack size is known b) determine critical crack size, when the stress is known 60 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 30
- 31. Fracture mechanics - fatigue When the speed at which a crack grows is known, then the fatigue life can be estimated if the stress intensity factor is known for the particular load the part is subjected to. The crack growth rate can be determined in tests on standardized specimens (ASTM, BS). 61 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Testing to determine crack growth rate 62 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 31
- 32. Influence of R Ratio on crack growth R=0 R=0.5 1 R=-1 0 -1 • Largest Influence near the threshold • Decreasing threshold with increasing R ratio. 63 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Integrating the crack growth law gives the fatigue life N da / dN C (K ) m af da N C (K )m ai af ai Y = const. K=Yσ πa Assume that da C Y a m a1fm / 2 ai1m / 2 C Y m (1 m / 2) (m 2) By inputting values of ai and af: N C0 m Or: Stress range, Δ 1 m log N log C m log S Log C0 N This is the equation for an S-N curve with slope - 1/m 64 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 32
- 33. Relationship between the crack growth diagram and the S-N curve log log da dN KmaxKc m 1 Paris: da = C(K)m dN Kth Fatigue limit: 65 1 Fatigue limit m o o= f(Kth, ai) log K log N σE ΔK th = YΔσE πa Fatigue design of welded structures - Norsok and Eurocode 3 2011 ΔK th πai P J Haagensen Example 1 Crack growth prediction Crack in a Finite Width Plate K= (sec(a/W)) Smin=0, Smax=50 MPa, W=100 mm t=10 mm ai=4 mm 2ai Material 355 YS Yield =370 MPa, KIC= 55 MPam Crack Growth Data C=1.37x10-14 m=3.3 66 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 33
- 34. Example 1 Crack length development 50 45 Crack Length a (mm) 40 35 da/dN=C Km a= (C Km) dN 30 25 20 15 10 5 0 0.0E+00 2.0E+06 4.0E+06 6.0E+06 8.0E+06 Cycles Fatigue life ? 67 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 500 450 400 350 300 250 200 150 100 50 0 Yield Strength = 355 MPa K 0 σLig = 68 50 45 40 35 30 25 20 15 10 5 0 F W - 2ai t 10 20 30 40 Crack Length (mm) 50 Failure occurs by plastic collapse when σLig =355 MPa =YS Critical Crack Length = ~ 42 mm Fatigue design of welded structures - Norsok and Eurocode 3 K (MPa m 1/2 ) Ligament (MPa) Example 1 Failure mode 2011 P J Haagensen 34
- 35. Structural implications Slow growth up to 10 mm, fast growth beyond 20 mm Actions: Establish failure criteria, apply safety factor (SF) to the critical crack length (ac) i.e. 42 mm / SF of 2.0; which gives allowable crack length = 21 mm Establish inspection and maintenance schedules up to the allowable crack length. When the crack length (a) reaches 21 mm: Remove component from service 69 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Fracture mechanics - summary Advantages: Applicable to any type of structure with life dominated by crack growth FEM, BEM or formulas can be used to determine SIF Prediction of tolerable crack sizes in structure Provide maintenance and inspection intervals Disadvantages: Requires detailed information of structure geometry Cycles to failure dependent on initial flaw geometry Implementation at the design stage difficult Determining SIFs can be involved and require special numerical techniques 70 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 35
- 36. The BS 7910 standard 71 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen The critical value of the stress intensity factor for brittle materials is the fracture toughness of the material, i.e. fracture occurs when K KIC The critical value of the crack tip opening displacement (CTOD = ) is C i.e. ductile fracture occurs for when C 72 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 36
- 37. Guidance assessing the risk for unstable fracture: • Methods for calculating stresses, external and interior (or residual stresses) • Calculation of SIFs for defect in question • Materials data Use Level 1 or 2 fracture assessment 73 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Guidance needed for fatigue crack growth calculations: Methods for calculating stresses, external and interior (residual stresses) Calculation of SIFs Materials data (crack growth curves) Objectives Acceptable flaw sizes Remaining life Inspection planning – length of inspection periods 74 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 37
- 38. Stress calculations – BS 7910 75 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Crack growth data - schematic 76 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 38
- 39. Crack growth data - schematic Environmental effects 77 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Crack growth data, BS 7910 78 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 39
- 40. Crack growth data constants, BS 7910 79 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 2011 P J Haagensen SIF calculations 80 Fatigue design of welded structures - Norsok and Eurocode 3 40
- 41. Quality category S-N curves 81 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen Symmary – Fracture mechanics BS 7910 gives comprehensive guidance for assessing the criticality of cracks or crack-like defects in welded structures with respect to fracture and fatigue The assessment can be made at different levels of complexity The effects of environment can be included in the assessments 82 Fatigue design of welded structures - Norsok and Eurocode 3 2011 P J Haagensen 41

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