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Fatigue & Fracture
- 1. Veermata Jijabai Technological Institute Fatigue & Fracture Presented By Chetan Fulaware
- 2. Contents ◎Introduction ○ Fatigue ○ Fracture ◎Literature review ◎Derivation ◎Numerical Example ◎Conclusion
- 3. Introduction ◎Fatigue Def : Fatigue is the response of a material to dynamic loading conditions. Components fail under fluctuation stresses at stress magnitude which is lower that the ultimate strength of material. Sometimes, it is lower than yield strength [1] ◎Fracture Def: A failure which is the result of a static overload. It is described as either ductile or brittle fracture. [1]
- 4. Introduction - History ◎History of Fatigue ○ In the 1800s, Europe, several investigators observed that bridge and railroad components were cracking when subjected to repeated loading. [2] ◎History of Fracture: ○ It is difficult to identify exactly, however, fracture failures that cause loss of life have recorded for over 100 years. [2]
- 5. ◎A spectacular example of this problem was the S. S. Schenectady, whose hull completely fractured.
- 6. Fatigue
- 7. Literature Review - Fatigue ◎So how this fatigue takes place ?? The process of fatigue consists of three stages ○ Stage I - crack initiation ○ Stage II - crack propagation ○ Stage III – Sudden fracture Ref: [2]
- 8. ◎Phase I – Crack Initiation ○ Form at the points of maximum local stress and minimum local strength – e.g. scratches, marks.. ○ Occur due to the formation of persistent slip bands (PSB). ○ Slip bands are a result of the systematic build-up of fine slip movements, on the order of only 1 nm.
- 9. ◎The crack initially follows the slip bands at approximately 45° to the principal stress direction ◎Becomes perpendicular to the principal stress, and the crack enters stage II ◎The crack propagation rate during stage I is very low (1 nm per cycle) ◎Consideration of environment-related mechanisms ◎Its rate and direction of growth are controlled by localized stresses
- 10. ◎Phase II – Crack Propagation ○ When the stage I crack changes direction and propagates in a direction normal to the applied stress ○ The plateaus are usually normal to the direction of maximum tensile stress
- 11. ○ Crack growth proceeds by a continual process of crack sharpening followed by blunting ○ crack growth often produces a pattern of fatigue striation (a) (b)
- 12. ◎Phase III - Final Fracture ○ Occurs when remaining cross section can no longer support the applied load ○ Size of fracture zone ○ Fracture of 2 distinct modes
- 13. Research Paper “Small fatigue crack initiation mechanisms and growth behavior of 304 stainless steel at room temperature” [3] ◎Introduction ○ Most of the total fatigue life could be spent in the initiation and small crack growth stages ○ Fatigue fracture is one of the main causes of failure for these components due to the dynamic or alternating stresses which they are often subjected to
- 14. ◎Experimental Procedure ○ The yield strength and ultimate tensile strength 297.55 MPa and 668.64MPa ○ Information such as the initiation, growth and coalescence behavior of small cracks ○ Using surface replicas and photomicrographs Ref: [3]
- 15. ◎Analysis ○ Eight major cracks initiated on the specimen ○ Depends on the grain boundary and the localization of plastic deformation Ref: [3]
- 16. ◎The slope of the major crack length did not change < 0.2mm ◎Critical small crack size for the transition to rapid crack growth was around 0.2mm Ref: [3] (a) (b)
- 17. ◎Paper - Conclusion ○ Grain boundaries - main factor that influence the growth rates ○ For critical crack size of 0.2 mm, rapid growth of this crack occurs
- 18. Derivation for Fatigue life ◎Cracks grow from an initial size (ao) to a critical size (ac) ◎The crack growth ratio ( da dn ) can be determined from the slope of the curve ◎The amount of crack extension per loading cycle, is correlated with the stress-intensity parameter (K ) 𝑑𝑎 𝑑𝑛 = 𝐶. ∆𝐾𝑚 a : flaw or crack size; n : No. of cycles; C and m are constants related to material variables, environment, temperature, and fatigue stress c conditions ΔK = Kmax –Kmin Ref: [2]
- 19. ◎During region II growth in the linear crack growth region, the Paris law can be used to determine the number of cycles to failure ○ ΔK can be expressed in terms of Δσ Y depends on the specific specimen geometry • To predict the fatigue life of structures
- 20. ◎Substitution of the expression for ΔK It is assumed that Δσ (or σmax − σmin) is constant and that Y depends on the crack length and therefore cannot be removed from within the integral. ◎While solving problem by integrating we will get fatigue life
- 21. Problem ◎ Calculate fatigue life Q. The crack growth rate of ferritic/pearlitic steels is given where ΔK is given in units of MPa√m ., and da dn is in units of m/cycle. Assume that a part contains an edge crack that is 0.05mm. long. The stresses vary from 0 to 50 Mpa, and the fractur toughness is 100 MPa√m. Compute the life of the part. Ref: [2]
- 22. ◎Solution: As we know, ∆𝐾 = 𝜎 𝜋 × 𝑎 As m =3 from question, and substituting the other values, we get 𝑑𝑎 𝑑𝑛 = 3.52 × 10−4 × 𝑎3/2 On integrating, we get 𝑑𝑎 𝑑𝑛 = 𝐶. ∆𝐾𝑚
- 23. ◎af depends on the fracture toughness and maximum stress Substituting this in above expression of life gives ◎Thus, the part is expected to last almost 20,000 cycles 𝑎𝑓 = 1 𝜋 × ( 𝐾 𝜎 )2 = 1 3.14 ( 100 1.12 × 50 )2 = 1.02
- 24. Fracture
- 25. Fracture ◎Fractures which are the result of a static overload are described as either ductile or brittle. ◎Ductile fracture - plastic deformation prior to failure. ◎Brittle fracture - little plastic deformation prior to fracture. Ref: [5]
- 26. Literature Survey - Fracture ◎Characteristics of Ductile Fracture ○ Considerable gross permanent or plastic deformation in the region of ductile fracture ○ Ductile fractures proceed only as long as the material is being strained ○ The characteristic appearance of the surface of a ductile fracture is dull and fibrous Ref: [2]
- 27. ◎Ductile fractures are those in which the shear stress exceeds the shear strength before any other mode of fracture can occur ◎The narrowing, or necking, indicates that there has been extensive stretching, or elongation ◎A ductile fracture starts near the centre of the reduced section in tensile loading
- 28. ◎Slant fracture – Shear lip ◎A tensile cup-and-cone fracture originates with many tiny internal fractures called micro voids
- 29. ◎Characteristics of Brittle Fracture ○ Once a brittle crack is initiated, it propagates at the speed of sound ○ There is no gross permanent or plastic deformation of the metal in the region of brittle fracture Ref: [2]
- 30. ○ The surface of a brittle fracture is perpendicular to the principal tensile stress ○ Characteristic markings on the fracture surface frequently, but not always, point back to the location from which the fracture originated.
- 31. Fracture Mechanics ◎Fracture mechanics is the science of predicting the influence of cracks and crack like defects on the fracture of components. ◎Fracture mechanics has its origin in the work of A. A. Griffiths, who proved that the fracture strength of a brittle material, like glass, is inversely proportional to the square root of the crack length. Ref: [4]
- 32. ◎A crack is regarded as a mathematical section in fracture mechanics ◎Three basic crack loading types ○ Mode I ○ Mode II ○ Mode III Ref: [6]
- 33. ◎Mode-I - the opening or tensile mode ◎Mode-II - sliding or in plane shearing mode ◎Mode-III - tearing mode Ref: [6]
- 34. Griffith’s theory of Brittle Fracture ◎A.A. Griffith, while testing glass rods, observed that the longer the rod, the lower the strength. ○ This led to the idea that the strength variation in the glass rods was due to defects, primarily surface defects ◎These flaws lower the fracture strength because they amplify the stress at the crack tip ◎The stress-concentration factor (Kt) increases with increasing crack length (a) and decreasing crack radius (ρt). Therefore, all cracks, if present, should be kept as small as possible. 𝐾𝑡 = 𝜎𝑚 𝜎0 = 2 . ( 𝑎 𝜌𝑡 )1/2 Ref: [2]
- 35. Problem on fracture ◎A wall bracket with a rectangular cross-section is shown in Figure. The depth of the cross-section is twice of the width. The force P acting on the bracket at 600 to the vertical is 5 kN. The material of the bracket is grey cast iron FG 200 and the factor of safety is 3.5. Determine the dimensions of the cross-section of the bracket such that it should not fracture. Assume maximum normal stress theory of failure. Ref: [4]
- 36. ◎Solution Given P, load = 5 kN Sut = 200 N/ mm2 , FOS = 3.5, Height to Width ratio of c/s = 2 ◎Step I Calculation of permissible stress 𝜎max =Sut/ FOS = 200/3.5 = 57.14 N/𝑚2 ◎Step II The force P is resolved into two components—horizontal component Ph and vertical component Pv. Ph = P sin 60° = 5000 sin 60° = 4330.13 N Pv = P cos 60° = 5000 cos 60° = 2500 N The bending moment at the section XX is given by Mb = Ph x 150 + Pv x 300 = 4330.13 x 150 + 2500 x 300 = 1399.52 x 103 N-mm
- 37. ◎𝜎𝑏 = 𝑀𝑏 𝑥 𝑌 𝐼 = 1399520 𝑥 𝑡 𝑡 𝑥 2𝑡3 12 = 2099280 𝑡3 ◎The direct tensile stress due to component Ph is given by, 𝜎𝑡 = 𝑃ℎ 𝐴 = 4330.13 2𝑡2 The vertical component Pv induces shear stress at the section XX. It is however small and neglected. ◎Step III Calculation of dimensions of c/s. The resultant tensile stress s max. at the point A is given by 𝜎𝑚𝑎𝑥 = 𝜎𝑏 + 𝜎𝑡 = 2099280 𝑡3 + 4330.13 2𝑡2 𝑡3 – 37.89 t – 36739.24 = 0 t = 33.65 mm ≈ 35 mm The dimensions of the cross-section to avoid fracture are 35 x 70 mm.
- 38. Conclusion ◎Fatigue cracks form at the point(s) of maximum local stress and minimum local strength ◎Most of the total fatigue life could be spent in the crack initiation ◎Three basic crack loading modes exist for all cracks appearing in components and structures ◎Surface defects like flaws lower the fracture strength because they amplify the stress at the crack tip
- 39. References [1] Engineering Materials, V. B. John, Chapter 10 [2] Fatigue and Fracture Understanding the Basics by F. C. Campbell, 2012 edition, [3] Paper: Small fatigue crack initiation mechanisms and growth behaviour of 304 stainless steel at room temperature, Author: G.J. Deng, S.T. Tu, X.C. Zhang, Q.Q. Wang, F.Z. Xuan [4] Design of machine elements by V. B. Bhandari, Page 151 [5] Springer series, Solid Mechanics and Its Applications, Volume 227, ‘Fatigue Crack Growth’ , Hans Albert Richard, Manuela Sander, [6] ‘Mechanical Behavior of Materials’, Engineering Methods for Deformation, Fracture, and Fatigue, Fourth Edition, Norman E. Dowling, Page 344
Editor's Notes
- -- //Fatigue is the response of a material to dynamic loading conditions. Components fail under fluctuation stresses at stress magnitude which is lower than the ultimate strength of material.// Sometimes, it is lower than yield strength. Further it has been found that the magnitude of stress causing fatigue failure decreases as number of stress cycles increases. This phenomenon of decreased resistance of the materials to fluctuating stresses is the main characteristic of fatigue failure -- And //Fracture is a failure which is the result of a static overload. It is described as either ductile or brittle fracture.// As we can see in the figure that ductile fractures are characterized by extensive plastic deformation prior to and during crack propagation. On the other hand, brittle fracture takes place at stresses below the net section yield strength, with very little observable plastic deformation and a minimal absorption of energy.
- History of Fatigue --The discovery of fatigue occurred //in the 1800s when several investigators in Europe observed that bridge and railroad components were cracking when subjected to repeated loading// -- //It is difficult to identify exactly when the problems// of failure of structural and mechanical equipment became of critical importance; //however, failures that cause loss of life have occurred for over 100 years.// Throughout the 1800s, stories could be heard of bridges fell, and pressure vessels blew up in UK and USA As the century progressed and the use of metals expanded with the increasing use of machines, more and more failures of components subjected to repeated loads were recorded. Even though much progress has been made, developing design procedures to prevent failure from the application of repeated loads is still unpredictable.
- --//A spectacular example of this problem was the S. S. Schenectady, whose hull completely fractured,// while it was docked at its fitting-out time. The fractured ship is shown in Figure. In this case, the need for tougher structural steel was even more critical because welded construction was used in shipbuilding instead of riveted plate. In riveted plate construction, a running crack must reinitiate every time it runs out of a plate. In contrast, a continuous path is available for brittle cracking in a welded structure, which is why low notch toughness is a more critical factor for long brittle cracks in welded ships.
- Literature Review for Fatigue So how this fatigue takes place ?? It takes place in 3 stages --In Stage I - crack initiation -Initial fatigue damage leads to crack nucleation and crack initiation --next is…..Crack propagation – In this stage, Progressive cyclic growth of a crack occurs until the remaining uncracked cross section of a part becomes too weak to sustain the loads imposed And In Final Stage III - sudden fracture of the remaining cross section takes place..
- Lets understand crack initiation separately: --Fatigue cracks form at the points of maximum local stress and minimum local strength => usually, it is near the surface of the part. E.g. scratches, marks, burrs, and other fabrication flaws -- crack initiation will eventually occur due to the formation of persistent slip bands (PSB), it is so called because, traces of the bands persist even when the surface damage is polished away. -- Slip bands are a result of the systematic build-up of fine slip movements, on the order of only 1 nano meter. The back-and-forth movement of the slip bands leads to the formation of intrusions and extrusions at the surface, eventually this leads to the formation of a crack.
- --The crack initially follows the slip bands at approximately 45° to the principal stress direction. --When the crack length becomes sufficient for the stress field at the tip to become dominant, the overall crack plane changes and becomes perpendicular to the principal stress, and the crack enters stage II. -The crack propagation rate during stage I is very low, on the order of 1 nm per cycle, and produces a practically featureless fracture surface. -In observing locations of crack nucleation, the possibility of environment-related mechanisms, including pitting corrosion, stress-corrosion cracking, and other effects of a hostile environment, must be considered. For example, In any structure having mechanically fastened joints with some relative motion, fretting provides a possible failure origin -Once a fatigue crack has been nucleated, its rate and direction of growth are controlled by localized stresses and by the structure of the material at the tip of the crack.
- Phase II – Crack Propagation --In Stage II crack growth occurs when the stage I crack changes direction and propagates in a direction normal to the applied stress. --As we can see in figure (a), The transition is from one or two shear planes in stage I to many parallel platowz (plateaus) separated by longitudinal ridges in stage II. The platowz (plateaus) are usually normal to the direction of maximum tensile stress as we can seen in figure (b). A transition from stage I to stage II in a coarse-grained specimen of aluminum alloy 2024-T3 is shown in figure (c), In this image, the stage II area shows a large number of approximately parallel fatigue patches containing very fine fatigue striations that are not resolved at the magnification used.
- --Crack growth proceeds by a continual process of crack sharpening followed by blunting, as shown in the Figure (a). Crack propagation during crack growth often produces a pattern of fatigue striations as shown in figure (b). Each striation represents one cycle of fatigue. Although striations are indicative of fatigue, fatigue failures can occur without the formation of striations. Striations are microstructural details that are best examined with a scanning electron microscope and are not visible to the naked eye.
- --In final phase --Ultimate failure occurs when the fatigue crack becomes long enough that the remaining cross section can no longer support the applied load. Final fracture occurs when the crack has grown to the critical size for overload failure. --The size of the final fracture zone depends on the magnitude of the loads, and its shape depends on the shape, size, and direction of loading of the fractured part. The final fracture zone of a fatigue fracture surface is often fibrous. --In tough materials, with thick or round sections, the final fracture zone will consist of a fracture by two distinct modes: tensile fracture (plane-strain mode) extending from the fatigue zone and in the same plane, and shear fracture (plane-stress mode) at 45° to the surface of the part, bordering the tensile fracture --But In thin sheet metal pieces having sufficient toughness, final fracture occurs somewhat differently. As you can see this in figure(a), As the crack propagates from the fatigue zone, the fracture plane rotates around an axis in the direction of crack propagation until it forms an angle of approximately 45° with the loading direction and the surface of the sheet. And in figure (b) we can observe that, The fracture in plane inclined 45° to the load direction, can occur on either a single-shear or a double-shear plane.
- Research Paper --This paper discuss “Small fatigue crack initiation mechanisms and growth behavior of 304 stainless steel at room temperature” [3] --304 austenitic stainless steel is an alloy that has been widely used in process and power generating industries as piping and structural material. --Introduction --We will came to know that most of the total fatigue life could be spent in the initiation and small crack growth stages. -Fatigue fracture is one of the main causes of failure for these components due to the dynamic or alternating stresses which they are often subjected to.
- Experimental Procedure --They carried out a fatigue test which can be seen in figure. A single edge notch tensile (SENT) specimen, was used to produce naturally initiated cracks --The yield strength and ultimate tensile strength of the material were 297.55 MPa and 668.64MPa respectively. --They obtained quantitative information such as the initiation, growth and coalescence behavior of small cracks in 304 stainless steel via surface replicas and photomicrographs
- Analysis --In order to characterize the fatigue crack initiation mechanism of 304 stainless steel, the replicas were observed at different time intervals when the specimen was tested at 370MPa. It was found that there were eight major cracks initiated on the specimen. --the initiation and propagation of small cracks depended on both the grain boundary and the localization of plastic deformation along the slip bands. After nucleating at the grain boundaries, and then they propagated in a way perpendicular to the loading axis -
- --We can see in figure (a), shows the variation of the lengths of major crack, which may cause the ultimate fracture. --The slope of the major crack length curve almost did not change too much when the crack length was lower than 0.2 mm. Once the surface small crack length reached around 0.2 mm, the crack will propagate rapidly --it can be deduced that the critical small crack size for the transition to rapid crack growth was around 0.2 mm for 304 stainless steel. --Figure (b) showed the variation of the small fatigue crack growth rates along with crack lengths. It was easy to be seen that there was not a general increase in crack growth rate with increasing crack length, as was normally observed for long cracks. Based on the observation of the replicas, the fluctuations of crack growth rate were due to the blocking effect of grain boundaries
- They have concluded that 1.Grain boundaries are not only the initiation sites of cracks for austenitic 304 stainless steel, but also are the main factor that influence the growth rates of microstructurally small cracks. 2. Once the surface small crack length reaches the critical crack size of 0.2 mm, rapid growth of this crack occurs, resulting in final specimen fracture.