Chapter 14 Fatigue

Fatigue Fracture Surface Initiation region (usually at the surface) Propagation of fatigue crack (evidenced by beach markings) Catastrophic rupture when crack length exceeds a critical value at the applied stress.

Analysis of Fatigue: Approaches (i) Stress-life approach (ii) Strain-life approach (iii) Fracture mechanics approach

Parameters of the S N Tests cyclic stress range, σ = σmax − σ min cyclic stress amplitude, σa = (σmax − σmin)/2 mean stress, σm = (σmax + σmin)/2 stress ratio, R = σmin/σmax

Basquin’s Law : High cycle Fatigue

S–N (Wöhler) Curves (a) S (stress)–N (cycles to failure) curves. (A) Ferrous and (B) nonferrous metals; SL is the endurance limit. b) S–N curves for polymeric materials. Polymers that form crazes, such as polymethylmethacrylate (PMMA) and polystyrene (PS), may show a flattened portion in the very beginning, indicated as stage I. (c) An example of an actual S–N curve showing the three stages in the case of polystyrene.

Coffin-Manson Law: Low Cycle Fatigue Basquin + Coffin -Manson

S–N curves for typical metals and polymers

Fatigue Strength Superposition of elastic and plastic curves gives the fatigue life in terms of total strain. (Adapted with permission fromR. W. Landgraf, in American Society for Testing and Materials, Special Technical Publication (ASTM STP) 467 (Philadelphia: ASTM, 1970), p. 3.)

Fatigue Life: HCF and LCF Fatigue life in terms of strain for an 18%-Ni maraging steel from R. W. Landgraf, in ASTMSTP 467, ASTM,1970), p. 3.

Mean Stress on S-N curves Effect of mean stress on S–N curves Fatigue life decreases as the mean stress increases

Effect of Mean Stress on Fatigue Life Goodman Gerber Soderberg

Effect of Frequency on the Fatigue Life Effect of frequency on the fatigue life of a reactor pressure vessel steel. The fatigue life decreases at 1,000 Hz compared to that at 20 Hz. (Used with permission from P. K. Liaw, B. Yang, H. Tian et al., ASTM STP 1417 (West Conshohocken, PA: American Society for Testing and Materials, 2002.)

Cumulative Damage (a) Damage accumulation, in a high-to-low loading sequence. (Adapted with permission from B. I. Sandor, Fundamentals of Cyclic Stress and Strain (Madison, WI: University of Wisconsin Press, 1972.) (b) Sequence of block loadings at four different mean stresses and amplitudes.

Fatigue Crack Nucleation (a) Persistent slip bands in vein structure. Polycrystalline copper fatigued at a total strain amplitude of 6.4 × 10−4 for 3 × 105 cycles. Fatiguing carried out in reverse bending at room temperature and at a frequency of 17 Hz. The thin foil was taken 73 μm below the surface. (Courtesy of J. R. Weertman and H. Shirai.) (b) Cyclic shear stress, τ , vs. plastic cyclic shear strain, γ pl., curve for a single crystal of copper oriented for single slip. (After H. Mughrabi, Mater. Sci. Eng., 33 (1978) 207.) The terms γ pl,M. and γ pl,PSB refer to cyclic plastic shear strain in the matrix and persistent slip bands, respectively. (c) Intrusions/extrusions in a tin-based solder due to thermal fatigue. (Courtesy of N. Chawla and R. Sidhur.)

Maze Structure Well-developed maze structure, showing dislocation walls on {100} in Cu–Ni alloy fatigued to saturation. (From P. Charsley, Mater. Sci. Eng., 47 (1981) 181.)

Fatigue Crack Nucleation at Slip Bands (b) SEM of extrusions and intrusions in a copper sheet. (Courtesy of M. Judelwicz and B. Ilschner.)

Fatigue Crack Nucleation Some mechanisms of fatigue crack nucleation. (After J. C. Grosskreutz, Tech. Rep. AFML-TR-70–55 (Wright– Patterson AFB, OH: Air Force Materials Laboratory), 1970.)

Fatigue Life (a) Residual stress profile generated by shot peening of a surface; CS and TS indicate compressive and tensile stress, respectively. (b) Effect of shot peening on fatigue life, σ of steels with different treatments as a function of ultimate tensile strength, σUTS. (After J. Y. Mann, Fatigue of Materials (Melbourne, Melbourne University Press, 1967).)

Stages I, II, and III of fatigue crack propagation

Fatigue Striations Fatigue striations in 2014-T6 aluminum alloy; two-stage carbon replica viewed in TEM. (a) Early stage. (b) Late stage. (Courtesy of J. Lankford.)

Fatigue Crack Growth Fatigue crack growth by a plastic blunting mechanism. (a) Zero load. (b) Small tensile load. (c) Maximum tensile load. (d) Small compressive load. (e) Maximum compressive load. (f) Small tensile load. The loading axis is vertical (After C. Laird, in Fatigue Crack Propagation, ASTM STP 415 (Philadelphia: ASTM, 1967), p. 131.)

Microscopic Fracture Modes modes in fatigue. (a) Ductile striations triggering cleavage. (b) Cyclic cleavage. (c) α − β interface fracture. (d) Cleavage in an α − β phase field. (e) Forked intergranular cracks in a hard matrix. (f) Forked intergranular cracks in a soft matrix. (g) Ductile intergranular striations. (h) Particle-nucleated ductile intergranular voids. (i) Discontinuous intergranular facets. (Adapted from W. W. Gerberich and N. R. Moody, in Fatigue Mechanisms, ASTM STP 675 (Philadelphia: ASTM, 1979) p. 292.)

Fatigue Crack Path in Polymer Discontinuous crack growth through a craze at the tip of a fatigue crack. (After L. Konczol, M. G. Schincker and W. Do¨ ll, J. Mater. Sci., 19 (1984) 1604.)

Fracture Mechanics Applied to Fatigue Failure locus. (b) Schematic of crack length a as a function of number of cycles,N.

Crack Propagation Rate: Paris Erdogan Relationship

Paris Relationship: Integration

Fatigue Crack Propagation in an AISI 4140 Steel (a) Longitudinal direction (parallel to rolling direction). (b) Transverse direction (perpendicular to rolling direction). (Reprinted with permission from E. G. T. De Simone, K. K. Chawla, and J. C. Miguez Su´arez, Proc. 4th CBECIMAT (Florian ´ opolis, Brazil, 1980), p. 345)

Fatigue Crack Propagation in Polymers Fatigue crack propagation rates for a number of polymers. (After R. W. Hertzberg, J. A. Manson, and M. Skibo, Polymer Eng. Sci., 15 (1975) 252.)

Fatigue Crack Propagation for PMMA and PVC Variation in fatigue crack propagation rates, at fixed values of K (= 0.6 MPa m1/2) and test frequency v (= 10 Hz), as a function of reciprocal of molecular weight for PMMA and PVC. (After S. L. Kim, M. Skibo, J. A. Manson, and R. W. Hertzberg, Polymer Eng. Sci., 17 (1977) 194.)

Fatigue Crack Growth Under Cyclic Loading Fatigue crack growth rate da/dN in alumina as a function of the maximum stress intensity factor Kmax under fully reversed cyclic loads (v = 5 Hz). Also indicated are the rates of crack growth per cycle derived from static-load fracture data. (After M. J. Reece, F. Guiu, and M. F. R. Sammur, J. Amer. Ceram. Soc., 72(1989) 348.)

Fatigue Damage Intrinsic and extrinsic mechanisms of fatigue damage. (After R. O. Ritchie, Intl. J. Fracture, 100 (1999) 55.)

Fatigue Crack Propagation propagation rates for pyrolitic-carbon coated graphite specimens in a physiological environment; leaflet and compact-tension specimens. (Adapted from R. O. Ritchie, J. Heart Valve Dis., 5 (1996) S9.)

Hysteretic Heating in Fatigue Effect of the applied stress range σ on temperature rise in PTFE subjected to stress-controlled fatigue. The symbol x denotes failure of the specimen. (After M. N. Riddell, G. P. Koo, and J. L. O’Toole, Polymer Eng. Sci. 6 (1966) 363.)

Effects in Fatigue A schematic of fatigue crack propagation rate as a function of cyclic stress intensity factor in air and seawater. At any given K, the crack propagation rate is higher in seawater than in air.

Two-parameters Approach A fatigue threshold curve. (After A. K. Vasudevan, K. Sadananda, and N. Louat, Mater. Sci. Eng., A188 (1994) 1.)

Fatigue crack growth rates for long and short cracks

Fatigue Testing Various loading configurations used in fatigue testing. (a) In cantilever loading, the bending moment increases toward the fixed end. (b) In two-point beam loading, the bending moment is constant. (c) Pulsating tension, or tension–compression, axial loading.

Statistical Analysis of S-N Curves S–N curve showing log-normal distribution of lives at various stress levels.

q-values for S--N Data

Survival and Failure Family of curves showing the probability of survival or failure of a component.

Line diagram of a hydraulically operated closed-loop system

Block diagram of a low-cycle fatigue-testing system