1. Chapter 14
Fatigue

2. 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.

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

4. 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

5. Basquin’s Law : High cycle Fatigue

6. 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.

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

8. S–N curves for typical metals and polymers

9. 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.)

10. 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.

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

12. Effect of Mean Stress on Fatigue Life
Goodman
Gerber
Soderberg

13. 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.)

14. 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.

15. 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.)

16. 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.)

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

18. 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.)

19. 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).)

20. Stages I, II, and III of fatigue
crack propagation

21. 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.)

22. 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.)

23. 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.)

24. 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.)

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

26. Crack Propagation Rate:
Paris Erdogan Relationship

27. Paris Relationship: Integration

28. 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)

29. 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.)

30. 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.)

31. 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.)

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

33. 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.)

34. 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.)

35. 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.

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

37. Fatigue crack growth rates for long and short cracks

38. 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.

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

40. q-values for S--N Data

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

42. Line diagram of a hydraulically operated closed-loop system

43. Block diagram of a low-cycle fatigue-testing system