Chapter 14

Fatigue

• Initiation region (usually at thesurface)• Propagation of fatiguecrack (evidenced by beachmarkings)•Catastrophic rupture when crack lengthexceeds a critical value at theapplied stress.

Fatigue Fracture Surface

(i) Stress-life approach(ii) Strain-life approach

(iii) Fracture mechanics approach

Analysis of Fatigue: Approaches

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 (cyclesto failure) curves. (A) Ferrous and(B) nonferrous metals; SL is theendurance limit.

b) S–N curves forpolymeric materials. Polymers thatform crazes, such aspolymethylmethacrylate (PMMA)and polystyrene (PS), may show aflattened portion in the verybeginning, indicated as stage I.

(c) An example of an actual S–N curve showing the three stages in thecase of polystyrene.

Coffin-Manson Law: Low Cycle Fatigue

Basquin + Coffin -Manson

S–N curves for typical metals and polymers

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 Strength

Fatigue life in terms of strain for an 18%-Ni maraging steel

from R. W. Landgraf, in ASTMSTP 467, ASTM,1970), p. 3.

Fatigue Life: HCF and LCF

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

Mean Stress on S-N curves

Goodman

Gerber

Soderberg

Effect of Mean Stress on 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.)

Effect of Frequency on the Fatigue Life

(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.

Cumulative Damage

Fatigue Crack Nucleation

(a) Persistent slipbands in vein structure.Polycrystalline copper fatigued at atotal strain amplitude of 6.4 ×10−4 for 3 × 105 cycles. Fatiguingcarried out in reverse bending atroom temperature and at afrequency of 17 Hz. The thin foilwas taken 73 μm below thesurface. (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 copperoriented for single slip. (AfterH. Mughrabi, Mater. Sci. Eng., 33(1978) 207.) The terms γ pl,M. andγ pl,PSB refer to cyclic plastic shearstrain in the matrix and persistentslip bands, respectively.(c) Intrusions/extrusions in atin-based solder due to thermalfatigue. (Courtesy of N. Chawlaand R. Sidhur.)

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.)

Maze Structure

Fatigue Crack Nucleation at Slip Bands

(a) Fatigue crack nucleation at slip bands.

(b) SEM of extrusions and intrusions in acopper sheet.

(Courtesy of M. Judelwicz and B. Ilschner.)

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 Crack Nucleation

(a) Residual stressprofile generated by shot peeningof a surface; CS and TS indicatecompressive 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).)

Fatigue Life

Stages I, II, and III of fatigue crack propagation

Fatigue striations in2014-T6 aluminum alloy; two-stagecarbon replica viewed in TEM. (a)Early stage. (b) Late stage.(Courtesy of J. Lankford.)

Fatigue Striations

Fatigue crack growthby 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 tensileload. The loading axis is vertical

(After C. Laird, in Fatigue CrackPropagation, ASTM STP 415(Philadelphia: ASTM, 1967),p. 131.)

Fatigue Crack Growth

Microscopic fracture modes in fatigue. (a) Ductilestriations triggering cleavage. (b)Cyclic cleavage. (c) α − β interfacefracture. (d) Cleavage in an α − βphase field. (e) Forkedintergranular cracks in a hardmatrix. (f) Forked intergranularcracks in a soft matrix. (g) Ductileintergranular striations. (h)Particle-nucleated ductileintergranular voids. (i)Discontinuous intergranular facets.

(Adapted from W. W. Gerberichand N. R. Moody, in FatigueMechanisms, ASTM STP 675(Philadelphia: ASTM, 1979) p. 292.)

Microscopic Fracture Modes

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.)

Fatigue Crack Path in Polymer

(a) Failure locus. (b) Schematic of crack length a as a function of number of cycles,N.

Fracture Mechanics Applied to Fatigue

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) Transversedirection (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 an AISI 4140 Steel

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 in Polymers

Variation in fatigue crack propagation rates, at fixedvalues 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 Propagation for PMMA and PVC

Fatigue crack growth rate da/dN in alumina as a functionof the maximum stress intensity factor Kmax under fully reversedcyclic loads (v = 5 Hz). Also indicated are the rates of crackgrowth 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 Crack Growth Under Cyclic Loading

Intrinsic and extrinsic mechanisms of fatigue damage.

(After R. O. Ritchie, Intl. J. Fracture, 100 (1999) 55.)

Fatigue Damage

Fatigue crackpropagation rates forpyrolitic-carbon coated graphite specimens in a physiological environment; leaflet andcompact-tensionspecimens.

(Adapted from R. O. Ritchie, J.Heart Valve Dis., 5 (1996) S9.)

Fatigue Crack Propagation

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.)

Hysteretic Heating 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.

Effects in Fatigue

A fatigue threshold curve.

(After A. K. Vasudevan, K. Sadananda, and N. Louat, Mater. Sci. Eng., A188 (1994) 1.)

Two-parameters Approach

Fatigue crack growth rates for long and short cracks

Various loadingconfigurations used in fatiguetesting. (a) In cantilever loading,the bending moment increasestoward the fixed end. (b) Intwo-point beam loading, thebending moment is constant. (c)Pulsating tension, ortension–compression, axialloading.

Fatigue Testing

S–N curve showinglog-normal distribution of lives at various stress levels.

Statistical Analysis of S-N Curves

q-values for S--N Data

Family of curvesshowing the probability of survivalor failure of a component.

Survival and Failure

Line diagram of a hydraulically operated closed-loop system

Block diagram of a low-cycle fatigue-testing system