Chapter 14

Fatigue

Schematicrepresentation of a fatigue fracturesurface in a steel shaft, showingthe initiation region (usually at thesurface), the propagation of fatiguecrack (evidenced by beachmarkings), and catastrophicrupture when the crack lengthexceeds a critical value at theapplied stress.

Fatigue Surface

Fatigue Parameters

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 curveshowing the three stages in thecase of polystyrene.

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 ofstrain for an 18%-Ni maragingsteel. (Adapted with permissionfrom R. W. Landgraf, in AmericanSociety for Testing and Materials,Special Technical Publication (ASTMSTP) 467, (Philadelphia: ASTM,1970), p. 3.)

Fatigue Life

Effect of mean stresson S–N curves. The fatigue lifedecreases as the mean stressincreases.

Mean Stress on S-N curves

(a) Effect of mean stress on fatigue life. (b) Gerber,Goodman, and Soderberg diagrams, showing mean stress effect on fatigue life.

Effect of Mean Stress on Fatigue Life

Effect of frequency on the fatigue life of a reactorpressure vessel steel. The fatigue life decreases at 1,000 Hz compared to that at 20 Hz. (Usedwith 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-lowloading sequence. (Adapted with permission from B. I. Sandor, Fundamentals of Cyclic Stress andStrain (Madison, WI: University of Wisconsin Press, 1972.) (b) Sequence of block loadings at fourdifferent 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 mazestructure, showing dislocationwalls on {100} in Cu–Ni alloyfatigued to saturation. (FromP. Charsley, Mater. Sci. Eng., 47(1981) 181.)

Maze Structure

Fatigue Crack Nucleation at Slip Bands

(a) Fatigue cracknucleation at slip bands. (b) SEM ofextrusions and intrusions in acopper sheet. (Courtesy ofM. Judelwicz and B. Ilschner.)

Some mechanisms offatigue crack nucleation. (AfterJ. C. Grosskreutz, Tech. Rep.AFML-TR-70–55 (Wright–Patterson AFB, OH: Air ForceMaterials 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 shotpeening on fatigue life, σ of steelswith different treatments as afucntin of ultimate tensile strength,σUTS. (After J. Y. Mann, Fatigue ofMaterials (Melbourne, MelbourneUniversity 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) Smallcompressive load. (e) Maximumcompressive 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 crackgrowth through a craze at thetip of a fatigue crack. (AfterL. Konczol, M. G. Schincker andW. Do¨ ll, J. Mater. Sci., 19 (1984)1604.)

Fatigue Crack Path

(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

Fatigue crackpropagation in an AISI 4140 steel.(a) Longitudinal direction (parallelto rolling direction). (b) Transversedirection (perpendicular to rollingdirection). (Reprinted withpermission from E. G. T. DeSimone, 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 fatiguecrack propagation rates, at fixedvalues of K (= 0.6 MPa m1/2) andtest frequency v (= 10 Hz), as afunction of reciprocal of molecularweight for PMMA and PVC. (AfterS. 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 growthrate da/dN in alumina as a functionof the maximum stress intensityfactor Kmax under fully reversedcyclic loads (v = 5 Hz). Alsoindicated are the rates of crackgrowth per cycle derived fromstatic-load fracture data. (AfterM. 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 graphitespecimens in a physiologicalenvironment; leaflet andcompact-tension specimens.(Adapted from R. O. Ritchie, J.Heart Valve Dis., 5 (1996) S9.)

Fatigue Crack Propagation

Effect of the applied stress range σ on temperaturerise in PTFE subjected to stress-controlled fatigue. Thesymbol x denotes failure of the specimen. (After M. N. Riddell, G. P. Koo, and J. L. O’Toole, PolymerEng. Sci. 6 (1966) 363.)

Hysteretic Heating in Fatigue

A schematic of fatigue crack propagagtion 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 atvarious stress levels.

Statistical Analysis of S-N Curves

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.