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
(a) 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
Microscopic fracture
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
(a) 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
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
Fatigue crack
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