Fatigue

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.

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(i) Stress-life approach(ii) Strain-life
approach(iii) Fracture mechanics approach
Analysis of Fatigue Approaches
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Parameters of the S N Tests
cyclic stress range, s smax - s min cyclic
stress amplitude, sa (smax - smin)/2 mean
stress, sm (smax smin)/2 stress ratio, R
smin/smax
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Basquins Law High cycle Fatigue
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SN (Wöhler) Curves
(a) S (stress)N (cycles to failure) curves. (A)
Ferrous and (B) nonferrous metals SL is
the endurance limit. b) SN 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 SN curve showing the
three stages in the case of polystyrene.
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Coffin-Manson Law Low Cycle Fatigue
Basquin Coffin -Manson
8
SN 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.
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Mean Stress on S-N curves
Effect of mean stress on SN curves Fatigue life
decreases as the mean stress increases
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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.
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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, t , vs. plastic
cyclic shear strain, ? pl., curve for a single
crystal of copper oriented for single slip.
(After H. Mughrabi, Mater. Sci. Eng., 33 (1978)
207.) The terms ? pl,M. and ? 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 CuNi alloy
fatigued to saturation. (From P. Charsley,
Mater. Sci. Eng., 47 (1981) 181.)
17
Fatigue Crack Nucleation at Slip Bands

• 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-7055 (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, s of steels with
different treatments as a function of ultimate
tensile strength, sUTS. (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.)
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Microscopic Fracture Modes
Microscopic fracture modes in fatigue. (a)
Ductile striations triggering cleavage.
(b) Cyclic cleavage. (c) a - ß interface fracture.
(d) Cleavage in an a - ß 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.)
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Fracture Mechanics Applied to Fatigue

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

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Crack Propagation Rate Paris Erdogan
Relationship
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Paris Relationship Integration
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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 Suarez,
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.)
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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.)
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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.)
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Fatigue Damage
Intrinsic and extrinsic mechanisms of fatigue
damage. (After R. O. Ritchie, Intl. J. Fracture,
100 (1999) 55.)
33
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.)
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Hysteretic Heating in Fatigue
Effect of the applied stress range s 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. OToole, 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.
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Two-parameters Approach
A fatigue threshold curve. (After A. K.
Vasudevan, K. Sadananda, and N. Louat, Mater.
Sci. Eng., A188 (1994) 1.)
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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 tensioncompression, axial loading.
39
Statistical Analysis of S-N Curves
SN curve showing log-normal distribution of
lives at various stress levels.
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q-values for S--N Data
41
Survival and Failure
Family of curves showing the probability of
survival or failure of a component.
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Line diagram of a hydraulically operated
closed-loop system
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Block diagram of a low-cycle fatigue-testing
system