MSE 2203

Mechanical Behavior of Materials

3. Fatigue of Metals

Jahirul Islam
Lecturer
Dept. of Materials Science and Engineering
Khulna University of Engineering & Technology
Khulna-9203
 Fatigue of Metals

Reference:
Chapter-12: Mechanical Metallurgy By G. E. Dieter
 Introduction
• Failures occurring under conditions of dynamic and fluctuating loading
are called fatigue failures.
• 90% of the failures are accounted for fatigue failure.
• A fatigue failure is particularly insidious because it occurs without any
obvious warning.
• Fatigue results in a brittle-appearing fracture, with no gross deformation at
the fracture.
• Appearance of fractured surface:
1. smooth region (beach marks)
2. rough region
• Three basic factors of fatigue failure:
1. a sufficiently high tensile stress,
2. a large variation of applied stress, and
3. a sufficiently number of cycles of the
applied stress.
 Stress Cycles
The general types of fluctuating stresses cycles
1. Completely reversed cycle of stress (sinusoidal
form)
2. Repeated stress cycle in which the maximum
stress, σmax and minimum stress, σmin are not equal
3. Complicated stress cycle (e.g. aircraft wing)
• Two stress component:
(1) mean stress σm (steady stress)
(2) alternating stress, σa (variable stress)
• Range of stress,
σr =σmax – σmin
• Stress Ratio,
R = σmin / σmax
• Amplitude ratio,
A = σa / σm = (1 -R)/(1+R)
 The S-N Curve
• The S-N curve, a plot of stress, S (e.g. σmax , σmin, σα ) against the number of
cycles to failure N (usually in log scale).
• Two type test:
1. High cycle fatigue (N>105) (@ low σ)
2. Low cycle fatigue (N<105) (@ high σ)
• Fatigue Limit/ endurance limit: Limiting stress level below which fatigue
failure will not occur.
• Fatigue strength: The stress level at which failure will occur for some
specified number of cycles (@ fixed N, e.g. 10 8).
• Fatigue life Nf: The number of
cycles to cause failure at a σm = 0
specified stress level.
The S-N curve plot process
• Start at a high stress (2/3 of UTS)
• Progressively decrease σ, until σ =
constant with N i.e. fatigue limit
• If no fatigue limit, stop test at
N=108 or 5x108 (Fatigue strength) Figure 12-3 Typical fatigue curves for ferrous
and nonferrous metals.
 Effect Of Mean Stress On Fatigue (if σm ≠ 0)

• If σm ≠ 0, common two way of representing

the S-N curve
1. σmax vs N @ constant Stress Ratio, R and
2. σα vs N @ constant Mean Stress, σm
• Change σmax and adjust σmin to keep constant,
R or σm
• R = σmin / σmax; σm = (σmax + σmin)/2;
• σa = (σmax - σmin)/2
• When, R ↑, σm ↑
• When, σm ↑, σa ↓
• Other ways of plotting S-N curve these data
are:
✓σmax vs N @ constant Mean Stress, σm
✓σmax vs N @ constant minimum Stress, σmin
 Effect Of Mean Stress On Fatigue (if σm ≠ 0)
• The problem with the earlier mentioned approach is that for each value of
mean stress there is a different value of the limiting range of stress, σmax - σmin,
which can be withstood without failure.
• J. Goodman (1899) first made the contribution to address this problem.

Figure 12-7 Goodman Diagram

(dependency of stress range with
mean stress )
 Effect Of Mean Stress On Fatigue (if σm ≠ 0)
• Relationship of σα and σm

where, x = l for Goodman line,

x = 2 for the Gerber parabola,
and σe is the fatigue limit for
completely reversed loading.
• If the design is based on the
yield strength, as indicated
by the dashed Soderberg line
in Fig. 12-8, then σ0 should Figure 12-8 Alternative method
be substituted for σu in Eq. of plotting the Goodman diagram.
(12-7). This is sometimes known as the
Haig-Soderberg diagram.
 Cyclic Stress-Strain Curve
• During initial loading the stress-strain curve is O-A-
B.
• On unloading yielding begins in compression at a
lower stress C due to the Bauschinger effect.
• In reloading in tension a hysteresis loop develops.
• The dimensions of the hysteresis loop arc described
by its width Δε, the total strain range, and its height
Δσ, the stress range.
• The total strain range Δε consists of the elastic strain
component Δεe= Δσ/Ε plus (+) the plastic strain
component Δεp.
• The width of the hysteresis loop will depend on the Figure 12-10 Stress-Strain
level of cyclic strain. curve under constant strain
condition.

• Since the plastic deformation is not completely reversible, due to cyclic

straining condition there are some structural changes occur as a results.
• This change of structure may cause may effect either cyclic softening, cyclic
hardening or remain stable.
Cyclic Stress-Strain Curve

• Cyclic hardening
would lead to a
decreasing peak
strain increasing
cycles.
• Cyclic softening
would lead to a
continually
increasing strain
range and early
fracture.
 Low Cycle Fatigue
• At high stress level a material may fail at a low cyclic stress.
• Example- thermal stress fatigue, where a material is failed due to
cyclic strain rather than cyclic stress.
• Due to temperature effect, the material is undergoes a cyclic thermal
expansion-contraction for a fixed length.
• The usual way of presenting low-cycle fatigue test results is to plot the
plastic strain range Δεp against N.

Figure 12-13 Low-cycle

fatigue curve (Δεp vs. N )
for Type 347 stainless steel.
Coffin-Manson relation
Low Cycle Fatigue
 Structural Feature of Fatigue (Structural
changes due to fatigue)
• The fatigue proceed as the following steps:
1. Crack initiation: originated from surface roughness, crack etc.
2. Slip-band crack growth → Stage I: deepening of initial crack via
shear stress.
3. Crack growth on planes of high tensile stress → Stage II:
propagation of well-defined crack (formed through stage I) via tensile
stress.
4. Ultimate ductile failure: as the crack growth to a sufficient length, the
remaining part of the body ruptured due to applied load.
• In high stress, low-cycle fatigue the stage II is relatively longer whereas
in low stress, high cycle fatigue stage I is the longer stage.
• If the initial stress level is high and the material has a sharp crack, the
stage I will not be observed at all.
• Fatigue crack normally initiated at outer fresh surface (exception, until
there present any interface e.g. TMT bar).
 Structural Feature of Fatigue (Structural
changes due to fatigue)
• During fatigue, due to deformation, slip happen at the same atomic planes
and in the same crystallographic direction.
• Successive cyclic deformation produce additional slip band i.e. thickening
of slip band or heavy slip formation which further lead to the formation of
crack.
• Once the crack is formed, it propagate initially along the slip planes.
• W. A. Wood (1955) proposed a model where he showed that due to the
cyclic strain, the back and forth movement of the slip planes creates a
surface notch either intrusion or extrusion.
• These may lead to the start of a fatigue crack.

Figure 12-15 W. A. Wood’s concept of microdeformation leading to formation of fatigue

crack , ( a ) Static deformation; ( b) fatigue deformation leading to surface notch
(intrusion); ( c) fatigue deformation leading to slip-band extrusion.
 Structural Feature of Fatigue (Structural
changes due to fatigue)
• The stage I crack propagate initially along
the persistent slip band.
• The rate of stage I crack propagation (few
nm per cycle) is slower as compared to
the stage II (few μm per cycle) crack
propagation.
• The fracture surface of stage I, is actually
featureless (no visible appearance to
describe).
• Whereas fracture surface of stage II,
appears as ripples or fatigue fracture
striation.
• Each striation is produced by a single
cycle of fatigue.
 Structural Feature of Fatigue (Structural
changes due to fatigue)
C. Laird proposed a mechanism how crack
propagate in stage II.
a) At start of the loading the crack tip is sharp.
b) Due to applied tensile stress the crack tip
slip along planes at 45° to the planes of the
crack.
c) As the crack widens to its maximum
extension its tips becomes blunted.
d) When the loading direction is changed to
compression, the slip direction in the end
zones is reversed.
e) As a results, the previously blunted face is Tensile Compression
crashed together and a new crack surface is loading cycle loading cycle
created with a re-sharpen crack tip by
buckling action. Figure 12-17 Plastic blunting
f) The re-sharpened crack is then ready process for growth of stage II
to advance and be blunted in the next stress fatigue crack.
cycle.
• The fatigue crack is progressed through by
above mentioned process.
 Effect of Stress Concentration on Fatigue
• Fatigue strength is seriously reduced due to the presence of stress raiser such
as notch or hole, surface roughness, porosity, inclusion etc.
• These can be reduced by careful design and avoiding metallurgical stress
raiser.
• The effect of notches on fatigue strength is determined by comparing the S-N
curve of notched and un-notched specimen.
• Fatigue-notch factor/ Fatigue-strength reduction factor, Kf : is the ratio of
fatigue limit of the un-notched to the notched specimen.
• Kf should be equal or greater than 1.
• Kf depends on:
1. Severity of the notches
(size/depth)
2. Type of the notches
(sharp/blunt)
3. Materials
4. Loading type
5. Stress level
 Effect of Stress Concentration on Fatigue
• Theoretical Stress-concentration factor, Kt: is the ratio
of maximum stress to the nominal stress.
• Kf is usually less than Kt
• Notch sensitivity factor,

• When Kf =1; q = 0 and when Kf = Kt; q = 1

• Kt ↑(sharpest the crack), q↓ (lower the fatigue
sensitivity).

• Higher the strength, higher the q.

• Therefore, increasing the hardness
or tensile strength may decrease
the fatigue performance in terms
of notch sensitivity.
 Effect of Material’s Size on Fatigue Behavior
• It is difficult to predict the real performance of a large machine while test a
small piece of it in the laboratory via fatigue test.
• Experience has shown that in most cases a size effect exists i.e. the fatigue
strength is lower for a larger material in general.
• Changing the actual size of the sample create variation of result in two way:
1. Size ↑, surface area ↑ as fatigue largely depends on surface area.
2. Size ↑, change the stress gradient across the cross sectional area i.e.
increases the material’s volume under the stressed condition.
• For reversed bending and torsion there is no effect on size of the material
however for most instance fatigue limit decreases with increasing diameter.
 Surface Effects and Fatigue
• In practically all fatigue crack starts from surface and is very sensitive
surface property.
• During bending and torsion loading the surface is the stressed most there
for fatigue crack start from surface in those condition.
• Surface factors that affecting fatigue property are: (1) surface roughness
(2) change in surface strength from the bulk (3) surface residual stress.
1. Surface roughness:
✓Surface roughness ↑, fatigue life ↓
 Surface Effects and Fatigue
2. Change in surface (strength) properties:
✓Anything that cause change in surface strength will change the fatigue
property.
✓Higher the strength at the surface, higher will be the fatigue limit.
✓Example- decarburization of heat-treated steel decreases the fatigue
strength.
✓Similarly, applying soft aluminum coating to the stronger age-harden
aluminum alloy will reduce fatigue life.
✓Carburizing and Nitriding will improve the fatigue properties by
forming a harder surface.
✓As there is a strength variation across the cross-section therefore the
fatigue crack start from the high strength and low strength interface
rather than at the surface.
✓Electroplating of a surface generally reduces the fatigue properties as
it causes large changes in residual stress, adhesion, porosity and
hardness of the coating to the substrate.
3. Surface Residual Stress
✓Increasing the surface residual stress will increase fatigue performance of
a material.
✓This residual stress region act as a stress-absorber or stress-locker which
reduces the stress that is applied to the material.

A material with no residual

stress after bending a stress
less than elastic limit

A material with surface

residual stress developed
due to shot peening

The same material after

shot peening subjected to a
bending force

✓Introducing residual compressive stress to the surface can be done by

surface rolling and shot peening however a post surface cleaning is
necessary to remove surface roughness.
 Effect of Metallurgical Variables on Fatigue
• As fatigue is quite structural/design sensitive, it is less dependent on
metallurgical variables such as strength, heat treatment.
• Fatigue properties are less sensitive on tensile strength of the materials e.g.
fatigue limit of cast and wrought steel is 50% of UTS where as for Ni, Cu
and Mg it is 35% of UTS.
• As yield/UTS increases, fatigue limit is also increased but does not follow
any relationship.
• However, Fatigue limit is microstructure sensitive e.g. spheroidite cast iron
and coarse pearlitic steel have same UTS but fatigue limit is lower for the
later one. WHY??
• Fatigue resistance can be increased by avoiding any possible stress
concentration or in other way homogenizing the slip deformation so that
the dislocations are constrained to move in the same plane.
• This can be achieved by lowering the stacking fault energy (energy
associated while stacking in a faulty manner) so that cross slip is less
favorable and dislocations are bounded to move in the same plane which
ultimately raises the fatigue strength of the materials.
 Effect of Metallurgical Variables on Fatigue
• The material with high stacking fault
energy (e.g. Al, Cu) usually the
dislocations cross slipped easily and
form cell like structure inside the grain
that suppress the effect of grain size of
the material (vice versa).
• Fatigue limit increases with increasing
materials hardness.
• Fatigue limit are greatly depends on
presence of foreign elements in that
material.

Figure 12-23 Steps in the development of a

material with a fatigue limit (schematic): A
(pure metal), B (effect of solid solution
elements on A ), C (fatigue limit due to
strain aging from interstitials), D (increased
fatigue limit from enhanced strain aging.
 Corrosion Fatigue
• The simultaneous action of cyclic stress and chemical attack is known as
corrosion fatigue.
• Two common types chemical attack are: pitting and fretting corrosion.
• Pits act as notches and reduces the fatigue strength.
• When corrosion and fatigue occur simultaneously, the chemical attack
greatly accelerates the rate at which fatigue cracks propagate.
• Materials which show definite fatigue limit at room temperature when tested
in air, but do not show any limit while tested in a corrosive environment.
• Corrosion fatigue is dependent on frequency/speed of the test while the
conventional test doesn't depends on test time (shorter the test time, lower
will be the severity).
• The action of the cyclic stress causes localized disruption of the surface
oxide film so that corrosion pits can be produced. Many more small pits
occur in corrosion fatigue than in corrosive attack in the absence of stress.
• The bottom of the pits are more anodic (active) as compared to remaining
surface → the bottom of the pits got corroded and removed further by cyclic
stress action → crack will occur when the crack becomes enough sharp.
 Fatigue due to Fretting

• Fretting is the surface damage which result when two surfaces in contact
experience slight periodic relative motion.
• Fretting is frequently found on the objects that are closely fitted together
and there is no chance for the corrosion products to be removed.
• The corroded product stay in the closely fitted joint and cause further
destruction by grinding action or by the alternate welding and tearing
away of the high spots.
• The removed particles become oxidized and form an abrasive powder
which continues the destructive process.
• Oxidation of the metal surface occurs and the oxide film is destroyed by
the relative motion of the surfaces, although oxidation is not essential to
fretting.
 Effect of Temperature on Fatigue
Low-Temperature Fatigue:
• Fatigue strength increases with decreasing the temperature as at lower
temperature the vacancy formation and condensation rate is much lower
than higher temperature.
High-Temperature Fatigue:
• We know, T ↑, Fatigue strength ↓ but mild steel is exceptional and show
a maximum fatigue strength at 200 to 300 °C due to strain hardening
effect.
• When the T is high enough, the fracture mode is changed from fatigue
to creep failure where the fracture occur at inter-granular manner rather
than transgranular manner of fatigue failure.
• At high T, local grain boundary oxidation can contribute significantly to
crack initiation.
• Example- Mild steel show definite fatigue limit at room temperature but
when tested above 430 °C, does not show any fatigue limit.
 Thermal Fatigue
• At high T, additional stress source is generated due to thermal stress which
will be added with mechanical stress (if present).
• During thermal fatigue, no additional mechanical stress is involved only
the thermal stress.
• Thermal stress result when the change in dimension of a member as a the
result of a temperature change is prevented by some kind of constraint e.g.
fixed end supported bar at high temperature cause to develop a thermal
stress of, σ = αEΔΤ
Where,
α = linear thermal co-efficient of expansion
E = modulus of elasticity
• If failure occurs by one application of thermal stress, the condition is
called thermal shock. However, if failure occurs after repeated
applications of thermal stress, of a lower magnitude, it is called thermal
fatigue.
• Austenitic SS is not good for high temperature application as it has low
thermal conductivity and high thermal expansion.