Fatigue of Materials
Fatigue
Definition: Damage accumulated through the
application of repeated stress cycles
Variable amplitude loadings cause different
levels of fatigue
Fatigue is cumulative through the life of an
engineering element
Factors Affecting Fatigue Life
Loading Conditions


Type of stress
Stress amplitude, mean value
Condition of Specimen/Structural Member


Stress concentrations
Surface finish
Material

Thermal history (e.g. grain size in metals)
Environmental conditions


Temperature
Corrosion effects
Loading Characteristics
Effect of Mean Stresses
sult
sm=0
sa
No mean stress
sm>0
sa
Mean Stresses
reduce the stress
range
Stress Amplitude vs. Mean
Goodman Relationship: lower the mean
stresses, the greater the allowable
stress amplitude for the same life.
sa sm

1
s f su
sa
sf
su
sm
Example: Goodman Diagram
If sf=su/2, sm=su/2,
What is the max and min s that can be
applied?
sa
su/2sf
smin= su/4
smax= 3su/4
su/4sf
su/2sm
su
sm
Stress vs. Number of Cycles
S-N Diagram
Lower mean stress
Miner’s Rule
Damage from variable loadings is related to the
life consumed by number of cycles at each
particular STRESS RANGE. The summation of life
consumed at each stress range must be less than
1 to avoid failure.
where:
S ni/Nfi  1
= number of repetitions applied at si
Nfi = number of repetitions to cause failure at a stress
range, si
(ni < Nfi)
ni
Example problem - Miner’s Rule
Stress Range,
si (ksi)
No. Applied
Cycles, Ni
No. Cycles to
Failure,Nfi
3
5
900
50
10,000
500
SNi/Nfi = 900/10,000 + 50/500
= 0.09 + 0.10
= 0.19
0.19 < 1.0  OK
Used 19% of fatigue life,
81% remains
5
3
500 10,000
Log N
Fatigue tests
1. Beam Fatigue
2. Tension- Compression
V
3. Others
M
2c
smax = Mc/I
M
Loading Patterns:
1. Reverse stresses, + to 2. Alternate zero to some maximum
3. Alternate above some base value