Fatigue refers to damage accumulated through repeated cyclic stresses over time. It is affected by factors like stress type/amplitude, surface finish, material properties, and environment. Fatigue life depends on the mean and amplitude of stresses based on relationships like the Goodman diagram. The Miner's rule states that the fraction of fatigue life consumed by stresses must be less than 1 to avoid failure. Fatigue tests involve repeated cyclic loading in tension, compression, bending, or other patterns to determine fatigue properties.

1. Fatigue of Materials

2. 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

3. 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

4. Loading Characteristics

5. Effect of Mean Stresses
sa
sm=0
sa
sm>0
sult
Mean Stresses
reduce the stress
range
No mean stress

6. Stress Amplitude vs. Mean
Goodman Relationship: lower the mean
stresses, the greater the allowable
stress amplitude for the same life.
1


u
m
f
a
s
s
s
s
sa
sm
sf
su

7. Example: Goodman Diagram
If sf=su/2, sm=su/2,
What is the max and min s that can be
applied?
sa
sm
su/2sf
su
su/4sf
su/2sm
smin= su/4 smax= 3su/4

8. Stress vs. Number of Cycles
S-N Diagram
Lower mean stress

9. 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:
ni = number of repetitions applied at si
Nfi = number of repetitions to cause failure at a stress
range, si
(ni < Nfi)
S ni/Nfi  1

10. Example problem - Miner’s Rule
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
Stress Range,
si (ksi)
No. Applied
Cycles, Ni
No. Cycles to
Failure,Nfi
3 900 10,000
5 50 500
Log N
5
500
3
10,000

11. Fatigue tests
2. Tension- Compression
Loading Patterns:
1. Reverse stresses, + to -
2. Alternate zero to some maximum
3. Alternate above some base value
V
M
1. Beam Fatigue
M
2c
smax = Mc/I
3. Others