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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
sa
sm=0
sa
sm>0
sult
Mean Stresses
reduce the stress
range
No mean stress
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
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
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:
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
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
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

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CE336-05-Fatigue.ppt

  • 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
  • 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