Fatigue of Materials

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Fatigue of Materials
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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

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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

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Loading Characteristics
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Effect of Mean Stresses
sult
sa
sa
smgt0
sm0
Mean Stresses reduce the stress range
No mean stress
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Stress Amplitude vs. Mean

• Goodman Relationship lower the mean stresses,
  the greater the allowable stress amplitude for
  the same life.

sa
sf
sm
su
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Example Goodman Diagram

• If ?f?u/2, ?m?u/2,
• What is the max and min ? that can be applied?

sa
smin su/4
smax 3su/4
su/2sf
su/4sf
sm
su
su/2sm
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Stress vs. Number of Cycles

• S-N Diagram

Lower mean stress
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Miners 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 lt Nfi)

S ni/Nfi ? 1
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Example problem - Miners Rule
Stress Range, si (ksi) No. Applied Cycles, Ni No. Cycles to Failure,Nfi
3 900 10,000
5 50 500

• Ni/Nfi 900/10,000 50/500
• 0.09 0.10
• 0.19
• 0.19 lt 1.0 ? OK
• Used 19 of fatigue life,
• 81 remains

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Fatigue tests
3. Others
Loading Patterns 1. Reverse stresses, to - 2.
Alternate zero to some maximum 3. Alternate
above some base value