Fatigue of Materials

FatigueDefinition: 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 LifeLoading 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

am=0

am>0

ult

Mean Stresses reduce the stress range

No mean stress

Stress Amplitude vs. MeanGoodman Relationship: lower the mean stresses, the greater the allowable stress amplitude for the same life.

1u

m

f

a

a

m

f

u

Example: Goodman Diagram

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

a

m

u/2f

u

u/4f

u/2m

min= u/4 max= 3u/4

Stress vs. Number of Cycles

S-N Diagram

Lower mean stress

Miner’s RuleDamage 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 i

Nfi = number of repetitions to cause failure at a stress range, i

(ni < Nfi)

ni/Nfi 1

Example problem - Miner’s Rule

Ni/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,

i (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 maximum3. Alternate above some base value

V

M

1. Beam Fatigue

M 2c

max = Mc/I

3. Others