Fatigue Considerations

Fatigue considerations are important because the consequent failure is generally sudden and at a stress level much lower than the ultimate stress.

Fatigue properties of materials are generally determined by producing Wohler /S-N Plots. These are simply plots with stress as the vertical axis and log (number of complete stress reversals) as the horizontal axis. A number of material specimens are tested and the points at which they break are plotted on the S-N curve.

It is a useful property of steel that when the stress level fall below a certain value the specimen is effectively never likely to fail. Generally other materials do not exhibit this effect.

The fatigue strength is the maximum completely reversed stress under which a material will fail after it has experienced the stress for a specified number of cycles. (The strength is accompanied by the number of cycles). ..Fatigue Strength (fixed number of cycles) = S_n,

The Fatigue limit is the maximum completely reversed stress for which it is assumed that the material will never fail regardless of the number of cycles. Fatigue Limit = S'_n

Experiments have shown little direct relationship between the fatigue limit and the yield strength ,ductility etc. However some relationship between the fatigue limit and the tensile strength Su has been established for unotched polished specimens tested using the rotating beam method. This method loads the specimens by reversed bending.

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S'n = 0.5 Su	for Wrought Steels where Su < 1400MPa
S'n = 690MPa	for Wrought Steels where Su > 1400MPa
S'n = 0.4 Su	for for cast steel and cast iron
S'n = 0.38 Su	for magnesium casting and wrought alloys (based on 106 cycle life)
S'n = 0.45 Su	for nickel and copper based alloys
S'n = 0.38 Su	for for wrought aluminium alloys up to a strength of 280 MPa (based on 5 x 108 cycle life)
S'n = 0.16 Su	for for cast aluminium alloys up to a strength of 350 MPa (based on 5 x 108 cycle life)

all of the above relationships are based on a 50% survival life.

The fatigue limit for reversed axial load of a polished,unnotched specimen is aboutt 15% lower than that for reversed bending.

The fatigue limit for torsional testing of polished unnotched specimens is

• about 0.58 x the fatigue limit in reversed bending for steel.

• about 0.8 x the fatigue limit in reversed bending for cast iron.

• about 0.48 x the fatigue limit in reversed bending for copper.

The above values are all experimentally derived under relatively ideal conditions.
These values should be modified using factors that take into account actual operating conditions.

Typically
The Modified working endurance limit
Se = Cr. x Cs x Cf x Cw x( 1/ Kf ) x S'n

Cr = Reliability factor
Cs = Size Reduction Factor
Cf = Surface Finish Correction
Cw = Weld Correction Factor
Kf = Fatigue stress concentration factor

All of the above factors have significant quantifiable negative effect on the fatigue strength of a metal.
Other factors can also have a significant non-quantifiable effect on the fatigue strength of metals.

Shot peening, cold rolling, case hardening and nitriding can also improve the fatigue strength and reduce the effect of stress concentrations. Fretting, corrosion etc reduce the fatigue strength.