A material subjected to a repeating constant amplitude strain eventually creates a repeating stable stress/strain hysteresis loop. You can plot several of these hysteresis loops, created at various strain amplitudes, on the same axes. Then, if a curve is plotted through the tips of all of the hysteresis loops, a 'cyclic stress-strain' curve is generated. The intent of this artificial curve is to represent the stable behavior of the material (after initial cyclic softening or hardening).

The cyclic stress strain curve is defined as:

K' = cyclic strain hardening coefficient

n' = cyclic strain hardening exponent

*Local Strain Based Fatigue-Life Relationship*

You can cycle a smooth test specimen between fixed strain limits until it develops a crack. If you cycle several such specimens between various elastic strain limits, you can plot the resulting number of cycles to crack against elastic strain amplitude. If you plot them on a log-log axes, then the points approximate to a straight line. Basquin first proposed this relationship.

Manson and Coffin later proposed that a similar relationship exists between the plastic strain amplitude and number of cycles to failure.

The total strain-life relationship can therefore be defined as:

Two methods of defining these strain-based material constants are provided within the Fatigue Wizard.

The parameters are entered directly to the Fatigue Wizard to define the strain-based fatigue life relationship.

The Fatigue Wizard approximates the parameters based on your input for the material tensile strength and the type of material (steel or other). Seeger's method is used to calculate appropriate material constants, and details are available in standard texts. This technique is an approximation. Use it only in the absence of actual test data.

The Seeger technique approximates the strain life curve (strain based coefficients) using the following formulae:

- K' = 1.65 * UTS
- n' = 0.15
- Sf = 1.5 * UTS
- b= -0.087
- c= -0.58
- Ef = 0.59 (if UTS/E<0.003)
- Ef = 0.59*(1.375-125*UTS/E)

- K' = 1.61 * UTS
- n' = 0.11
- Sf = 1.67 * UTS
- b= -0.095
- c= -0.69
- Ef = 0.535

Several methods of accounting for the effect of mean stress in the cycle are proposed for the local strain-based fatigue-life relationship. The Fatigue Wizard utilizes two methods; the Morrow correction and the Smith-Watson-Topper correction.

The elastic part of the strain-life relationship is corrected by subtracting the cycle mean stress. This correction is based on the observation that the effect of mean stress is greater at long lives.

*Smith-Watson-Topper Correction*

Smith Watson and Topper suggest that fatigue life is a function of the product of the strain amplitude and maximum stress in the cycle. This factor leads to a strain-life relationship of the following form: