Goodman relation

In materials science and fracture mechanics, the Goodman relation is an equation used to quantify the effect of mean stress on the fatigue life of a material.

Mathematical description

The Goodman relation can be represented mathematically as:

:$sigma\_\; ext\{a\}\; =\; sigma\_\; ext\{fat\}\; imesleft(1-frac\{sigma\_\; ext\{m\{sigma\_\; ext\{ts\; ight).$

Where $sigma\_\; ext\{a\}$ is the applied stress, $sigma\_\; ext\{m\}$ is the mean stress, $sigma\_\; ext\{fat\}$ is the fatigue stress, and $sigma\_\; ext\{ts\}$ is the ultimate tensile stress of the material. The general trend given by the Goodman relation is one of decreasing fatigue life with increasing mean stress for a given level of applied stress. The relation can be plotted to determine the safe cyclic loading of a part; if the coordinate given by the mean stress and the applied stress lies under the curve given by the relation, then the part will survive. If the coordinate is above the curve, then the part will fail for the given stress parameters.

References

*Hertzberg, Richard W. Deformation and Fracture Mechanics and Engineering Materials. John Wiley and Sons, Hoboken, NJ: 1996.