Fatigue

Definition

Let a specimen of a material be loaded cyclically, so that the stress at a point oscillates between $\sigma_{\min}$ and $\sigma_{\max}$. The stress amplitude is $\sigma_a = (\sigma_{\max} - \sigma_{\min})/2$ and the mean stress is $\sigma_m = (\sigma_{\max} + \sigma_{\min})/2$. Fatigue is the progressive and localized damage of the material under such loading, by crack initiation and crack growth. It leads to fracture after a finite number of cycles, even when $\sigma_{\max}$ is below the static tensile strength. The fatigue life $N_f(\sigma_a, \sigma_m)$ is the number of cycles to failure, and the graph of $N_f$ against $\sigma_a$ at fixed $\sigma_m$ is the S–N curve. The endurance limit, when it exists, is the amplitude below which $N_f = \infty$.