Wei, Z., Luo, L., Lin, S., Gao, L. et al., "Probabilistic Life and Damage Assessment of Components under Fatigue Loading," SAE Int. J. Commer. Veh. 8(2):355-363, 2015, doi:10.4271/2015-01-2759.
This study presents a probabilistic life (failure) and damage assessment approach for components under general fatigue loadings, including constant amplitude loading, step-stress loading, and variable amplitude loading. The approach consists of two parts: (1) an empirical probabilistic distribution obtained by fitting the fatigue failure data at various stress range levels, and (2) an inverse technique, which transforms the probabilistic life distribution to the probabilistic damage distribution at any applied cycle. With this approach, closed-form solutions of damage as function of the applied cycle can be obtained for constant amplitude loading. Under step-stress and variable amplitude loadings, the damage distribution at any cycle can be calculated based on the accumulative damage model in a cycle-by-cycle manner. For Gaussian-type random loading, a cycle-by-cycle equivalent, but a much simpler closed-form solution can be derived. Several case studies are provided to demonstrate the effectiveness of the approach.