Stochastic Models Related to Fatigue Damage of Materials

The stochastic models for the fatigue damage phenomena are proposed. They describe the uncertainty caused by inhomogeneity of materials for fatigue crack propagation of metals and fatigue damage of carbon fiber composite (CFRP). The models are given by the stochastic differential equations derived from the randomized Paris-Erdogan’s fatigue crack propagation law and Kachonov’s equation of fatigue damage. The sample paths and life distribution of fatigue crack propagation in metals or of damage accumulation in CFRP are obtained by using the solution of the stochastic differential equation and the probability density function, respectively. These theoretical results are compared with the actual experiments—fatigue crack propagation of high tensile strength steel APFH 60 and fatigue test for a carbon eight-harness-satin/epoxy laminate—through numerical experiments.