Abstract
A stochastic model for fatigue crack propagation is proposed in consideration of random propagation resistance. It is based on Paris-Erdogan's propagation law of fatigue crack. By adding Gaussian white noise to the propagation resistance, the propagation law is randomized. A stochastic differential equation of the Itô type is derived from the randomized Paris-Erdogan's law by a change of variable in the law, and Wong and Zakai's theorem. By using the solution of the stochastic differential equation and its probability density, a sample process and life distribution of fatigue crack propagation are obtained, respectively. These theoretical results are compared with the experimental data for high tensile strength steel APFH 60. Through the comparison, an improvement in the above model is made.
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