Formulation of a Stochastic Fatigue Crack Growth Model and its Numberical Analysis.

Abstract

Fatigue crack growth is a major factor that must be considered in the design and life prediction of fatigue-critical structures, yet recent studies suggest that much of fatigue crack growth data exhibit a large amount of statistical variability and deterministic models do not adequately describe the crack propagation behavior. Thus, the need to use probabilistic methods to predict fatigue crack growth becomes evident. In this paper, focus is centered on the formulation of a stochastic fatigue crack growth model. With the use of the diffusion Markov process theory, a partial differential equation called the Fokker-Planck equation which satisfies the probability density of the random time to reach a given crack size is introduced. Then, the equation is numerically solved by the finite differential method, and the statistical properties of crack growth fatigue life are evaluated.