A New Probabilistic Model for Random Fatigue Crack Growth Based upon a Random Field
Hiroaki TANAKA
Abstract:A new probabilistic model describing the random fatigue crack growth is proposed based upon a spatially random differential equation driven by a random field. First, a basic equation to describe the random crack growth is formulated as a system of spatially random differential equations by modeling the random propagation resistance in the well-known Paris law as a homogeneous random field. The probability of failure against the fatigue crack growth is then formulated as a functional integral form by the use of its solution. Next, validity of the proposed model is quantitatively verified by comparing with statistical experimental data reported by Ichikawa et al. Next, an importance sampling simulation scheme is constructed by the use of the Girsanov theorem to make an efficient estimation for the probability of failure. A numerical example is finally given, which shows that the proposed simulation scheme can give accurate estimations for extremely small probability of failure. Key Words:Fatigue crack growth, Random crack growth, Probabilistic model, Random field, Random differential equation, Monte Carlo simulation, Importance sampling method