Stochastic modelling and prediction of fatigue crack propagation using piecewise-deterministic Markov processes
Résumé
Fatigue crack propagation is a stochastic phenomenon due to the inherent uncertainties originating from material properties, environmental conditions and cyclic mechanical loads. Stochastic processes offer thus an appropriate framework for modelling and predicting crack propagation. In this paper, we propose to model and to predict the fatigue crack growth by a piecewise-deterministic Markov process associated with deterministic crack laws. First, we propose a regime-switching model to express the transition between Paris' regime and rapid propagation which occurs before failure. Both regimes of propagation are governed by a deterministic equation whose parameters are randomly selected in a finite state space. This one has been adjusted from real data available in the literature. The crack growth behaviour is well-captured and the transition between both regimes is well-estimated by a critical stress intensity factor range. The second purpose of our investigation deals with the prediction of the fatigue crack path and its variability based on measurements taken at the beginning of the propagation. We show that our method based on this class of stochastic models associated with an updating method provides a reliable prediction and can be an efficient tool for safety structures in a large variety of engineering applications. In addition, the proposed strategy requires only few information to be effective and is not time-consuming.
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