Stochastic modelling and prediction of fatigue crack propagation using piecewise-deterministic Markov processes

Abstract : Fatigue crack propagation is a stochastic phenomenon due to the inherent uncertainties originating from material properties, environmental conditions and loads. Stochastic processes offer an appropriate framework for modelling and predicting crack propagation. In this work, we propose to model and to predict the fatigue crack growth with Piecewise Deterministic Markov Processes (PDMP) associated with deterministic crack laws. First, we propose a regime-switching model with one jump to express the transition between Paris' regime and rapid crack propagation which occurs before failure. Parameters are adjusted from real data available in the literature. For this, we have to capture the change of regime of the observed failure trough an optimisation algorithm. The second purpose of this investigation is to predict the fatigue crack path and its variability based on the global model and knowledge of some informations retrieved at the beginning of crack propagation. We show that our method based on PDMP 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 cheaper in terms of computing time.