Section: New Results

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

Participants : Romain Azaïs, Anne Gégout-Petit.

Fatigue crack propagation is a stochastic phenomenon in nature due to the inherent uncertainties coming from material properties, environmental conditions and loads. Stochastic processes offer an appropriate framework for modelling crack propagation since it is intended to include sources variabilities. In this work, we propose to model crack propagation mechanism with Piecewise Deterministic Markov Process (PDMP) using usual random crack laws. Conventional laws proposed in the literature seem inadequate for describing the whole fatigue crack trajectory mainly when the crack extends in a rapid manner. To overcome this drawback, a new modelling is proposed that consists in using more than one law as each one is more suitable for a specific phase during crack propagation. Regime-switching models seem very attractive and with our modelling assessed crack growth rates and crack lengths are very close to experimental values. Moreover, behaviour just before failure is well captured and can be discussed. Empirical curves from literature are used to adjust the parameters associated to the proposed modelling. Statistical observations and numerical simulations show the efficiency of the proposed approach to model and to simulate fatigue crack growth. This work has been presented in an international congress [34] and is the object of a paper which will be submitted very soon.