A Stochastic Model for Slow Crack Growth in Brittle Materials

Abstract

In the last decade, progress in brittle material technology (CC-composites, ceramics, ceramic composites, etc) made these so attractive for structural applications that one has to put up with their tendency to fail unpredictably, provided that one can predict with confidence probabilities of failure. The present paper addresses prediction of life-time scatter for brittle materials. In the paper, we model a commonly observed mode of slow crack growth in brittle materials, namely a Markovian stochastic pattern of a microscopic random jump, followed by a random waiting time, followed by a random jump, and so on. The waiting times are related, on physical grounds, to random energy barriers at the arrest points, whereas random magnitudes of the jumps are treated within the existing framework of Crack Diffusion Theory. This leads to a description of crack growth as a random process whose transition probability density satisfies a hyperbolic PDE. Relation to probabilistic life-time prediction is discussed and a simple illustrative example considered.