Non-Linear Damage Evolution and Failure in Materials

Abstract

Damage evolution and time-to-failure are investigated for a model material in which damage formation is a stochastic event. Specifically, the probability of failure at any site i at time t is ∝ σ_i(t)^η where σ_i(t) is the local stress at site i at time t, and differs from the applied stress because of the stress redistribution from prior damage. Numerical simulations in 2-dimensional systems demonstrate interesting and non-linear behavior. Of particular interest is η≥3, for which failure occurs by rapid damage growth after a “nucleation” period during which a large damage cluster develops to the critical size. An analytic model of the damage process predicts this “avalanche” failure, as well as (i) more abrupt failure with increasing η, (ii) failure times scaling inversely with system size, and (iii) broadening of the distribution of failure times, so that the failure becomes less predictable. These features are all observed in the simulations. The model also predicts the onset time for the rapid growth, offering the possibility of early detection of impending failure.