Failure time in heterogeneous systems

Abstract

We show that the failure time $τ_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $δ$ and the stress release range $R$ in the system. For $R$ beyond a critical value $R_c$ the distribution of $τ_f$ follows Weibull form. In this region, the average $τ_f$ shows the variation $τ_f \sim L^α$ where $L$ is the system size. For $R<R_c$, $τ_f\sim L/R$. We find that the crossover length scale has the scaling form $R_c \sim L^{1-α}$. This scaling has been found to be valid for various disorder distributions. For $δ<δ_c$, $α$ is an increasing function of $δ$. For all $δ\ge δ_c$, $α$=1/3.