Failure time in heterogeneous systems

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