Failure time in heterogeneous systems

We show that the failure time τ_{f} in the 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 model. In the mean-field limit, the distribution of τ_{f} is log-normal. In this limit, the average failure time shows the variation τ_{f}∼L^{α(δ)}, where L is the system size. The exponent α has a constant value above a critical disorder δ_{c} (=1/6), while it is an increasing function of δ in the region δ