Failure Time In Heterogeneous Systems

We show that the failure time tau(f) in the fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder d and the stress release range R in the model. In the mean-field limit, the distribution of tau(f) is log-normal. In this limit, the average failure time shows the variation tau(f) similar to L-alpha(delta), where L is the system size. The exponent a has a constant value above a critical disorder delta(c) (= 1/6), while it is an increasing function of d in the region delta < delta(c). On the other hand, in the limit where the local stress concentration plays a crucial role, we observe the scaling t(f) similar to L-alpha(delta) similar to Phi R/L1-alpha(delta)), where R is the stress release range. We find that the crossover length scale Rc, between the above two limiting cases, scales as R-c similar to L-1-alpha(delta).