Criticality in Fiber Bundle Model

Abstract

We report a novel critical behavior in the breakdown of an equal load sharing fiber bundle model at a dispersion $δ_c$ of the breaking threshold of the fibers. For $δ< δ_c$, there is a finite probability $P_b$, that rupturing of the weakest fiber leads to the failure of the entire system. For $δ\geq δ_c$, $P_b = 0$. At $δ_c, P_b \sim L^{-η}$, with $η\approx 1/3$, where $L$ is the size of the system. As $δ\rightarrow δ_c$, the relaxation time $τ$ diverges obeying the finite size scaling law: $τ\sim L^β(|δ-δ_c| L^α)$ with $α, β= 0.33 \pm 0.05$. At $δ_c$, the system fails, at the critical load, in avalanches (of rupturing fibers) of all sizes $s$ following the distribution $P(s) \sim s^{-κ}$, with $κ= 0.50 \pm 0.01$. We relate this critical behavior to brittle to quasi-brittle transition.

4 pages, 5 figures