Scaling in the time-dependent failure of a fiber bundle with local load sharing

TL;DR

This paper investigates the scaling laws governing time-dependent failure in a fiber bundle model with local load sharing, revealing universal and non-universal scaling behaviors near complete failure.

Contribution

It introduces a detailed analysis of the divergence of fiber breaking rate and the system size scaling of lifetime in a local load sharing fiber bundle model.

Findings

Breaking rate diverges as (T_f - t)^(-1) near failure

Lifetime scales with system size as N^(-δ)

Scaling exponent ξ is approximately 1.0 and universal

Abstract

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$ is the lifetime of the bundle, and $\xi \approx 1.0$ is a quite universal scaling exponent. The average lifetime of the bundle $<T_f>$ scales with the system size as $N^{-\delta}$, where $\delta$ depends on the distribution of individual fiber as well as the breakdown rule.