Local load sharing fiber bundles with a lower cutoff of strength disorder

TL;DR

This study investigates how a lower cutoff in fiber strength affects failure behavior in fiber bundles with varying load sharing ranges, revealing a critical cutoff where the bundle becomes perfectly brittle and burst size distributions follow a universal power law.

Contribution

It extends mean field models by analyzing the impact of a lower strength cutoff on failure modes across different load sharing interactions.

Findings

Existence of a critical cutoff strength leading to brittle failure.

Universal burst size distribution with a 3/2 power law exponent near the critical cutoff.

Failure behavior transitions from ductile to brittle at the critical cutoff.

Abstract

We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations revealed that at any range of load redistribution there exists a critical cutoff strength where the macroscopic response of the bundle becomes perfectly brittle, i.e. linearly elastic behavior is obtained up to global failure, which occurs catastrophically after the breaking of a small number of fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95, 125501 (2005)], we demonstrate that approaching the critical cutoff, the size distribution of bursts of breaking fibers shows a crossover to a universal power law form with an exponent 3/2 independent of the range of interaction.