Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

TL;DR

This study examines how a lower cutoff in fiber threshold distribution influences failure behavior in fiber bundle models, revealing modifications in critical strength, avalanche dynamics, and size effects.

Contribution

It provides analytical insights into the impact of lower cutoff thresholds on failure properties in both equal load sharing and local load sharing fiber bundle models.

Findings

Critical strength bounded by an upper limit due to lower cutoff

Avalanche size distribution deviates from mean-field power law

Failure threshold and avalanche statistics depend on lower cutoff level

Abstract

Presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility both in a equal load sharing (ELS) fiber bundle model and in local load sharing (LLS) one. We show analytically that in ELS model, the critical strength gets modified due to the presence of lower cutoff and it becomes bounded by an upper limit. Although the dynamic exponents for the susceptibility and relaxation time remain unchanged, the avalanche size distribution shows a permanent deviation from the mean-fiels power law. In the LLS model, we analytically estimate the upper limit of the lower cutoff above which the bundle fails at one instant. Also the system size variation of bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.