Critical behaviour of random fibers with mixed Weibull distribution

TL;DR

This paper investigates the critical failure behavior of a fiber bundle model with mixed Weibull distributions under global load sharing, revealing how mixing influences critical stress while preserving universal avalanche statistics.

Contribution

It introduces a mixed Weibull fiber bundle model and analyzes how the mixture affects critical stress and avalanche behavior under quasistatic loading.

Findings

Critical stress varies with mixing parameter, linearly in a special case.

Critical exponents and burst avalanche distributions remain unchanged by mixing.

Mixing tunes the bundle's failure threshold without altering universality classes.

Abstract

A random fiber bundle model with a mixed Weibull distribution is studied under the Global Load Sharing (GLS) scheme. The mixed model consists of two sets of fibers. The threshold strength of one set of fibers are randomly chosen from a Weibull distribution with a particular Weibull index, and another set of fibers with a different index. The mixing tunes the critical stress of the bundle and the variation of critical stress with the amount of mixing is determined using a probabilistic method where the external load is increased quasistatically. In a special case which we illustrate, the critical stress is found to vary linearly with the mixing parameter. The critical exponents and power law behaviour of burst avalanche size distribution is found to remain unaltered due to mixing.