Failure process of fiber bundles with random misalignment

TL;DR

This paper analyzes how structural disorder from random fiber misalignment influences the failure process of fiber bundles, revealing a transition from brittle to quasi-brittle failure modes and characterizing avalanche size distributions.

Contribution

It introduces an analytical and simulation-based study of failure in fiber bundles with misalignment disorder, identifying a transition in failure behavior and avalanche statistics.

Findings

Transition from brittle to quasi-brittle failure with increasing disorder

Avalanche size distribution follows a power law with exponents 3/2 and 5/2

Analytical mapping to aligned fiber bundles with strength disorder

Abstract

We investigate the failure process of fiber bundles with structural disorder represented by the random misalignment of fibers. The strength of fibers is assumed to be constant so that misalignment is the only source of disorder, which results in a heterogeneous load distribution over fibers. We show by analytical calculations and computer simulations that increasing the amount of structural disorder a transition occurs from a perfectly brittle behaviour with abrupt global failure to a quasi-brittle phase where failure is preceded by breaking avalanches. The size distribution of avalanches follows a power law functional form with a complex dependence of the exponent on the amount of disorder. In the vicinity of the critical point the avalanche exponent is 3/2, however, with increasing disorder a crossover emerges to a higher exponent 5/2. We show analytically that the mechanical behaviour of the bundle of misaligned fiber with no strength disorder can be mapped to an equal load sharing fiber bundle of perfectly aligned fibers with properly selected strength disorder.