Failure avalanches in fiber bundles for discrete load increase

TL;DR

This paper investigates how the size distribution of failure bursts in fiber bundles changes with different load application methods, revealing a shift in power-law exponents depending on whether load is increased continuously or discretely.

Contribution

It provides an analytical framework showing the dependence of avalanche size distribution exponents on load application mode in fiber bundle failure models.

Findings

Power-law exponent is 5/2 for continuous load increase.

Exponent shifts to 3 when load is increased in discrete steps.

The analysis applies to general fiber threshold distributions.

Abstract

The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-\xi}$, for large avalanches. The exponent $\xi$ depends upon how the avalanches are provoked. While it is known that when the load on the bundle is increased in a continuous manner, the exponent takes the value $\xi=5/2$, we show that when the external load is increased in discrete and not too small steps, the exponent value $\xi=3$ is relevant. Our analytic treatment applies to bundles with a general probability distribution of the breakdown thresholds for the individual fibers. The pre-asymptotic size distribution of avalanches is also considered.