Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure

TL;DR

This paper investigates the avalanche size distribution in fiber bundles and fuse models, revealing a crossover in power-law behavior that signals imminent failure, with implications for predicting catastrophic breakdowns.

Contribution

It identifies a crossover in avalanche size distribution power laws as a signature of imminent failure in fiber bundles and fuse models, providing conditions for this behavior.

Findings

Crossover from Delta^(-3/2) to Delta^(-5/2) in avalanche distributions.

Crossover signals imminent catastrophic failure.

Applicable to fiber bundle and fuse models.

Abstract

Bundles of many fibers, with statistically distributed thresholds for breakdown of individual fibers and where the load carried by a bursting fiber is equally distributed among the surviving members, are considered. During the breakdown process, avalanches consisting of simultaneous rupture of several fibers occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. We show that there is, for certain threshold distributions, a crossover behavior of D(Delta) between two power laws D(Delta) proportional to Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic behavior, and we give the condition for which the D(Delta) proportional to Delta^(-3/2) behavior is seen. This crossover is a signal of imminent catastrophic failure in the fiber bundle. We find the same crossover behavior in the fuse model.