Crossover behavior in failure avalanches

TL;DR

This paper investigates the crossover in failure avalanche distributions in composite materials and fuse networks, revealing distinct power-law exponents near and away from catastrophic failure, which can signal imminent breakdown.

Contribution

It analytically demonstrates the crossover in avalanche size distribution exponents in fiber bundles and fuse networks, linking it to failure prediction.

Findings

Power-law exponent near breakdown: 3/2 for fiber bundles, 2 for fuse networks.

Power-law exponent away from breakdown: 5/2 for fiber bundles, 3 for fuse networks.

Crossover behavior signals imminent catastrophic failure.

Abstract

Composite materials, with statistically distributed threshold for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution $D(\Delta)$ of the magnitude $\Delta$ of such avalanches. The distribution is typically a power law $D(\Delta)\propto\Delta^{-\xi}$. For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent $\xi$ in the vicinity of complete breakdown and a larger exponent $\xi$ for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case $\xi=3/2$ near the breakdown point and $\xi=5/2$ away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find $\xi=2$ near the catastrophic failure and $\xi=3$ away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.