Burst statistics as a criterion for imminent failure

Abstract

The distribution of the magnitudes of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded close to the point at which the system fails catastrophically, we find that the power law has an exponent which differs from the one characterizing the size distribution of all avalanches. We demonstrate this analytically for bundles of many fibers with statistically distributed breakdown thresholds for the individual fibers. In this case the magnitude distribution $D(\Delta )$ for the avalanche size $\Delta$ follows a power law ${\Delta }^{-\xi }$ with $\xi =3/2$ near complete failure, and $\xi =5/2$ elsewhere. We also study a network of electric fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere. We propose that this crossover in the size distribution may be used as a signal for imminent system failure.

10 pages, 10 figures To appear in proceedings from "Symposium on Scaling in Solid Mechanics" Cardiff, 2007