Failure avalanches in fiber bundles for discrete load increase

Abstract

The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-ξ}$, for large avalanches. The exponent $ξ$ 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 $ξ=5/2$, we show that when the external load is increased in discrete and not too small steps, the exponent value $ξ=3$ 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.