Noise induced rupture process: Phase boundary and scaling of waiting time distribution

TL;DR

This paper models fiber bundle rupture under stress and noise, revealing a phase boundary between continuous and intermittent fracture regimes, with avalanche and waiting time distributions showing power-law and Gamma scaling, respectively.

Contribution

It introduces a phase boundary in fiber bundle rupture models and characterizes the statistical properties of avalanches and waiting times.

Findings

Existence of a robust phase boundary between fracture regimes.

Waiting times follow a Gamma distribution.

Avalanche sizes exhibit power-law scaling.

Abstract

A bundle of fibers has been considered here as a model for composite materials, where breaking of the fibers occur due to a combined influence of applied load (stress) and external noise. Through numerical simulation and a mean-field calculation we show that there exists a robust phase boundary between continuous (no waiting time) and intermittent fracturing regimes. In the intermittent regime, throughout the entire rupture process avalanches of different sizes are produced and there is a waiting time between two consecutive avalanches. The statistics of waiting times follows a Gamma distribution and the avalanche distribution shows power law scaling, similar to what have been observed in case of earthquake events and bursts in fracture experiments. We propose a prediction scheme that can tell when the system is expected to reach the continuous fracturing point from the intermittent phase.