From nucleation to percolation: the effect of system size when disorder and stress localization compete

TL;DR

This paper explores how system size influences failure modes in a fiber bundle model with competing disorder and stress localization, revealing a phase diagram with nucleation, avalanche, and percolation failure regimes.

Contribution

It introduces a comprehensive phase diagram for a fiber bundle model considering system size, disorder, and stress relaxation, highlighting the transition between failure modes.

Findings

Failure mode depends on system size, disorder, and stress relaxation.

Nucleating failure dominates in the thermodynamic limit unless parameters favor mean-field behavior.

Complex phase diagram shows distinct failure regimes: nucleation, avalanche, and percolation.

Abstract

A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - (I) nucleation, (II) avalanche, and (III) percolation, depending on the spatial correlation observed during the failure process.