Phase transitions and correlations in fracture processes where disorder and stress compete

TL;DR

This paper investigates how disorder and stress influence fracture processes using a fiber bundle model, revealing a phase transition between localized and non-localized states with distinct critical behaviors.

Contribution

It introduces a disorder distribution with an adjustable parameter, identifies a phase transition, and characterizes the critical exponents and correlations in the localized phase.

Findings

The model exhibits a localization transition controlled by disorder.

Critical exponents near the second order transition resemble percolation.

Correlation functions follow power laws similar to invasion percolation.

Abstract

We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.