Damage Growth in Random Fuse Networks

TL;DR

This paper investigates how microfractures grow and correlate in random fuse networks, revealing a transition towards mean-field-like fracture behavior as the system approaches failure, with implications for understanding damage localization.

Contribution

It provides new insights into the correlation lengthscale of microfracture growth and demonstrates the asymptotic mean-field nature of fracture in large systems.

Findings

Microfracture correlations are uncorrelated above a growing lengthscale.

Damage profile becomes statistically constant except at the final crack.

The process approaches mean-field-like behavior with increasing sample size.

Abstract

The correlations among elements that break in random fuse network fracture are studied, for disorder strong enough to allow for volume damage before final failure. The growth of microfractures is found to be uncorrelated above a lengthscale, that increases as the the final breakdown is approached. Since the fuse network strength decreases with sample size, asymptotically the process resembles more and more mean-field-like (``democratic fiber bundle'') fracture. This is found from the microscopic dynamics of avalanches or microfractures, from a study of damage localization via entropy, and from the final damage profile. In particular, the last one is statistically constant, except exactly at the final crack zone (in contrast to recent results by Hansen et al., Phys. Rev. Lett. 90, 045504 (2003)), in spite of the fact that the fracture surfaces are self-affine.