Size scaling of failure strength with fat-tailed disorder in a fiber bundle model

TL;DR

This paper explores how the failure strength of heterogeneous materials modeled by fiber bundles scales with size when the microscopic disorder follows a fat-tailed distribution, revealing a non-traditional size effect.

Contribution

It introduces a fiber bundle model with power law distributed fiber strengths and analytically and numerically uncovers a unique size-dependent failure strength behavior.

Findings

Small systems show increasing strength with size.

A characteristic size marks the transition to usual decreasing strength.

A scaling law describes strength dependence on disorder parameters.

Abstract

We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the limit of equal load sharing an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect of heterogeneous materials is only restored beyond a characteristic size. We show analytically that the extreme order statistics of fibers' strength is responsible for this peculiar behavior. Analyzing the results of computer simulations we deduce a scaling form which describes the dependence of the macroscopic strength of fiber bundles on the parameters of microscopic disorder over the entire range of system sizes.