Role of disorder in the size-scaling of material strength

TL;DR

This paper investigates how disorder influences the size-dependent strength of materials, revealing a crossover between disorder-driven fluctuations and stress concentration effects through numerical simulations and scaling laws.

Contribution

It introduces a new scaling law for material strength that accounts for disorder and stress concentrations, validated by simulations and experimental data.

Findings

Identifies a crossover in strength behavior due to disorder and stress concentration

Develops a scaling law involving a statistical fracture process zone

Matches simulation results with experimental data from paper samples

Abstract

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.