Modeling crack propagation in heterogeneous materials: Griffith's law, intrinsic crack resistance and avalanches

TL;DR

This paper investigates how initial cracks influence fracture behavior in heterogeneous materials using a fiber bundle model, revealing three regimes of crack growth and the impact of heterogeneity on critical stress and crack size.

Contribution

It introduces a detailed analysis of crack dynamics in a fiber bundle model, highlighting the dependence of fracture regimes on heterogeneity and stress relaxation.

Findings

Three distinct fracture regimes depending on initial crack size

Critical stress varies with crack size following a power-law

Heterogeneity strength influences crack growth and critical parameters

Abstract

Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in heterogeneous materials, known as the fiber bundle model. We find three distinct regimes for fracture dynamics depending on the initial crack size. If the initial crack is smaller than a certain value, it does not affect the rupture dynamics and the critical stress. While for a larger initial crack, the growth of the crack leads to a breakdown of the entire system, and the critical stress depends on the crack size in a power-law manner with a nontrivial exponent. The exponent, as well as the limiting crack size, depend on the strength of heterogeneity and the range of stress relaxation in the system.