Fracture size effects from disordered lattice models

TL;DR

This paper investigates how the size of disordered lattice samples influences fracture strength, identifying a crossover between disorder-driven and stress-concentration regimes through numerical simulations.

Contribution

It introduces a scaling law describing the crossover between disorder-induced and fracture mechanics regimes, incorporating the fracture process zone in lattice models.

Findings

Identifies a crossover governed by a scaling law.

Quantifies the fracture process zone development.

Shows similar results across different lattice models.

Abstract

We study size effects in the fracture strength of notched disordered samples using numerical simulations of lattice models for fracture. In particular, we consider the random fuse model, the random spring model and the random beam model, which all give similar results. These allow us to establish and understand the crossover between a regime controlled by disorder-induced statistical effects and a stress-concentration controlled regime ruled by fracture mechanics. The crossover is described by a scaling law that accounts for the presence of fracture process zone which we quantify by averaging over several disordered configurations of the model. The models allow to study the development of the fracture process zone as the load is increased and to express this in terms of crack resistance (R-curve).