Role of crystal lattice structure in predicting fracture toughness

TL;DR

This paper investigates how the atomic lattice structure influences the fracture toughness of brittle crystals, revealing that traditional models do not account for lattice geometry effects and proposing a new predictive approach based on atomistic parameters.

Contribution

It introduces a novel analytical and numerical framework linking lattice geometry to fracture toughness, extending predictive capabilities to materials like graphene.

Findings

Fracture toughness depends on lattice geometry, not just surface energy.

A new asymptotic form of the displacement field predicts toughness from atomistic parameters.

Application demonstrated for graphene, showing practical relevance.

Abstract

We examine the atomistic scale dependence of material's resistance-to-failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a way incompatible with Griffith's relationship between fracture and free surface energy. Its value finds its origin in the matching between the continuum displacement field at the engineering scale, and the discrete nature of solids at the atomic scale. The generic asymptotic form taken by this field near the crack tip provides a solution for this matching, and subsequently a way to predict toughness from the atomistic parameters with application to graphene.