Atomistic modelling of near-crack-tip plasticity

TL;DR

This paper develops an atomistic model for near-crack-tip plasticity on a lattice, incorporating a new geometric framework that accounts for crack surfaces and dislocations, establishing stable configurations without minimum separation constraints.

Contribution

It introduces a novel lattice manifold complex framework that fully incorporates crack surfaces and dislocations, providing a rigorous foundation for studying near-crack-tip plasticity.

Findings

Existence of stable equilibrium configurations with cracks and dislocations.

No minimum separation needed between dislocation cores and crack surfaces.

Framework sets the stage for further rigorous studies on crack-tip plasticity.

Abstract

An atomistic model of near-crack-tip plasticity on a square lattice under anti-plane shear kinematics is formulated and studied. The model is based upon a new geometric and functional framework of a lattice manifold complex, which ensures that the crack surface is fully taken into account, while preserving the crucial notion of duality. As a result, existence of locally stable equilibrium configurations containing both a crack opening and dislocations is established. Notably, with the boundary in the form of a crack surface accounted for, no minimum separation between a dislocation core and the crack surface or the crack tip is required. The work presented here constitutes a foundation for several further studies aiming to put the phenomenon of near-crack-tip plasticity on a rigorous footing.