Discrete models of dislocations and their motion in cubic crystals

TL;DR

This paper introduces a discrete lattice model for dislocations in cubic crystals that aligns with linear anisotropic elasticity and enables simulation of static and dynamic dislocation behaviors, including crack propagation.

Contribution

The paper presents a novel discrete model incorporating crystal symmetry and a periodic function to simulate dislocation dynamics in cubic crystals.

Findings

Simulation of static and moving dislocations with realistic cores and profiles

Observation of dislocation loops and dipoles in numerical experiments

Crack initiation and propagation from dislocation dipoles

Abstract

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their cores and profiles. Dislocation loops and dipoles are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.