A Non-Local Formulation of the Peierls Dislocation Model

TL;DR

This paper introduces a non-local Peierls-Nabarro model derived from atomistic data, improving the accuracy of dislocation energetics while maintaining core structure predictions.

Contribution

It develops a non-local formulation of the Peierls-Nabarro model based on atomistic calculations, enhancing defect energy predictions.

Findings

Non-local model aligns better with atomistic energetics.

Core structure remains similar to local models.

Significant improvements in dislocation energy descriptions.

Abstract

Cohesive zone models provide an illuminating and tractable way to include constitutive nonlinearity into continuum models of defects. Powerful insights have been gained by studying both dislocations and cracks using such analyses. Recent work has shown that as a result of the locality assumption present in such cohesive zone models, significant errors can be made in the treatment of defect energies. This paper aims to construct a non-local version of the Peierls-Nabarro model in which the atomic level stresses induced at the slip plane depend in a non-local way on the slip degrees of freedom. The non-local interplanar kernel is computed directly from atomistics and is used to evaluate both the structure and energetics of planar dislocations. The non-local formulation does not significantly change the dislocation core structure from that obtained with the local model, but the new formulation leads to significant improvements in the description of dislocation energetics for dislocations with planar cores.