Peach-Koehler forces within the theory of nonlocal elasticity

TL;DR

This paper applies Eringen's nonlocal elasticity theory to dislocations, deriving nonlocal Peach-Koehler forces that eliminate classical singularities and reveal force extrema near dislocation lines.

Contribution

It introduces a nonlocal elasticity framework for calculating dislocation forces, removing singularities present in classical models.

Findings

Nonlocal stresses for screw and edge dislocations are derived.

Classical singularities in Peach-Koehler forces are eliminated.

Force extrema are identified near dislocation lines.

Abstract

We consider dislocations in the framework of Eringen's nonlocal elasticity. The fundamental field equations of nonlocal elasticity are presented. Using these equations, the nonlocal force stresses of a straight screw and a straight edge dislocation are given. By the help of these nonlocal stresses, we are able to calculate the interaction forces between dislocations (Peach-Koehler forces). All classical singularities of the Peach-Koehler forces are eliminated. The extremum values of the forces are found near the dislocation line.