Self-energy of dislocations and dislocation pileups

TL;DR

This paper introduces a continuum model for dislocation pileups that incorporates self-energy, revealing a critical stress threshold and non-linear dislocation behavior, advancing understanding of dislocation interactions in materials.

Contribution

It presents an analytical solution for dislocation distribution considering self-energy, highlighting new non-linear effects and a critical stress threshold in pileup equilibrium.

Findings

Existence of a critical threshold stress for dislocation equilibrium.

Non-linear regime where dislocation number does not scale linearly with external stress.

Analytical solution describing dislocation distribution in equilibrium.

Abstract

A continuum model of dislocation pileups that takes the self-energy of dislocations into account is proposed. An analytical solution describing the distribution of dislocations in equilibrium is found from the energy minimization. Based on this solution we show (i) the existence of a critical threshold stress for the equilibrium of dislocations within a double pileup, and (ii) the existence of a non-linear regime in which the number of dislocations in a double pileup does not scale linearly with the resolved external shear stress, contrary to the classical double pileup model.