The probability distribution of internal stresses in externally loaded 2D dislocation systems

TL;DR

This paper investigates the distribution of internal shear stresses in 2D dislocation systems under external load, combining analytical calculations and simulations to understand stress behavior and the influence of dislocation multipoles.

Contribution

It extends previous work by analytically and numerically analyzing how external shear stress affects internal stress distributions in 2D dislocation systems, including the role of dislocation multipoles.

Findings

Analytical stress distribution matches numerical simulations.

Dislocation multipoles significantly influence stress distributions in relaxed configurations.

Theoretical framework applies despite complexities introduced by multipoles.

Abstract

The distribution of internal shear stresses in a 2D dislocation system is investigated when external shear stress is applied. This problem serves as a natural continuation of the previous work of Csikor and Groma (Csikor F F and Groma I 2004 Phys. Rev. B 58 2969), where analytical result was given for the stress distribution function at zero applied stress. First, the internal stress distribution generated by a set of randomly positioned ideal dislocation dipoles is studied. Analytical calculations are carried out for this case. The theoretical predictions are checked by numerical simulations showing perfect agreement. It is found that for real relaxed dislocation configurations the role of dislocation multipoles cannot be neglected, but the theory presented can still be applied.