Depinning of a discrete elastic string from a two dimensional random array of weak pinning points

TL;DR

This paper develops a statistical theory for the force needed to move an elastic string through a 2D lattice with randomly distributed obstacles, matching simulations and theory for various obstacle densities and lattice shapes.

Contribution

It provides an analytical framework for understanding dislocation glide in solid solutions with weak obstacles, validated by numerical simulations across different conditions.

Findings

Strong agreement between theory and simulations for obstacle densities 1-50%

Theory effective when obstacle-string interaction is weak

Applicable to various lattice aspect ratios

Abstract

The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a problem, we compute analytically the external force required to drag an elastic string along a discrete two-dimensional square lattice, where some obstacles have been randomly distributed. The corresponding numerical simulations allow us to demonstrate a remarkable agreement between simulations and theory for an obstacle density ranging from 1 to 50 % and for lattices with different aspect ratios. The theory proves efficient on the condition that the obstacle-chain interaction remains sufficiently weak compared to the string stiffness.