A screw dislocation in a functionally graded material using the translation gauge theory of dislocations

TL;DR

This paper develops an analytical gauge theory framework to model screw dislocations in functionally graded materials with exponentially varying properties, providing explicit expressions for dislocation fields and stresses.

Contribution

It introduces a novel analytical solution for screw dislocations in inhomogeneous media using gauge theory, accounting for material gradation and intrinsic length scales.

Findings

Explicit formulas for elastic distortions and stresses in graded media

Dislocation density and pseudomoment stresses depend on gradation moduli

Analytical solutions enhance understanding of dislocation behavior in complex materials

Abstract

The aim of this paper is to provide new results and insights for a screw dislocation in functionally graded media within the gauge theory of dislocations. We present the equations of motion for dislocations in inhomogeneous media. We specify the equations of motion for a screw dislocation in a functionally graded material. The material properties are assumed to vary exponentially along the x and y-directions. In the present work we give the analytical gauge field theoretic solution to the problem of a screw dislocation in inhomogeneous media. Using the dislocation gauge approach, rigorous analytical expressions for the elastic distortions, the force stresses, the dislocation density and the pseudomoment stresses are obtained depending on the moduli of gradation and an effective intrinsic length scale characteristic for the functionally graded material under consideration.