The displacement field of a rectangular Volterra dislocation loop

Abstract

The displacement field of a rectangular Volterra dislocation loop having three non-zero Burgers vector components is obtained in an analytical closed form. The solution is obtained via integrating the Burgers equation for the displacement field of any closed dislocation curve and is expressed in a relatively compact form. The current solution has utility in a number of problems including dislocation-particle interaction problems, where the boundary condition involved imposes certain restrictions on the displacements in the medium, and modelling of cracks of arbitrary shapes. The solution is also useful in benchmarking newly emerging dislocation dynamics codes which discretize a curved dislocation line in some form or another. Several verification steps of the solution correctness are made including a comparison with the displacement and stress fields of a circular Volterra dislocation loop of equal Burgers vector and comparable size.