A numerical method for the treatment of image stresses in dislocation dynamics simulations

In this work a newly developed method for the treatment of dislocation image stresses resulting from the presence of nearby traction-free surfaces is presented. The method is particularly suited for three-dimensional dislocation dynamics simulations. In this method, a finite-area free surface is meshed into an N number of elements, each of which represents a generally prismatic dislocation loop (i.e. one whose Burgers vector is inclined to its normal). The unphysical tractions created at surface collocation points by sub-surface crystal dislocations are annulled by proper selection of the loops' Burgers vectors. The image stresses on a dislocation segment are simply then those resulting from surface loops.