A distributed-dislocation method for treating free-surface image stresses in three-dimensional dislocation dynamics simulations

Abstract

This work reports on a recent advancement in three-dimensional dislocation dynamics modelling. A method is presented for the treatment of dislocation image stresses resulting from the presence of nearby traction-free surfaces. The image stress-field of a dislocation segment below a finite-sized free surface is obtained by the distribution of N generally prismatic rectangular or square dislocation loops padding the area (the external bounding surfaces of the simulation box). The unphysical tractions created at surface collocation points by sub-surface crystal dislocations are annulled by proper determination of the loops' Burgers vectors. The image stresses on a dislocation segment are simply those stresses resulting from the surface loops. The accuracy can be improved by increasing the number of collocation points (i.e. surface loop density).