Recent advances in 3-dimensional dislocation dynamics included the treatment of free surfaces. Dislocation interaction and slip were treated as a boundary-value problem for which a zero-traction condition was enforced at the external surfaces of the simulation box. A new rigorous method was presented here for such treatments. The method was semi-analytical cum numerical in nature, in that a zero traction condition was enforced at select collocation points on a surface. The accuracy could be improved by increasing the number of collocation points. In this method, the image stress-field of a sub-surface dislocation segment near to a free surface was obtained by an image segment and by a distribution of prismatic rectangular dislocation loops padding the surface. The loop centers were chosen to be the collocation points of the problem. The image segment, with properly selected Burgers-vector components, annulled unwanted shear stresses at the surface. The distributed loops annulled the unwanted normal stress component at the collocation points and, in doing so, created no undesirable shear stresses.

Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modelling. T.A.Khraishi, H.M.Zbib: Journal of Engineering Materials and Technology, 2002, 124[3], 342-51