The proper treatment of the planar traction-free surfaces which typically bounded a computational box in 3-dimensional dislocation dynamics was considered. The present work presented an alternative to the use of the finite-element method for this purpose. In order to annul the tractions which were produced by a sub-surface dislocation segment on a finite-area free surface, S, the combination of an image dislocation segment and a distribution of N prismatic rectangular Volterra dislocation loops which meshed with S was used. The image dislocation segment, with a proper selection of the sign of the Burgers vector components, annulled the shear stresses. The normal stress component was annulled discretely at N collocation points which represented the centers of the loops. The unknown quantities in the problem were the magnitudes of the N Burgers vectors for the loops. When these were determined, it was possible to deduce the Peach-Koehler force which acted upon the sub-surface segment and represented the effect of the free surface. The accuracy of the method improved as the loops were continuously decreased in size.

The Treatment of Traction-Free Boundary Condition in Three-Dimensional Dislocation Dynamics using Generalized Image Stress Analysis. T.A.Khraishi, H.M.Zbib, T.Diaz de la Rubia: Materials Science and Engineering A, 2001, 309-310, 283-7