The treatment of traction-free boundary condition in three-dimensional dislocation dynamics using generalized image stress analysis

Recent attention has been given to the proper treatment of the planar tract ion-free surfaces which typically bound a computational box in three-dimens ional dislocation dynamics. This paper presents an alternative to the use o f the finite-element method for this purpose. Here, to annul the tractions produced by a sub-surface dislocation segment on a finite-area free surface S, a combination of an image dislocation segment, and a distribution of N prismatic rectangular Volterra dislocation loops meshing S is utilized. The image dislocation segment, with the proper sign selection of the Burgers v ector components, annuls the shear stresses, and the normal stress componen t is annulled discretely at N collocation points representing the centers o f the loops. The unknowns in this problem are the magnitudes of the N Burge rs vectors for the loops. Once these are determined, one can back calculate the Peach-Koehler force acting on the sub-surface segment and representing the effect of the free surface. As expected, the accuracy of the method im proves as the loops continuously decrease in size. (C) 2001 Elsevier Scienc e B.V. All rights reserved.