Dislocations intersecting free surfaces presented a challenge for numerical implementation of traction-free boundary conditions in dislocation dynamics simulations. The difficulty arose when singular analytic expressions of dislocation stress fields need to be used in combination with numerical methods to calculate image stress fields due to the free surfaces. A new hybrid method was developed here in which the singular and non-singular parts of the image stress were dealt with separately. The analytic solution for a semi-infinite straight dislocation intersecting the surface of elastic half-space was used to account for the singular part of the image stress, while the remaining non-singular part was treated using the standard finite element method. The numerical advantages of this decomposition were demonstrated with examples.

A Hybrid Method for Computing Forces on Curved Dislocations Intersecting Free Surfaces in Three-Dimensional Dislocation Dynamics. M.Tang, W.Cai, G.Xu, V.V.Bulatov: Modelling and Simulation in Materials Science and Engineering, 2006, 14[7], 1139-51