A numerical method was used to solve the interaction force between a dislocation line and a 3-dimensional particle, e.g. a spherical and a cubical particle. The numerical method used involved the decomposition of an elastic composite containing dislocations. The numerical method was validated in a cylindrical case by comparing the numerical solutions with known analytical solutions. The image (interaction) force profiles which were solved for a rigid and a void spherical particle showed that the area of significant image forces was more confined as compared with the corresponding cylindrical particle, and that the profiles were well represented by x-β. The image forces along the climb direction of an edge dislocation were also computed, and it was found that a cubical particle with a habit plane of {111} induced much smaller forces than did a spherical particle. The computed results were compared with the analytical solutions obtained from the same configuration.

Three-Dimensional Computation of the Interaction between a Straight Dislocation Line and a Particle. C.Shin, M.Fivel, W.W.Kim: Modelling and Simulation in Materials Science and Engineering, 2005, 13[7], 1163-73