A numerical method was used to solve the interaction force between a dislocation line and a 3-dimensional particle: spherical or cubic. The numerical method involved the decomposition of an elastic composite containing dislocations. The numerical method was validated in the 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 cubic particle with a habit plane of {111} induced much smaller forces than did a spherical particle.

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