The influence of surface corrections on 3-dimensional dislocation dynamics was investigated by considering a curved dislocation which intersected a plane free surface. The Boussinesq–Cerruti formalism was used to determine the image field for this problem. An heuristic method for simultaneously regularizing the self-interaction and the image-field singularity permitted curvature and image effects to compete dynamically. A comparison of this implementation with analytical predictions for the critical strain in a strained layer with a free surface yielded excellent agreement. It was found that, while the image corrections determined the angle at which the dislocation entered the boundary, their overall effect upon a curved dislocation was surprisingly small; varying from a few % for a 1µm half-loop at the surface, to at most 40% for a half-loop with a radius as small as 1nm. It was concluded that for many dislocation problems, especially those involving just a few dislocations within a confined geometry, it was a meaningful first approximation to neglect completely the long-range image effects. The errors became large only at scales which were comparable to the Burgers vector. One way of using this approximation in the case of a free surface was to estimate an image force by using a formula given by Lothe, and to apply it only to the surface intercept point.

Modelling of Dislocations Intersecting a Free Surface. X.H.Liu, K.W.Schwarz: Modelling and Simulation in Materials Science and Engineering., 2005, 13[8], 1233-47