The dynamic interaction between dislocations moving on parallel slip planes was considered. It was shown that the average interaction stress could be expressed in terms of second-order gradients of the mobile dislocation density, and the logarithm of the dislocation velocity. The derivation could be used as a basis for the justification of the newly popular gradient-dependent plasticity models. It could also be seen as providing further insights into earlier models of gradient dislocation dynamics. The implications of the derived gradient terms for the spatial organization and propagation of slip, after yielding, were considered.

On the Dynamic Interaction between Moving Dislocations. M.Zaiser, E.C.Aifantis: Applied Physics A, 1998, 66[4], 393-7