Interaction between a Dislocation and an Assembly of Dislocation Arrays

Abstract

The force exerted upon a lone dislocation by an assembly of dislocation arrays is discussed in the continuum approximation. The arrays are parallel and in equilibrium with a constant applied stress, but no further restrictions are imposed. For both edge and screw dislocation arrays, the force parallel to the glide planes can exhibit absolute maxima and minima only at the glide planes, and the sign of the force throughout the medium is governed by the distribution functions evaluated at the glide plane ends. Some numerical results in agreement with the analysis are given for screw dislocations upon two parallel glide planes; a ``shadow effect'' is also demonstrated for this case. The analysis is also valid for the interaction between a dislocation and an assembly of parallel cracks.