The de-pinning transition which occurred in dislocation assemblies was investigated. Particular consideration was given to the cases of regularly spaced pile-ups and low-angle grain boundaries which interacted with a disordered stress landscape that was provided by solute atoms; or by other immobile dislocations that were present in non-active slip systems. By using linear elasticity theory, calculations were made of the stress which was produced by small deformations of these assemblies and of the corresponding energy cost in 2 and 3 dimensions. Contrary to the case of isolated dislocation lines, which were usually approximated as elastic strings with an effective line-tension, the deformation of a dislocation assembly could not be described by local elastic interactions with a constant tension or stiffness. A non-local elastic kernel resulted as a consequence of long-range interactions between dislocations. In view of this result, statistical de-pinning theories of dislocation assemblies were revised, and the theoretical results were compared with numerical simulations and experimental data.

Depinning Transition of Dislocation Assemblies – Pile-Ups and Low-Angle Grain Boundaries. P.Moretti, M.C.Miguel, M.Zaiser, S.Zapperi: Physical Review B, 2004, 69[21], 214103 (11pp)