Fluctuations in the stress field, which were introduced by a pair of infinite walls of uniform-randomly distributed dislocations that were coupled into dipoles, were considered. This type of disorder most realistically modelled the structures of dislocation arrays which formed in grain, cell or sub-grain boundaries during the plastic deformation of materials with an internal microstructure. It was found that, near to each wall, the fluctuations decayed as (x-h)-½, where x was the distance from a wall and h was equal to half of the inter-wall spacing. At distances, x, which were much larger than the separation of the walls, the stress fluctuations decreased as x-3/2. In the general case of the deformation of polycrystals, the slip lines were inclined with respect to the grain boundaries and the dislocations had both normal and tangential Burgers vector components. Hence, dislocations which constituted a dipole deviated with respect to each other. The present consideration could be extended to this general case, and it could be shown that the stress fluctuations diminished according to the same laws.

Stress Fields of Disordered Dislocation Arrays: a Double Wall Consisting of Dislocation Dipoles. A.A.Nazarov: Philosophical Magazine Letters, 1995, 72[1], 49-53