The internal elastic stress fields which were associated with dislocation cells were studied by using 3-dimensional numerical simulations. Only static dislocation arrangements were considered, and they were treated as line defects that were embedded in an otherwise linear isotropic elastic medium. The dislocation lines were decomposed into piece-wise straight segments, and 2 types of 3-dimensional dislocation ensemble were investigated. The first arrangement represented a conventional sub-grain structure. It consisted of pure low-angle tilt and twist boundaries with alternating senses of misorientation. The second consisted of interface dislocations. The stress fields of both types of cell structure were calculated, with and without screw dislocations. The simulations confirmed that, in the first case (Kuhlmann-Wilsdorf), the contribution which arose from screw dislocations was negligible. In the second case (Mughrabi), the screw dislocations led to a 67% increase in the maximum shear stress in the cell interior. The total value of the maximum shear stress which arose from screw and edge dislocations, 3D, could be described here by the expression, 3D = 2D + 2D(1-), where 2D represented the contribution that was made by edge dislocations and 2D(1-) was the contribution that was made by screw dislocations. It was shown that the stress fields of 3-dimensional dislocation arrangements had to be calculated for cells which were embedded in larger translational 3-dimensional grids in order to provide sufficiently accurate boundary conditions.

D.Raabe: Philosophical Magazine A, 1996, 73[5], 1363-83