Long-range internal stresses in dislocation sub-grain structures were proposed to be a consequence of a plastic incompatibility that was caused by dislocations bowing out between sub-grain boundaries, which acted as obstacles to dislocation glide. A plane-strain model for incompatible plastic deformation was formulated by assuming that elliptically bowed dislocations existed on 2 slip systems. The internal stresses were calculated by using a numerical method which was based upon the fast Fourier transform. Considerable internal stresses arose, especially in sub-grain structures with sub-grain boundaries that were inclined with respect to the glide planes.

Internal Stresses in Dislocation Sub-Grain Structures. R.Sedlacek, W.Blum: Computational Materials Science, 1998, 13[1-3], 148-53