The effect of geometrically necessary dislocations on the flow stress of deformed crystals containing a heterogeneous dislocation distribution

Abstract

In deformed crystals, long-range internal stresses develop during deformation as a consequence of the heterogeneity of the distribution of the dislocations which frequently form a cell structure. The composite model describes these internal stresses in a natural manner in terms of the elastic/plastic strain mismatch between the hard cell walls and the soft cell interiors. This mismatch is closely related to a well-defined density of so-called interface dislocations at the hard–soft region interfaces. The interface dislocations are geometrically necessary dislocations in Ashby's terminology [M.F. Ashby, Phil. Mag. 21 (1970) 399]. According to the composite model, their main role is to provide the internal stresses, which are necessary for the simultaneous compatible deformation of hard and soft regions. The interface dislocations do not, in general, contribute to the flow stress. Hence, their density does not appear explicitly in the flow-stress equation. It is shown that this is strictly true for single-slip deformation. In the case of multiple slip, a different situation prevails, since some of the interface dislocations of one glide system can act like forest dislocations for glide dislocations of another slip system. This situation is analyzed in more detail for a simple model cell structure. It is found that the interaction of the glide dislocations with the interfacial forest dislocations makes only a negligible contribution to the overall flow stress. This holds for both glide dislocations bowing into and for glide dislocations bowing out of the walls.