Modelling the evolution of geometrically necessary boundaries at large plastic strains

Abstract

In polycrystals undergoing large plastic strains, the strain compatibility between adjacent misoriented areas is usually ensured by the activation of different slip system combinations leading to localised orientation gradients. The latter are accommodated by GNBs, or Geometrically Necessary Boundaries, of increasing misorientation. A new model is developed for the evolution of a GNB between two crystallites under multiple slip conditions. This model takes the crystal plasticity of each cell block into account (using a Taylor–Bishop–Hill approach) and leads to a dynamic accommodation of the boundary disorientation on the basis of dislocation arrays. In particular the optimal dislocation configuration of the GNBs is obtained by minimising the sub-boundary energy within the range of conditions imposed by the slip system kinematics. Applied to the case of plane strain compression of fcc crystals, the model shows that the GNB dislocation lattice is very sensitive to the initial grain orientations, stable texture components like Brass {110}〈112〉 or S {123}〈634〉 leading to the lowest dislocation densities. The strain path and the relative positions of the misorientation axis and boundary plane normal also have an influence on the final dislocation structure, albeit to a smaller extent.