Bicrystals with Strain Gradient Effects

Abstract

ABSTRACTThe boundary between two perfectly bonded single crystals plays a very important role in determining the deformation of the bicrystal. This work addresses the role of the grain boundary by considering the elevated hardening of a slip system due to a slip gradient. The slip gradients are associated with geometrically necessary dislocations and their effects become pronounced when a representative length scale of the deformation field is comparable to the dominant microstructural length scale of a material. A new rate-dependent crystal plasticity theory is presented and has been implemented within the finite element method framework. A planar bicrystal under uniform in-plane loading is studied using the new crystal theory. The strain is found to be continuous but non-uniform within a boundary layer around the interface. The lattice rotation is also non-uniform within the boundary layer. The width of the layer is determined by the misorientation of the grains, the hardening behavior of slip systems, and most importantly by the characteristic material length scales. The overall yield strength of the bicrystal is also obtained. A significant grain-size dependence of the yield strength, the Hall-Petch effect, is predicted.