Theory of grain boundary structure effects on mechanical behaviour

Described in this paper are elements of emerging theories for the mechanical behavior of polycrystals which influence elastic and plastic behavior through details of the spatial placement of lattice orientation. The approach taken here is through the two-point statistics of placement of lattice orientation. Although explicit connections between statistical and exact representations of microstructure are not achieved, it is argued that grain boundary structure plays a dominant role, in theories which extend beyond the well-known first-order theories which incorporate only a volume-fraction representation of microstructure. As an example the effects which are predicted by the theory, the spatial placement of the well-known copper and brass components of rolling texture in fcc metals is considered. It is demonstrated that spatial placement of lattice orientation can have strong effects upon components of the effective elastic stiffness tensor, yield strength, the local curvature of the yield surface, and the scatter of these properties.