An attempt was made to determine whether there was a physically natural method of characterizing the possible interactions between the slip-systems of 2 grains that met at a grain boundary. A positive result was obtained; based upon the notion of a Burgers vector as described by a tensor field G on the grain boundary. It was shown that the magnitude of G could be expressed in terms of two types of moduli: inter-grain moduli that characterize slip-system interactions between the two grains; intra-grain moduli that for each grain characterize interactions between any two slip systems of that grain. The theory was based upon microscopic force balances derived using the principle of virtual power, a version of the second law in the form of a free-energy imbalance, and thermodynamically compatible constitutive relations dependent upon G and its rate. The resulting microscopic force balances represent flow rules for the grain boundary; and what was most important, these flow rules account automatically - via the intra- and inter-grain moduli - for the relative misorientation of the grains and the orientation of the grain boundary relative to those grains.

A Theory of Grain Boundaries that Accounts Automatically for Grain Misorientation and Grain-Boundary Orientation. M.E.Gurtin: Journal of the Mechanics and Physics of Solids, 2008, 56[2], 640-62