The deformation of a polycrystalline aggregate may be regarded as consisting of two components: a strain component which is uniform across the aggregate, and a component arising from relative motion of grains normal and parallel (grain-boundary sliding) to their boundaries. The latter causes local discontinuities in the total strain tensor. It is shown that the sum of these components is equal to the mean strain of an individual grain provided certain coherency conditions are satisfied. In particular, grain-boundary sliding does not allow the aggregate to have a greater total strain than the mean strain of an individual grain.
