The response of periodic microstructures to deformation could be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons were shown to be anisotropic in their rheology. Analytic solutions were derived in which grain rotation was a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity was extremely anisotropic. There were two orthogonal directions of zero strength: sliding and rotation cooperate to allow strain parallel to these directions to be accomplished without any dissolution or plating. When a linear velocity/shear stress relationship was introduced for grain boundaries, the anisotropy was less extreme, but two weak directions still exist along which polycrystal strength was controlled only by the grain boundary “viscosity”. Irregular hexagons were characterised by four parameters. A particular subset of hexagons defined by two parameters, which includes regular hexagons as well as some elongate shapes, exhibited singular behaviour. Grain shapes that were close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there was a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equiaxed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.

Anisotropic Rheology during Grain Boundary Diffusion Creep and its Relation to Grain Rotation, Grain Boundary Sliding and Superplasticity. J.Wheeler: Philosophical Magazine, 2010, 90[21], 2841-64