Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation, grain boundary sliding and superplasticity

John Wheeler (1)

1 Earth and Ocean Sciences

The response of periodic microstructures to deformation can be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons are shown to be anisotropic in their rheology. Analytic solutions are derived in which grain rotation is a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity is extremely anisotropic. There are 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 is introduced for grain boundaries, the anisotropy is less extreme, but two weak directions still exist along which polycrystal strength is controlled only by the grain boundary "viscosity". Irregular hexagons are characterised by 4 parameters. A particular subset of hexagons defined by 2 parameters, which includes regular hexagons as well as some elongate shapes, shows singular behaviour. Grain shapes that are close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there is a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equi-axed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.

Mots clés: Physical Sciences

John Wheeler. Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation, grain boundary sliding and superplasticity. Philosophical Magazine, 2010, 90 (21), pp.2841-2864. ⟨10.1080/14786431003636097⟩. ⟨hal-00597800⟩