A model was developed for elasticity, plasticity and twinning in anisotropic single

crystals subjected to large deformations. Dislocation glide and deformation

twinning were dissipative, while energy storage mechanisms associated with

dislocation lines and twin boundaries were described via scalar internal state variables. Concepts from continuum crystal plasticity were invoked, with shearing

rates on discrete glide and twinning systems modelled explicitly. The model

describes aspects of thermomechanical behaviour of single crystals of alumina over

a range of loading conditions. Resolved shear stresses necessary for glide or twin

nucleation at low to moderate temperatures were estimated from nonlinear elastic

calculations, theoretical considerations of Peierls barriers and stacking fault

energies and observations from shock physics experiments. These estimates were

combined with the existing data from high-temperature experiments to provide

initial yield conditions spanning a wide range of temperatures. The model reflects

hardening of glide and twin systems from dislocations accumulated during basal

slip. Residual elastic volume changes, predicted from nonlinear elastic

considerations and approximated dislocation line energies, were positive and

proportional to the dislocation line density. While the model suggested that

generation of very large dislocation densities could influence the pressure–volume

response, volume increases from defects were predicted to be small in crystals

deformed via basal glide on a single system.

A Continuum Description of Nonlinear Elasticity, Slip and Twinning, with

Application to Sapphire. J.D.Clayton: Proceedings of the Royal Society A, 2009,

465[2101], 307-34