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