Deformation Twinning in Single Crystals

Abstract

A continuum theory is formulated to simultaneously address thermoelasticity, plasticity, and twinning in anisotropic single crystals subjected to arbitrarily large deformations. Dislocation glide and deformation twinning are dissipative mechanisms, while energy storage mechanisms associated with dislocation lines and twin boundaries are described via scalar internal state variables. In the inelastic regime, for highly symmetric orientations and rate independent shear strength, the Rankine--Hugoniot conditions and constitutive relations can be reduced to a set of algebraic equations to be solved for the material response. In a case study, the model describes the thermomechanical behavior of single crystals of alumina, i.e., sapphire. Resolved shear stresses necessary for glide or twin nucleation are estimated from nonlinear elastic calculations, theoretical considerations of Peierls barriers and stacking fault energies, and observations from both quasi-static and shock compression experiments. Residual elastic volume changes, predicted from nonlinear elastic considerations and approximated dislocation line energies, are positive and proportional to the dislocation line density and twin boundary area density. Analytical solutions to the planar shock problem are presented for c-axis compression of sapphire wherein rhombohedral twinning modes are activated.