A continuum description of nonlinear elasticity, slip and twinning, with application to sapphire

Abstract

A model is developed for elasticity, plasticity and twinning in anisotropic single crystals subjected to large deformations. Dislocation glide and deformation twinning are dissipative, while energy storage mechanisms associated with dislocation lines and twin boundaries are described via scalar internal state variables. Concepts from continuum crystal plasticity are 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 are estimated from nonlinear elastic calculations, theoretical considerations of Peierls barriers and stacking fault energies and observations from shock physics experiments. These estimates are 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, are positive and proportional to the dislocation line density. While the model suggests that generation of very large dislocation densities could influence the pressure-volume response, volume increases from defects are predicted to be small in crystals deformed via basal glide on a single system.

Shock compression of metal single crystals modeled via Finsler-geometric continuum theory

“…Excellent agreement between model predictions and experiment is evident. Post-yielding, shock stress is higher for the case when inelastic density change is included (k > 0), in agreement with predictions for other solids [45]. Stress P is largest for the isentrope since inelastic deformation by slip that would otherwise relieve elastic strain is excluded.…”

A phase field model of deformation twinning: Nonlinear theory and numerical simulations

“…The theory presented here does not address plastic slip, i.e., glide of full and/or partial dislocation lines and loops not associated with twinning. Additional model features are required to simultaneously address plastic slip and twinning [16,36].…”

“…More generally, the interfacial energy of a growing or shrinking twin also includes elastic and core energies of twinning dislocations comprising such interfaces [9,13,14]. Continuum mechanics models for deformation twinning have been developed in the context of crystal plasticity theory [15,16], wherein at each continuum material point, the volume/mass fraction of a particular twin system is evolved via a kinetic relation usually involving a resolved shear stress criterion. Intended goals of such models include predictions of macroscopic stress-strain behavior and crystallographic texture.…”

Modeling and Simulation of Ballistic Penetration of Ceramic-Polymer-Metal Layered Systems

“…Cohesive zone representations of interfacial separation [23][24][25] offer the potential for more realistic modeling of interfacial physics than the fully bonded or free surface interactions prescribed herein among layers. Constitutive models with a more rigorous basis in finite deformation kinematics [26] and thermodynamics [21] may enable improvements in descriptions of the bulk behavior of metals [23,27] and ceramics [28], albeit at increased model complexity and computational expense. Phase field models [29] of structural transformations (e.g., for high-pressure phase transitions [17] and fracture in AlN) and nonlocal models for inelasticity and damage mechanisms [30] may also offer improvement over usual continuum mechanical treatments available in simulation codes such as EPIC, for example, potential benefits with regard to regularization of numerical solutions.…”