Continuum Thermodynamic Modeling and Simulation of Additional Hardening due to Deformation Incompatibility

Abstract

The purpose of this work is the formulation and investigation of a phenomenological constitutive model for the inelastic material behavior of single crystals and polycrystals including the possible effects of incompatibility in the local inelastic deformation on this behavior. In particular, attention is focused here on additional hardening caused by the production of additional dislocations (i.e., geometrically-necessary dislocations) accommodating such incompatibility. In the context of crystal plasticity, such local inelastic deformation is represented by the glide-system (scalar) slips. As it turns out, this quantity can be used as a basis on which to formulate a non-local continuum thermodynamic generalization of standard crystal plasticity in order to account for the effects of such incompatibility on the material behavior. The corresponding continuum thermodynamic formulation yields a generalized Ginzburg-Landau or Cahn-Allen-type evolution/field relation for the scalar glide-system slip whose form is determined by that of the free energy, a dissipation potential, and that of the evolution relations for the inelastic state variables. In the last part of the work, the behavior of the model is elucidated in the context of the constrained simple shear of a crystalline strip containing one or two glide systems.