Elastic-plastic crystal mechanics for low symmetry crystals

Abstract

A method of averaging the elastic-viscoplastic aggregate behavior of low symmetry materials is developed. The single crystal constitutive model includes both elasticity and rate dependent crystallographic slip. The constraint conditions imposed on the local deformations are discussed and developed in a form that allows elastic deformation without crystallographic slip in the constrained directions. The interaction law between the macroscopic and local deformations is achieved by a modified Taylor type model in which macroscopic equilibrium and compatibility are maintained, but local compatibility is not considered. Deformations in the constrained directions are posed as Lagrange multipliers rigorously enforcing a minimum work rate throughout the aggregate. The constitutive model is used to predict deformation response and texture evolution in a broad class of low symmetry materials lacking the five independent slip systems required to accommodate a general deformation. The predictions are compared to experimental data for the various materials. By including elasticity into the new model, predictive capabilities are now expanded to include a broad range of phenomena critical to the processing of such low symmetry crystals (i.e. yield surfaces, residual stresses, etc.).