A two-dimensional polycrystal model in a `deep' space representation (Q1905584)

The authors propose a model which links macroscopic deformations with changes in crystalline texture. To describe the state of the polycrystal, the model calls upon microstructural variables; their time-rates, together with the corresponding microstresses, enter the expression for virtual power. Appropriate supplementary terms also appear in the equations of balance of energy and entropy. Schmid's law for single slip systems is invoked to provide one of the additional constitutive equations. A constitutive statement similar to the Taylor-Bishop-Hill criterion for polycrystals is introduced to relate the velocity gradient and the lattice spin via the active spin combination. The model is applied to a Taylor planar polycrystal for a particular choice of constitutive laws for the microstresses.