Finite Deformation Elastoplasticity for Rate and Temperature Dependent Polycrystalline Metals

An elastoplasticity model is formulated and demonstrated in one-dimension (1D) for modeling finite deformations in poly-crystalline metals. Quasi-static to high strain rate effects as well as temperature sensitivity are included. A multiplicative decomposition of the deformation gradient into elastic, plastic, and thermal parts, that includes a volumetric/isochoric split of the elastic stretching tensor is assumed. The kinematics and thermodynamic formulation lead to constitutive equations, stresses, and constraints on the evolution of the internal state variables. The model accounts for (i) dislocation drag effects on flow stress, and (ii) generation (hardening) and annihilation (recovery) of statistically-stored dislocations (SSDs). The resulting model is normalized to dimensionless form to allow dimensionless material parameters fit for one metal to approximate the behavior of another metal of similar lattice structure, if data are limited. One dimensional material parameter fitting is demonstrated for two refractory metals, body centered cubic (bcc) Tantalum and Tungsten.