Modeling of polycrystals using a gradient crystal plasticity theory that includes dissipative micro-stresses

This study investigates thermodynamically consistent dissipative hardening in gradient crystal plasticity in a large-deformation context. A viscoplastic model which accounts for constitutive dependence on the slip, the slip gradient as well as the slip rate gradient is presented. The model is an extension of that due to Gurtin (Gurtin, M. E., J. Mech. Phys. Solids, 52 (2004) 2545–2568 and Gurtin, M. E., J. Mech. Phys. Solids, 56 (2008) 640–662)), and is guided by the viscoplastic model and algorithm of Ekh et al. (Ekh, M., Grymer, M., Runesson, K. and Svedberg, T., Int. J. Numer. Meths Engng, 72 (2007) 197–220) whose governing equations are equivalent to those of Gurtin for the purely energetic case. In contrast to the Gurtin formulation and in line with that due to Ekh et al., viscoplasticity in the present model is accounted for through a Perzyna-type regularization. The resulting theory includes three different types of hardening: standard isotropic hardening is incorporated as well as energetic hardening driven by the slip gradient. In addition, as a third type, dissipative hardening associated with plastic strain rate gradients is included. Numerical computations are carried out and discussed for the large strain, viscoplastic model with non-zero dissipative backstress.