Comparison of equilibrium-based plasticity models and a Taylor-like hybrid formulation for deformations of constrained crystal systems

• Published in: Modelling and simulation in materials science and engineering Vol. 3; no. 2; pp. 215 - 234
• Main Authors: Prantil, V C, Dawson, P R, Chastel, Y B
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.03.1995
• ISSN: 0965-0393; 1361-651X
• DOI: 10.1088/0965-0393/3/2/006

A class of equilibrium-based plasticity models are compared with a hybrid formulation developed for systems with internal constraints. The response of a constrained HCP polycrystal is modeled in the absence of pyramidal slip and twinning so the crystal c-axis becomes inextensible. The inherent inhomogeneity of the deformation over the aggregate is accommodated differently by the two approaches. The constrained hybrid formulation prescribes the partitioning of deformation among the individual crystals using a kinematic rule that, crystal by crystal, filters out the component of the motion in each crystal's constraint direction. This part of the motion must then be sustained by neighboring crystals which are more favorably oriented. The equilibrium-based formulations explicity satisfy intergranular equilibrium by assuming that all crystals experience the macroscopic stress. The magnitude of this stress is determined by enforcing the average crystal deformation to be equal to the macroscopically impoed motion. Over the full range of rate sensitivity, the stress response of the constrained hybrid model is bracketed by the equilibrium-based predictions which provide a lower bound and a Taylor analysis with hard pyramidal slip which provides an upper bound. The response of an aggregate undergoing plane strain compression is examined for two significantly different rate sensitivities.