A time integration algorithm for elasto-viscoplastic cubic crystals applied to modelling polycrystalline deformation

An algorithm for integrating the constitutive equations for an elasto-viscoplastic cubic crystal is presented which is shown to be easily employed in a polycrystalline analysis. Anisotropic elastic behaviour is incorporated into the standard constitutive equations for ductile single crystals. The algorithm is shown to be efficient, robust and general. The primary advantage of this algorithm is that is provides an implicit integration of the plastic deformation gradient while including the elastic response. This permits taking large time steps while maintaining accuracy and stability. Several polycrystalline examples are presented to demonstrate the effect of the time step on the solution. Examples also are presented which compare the algorithm described herein to an algorithm which neglects the elastic part of the deformation. In addition, the effect of the anisotropic component of the elasticity is investigated by comparing the results with those obtained assuming isotropic elasticity.