Self-consistent polycrystal models: a directional compliance criterion to describe grain interactions

Viscoplastic self-consistent polycrystal models have been successful in addressing and explaining features of plastic deformation which cannot be treated with the Taylor condition of isostrain. In particular, these models have been applied to the simulation of plastic deformation and texture development in materials with hexagonal, trigonal, orthorhombic and triclinic symmetry.

An important assumption required to solve the equilibrium equation within self-consistent formulations is that the strain-rate varies linearly with the stress in the homogeneous effective medium surrounding the inclusion. The characteristic of such a linear relation has been a matter of debate and two extreme cases can be identified: the tangent and the secant approaches. The secant approach has associated with it a stiffer inclusion-matrix interaction than the tangent approach and is closer to the Taylor approach.

In this work we perform a systematic study of the implications of both assumptions on the response of cubic and hexagonal materials (texture development, system activity, stress and strain-rate deviations). In addition, we argue that the strength of the matrix-inclusion interaction should not be constant but should depend on the capability of each orientation to accommodate the particular deformation mode imposed externally. As a consequence, we propose a relative directional compliance (RDC) criterion for defining a variable interaction between grain and matrix depending on their relative compliances and compare the predictions of the RDC approach with the predictions of the secant and the tangent schemes.