Theory of orientation gradients in plastically strained crystals

We suggest a theory of in-grain orientation gradients in plastically strained metals. It is an approach to explain why initially uniformly oriented crystals can-under gradient-free external loadings-build up in-grain orientation gradients during plastic deformation and how this phenomenon depends on intrinsic factors (crystal orientation) and extrinsic factors (neighbor grains). The intrinsic origin (orientation dependence) of in-grain orientation gradients is investigated by quantifying the change in crystal reorientation upon small changes in initial orientation. This part of the approach is formulated by applying a divergence operator to reorientation rate vector fields (in the present paper calculated by using strain-rate homogenization Taylor-Bishop-Hill theory). The obtained scalar divergence function (but not the reorientation vector field itself) quantifies the kinematic stability of grains under homogeneous boundary conditions as a function of their orientation. Positive divergence (source in the reorientation rate vector field) characterizes orientations with diverging non-zero reorientation rates which are kinematically unstable and prone to build up orientation gradients. Zero divergence indicates orientations with reorientation rate identity with the surrounding orientations which are not prone to build up orientation gradients. Negative divergence (sink in the reorientation rate vector field) characterizes orientations with converging non-zero reorientation rates which are kinematically stable and not prone to build up orientation gradients. Corresponding results obtained by use of a crystal plasticity finite element formulation are in good agreement with the reorientation field divergence function derived by homogenization theory. The extrinsic origin of in-grain orientation gradients (influence of grain-neighbor interaction) is addressed using a crystal plasticity finite element bicrystal model. The simulations show that a significant dependence of orientation gradients on the neighbor crystals occurs for grains with high positive divergence. The build-up of orientation gradients in grains with close to zero or negative divergence is in body centered cubic crystals less sensitive to the presence of neighbor orientations than in face centered cubic crystals (Goss and cube orientation). (C) 2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.