Prediction of ideal orientations in velocity gradient-driven processes for large plastic deformations of crystals
We focus on the crystal lattice ideal orientations, also referred to as preferred or attractor orientations, in crystalline materials, and how they can be used to predict the final texture of polycrystals after manufacturing processes. The simplified crystal plasticity (CP) models used here capture the main features of microstructural evolution in monocrystalline and polycrystalline materials undergoing velocity-gradient-driven processes, without considering hardening or softening effects. The evolution of the lattice orientation is described by a nonlinear ordinary differential equation, and a linear stability analysis is performed to identify the permanent orientations that act as attractors (i.e., the ideal or preferred orientations). Although our linear stability analysis is generally applicable, it is detailed using a simplified two-dimensional model with three slip systems. This approach successfully predicts lattice orientation attractors for large strains by analyzing the interplay between deformation and rotation, initial orientation, and the interaction between different slip systems under applied loads. Three fundamental problems in CP illustrate the effectiveness of the theory: polycrystal deformation under homogeneous velocity gradient loading, void evolution under radial loading, and slip band formation in a monocrystal. High-resolution CP numerical simulations, enhanced using re-meshing techniques, provide further validation of our findings concerning the impact of initial crystallographic orientations, deformation mechanisms, and loading conditions on the evolution of orientation attractors and the final crystal texture.