Compact reconstruction of orientation distributions using generalized spherical harmonics to advance large-scale crystal plasticity modeling: Verification using cubic, hexagonal, and orthorhombic polycrystals

Abstract Compaction of crystallographic texture data is highly desirable in crystal plasticity simulations because the computational time involved in such calculations scales linearly with the number of crystal orientations. In a recent publication, we have reported a rigorous procedure for reducing large datasets of crystal orientations for cubic-orthotropic and hexagonal-orthotropic polycrystalline metals using symmetrized generalized spherical harmonics (GSH) functions. The procedure relies on a quantitative description of crystallographic texture using an orientation distribution function (ODF) and its series representation using GSH. The core procedure consists of matching the spectral representation of a full-size ODF containing any number of crystal orientations with that of an ODF containing a compact set of orientations. In this paper, we generalize the procedure to any crystal structure with no restrictions to sample symmetry. These major extensions are accompanied by dealing with significantly more dimensions as well as imaginary terms. Two approaches for generating an initial set of orientations in the compact ODF are explored, one based on binning of a given fundamental zone in the Bunge-Euler orientation space and another that takes advantage of MTEX to maximize the compaction. The overall procedure has been successfully applied to compaction of large ODFs for cubic, hexagonal, and orthorhombic polycrystalline metals with orthotropic and no sample symmetry. It is quantitatively demonstrated that texture evolution, twin volume fraction evolution, stress-strain response, and geometrical changes of samples can be accurately simulated to large plastic strains with compact ODFs using crystal plasticity finite element models.