Investigation of crystallographic textures in multi-level models for polycrystalline deformation using clustering techniques - Ostapovich, Kirill Vadimovich; Trusov, Petr Valentinovich (Computational Continuum Mechanics, 2019)
The feasibility of applying clustering techniques to describe and investigate crystallographic textures by using numerical results simulated for crystallite (grain, subgrain) lattice orientations with the help of multi-level crystal elasto-visco-plasticity models is considered. The texture clustering problem is stated as partitioning a given sample of crystal lattice orientations into disjoint subsets of elements which are close to each other in a certain sense. To formalize this concept of closeness, a special pseudo-metric distance taking into account rotational lattice symmetry is introduced in the space of orientations. This distance being induced by the natural Riemann metrics determines the minimal rotation angle between the symmetrically equivalent orientations of the arguments. A heuristic algorithm based on alternating well-known clustering methods is formulated to solve the stated problem. The proposed approach allows identifying, for a polycrystalline aggregate, the regions in the space of orientations with the higher density of elements, as well as evaluating some of their effective characteristics for such regions. The developed procedure includes the following stages: dividing a sample of orientations into layers; clustering by reachability (in the sense of the transitive closure of the closeness criterion being adopted for orientations); the so-called medoid-based clustering; splitting weakly localized clusters. The application of the presented clustering technique is demonstrated by considering simple shear and axial compression textures obtained through modeling the inelastic deformation of a representative volume element for polycrystalline copper. In the examined cases, local one-parameter approximations of a given form are found for the density of distribution of the angles between orientations and medoids (conditional centers) of the related clusters. Also, the statistical significance of these approximations is tested using equiprobable intervals.