Investigation of crystallographic textures in multi-level models for polycrystalline deformation using clustering techniques

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...