Reduced Statistical Representation of Crystallographic Textures Based on Symmetry-Invariant Clustering of Lattice Orientations

As proven in numerous experimental and theoretical studies, physical mechanical properties of materials are determined by their internal structure. In the particular case polycrystalline metals alloys, an important role is given to orientation distributions crystalline lattices, or, other words, crystallographic textures. Physically reasonable models texture formation highly demanded modern Material Science Engineering since they can provide efficient tool for designing products with improved operational characteristics. Models interest be obtained on basis statistical formulations multilevel approaches crystal elasto–visco–plasticity theories (in particular, Taylor–Bishop–Hill various modifications appropriate here). such a framework, representative volume element polycrystal numerically implemented as finite aggregate crystallites (grains or subgrains) homogenized response at macro-scale. Quantitative analysis this requires estimating statistically stable features distribution. The present paper introduces clustering-based approach executing task regard preferred orientations. proposed procedure operates weighted sample orientations representing divides it into clusters, i.e., disjoint subsets close elements. closeness criterion supposed defined help special pseudometric distance, which takes rotational symmetry lattice account. A specific illustrative example provided better understanding developed procedure. clustered described reductively terms effective characteristics distinguished clusters. Several possible reduced-form representations considered investigated from viewpoint aggregating elastic application some simulated