Abstract:The products made by the forming of polycrystalline metals and alloys, which are in high demand in modern industries, have pronounced inhomogeneous distribution of grain orientations. The presence of specific orientation modes in such materials, i.e., crystallographic texture, is responsible for anisotropy of their physical and mechanical properties, e.g., elasticity. A type of anisotropy is usually unknown a priori, and possible ways of its determination is of considerable interest both from theoretical and practical viewpoints. In this work, emphasis is placed on the identification of elasticity classes of polycrystalline materials. By the newly introduced concept of "elasticity class" the union of congruent tensor subspaces of a special form is understood. In particular, it makes it possible to consider the so-called symmetry classification, which is widely spread in solid mechanics. The problem of identification of linear elasticity class for anisotropic material with elastic moduli given in an arbitrary orthonormal basis is formulated. To solve this problem, a general procedure based on constructing the hierarchy of approximations of elasticity tensor in different classes is formulated. This approach is then applied to analyze changes in the elastic symmetry of a representative volume element of polycrystalline copper during numerical experiments on severe plastic deformation. The microstructure evolution is described using a two-level crystal elasto-visco-plasticity model. The well-defined structures, which are indicative of the existence of essentially inhomogeneous distribution of crystallite orientations, were obtained in each experiment. However, the texture obtained in the quasi-axial upsetting experiment demonstrates the absence of significant macroscopic elastic anisotropy. Using the identification framework, it has been shown that the elasticity tensor corresponding to the resultant microstructure proves to be almost isotropic.

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

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An approach based on involving clustering techniques to identify texture components for a given polycrystalline aggregate is formulated. A heuristic iterative clustering algorithm operating only with a sample of lattice orientations and the concept of closeness between them is proposed for this task. The mentioned closeness concept is introduced via a special pseudometric distance, which is induced by the natural Riemann metrics and takes the lattice symmetry into consideration. The developed procedure allows representing an inhomogeneous orientation distribution by localized clusters in the space of orientations and thus can be used to reduce the dimension of orientation distribution data in statistical crystal plasticity models. Two examples of such an application of the clustering procedure are provided.

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