Generalization of the Concept of Sample Symmetry‐ Fuzzy Symmetry,Symmetroids, Similarity

Abstract

The crystal orientation distribution function of polycrystalline materials, i.e. the texture, may exhibit internal symmetries due to symmetries of the production steps, or more generally, to the whole materials history. The “sharpness” of such symmetries can be quantified in terms of various symmetry parameters. If the symmetries of subsequent production processes are different, e.g. of sheet rolling and deep drawing, then these symmetries may still be recognized in the final texture. In the same way also similarities of textures and properties of different materials can be quantified. Symmetry parameters have many practical applications. Examples of that are the determination of rolling direction corrections, determination of the “plastic spin”, estimation of coarse-grained materials, or finding the “correct” (symmetry adapted) axis system in a material.