Applying Gaussian distributions on SO(3) for modeling the texture and predicting the properties of texturized polycrystalline materials

Abstract

This paper considers a quantitative description of the crystallographic texture. When the crystallographic texture is modeled, the generalized Gaussian distribution is applied on Riemannian manifolds. A simple model of the orientation distribution function (ODF) is obtained, which corresponds to the Gaussian distribution of the axial crystallographic texture. It is demonstrated that an equally probable distribution of crystallographic axes and an ideal axial texture are realized as special cases of the ODF model. An anisotropy evaluation of elastic modulus is carried out. The indicatrix transformation of Young's modulus is demonstrated. © 2016 Author(s).