Texture parameter variation region for orthotropic polycrystals with cubic symmetry of the crystal lattice

Abstract

The variation region of texture parameters (which are integral characteristics of the preferable orientation of crystallographic axes) allows solutions to be found for managing anisotropic properties, illustrating all possible textured states of an orthotropic polycrystalline material with a crystal lattice of cubic symmetry. Each point in this region is matched by certain anisotropy of both elastic and plastic properties. The region of texture parameter variation is defined both analytically and using a numerical experiment of statistic simulation. Analytically, the solution is found via determining the effective eigenvalues of the elasticity operator for a textured anisotropic cubic polycrystal. The algorithm to be followed for visualizing the region-forming elements implies determining the lines of intersection of planes with a conical surface. The numerical solution is based on the determination of texture parameters, i.e, on the starting assumption that the variation region is bounded and lies in the first octant. The task of constructing the variation region is solved via finding the texture parameters using the Monte-Carlo method according to the density of distribution of crystallographic axes in space. When modeling the variation region, octets are used, which are symmetrical reflections of randomly taken orientations in all the octants of space. The constructed regions have the required symmetry. The numerically obtained cloud of textured states and the analytically constructed variation region have geometric centers coinciding at the point corresponding to the non-textured state. At various stages of thermal and mechanical treatment of metallic materials, texture evolution can be represented geometrically as a texture state trajectory that is seen to be within the determined texture parameter variation region. © 2018 Author(s).