A New Approach to Describing Three-Dimensional Orientation Distribution Functions in Textured Materials–Part I: Formation of Pole Density Distribution on Model Pole Figures

Abstract

New method for simulation of orientation distribution functions of textured materials has been proposed. The approach is based on the concept to describe any texture class by a superposition of anisotropic partial fibre components. The texture maximum spread is described in a “local” coordinate system connected with the texture component axis. A set of Eulerian angles γ₁,γ₂,γ₃ are introduced with this aim. To specify crystallite orientations with respect to the sample coordinate system two additional sets of Eulerian angles are introduced besides γ₁,γ₂,γ₃. One of them, (Ψ₀,θ₀,ϕ₀), defines the direction of the texture axis of a component with respect to the directions of the cub. The other set, (Ψ₁,θ₁,ϕ₁), is determined by the orientation of the texture component and its texture axis in the sample coordinate system. Analytical expressions approximating real spreads of crystallites in three-dimensional orientation space have been found and their corresponding model pole figures have been derived. The proposed approach to the texture spread description permits to simulate a broad spectrum of real textures from single crystals to isotropic polycrystals with a high enough degree of correspondence.