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.
Highlights
The distribution of orientations in textured materials is known to be described by threedimensional functions f(gB), with the crystallite orientations gB being commonly specified by three Eulerian angles tp, and tp2, see Bunge (1969)
A specific crystallographic direction from the family is the texture axis of every specific preferred[uvw] orientation which is presented by a maximum in the space of angles gB (91,92) the specific values of rotations go/= (Woi,Ooi,tPoi) and gli= (lYli,Oli,(Pli) ga g g determined earlier will correspond to every texture maximum c Let us consider each maximum separately
",Pk Pk are the volume fractions of the texture components and. In this manner the model pole figures (PF), which correspond to the cube texture and to the hypothetical ones shown in Figure 3, may be obtained
Summary
New method for simulation of orientation distribution functions of textured materials has been proposed. The texture maximum spread is described in a "local" coordinate system connected with the texture component axis. A set of Euledan angles YI,Y2,Y3 are introduced with this aim. To specify crystallite orientations with respect to the sample coordinate system two additional sets of Euledan angles are introduced besides Y,Y-,Y3- One of them, (W0,00,%), defines the direction of the texture axis of a component with respect to the directions of the cub. The other set, (Wi,0,q), is determined by the orientation of the texture component and its texture axis in the sample coordinate system. 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
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