Computational Analysis of the Thermal States of BM-P and BM-LR Experimental Facilities

Abstract

   Approximation by standard functions is one of the methods to reconstruct the orientation distribution function of grains in polycrystalline materials from a set of experimentally measured pole figures. In practice, the central and canonical normal distributions are often used to solve this problem. The central distribution has a circular scattering character, whereas the canonical one is anisotropic. The orientation distribution function can have peak and axial components. The peak component is bell-shaped and has a single maximum in the orientational space. The axial component is the average of the peak component over rotations around the selected axis. The distribution functions for the orientations of the axial components of the central and canonical normal distributions have been calculated. Pole figures for the canonical normal distribution with different parameters are constructed. The exact and approximating expressions for the axial component of the central normal distribution have been compared quantitatively and qualitatively. It is appropriate to use an approximating function to simplify the calculation of the axial component for a normal distribution with circular and noncircular scattering patterns of the texture of polycrystals. Since real textures usually include several axial components with different parameters and weights, calculations of the orientation distribution function are greatly simplified when using the approximating expression.