Analytical method of constructing field of possible texture parameters changes

The proposed work is focused on polycrystalline materials with cubic symmetry of the lattice, subjected to thermomechanical treatment and having a crystallographic texture. As a subject of study the link of physical and mechanical properties anisotropy with integral characteristics of texture was examined. As integral texture characteristics (texture parameters) the authors selectedaverage values of certain combinations of the direction cosines defining the provisions of the crystallographic axes grain polycrystalline, in the laboratory system of axes. On the basis of the published data analysis a problem of findingborders of distribution of texture parameters that determine the anisotropy of the elastic properties of textured polycrystals was formulated. A vector-matrix algorithm for constructing the required piecewise smooth enclosed surface was proposed. The initial data for the area construction was used as restrictions imposed on the textural parameters, which derived from the condition of positivity of the weight coefficients in the corresponding problem of averaging - determining the weighted average degree of eigenvalues of a textured polycrystal elasticity operator. It was established that the distribution area of textural parameters has a fold symmetry axis and is limited by flat and conical elements. In the analytical form the equations of boundary surface elements and the lines of their intersection were obtained. Validation of the mathematical model for constructing the distribution area of texture parameters was performed by comparison with the empirical data. The empirical data on the evolution of the texture was obtained earlier, by an independent research in rolling of sheets of aluminum alloys at a multistand camp. It was established that the experimentally determined values of texture parameters belong to the trajectory lying inside the found analytical field. This will lead to a targeted control of technological processes in manufacturing items and semi-finished products of metal materials.