ЧИСЛЕННО-АНАЛИТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ДИФФУЗИОННЫХ ПРОЦЕССОВ В ОГРАНИЧЕННЫХ МНОГОКОМПОНЕНТНЫХ ТВЕРДЫХ ТЕЛАХ

Abstract

Results are presented of a symbolic and numerical modeling as well as experimental identification of the material properties of an alloy. A methodology is also proposed for an experiment that allows to exclude the effect of the boundaries of the alloy on the identification of the material properties. Results of the data processing are presented, which are obtained by means of numerical modelling of the experiments under various technological conditions. Considered were (1) a distribution of the impurities in the volume of a rectangular plate, (2) a distribution of impurities on the plate surface with the length covered partly and width fully, (3) a symmetric distribution of impurities, (4) a partially covered by a film plate, with the former being serving as the source of impurities. The influence was analyzed of the technological conditions at the boundary of the solids on the character of the diffusive processes. Distribution functions were found of the concentration of impurities in the material. This allows to solve a set of practically relevant problems such as the determination of the geometry of the diffusive coating, the time of homogenization, the amount of matter diffused through a boundary of a composite material, etc. It was found that for the identification of the characteristics of the diffusive process, it is advantageous to use fast varying distribution functions rather than slow ones. A numerical experiment was conducted using the commercially available package ANSYS. A rectangular plate was considered with various boundary and initial conditions. Analytical expressions for the distribution functions of the impurities under various boundary and initial conditions were obtained using the symbolic MAPLE software. A comparison of the symbolic and numerical simulations showed that there is a class of the boundary conditions for which the results of these simulations agree well.