Influence of composition, thermoelastic characteristics and concentration of components on average stresses in matrix composites reinforced by oriented fibers
A model is constructed in the work that allows predicting the influence of local stresses caused by changes in the volumes of the heterogeneity elements of two-component matrix composites with orthogonal reinforced (parallel to a fixed plane) fibers on average stresses over the material. The model is based on a generalized singular approximation of random field theory, used in solving a system of stochastic differential equilibrium equations for an elastic medium. When constructing the model, the concept of the stress concentration operator (fourth-rank tensor) is used, which connects the material average stresses with their local values within a single heterogeneity element. The generalized singular approximation allows you to obtain an explicit expression for the concentration operator, with the help of which a calculated relation is derived for determining average stresses in the considered matrix structures. The ratio allows you to take into account a number of factors. These include the composition and thermoelastic characteristics of the components of the composites, the volume concentration and orientation of the fibers in the matrix, as well as the difference factor in the magnitude of the change (jump) in temperature in various elements of the inhomogeneity of the material - the fibers and the matrix.For model composites with a silicon dioxide matrix and oriented fibers (copper, aluminum), numerical calculations were carried out to determine the values of the average material stresses in the directions of the axes of the laboratory coordinate system. The dependences of the indicated values on the volumetric content of fibers, as well as on variations in the magnitude of the temperature jump in the fibers and matrix, are studied. Model calculations showed that the difference in the magnitude of the temperature jump in the elements of heterogeneity and the volumetric concentration of fibers in the composites have a significant effect on the values of average stresses over the material.