The common operator expression for a tensor of effective thermal conductivity ${\rm {\bf k}}^{\ast }$ of the inhomogeneous textured material is derived. Assuming the inhomogeneous material to consist of ellipsoidal grains let us approximate the integral operator by the constant tensor ${\rm {\bf g}}$ related with the concrete inclusion and thus obtain the generalized singular approximation for ${\rm {\bf k}}^{\ast }$ on the base of the common operator expression. It is shown that in case of coincidence of axes of ellipsoidal inclusion with principal axes of a tensor of thermal conductivity of the comparison medium the components of a tensor ${\rm {\bf g}}$ may be expressed through components of a tensor of the generalized geometrical factors of the ellipsoid placed in the anisotropic external medium. The received generalized singular approximation is applied to calculation of a tensor ${\rm {\bf k}}^{\ast }$ of the multicomponent textured matrix composite with uniformly oriented inclusions. For a special case of the generalized singular approximation - a self-consistent approximation - the system of equations for finding of the main components of a tensor ${\rm {\bf k}}^{\ast }$ of this composite is derived. On the basis of the received system of equations numerical simulation of thermal conducting characteristics of the textured tribocomposite consisting of three components is made: epoxy ED-20 system as a matrix, polytetrafluoroethylene inclusions of spherical shape as an antifriction component and the prolate spheroidal glass inclusions as the reinforcing component. Dependences of the principal components of effective thermal conductivity tensor of this tribocomposite on volume fractions of reinforcing inclusions are given. It is shown what this tribocomposite has anisotropy of thermal-conducting properties, despite isotropic material characteristics of each components. It is also shown that values of the principal components of effective thermal conductivity tensor are less than volume average value of a thermal conductivity.

Выведено общее операторное выражение для тензора эффективной теплопроводности неоднородного текстурированного материала. Для указанного тензора получено обобщенное сингулярное приближение, применяемое при его вычислении в многокомпонентном матричном композите с эллипсоидальными включениями. Для частного случая обобщенного сингулярного приближения — метода самосогласования — выведена система уравнений для нахождения главных компонент тензора эффективной теплопроводности. Проведено численное моделирование теплопроводящих характеристик трибокомпозита на основе эпоксидной смолы ЭД-20, включений сферической формы ПТФЭ и одинаковым образом ориентированных вытянутых сфероидальных включений стекла. Приведены зависимости главных компонент тензора эффективной теплопроводности данного трибокомпозита от объемных долей элементов неоднородности.