On calculation of the effective thermal conductivity of textured matrix composites with high volume fraction of inclusions

In the generalized singular approximation the expression for a tensor $\mathbf{k}^{\ast }$ of effective thermal conductivity of a multicomponent matrix composite is received. Each component is considered consisting of isotropic ellipsoidal inclusions with orientations distributed under some probabilistic law. The shape of the inclusions of a given type (relating to the given component) is considered identical.On the basis of the received expression the method is developed for calculation of a tensor $\mathbf{k}^{\ast }$ of the three-component textured matrix tribocomposite with epoxy ED-20 system as a matrix, inclusions from a polytetrafluoroethylene of spherical shape as an antifrictional component and glass fibers as the reinforcing component. It is considered that glass fibers, have small dispersion in orientations around some axis - a texture axis, their volume fraction changes in the range from 0,4 to 0,7. The method uses fine tuning of parameter $k^{(c)}$ of the comparison medium depending on a volume fraction of glass fibers and a ratio between thermal conductivities of inclusions and of matrix. This tuning dependence is received by comparison of results of model and finite-differences calculations for a two-component matrix composite with glass fibers without dispersion of their orientations. The method is applied to a research of influence of size of dispersion in orientations of glass fibers to tensor $\mathbf{k}^{\ast }$ components. Dependences of principal components of tensor of the effective thermal conductivity of this tribocomposite on a volume fraction of the glass reinforcing inclusions are given at various sizes of dispersion in their orientations. It is shown that increase in dispersion in orientations of glass fibers leads to reduction of longitudinal component and to growth of transverse component of tensor $\mathbf{k}^{\ast }$ with respect to the texture axis. It is also shown that values of the principal components of a tensor of effective thermal conductivity are less than average on volume basis value of a thermal conductivity.