J.Appl.Phys. 94, 1539-1549
D. Duschlbauer, H.E. Pettermann and H.J. Böhm
Institute of Lightweight Structures and Aerospace
TU Wien, Vienna, Austria
An analytical approach is presented for solving the steady state thermal
conductivity problem of the following configuration.
An infinite matrix material contains a single inhomogeneous spheroidal
inclusion and a thermal resistance is present at the pertinent interface.
The matrix shows isotropic conductivity while the inclusion is transversally
isotropic, the principal material axes being aligned with the spheroid.
Analytical expressions are derived for the local gradient fields in the matrix and in the inclusion as well as for the temperature mismatch along the interface. An analytical method is developed which allows replacing the original imperfectly bonded inclusion by a less conductive but perfectly bonded inclusion. For the specific case of confocal distributions of the interface resistance the present approach yields the exact solution, i.e. the replacement operation leaves the matrix fields unchanged. For general spatial distributions of the interface properties (meeting the spheroidal symmetry properties) an approximate solution strategy is introduced providing estimates.
The further application of the present method for investigations of non-dilute composites is discussed in terms of homogenization and localization. The effect of the inclusion size in combination with an interface resistance on the conductivity of non-homogeneous systems is addressed, as well as critical inclusion dimensions.
The proposed method is compared with existing approaches from literature. Additionally, cross links to established models of coated inclusions are provided. As an example the material system of diamond inclusions in zinc sulfide matrix is considered. Predictions are compared with results from analytical approaches as well as numerical results from finite element analyses.