Effect of an inhomogeneous interphase on the thermal expansion coefficient of a particulate composite

This work is a study of the thermal properties of composite materials containing isotropic spherical inclusions surrounded by an inhomogeneous interphase, embedded in an isotropic matrix. By modelling the thermal and mechanical properties of the interphase as continuous radial functions, a replacement technique is used to derive a differential equation which models the thermal expansion coefficient of the composite. The results are generalised for a wide class of functions describing the inhomogeneous properties of the interphase. When the mechanical properties of the interphase are described by a power law profile a closed form solution is obtained for various thermal expansion profiles. The results are displayed graphically against various other theoretical models and with experimental results. A comparison of the results for different values of the problem parameters is also presented. The present model showed good agreement with the experimental results of Holliday and Robinson [Holliday L, Robinson J. Review: the thermal expansion of composites based on polymers. J Mater Sci 1973;8:301–11].