On the thermal expansion of composite materials and cross-property connection between thermal expansion and thermal conductivity

The paper focuses on the quantitative characterization of heterogeneous microstructures from the point of view of the material’s thermal expansion. First, we derive expression for the second rank thermal expansion contribution tensor of an inhomogeneity and specify it for various inhomogeneity shapes. Case of a spheroidal inhomogeneity in an isotropic material is discussed in detail. Thermal expansion contribution tensor is used as a basic building block to calculate effective thermal expansion of a heterogeneous material and to derive explicit cross-property connection between thermal expansion and thermal resistivity of a composite. We compare our results with experimental data available in literature and with other approaches.

► Expression for thermal expansion contribution tensor of an inhomogeneity is derived. ► Effective thermal expansion of a composite is calculated using various approximate schemes. ► Thermal expansion - thermal resistivity cross-property connection is derived. ► Comparison of theoretical results with experimental data is provided. ► Results are valid for materials with negative thermal expansion.