On the Effective Coefficient of Thermal Expansion in Thermal Bending of Composites Undergoing Linear Heat Flow

Abstract

It is suggested that the localized stresses and associated displacements resulting from the thermal conductivity mismatch of second-phase inclusions in dispersed phase-continuous matrix composites subjected to linear heat flow can contribute to the thermal bending (i.e., the curvature) of the composite at the continuum level. The original solutions of Tauchert for a single inclusion were used to derive an expression for the curvature and associated effective coefficient of thermal expansion of a matrix with spherical inclusions undergoing linear heat flow. The results are expressed in terms of the isothermal coefficient of thermal expansion, Young's modulus and thermal conductivity of the composite, which, in turn, depend on the relevant properties and volume fractions of the matrix and dispersed phase. Numerical examples are presented which indicate a significant effect. Thermal expansion mismatches between the matrix and dispersed phase are shown to play a particularly large role in either increasing or decreasing the degree of thermal bending, which may even become negative for matrices with near-zero expansion behavior. A numerical example based on a flat composite plate constrained from bending indicates that the above effect can have a large influence on the magnitude of maximum thermal stress.