Effect of Thermal Conductivity Mismatch on the Thermal Stresses in a Dispersed Phase-Continuous Matrix Composite Material Undergoing Steady-State Heat Flow

Abstract

Under conditions of heat flow a mismatch in the thermal conductivity of the components in a composite material gives rise to localized stresses and displacements not present under isothermal conditions. These localized displacements result in additional bending displacements (i.e., additional curvature) at the continuum level. When such curvature is constrained, additional thermal stresses will arise which are superposed on those based on conventional thermoelastic theory and the isothermal properties of the composite material. This phenomenon is referred to as the “thermal conductivity mismatch effect.” For any given composite material, this effect can be analyzed by numerical means. It is the purpose of this study to present an analytical approach to this problem based on an approximate analytical expression for the effective coefficient of thermal expansion in thermal bending under conditions of steady-state heat flow. The specific geometry selected for this analysis consisted of a short ring subjected to steady-state radial heat flow. The approach taken was to first calculate the thermal stresses based on isothermal thermal properties and then superpose the stresses resulting from the change in the coefficient of thermal expansion in thermal bending due to the presence of heat flow. Numerical examples for an aluminum oxide-aluminum composite material indicated that the thermal conductivity mismatch effect can play a significant role in the magnitude of the thermal stresses and can be positive or negative depending on the direction of mismatch. This latter finding suggests a solution for materials selection for engineering design involving high magnitudes of thermal stress.