Overall degradation of conductive solids with mesocracks

Abstract A continuum damage model for heat conduction is proposed in this work to account for the degradation of the bulk thermal conductivity due to the formation of subscale defects in the solid. Specifically, defects in the form of cracks, or mesocracks, have been considered. A field theory is developed analytically which isolates the effects of mesocracks in an added matrix of the thermal resistance. Followed by a general formulation, the concept of mesocrack damage in the process of heat transport is further illustrated by considering a three-dimensional and isotropic medium transferring the thermal energy according to Fourier's law of heat conduction. It is found that the amount of degradation of the bulk thermal conductivity increases linearly with the mesocrack density. In the case that the solid is saturated with mesocracks, a limiting value of thermal conductivity K being one-ninth of the intact value is obtained. A detailed discussion on this limiting value is then provided with emphasis placed on the identification of the damage parameters in the temperature-gradient model proposed earlier for assessing the mesocrack damage from a different point of view.