Temperature, thermal flux and thermal stress distribution around an elliptic cavity with temperature-dependent material properties

Temperature is an important factor affecting the physical and chemical properties of materials, especially when the temperature changes significantly, such as in the process of heat conduction. The corresponding changes of material properties greatly complicate the distribution of temperature and thermal stress, and make it much more difficult to accurately solve the thermal-elastic field. Using the generalized complex variable method, the thermal-elastic problem of an elliptic cavity embedded in an infinite medium has been analyzed in this paper, with the temperature dependence of thermal conductivity, elastic modulus and thermal expansion coefficient fully accounted for. The temperature, thermal flux and thermoelastic fields have been obtained analytically. The analytical and numerical results show that thermal flux solution is consistent with the temperature independent case, while the temperature and thermal stress solutions are much more complicated. When the elliptical cavity degenerates into a crack, Mode I thermal stress intensity factor K1 has a tiny negative value, which indicates that thermal flux can actually close the crack slightly. In addition, both K1 and K2 vary nonlinearly with remote thermal loads, and depend on 3/2,5/2 and 7/2 power of crack length. These results provide a powerful tool for the failure and reliability analysis of temperature dependent materials.