Mechanical Study of Nano-ceramic Thermal Barrier Coatings by the Equation of Phonon Radiative Transfer

Temperature filed, thermal stress, especially tensile stress and J-integral are important for thermal barrier coatings (TBCs) under thermal shock. At the micro- and nano-scale, the energy transport mechanisms are significantly different from those at the macro-scale. The temperature fields, which are obtained by combining the Equation of Phonon Radiative Transport (EPRT) (for the nano-scale ceramic TBCs)and the Fourier law (for the substrate), are used as the thermal loading in the thermal stress and J-integral of an edge in the TBCs analysis by the finite element method. The temperature field and thermal stresses as well as J-integral are compared with those which are calculated by applying the Fourier law to both the TBCs and the substrate. The influence of the physical heat properties of the TBCs on the temperature field and thermal stress and J-integral have been analyzed in this paper. It is concluded that the temperature, thermal stress, including the tensile and compressive components, and J-integral which are calculated with the EPRT, are lower than that calculated with the Fourier law in the TBCs. Moreover, thermal stress in the TBCs increase with increasing phonon speed and relaxation time, but J-integral at the crack tip is in the opposite