Anisotropy analysis of the thermal stresses and strain energies in BCC metal films

A thin polycrystalline film tightly bonded to a thick substrate of different thermal expansion coefficients will experience thermal stresses when the temperature is changed in applications. Calculations of these stresses and the corresponding strain energies for grains having various crystallographic orientations (hkl) relative to the film surface were made for a polycrystalline film composed of the BCC metal Cr, Fe, K, Li, Mo, Na, Nb, Ta, V and W, respectively. Neglecting W, which is isotropic, the stresses and strain energy densities are not grain orientation (hkl) dependence. The remaining BCC metals may be grouped into two classes. In the first group (Cr, Mo, Nb and V), the (1 0 0)-oriented grains have the highest stresses and strain energy densities and (1 1 1)-oriented grains the lowest, the stresses σ1 and σ2 in the film surface and strain energy densities in other (hkl)-oriented grains decrease linearly with increasing angle between (hkl) and (1 0 0), and have σ1<σ2 excepting in (1 0 0)- and (1 1 1)-oriented grains. The contrary conclusions are obtained for the second group (Fe, K, Li, Na and Ta).