The biaxial modulus of single crystal cubic thin films under an equibiaxial strain

Abstract

Formulae for the biaxial moduli and their principal values for (hkl) surface orientations of single crystal cubic thin films subjected to a state of equibiaxial strain when bonded to an isotropic substrate or cubic substrate with which it has a cube-cube orientation relationship are given. The assumption is made in this analysis that the single crystal film is thin enough that the traction-free surface leads to zero shear stresses throughout the film in suitably chosen coordinate systems. Expressions for the shear strains and the out-of-plane normal strain for (hkl) orientations are also given. It is shown that the stationary points of the biaxial modulus always lie on {hhl} orientations. Formulae for these stationary points are derived. The assumption of zero shear stresses throughout the film in suitably chosen coordinate systems produces values of the principal biaxial moduli that are in general different from those obtained in a prior work where the assumption of zero shear strains throughout the film in suitably chosen coordinate systems was made.