Biaxial modulus of fiber-textured cubic polycrystalline films with an arbitrary texture axis [hkl]

A simple method to estimate the effective biaxial modulus of cubic polycrystalline films with an arbitrary [hkl] fiber texture is presented. Analytic expressions of the Voigt [Lehrbuch der Kristallphysik (Teubner, Leipzig, 1910)] and the Reuss [Z. Angew. Math. Mech. 9, 49 (1929)] averages of the biaxial modulus are given in terms of the axis orientation [hkl] and single-crystal elastic constants. We then explain why the two averages of the fiber-textured films are identical to the corresponding appropriate biaxial modulus of the constituent grain. Finally, we show that for fiber axes equivalent to [100] or [111], the Voigt and Reuss averages coincide and are identical to the true effective biaxial modulus of the fiber-textured film. For other fiber axes, we further show that the Voigt-Reuss-Hill average of the biaxial modulus is an excellent theoretical estimation.