Effect of texture dispersion on the effective biaxial modulus of fiber-textured hexagonal, tetragonal, and orthorhombic films

The effective biaxial modulus $(Meff)$ of fiber-textured hexagonal, tetragonal, and orthorhombic films is estimated by using the Voigt–Reuss–Hill and Vook–Witt grain-interaction models. The orientation distribution function with Gaussian distributions of the two Euler angles $θ$ and $ϕ$ is adopted to analyze the effect of texture dispersion degree on $Meff$⁠. Numerical results that are based on ZnO, $BaTiO3$⁠, and yttrium barium copper oxide (YBCO) materials show that the Vook–Witt average of $Meff$ is identical to the Voigt–Reuss–Hill average of $Meff$ for the (001) plane of ideally fiber-textured hexagonal and tetragonal films. The $ϕ$ distribution has no influence on $Meff$ of the $(hkl)$-fiber-textured hexagonal film at any $θ$ distribution in terms of the isotropy in the plane perpendicular to the [001] direction. Comparably, tetragonal and orthorhombic films represent considerable actions of $ϕ$ dispersion on $Meff$⁠, and the effect of $ϕ$ dispersion on $Meff$ of a (001)-fiber-textured YBCO film is smaller than that for a (001)-fiber-textured $BaTiO3$ film since the shear anisotropic factor in the (001) shear plane of a YBCO film more closely approaches 1. Enhanced $θ$ and $ϕ$ distributions destroy the perfect fiber textures, and as a result, the films exhibit an evolution from ideal $(hkl)$ fiber textures to random textures with varying full widths at half maximums of $θ$ and $ϕ$⁠.