Effective biaxial modulus and strain energy density of ideally (h k l)-fiber-textured hexagonal, tetragonal and orthorhombic films

The effective biaxial modulus (Meff) and strain energy density (W/ε∥2) of hexagonal, tetragonal and orthorhombic polycrystalline films with ideally (h k l) fiber textures are evaluated using the Vook-Witt, inverse Vook-Witt, Voigt, Reuss and Voigt-Reuss-Hill grain interaction models. A two-dimensional Dirac delta function is employed to describe the orientation distribution function of these films. Numerical results show that the averages of Meff calculated with the five models are identical for the (0 0 1) plane of ideally fiber-textured hexagonal and tetragonal films. The evolution of Meff with Euler angle θc indicates that Meff of hexagonal films is related to θc only. However, tetragonal and orthorhombic films represent various Meff even if θc is uniform, which implies that both θc and ϕc contribute to the change of Meff.