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

The effective biaxial modulus (M _eff ) and strain energy density (W / ε{lunate} _∥ 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 M _eff calculated with the five models are identical for the (0 0 1) plane of ideally fiber-textured hexagonal and tetragonal films. The evolution of M _eff with Euler angle θ _c indicates that M _eff of hexagonal films is related to θ _c only. However, tetragonal and orthorhombic films represent various M _eff even if θ _c is uniform, which implies that both θ _c and φ{symbol} _c contribute to the change of M _eff .