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

Abstract

The effective biaxial modulus ( M eff) 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 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 c contribute to the change of M eff.