Effective biaxial modulus and strain energy density of ideally ( h k l)-fiber-textured cubic polycrystalline films

Abstract

The effective biaxial modulus ( M eff) and strain energy density ( W) of cubic polycrystalline films with ideally ( h k l) fiber textures are estimated using Vook–Witt (VW) grain interaction model and the data are compared with those derived from Voigt, Reuss and Voigt–Reuss–Hill (VRH) models. Numerical results show that the VW average of M eff for ideally (1 0 0)- or (1 1 1)-fiber-textured films is identical to the VRH average of M eff. For (1 1 0) and (1 1 2) planes, however, the VW average of M eff for (1 1 0)-fiber-textured film is larger than that of (1 1 2)-fiber-textured film when the Zener anisotropic factor ( A R) is not equal to 1. Furthermore, M eff and W exhibit incremental tendencies with the increase of the orientation factor (Γ h k l ) for the [ h k l] axis when A R > 1, implying that M eff and W have the minimums on the (1 0 0) plane. Reversely, M eff and W decrease with the increasing Γ h k l when A R < 1. This means that M eff and W on (1 1 1) plane have the minimums.