An equation is derived for the effective work function of a polycrystalline metal with a fiber texture. This equation contains two parameters: the temperature and the maximal tilt angle, i.e. the maximal deviation from the fiber axis. A linear relationship is assumed between the work function of a uniform lattice plane and the angle of a low index plane with respect to the uniform lattice plane. The proportionality constant D in the  zone is evaluated from experimental data for tungsten: D=0.035 * (eV/degree). It is expected that D has the same value in other bcc metals. For a given maximal tilt angle, a higher temperature results in a higher effective work function. A reasonable agreement is found for the calculated effective work functions of tungsten with 110 fiber textures of various sharpness and the experimentally determined work functions from the literature. Furthermore, the effective work function of texture-free polycrystalline tungsten is calculated. The agreement with the experimentally determined value reported in the literature is excellent.
Gubbels, G. H. M., & Metselaar, R. (1990). On the effective bare work function of bcc thermionic electrode materials. Surface Science, 226(3), 407-411. https://doi.org/10.1016/0039-6028%2890%2990503-Z, https://doi.org/10.1016/0039-6028(90)90503-Z