Materials design of elastic properties of multiphase polycrystalline composites using model functions

For a chosen combination of materials for a multiphase polycrystalline composite, a crystallite orientation distribution function for each phase is formulated as a superposition of analytic central model von Mises-Fisher functions. The chosen central model functions allow the analytic integration of orientation averages of arbitrarily anisotropic fourth-order tensors. Based on this result, the first-order bounds of Voigt and Reuss and the geometric average of the stiffness can be expressed explicitly in closed forms for arbitrarily anisotropic polycrystalline materials and number of phases depending on the volume fractions and the influence of the crystallographic texture of each constituent. These expressions can then be used for the materials design aiming the determination of volume fractions and orientation distribution of selected materials for prescribed effective properties. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)