Bounds and self-consistent estimates of overall properties for random polycrystals described by linear constitutive laws

Analytical solutions for bounds of overall properties are derived for singlephase polycrystalline materials of random texture, composed of grains with arbitrary anisotropy and described by the linear constitutive law. Self-consistent estimates are found for these materials and they are studied in more details when anisotropic grains are volumetrically isotropic. Reduction of the above solutions for incompressible materials or materials with constraint modes of deformation is also derived. Existence and uniqueness of the obtained solutions are discussed. In order to obtain the solutions, simultaneously the spectral and harmonic decomposition of fourth order Hooke's tensor are used. Utility of the obtained results is demonstrated on the examples of metals and alloys of high specific strength and stiffness.