Estimates for the elastic moduli of random orthorhombic polycrystals

Our variational bounds are suggested to provide estimates on the possible scatter ranges for the macroscopic elastic moduli of random polycrystalline materials. Explicit expressions for the random aggregates of orthorhombic crystals are derived and calculated. The complicated general bounds are well approximated by the simple ones for specific spherical cell polycrystals, which are proposed also to represent practical equi-axed particulate aggregates. Hence the latter could be recommended for practical uses. The results for a number of polycrystals indicate that their macroscopic moduli may be determined with the accuracy from two to four significant digits.