Improved three-point correlation estimates for the effective elastic moduli of random orthorhombic crystals and multicomponent materials

Abstract

Particular expressions of upper and lower bounds on the macroscopic elastic moduli of random cell orthorhombic polycrystalline materials are derived and computed for a number of practical crystals. The cell-shape-unspecified bounds, based on minimum energy principles and generalized polarization trial fields, appear close to the bounds for specific spherical cell polycrystals (the differences between the bounds are reduced a half compared to those from our previous bounds using Hashin-Shtrikman polarization trial fields). The results enforce our assessment to use our previous simple bounds for spherical cell polycrystals generally as good simple estimates for the scatter ranges of the elastic moduli of the random polycrystalline materials. Our previous three-point correlation bounds on the elastic shear modulus of -dimensional multicomponent materials (including those for symmetric cell mixtures) become singular in the case of 2D lower bound – the case is also re-examined in this paper.

Keywords:

• random cell polycrystal
• orthorhombic crystal
• isotropic multicomponent material
• bounds on effective elastic moduli

Acknowledgments

We thank the support of Vietnam’s Nafosted, Project N. 107.02-2013.20.