Effective elastic stiffness of polycrystalline solid with general imperfect interface

Abstract

The analytical self-consistent model of a polycrystalline solid with isotropic grains and a general imperfect interface has been developed. The grain-to-grain bonding conditions assume a jump of both the displacement and normal traction vectors across the interface. The model is consistent with the general theory of curved deformable interfaces in solids with nanometre-scale microstructure (Gurtin et al., 1998) that justifies its applicability to the elastic nanopolycrystals. The proper formulation of the self-consistent micromechanical model of polycrystal imperfect interface is discussed. The explicit formulas for the effective elastic moduli are derived from the multipole expansion solution to the model problem under the zero dipole moment condition of the imperfectly bonded inhomogeneity in the effective medium. The developed theory and numerical results are validated by comparison with the available results for the spring and membrane-type interfaces.