Thermal expansion of polycrystals with grain boundary sliding

Abstract

Anisotropic polycrystals in which the shear tractions vanish at several locations of the grain boundaries are considered. For three-dimensional polycrystals whose crystals belong to the tetragonal, hexagonal or trigonal class, it is shown that the effective thermal expansion tensor is given in terms of its effective elastic compliance and the properties of the constituent crystals. If the crystals are cubic, it is shown that the components of the effective compliance tensor obey a constraint condition whereas the effective thermal expansion tensor is equal to that of the constituent crystals. Polycrystals containing an inclusion phase and exhibiting grain boundary sliding at possible locations of the crystal-crystal and crystal-inclusion boundaries are also considered. For such polycrystals microstructure independent relations for the effective thermal expansion tensor are derived under the restriction that both the crystals and the inclusion phase are cubic. Corresponding results for planar polycrystals in plane stress or plane strain conditions are also presented.