Variations in the second- and third-order elastic constants in polycrystalline aggregates

Abstract

Expressions for the expected variation in the effective second- and third-order elastic constants of statistically isotropic polycrystalline aggregates with a finite number of crystallites are developed. The analysis is based on the Voigt approach for the effective response of an aggregate and is valid for cubic crystals of the highest symmetry (m3m,432,4̄3m). In this approach, the effective stiffnesses are the averages of the stiffnesses in the constituent crystals. It is shown that the expected variance in the effective elastic stiffness is inversely proportional to the number of crystallites contributing to the average. Numerical evaluations for crystals of various materials show that the variations in the third-order stiffnesses are substantially larger than the variations in the second-order stiffnesses.