On the size of the Representative Volume Element for isotropic elastic polycrystalline copper

Abstract

A computational homogenization strategy is developed to determine the number of grains necessary to estimate the effective elastic properties of isotropic polycrystalline copper with a given precision. Finite element simulations of polycrystalline aggregates are presented for both homogeneous and periodic boundary conditions. For different volumes, several realizations are considered. The mean apparent shear modulus and the associated dispersion are estimated as a function of the number of grains. Periodic conditions lead to rapid convergence of the result towards the wanted effective shear modulus. The Representative Volume Element (RVE) size is then related to the evolution of the standard deviation of the apparent shear modulus, via an extension of the notion of integral range A3. For a precision of 1% and 10 realizations, a minimal RVE size of 445 grains is found. The found value A3 = 1.43 can be compared to the integral range for other microstructures and physical properties. © 2007 Springer.