A modified voigt method for calculation of the elastic constants of ensembles selected by diffraction methods

Abstract

The Voigt assumption describes a polycrystalline material under load as having an isotropic strain tensor in all grains. Consequently the corresponding stiffness tensor is isotropic according to Voigt. Extension of the Voigt limit to the calculation of elastic compliances used with diffraction stress determination techniques by Moller and Martin yielded values that are independent of the reflection used for the measurement. Since the data obtained by diffraction originated solely from the domains that satisfy Bragg’s law, one can modify the Voigt assumption by requiring that the strain tensors of the diffracting grains be equal to an average strain (ϵij)hklfor the particular reflection, where this average is different from the macroscopic average strain of the aggregate. In this paper this calculation is discussed. It is shown that this modification of the Voigt assumption yields compliances that are dependent on the crystallographic orientation of the diffracting crystallites. The isotropic nature of previously calculated Voigt constants is reproduced as a special case of this more general tensor. The modified Voigt diffraction elastic constants for (h00) and (hhh) reflections are also equivalent to those derived using the traditional Reuss treatment due to Neumann’s principle of symmetry. © 1999 Taylor & Francis Group, LLC.