Polycrystal piezoelectricity: revisiting the Voigt-Reuss-Hill approximation

A tensor formalism for the calculation of effective polycrystal properties associated with polar tensors of up to 4th rank is presented. Sample fiber symmetry is assumed. The Hill approach, via Voigt and Reuss approximations, is followed. The article contains a compact summary of the required mathematical background. The necessary considerations for the treatment of the so-called coupling properties, particularly piezoelectricity, are considered. Focus is put on the elasto-piezo-dielectric case. The analysis of an experimental study from the literature is presented. The article includes a link to the system of programs developed during the investigation. The methodology and the programs described in this article represent tools for the approximate prediction of the properties to be expected in piezoceramics.