P3L-1 Elastic Moduli, and their Temperature Coefficients, of Piezoelectric and Nonpiezoelectric Polycrystalline Aggregates

Classical procedures for computing average isotropic elastic moduli of polycrystalline aggregates are associated with the names of Voigt, Reuss, and Hill. The Voigt-Reuss-Hill (VRH) procedures apply to averaging moduli subject solely to mechanical boundary conditions. Piezoelectrics in general, are required to be characterized by both mechanical and electrical boundary conditions. This paper describes proper averaging for piezoelectrics, along with an advanced averaging method. Numerical values are provided for examples using materials with strong piezocoupling values. The examples demonstrate that the piezoelectric effect must be taken into account in the averaging process. Associated temperature coefficients of the elastic moduli are also supplied for some technologically important piezoelectric and nonpiezoelectric substances