Micro-Electromechanical Determination of the Possible Remanent Strain and Polarization States in Polycrystalline Ferroelectrics and the Implications for Phenomenological Constitutive Theories

The micro-electromechanical constitutive model for polycrystalline ferroelectric ceramics is implemented to determine the remanent strain and remanent polarization states that are possible in a ferroelectric polycrystal. The underlying crystal structure of the single crystals is assumed to be tetragonal, but the methods developed in this paper can be applied to other crystal structures as well. The full multi-axial set of remanent strain saturation states possible in an untextured polycrystal is determined. It is argued and demonstrated that the remanent polarization saturation level is dependent on the prevailing remanent strain state. The possible uniaxial combinations of remanent strain and polarization are determined from the micro-electromechanical model. The results of these investigations are then applied within the phenomenological constitutive framework and the constitutive response under coupled electromechanical loading is predicted.