Microstructural model of a ferroelectrоelastic material taking into account the evolution of defects

Abstract

For the description of the hysteresis behavior of ferroelectrics/ferroelastics under complex multiaxial combined electrical and/or mechanical loading, a thermodynamically consistent microstructural model of a ferroelectroelastic material is proposed taking into account the presence and evolution of polar point defects. The model also takes into account multiphase composition (tetragonal, rhombohedral and orthorhombic phases and their mixtures), anisotropy of properties, domain structure, and dissipative motion of domain walls. The linear theory of the evolution of charged point defects is proposed based on the free energy of defects in the form of a quadratic form of the polarization vector and strain tensor of defects. The evolution equations of which are obtained on the base of the dissipation inequality. The cases of changing and unchanging (frozen) defects are considered. Their influence on switching processes is investigated. The dependence of the hysteresis loop shift (due intern bias field) on the parameters of the free energy of defects is shown. The mutual influence of crystallites in a polycrystal is taken into account by using the method of two-level finite element homogenization. Comparison of the computation results with experimental curves of dielectric, mechanical, and electromechanical hysteresis for polycrystalline piezoelectric PZT PIC-151, polycrystalline BaTiO3, single-crystal PMN-PZT and KTS doped with acceptor additives, showed a showed good agreement.

Keywords

• polycrystalline piezoceramics
• point defect
• constitutive equation
• hysteresis
• finite element homogenization