POSSIBILITIES OF THE MODEL OF IRREVERSIBLE DEFORMATION AND POLARIZATION PROCESSES USING EXAMPLES OF THE MUTUAL INFLUENCE OF MECHANICAL AND ELECTRIC FIELDS

Abstract

The paper presents the capabilities of a model for irreversible deformation and polarization processes in polycrystalline ferroelectric materials exposed to intense mechanical stresses and electric fields. The paper presents the main provisions of a generalized three-dimensional model, which is a development of the one-dimensional Giles – Atherton polarization model for the case of mutual action of mechanical stresses and electric fields. It is based on a statistical approach of accounting the micromechanical switching of domains by an electric field, proposed by I.E. Tamm, which is supplemented by the effect of mechanical stresses on this process. The main stages are considered, and energy costs are estimated for each of them. The energy required to break the domain pinning mechanisms is determined, the work required for their simple rotation to a new direction is calculated, and the total energy losses in the real process of deformation and polarization are determined. All energy estimates are made for a representative volume and expressed through the integral characteristics of reversible and irreversible parameters. An energy balance has been obtained, which has made it possible to obtain constitutive relations for the residual strain tensor and residual polarization vector in the form of a system of equations in differentials. Reversible components in the form of algebraic tensor equations obtained by the methods of thermodynamics of irreversible processes have been added to the residual parameters. The result of the model are constitutive relations, which consist of equations in differentials for irreversible components and algebraic tensor relations for reversible components, with the difference that the physical modules in the tensor equations depend on the current values of the residual parameters. General dependencies between the sought and constitutive parameters are constructed by successive integration. For cyclic external fields, such dependencies are called hysteresis curves. The proposed model allows one to calculate all currently known experimental dependencies and select the model parameters so that not only qualitative but also quantitative coincidences are obtained. Hysteresis dependencies for various mechanical stresses and electric fields are given.