Constitutive relations of ferroelectric ceramics

The objective of this thesis is to obtain a better understanding on the fundamental constitutive behavior of ferroelectric ceramics based on the physics of phase transition, micromechanics of heterogeneous materials, and principles of irreversible thermodynamics. Within this framework, a self-consistent model is developed to investigate the electromechanical responses of ferroelectric polycrystals under temperature change and electromechanical loading. Cooling of a paraelectric crystal below its curie temperature T_c would result in spontaneous polarization, whereas electromechanical loading on a poled crystal could lead to domain switch. Domain growth and reorientation inside ferroelectric crystals are studied in light of these phase transition and domain switch. In this process, the change of the effective elastic, dielectric and piezoelectric constants during the evolution of microstructures are examined. In addition, hysteresis loops for the electric displacement and other related phenomena are computed under cyclic electric load.; On top of all methods implemented in this work, the kinetic equation derived from the irreversible thermodynamics is the key to study the domain evolution in ferroelectric crystals. The kinetic relation not only governs the growth of new domain in a ferroelectric crystal, but it also determines the onset of phase transition. This characteristic is used to study the effect of hydrostatic pressure on the shift of Curie temperature of a ferroelectric crystal. Based on the derived expressions, it is observed that the deriving force can increase or decrease upon applied hydrostatic mechanical loading, depending on the change of electromechanical moduli, eigenstrain and electro-polarization. Several typical cases are computed and it is found that the change of the electromechanical moduli during phase transformation plays the key role in the shift of Curie temperature.; Since ferroelectric ceramics are in a polycrystal form, a self-consistent model is used to examine the issues involved. In this model, each grain is represented by a spherical inclusion embedded in an infinitely extended piezoelectric matrix, and the inclusion further possesses an eigenstrain and eigen polarization. Secant relations between the polycrystal-matrix and the embedded inclusion are established by extending Hill's [1] incremental relations. An iterative computational program is developed for this self-consistent model.