The Constitutive Relations Of Ferroelectric Composites

This dissertation studies the macroscopic and microscopic electric-mechanical coupling behavior of ferroelectric composites in systematic manner. The work is focused on the following five aspects:1. The problem of a ferroelectric ellipsoidal inclusion embedded in an infinite non-piezoelectric matrix is analyzed via the Green's function technique. The closed-form solutions of the electroelastic Eshelby's tensors can be expressed by the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby's tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics respectively, the electroelastic Eshelby's tensors can be gotten conveniently. Using these results, the closed-form solutions of the constraint elastic fields and constraint electric fields inside ferroelectric ellipsoidal are also obtained. The closed-form solutions can be readily utilized in analyzing the relations between the constraint electroelastic fields in the inclusion and applied electroelastic fields, which are the base of the switching criterion when the interactions among inclusions are considered, In this part, the analytical solutions of electroelastic Eshelby's tensors are obtained for the cylinder inclusion and the spherical inclusion which are transversely isotropic.2. Based on the generalized Budiansky's energy-equivalence framework and the results obtained in part I, the linear electric-mechanical coupling behavior of ferroelectric composites is studied systematically. The closed-form solutions of the effective properties of piezocomposites are given. The solutions can be used to analyze non-interaction or interaction among piezoelectric inclusions as well as the different connectivity patterns. The closed-form solutions of the effective properties of piezocomposites with non-piezoelectric inclusions are also obtained. In this part, the analytical solutions of the effective electroelastic moduli are obtained by means of the dilute solution for the 0-3 piezocomposite with the transversely isotropic piezoelectric spherical inclusion and by the dilute solution and the Mori-Tanaka's method for the 1-3 piezocomposite with two kinds of transversely isotropicpiezoelectric cylinderical inclusions. The predicted results are compared with experimental data, which shows that the theoretical values agree quite well with the experimental ones.3. The non-linear electric-mechanical coupling behavior of ferroelectric composites is studied systematically by means of orientation distribution function (ODF) and its evolution and the domain switching of ferroelectric inclusions. The switching criterion which considers the interaction among the ferroelectric inclusions and the effect of material properties of constitutive phases is established. The free energy of the constitutive element is derived by micromechanics. Based on the above results, the constitutive law of ferroelectric composites is obtained, which can be used to analyze the poling problems and the non-linear electric-mechanical coupling problems of ferroelectric composites. The theoretical values are compared with experimental results, which shows that the constitutive law in this part can describe the principal properties of ferroelectric composites very well.4. The electric-mechanical coupling properties of the ferroelectric composites whose matrix is viscoelectric and exhibits dielectric relaxation are studied by means of Laplace transformation. The switching criterion and constitutive law is obtained which considers the interaction among the ferroelectric inclusions and the viscoelasticity and dielectric relaxations of the matrix. The predicted results are compared with experimental data, which shows that the constitutive law can describe the electric-mechanical coupling behavior of these kinds of ferroelectric composites.5. The experimental research for ferroelectric composites is carried out and new experimental data are obtained.