| In this dissertation, models for the constitutive behavior of ferroelectric ceramics are developed. Constitutive laws for single crystals are proposed based on the knowledge that domain wall motion is responsible for polarization switching and that this motion is a dissipative process. The criterion that is used for single crystal switching is that the motion of the domain wall must dissipate a critical amount of energy. Consequences of this assumption lead to the derivation of the tangent moduli (elastic stiffnesses, piezoelectric coefficients and dielectric permittivities) of the single crystal. Once the single crystal behavior is developed, a self consistent scheme is used to predict the response of a polycrystalline ferroelectric ceramic made up of randomly oriented single crystals. The self consistent model assumes that each single crystal can be represented as a spherical inclusion embedded in a matrix. Far field electric fields and mechanical stresses are applied to the matrix and the incremental response of each inclusion is calculated accounting for the constraint that the matrix imposes on the inclusions and thus the electric field, electric displacement, strain and stress rates imposed on the matrix are in general different from those acting on the inclusions. The model is termed “self consistent” because the tangent moduli of the matrix are taken to be equal to the averaged tangential response of the single crystal inclusions. With this model, the strain and electric displacement in the material can be calculated given the history of electric field and stress loading on the material. Then, using the self-consistent model as a guide, a two dimensional, plane strain phenomenological constitutive model is constructed. The model contains many of the necessary features for a phenomenological law but is not entirely sufficient. Finally, asymptotic stress fields near a crack in a ferroelectric are investigated. |
