Characterization of Stress-Effects in Ferroelectrics with Application to Transducer Design

Abstract

The increasing investigation of smart material structures requires a more thorough understanding and characterization of the underlying physics in both the constituent materials and the adaptive structures as a whole. To this end, we focus our efforts on understanding the effects of stress on ferroelectric materials and the transducers which utilize them.

This dissertation addresses the development of constitutive models based on homogenized energy principles which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. Models characterizing the manufactured shape and quantifying the displacements generated in THUNDER (THin layer UNimorph ferroelectric DrivER and sensor) actuators in response to applied voltages for a variety of boundary conditions are developed utilizing the developed ferroelastic switching models.

To develop constitutive models, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 degree dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. Stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds.

Models characterizing the manufactured shape of THUNDER actuators and displacements resulting from applied voltages for fields are constructed using thin shell theory and Newtonian principles. The thermal stresses and strains due to repoling resulting in a prestressing of the PZT layer are also included in the model development. Attributes and limitations of the characterization framework are illustrated through comparison with experimental data.