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Theoretical modeling of small-scale domain switching and fracture of ferroelectric materials Zeng, Xianwei

Abstract

The intrinsic electromechanical properties and quick response to external excitations make ferroelectrics an ideal material for fabrication of sensors, actuators and adaptive (smart) structures. Ferroelectrics have been increasingly employed beyond the linear regime as characterized by linear piezoelectricity. Electric fields and forces required to achieve large actuation result in mechanical and electrical degradation. Understanding of coupled electromechanical behavior and fracture mechanics of ferroelectrics is very important to the reliability and efficient design of devices made out of them. Some problems related to fracture mechanics of ferroelectrics are investigated theoretically in this thesis. A unique feature of ferroelectrics is their ability to rotate the direction of spontaneous polarization (i.e. domain switching) by 180° or non-1800, when subjected to a large electric field or stress. Domain switching is the major source of material non-linearity and has a significant influence on crack-tip electroelastic field. By examining the change of free energy before and after switching of an elliptic crystallite in a poled ferroelectric, a domain switching criterion which predicts the critical loading to trigger polarization switching is proposed for ferroelectric materials. This new criterion considers the interaction of the applied field with the switching strains and polarization and the change of electroelastic properties of the switched domain. A theoretical model similar to transformation toughening of zirconia-containing ceramics is proposed to investigate the effects of small-scale domain switching at a crack tip on crack tip field intensity factors. The new domain-switching criterion is used to predict the switching zone around a crack tip. A fundamental solution for a crack interacting with stress-free transformation strains and electric field-free polarization is obtained by using the Leknitskii's formalism. A Reuss-type approximation is proposed to model polycrystalline ferroelectrics. The influence of electromechanical loading and polar direction on apparent fracture toughness is numerically investigated for insulating and conducting cracks and qualitatively compared with available experiments. The theoretical models are extended to analyze the electroelastic field at the tip of a closed insulating (or conducting) crack or an embedded electrode. The effect of domain switching on the near-tip field is examined. The tensile stress ahead of a closed crack tip may lead to crack growth, while the intensified stress at an electrode-ceramic interface may lead to segmentation cracks and electrode delamination as observed in experimental studies of multi-layer stack actuators.

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