Lead zirconate titanate (PZT) ferroelectric ceramics are widely applied in actuators, sensors, controlling devices and smart structures. Service conditions often involve combined mechanical-electrical loadings, which may deteriorate material properties and thus reduce reliability. Essentially, PZT ceramics are brittle and crack easily at all scales from domains to devices. Most industrial applications require the reliability of this type of piezoelectric materials to be well ensured. Thus fracture mechanics studies become an essential step for a better understanding of fracture behaviors of the materials.

Even though the response of ferroelectrics on applied fields is essentially nonlinear, linear analysis is still fundamental and important. We started from the linear electro-elastic theoretical analysis through Stroh's formalism and coordinate transformation, to investigate the crack driving force as a function of applied mechanical and electrical loadings for different crack orientations with respect to the poling direction. We found that the energy release rate for the propagation of a slit crack is related to the slit geometry and the ratio of dielectric constants. For an insulating crack, the energy release rate is smaller when the crack plane is closer to the poling direction, indicating that the material will be easily fractured when the poling direction is perpendicular to the crack plane. For a conducting crack, however, the energy release rate behaves differently in different loading conditions. But the tendency to crack is most likely along the crack plane parallel to the poling direction, along which the electric field is applied.

To explore the non-linearity around the crack tip in the piezoelectric material under the mixed mechanical and electric loadings, we studied the interaction of a piezoelectric screw dislocation with an insulating cavity and presented the general solution in series, using the image dislocation approach with consideration of the electric field in the cavity. When the cavity is reduced into a crack, three cases appear, which correspond to three different electrical boundary conditions along the crack faces, depending on the ratio of α/β, where α is the ratio of the minor semi-axis to the major semi-axis of the ellipse and β is the ratio of the dielectric constant of the cavity to the dielectric constant of the piezoelectric material. The crack is electrically impermeable when α/β→∞, while the crack becomes electrically permeable as α/β→0. Since the minimum of dielectric constant has a finite nonzero value and a real crack has also a nonzero width, the ratio of α/β will generally have a finite nonzero value, resulting in a semi-impermeable crack. Furthermore, the difference in the electric boundary conditions lead to great differences in the image force acting on the dislocation, and in the intensity factors and the energy release rate induced by the dislocation.

Experimentally we investigated the fracture behavior of conductive cracks in PZT-4 piezoelectric ceramics by using compact tension specimens under electrical and/or mechanical loading. Finite element calculations were conducted to obtain the energy release rate, the stress intensity factor and the intensity factor of the electric field strength for the specimens. The experimental results show that the critical energy release rate under either pure electrical or pure mechanical loading is a constant, independent of the ligament length. However, the critical energy release rate under combined electrical and mechanical loading depends on the weighting of the electrical load in comparison with the mechanical load. We normalized the critical stress intensity factor by the critical stress intensity factor under pure mechanical loading and normalized the critical intensity factor of electric field strength by the critical intensity factor of electric field strength under pure electric loading. Then, a quadratic function describes the relationship between the normalized critical stress intensity factor and the normalized critical intensity factor of the electric field strength, which can serve as a failure criterion of conductive cracks in piezoelectric ceramics under combined electrical and mechanical loading.

While a pure electric field can fracture poled ferroelectric ceramics, and electric fracture toughness exists for PZT ceramics, we then further studied how the electric fields effect depoled lead zirconate titanate ceramics with conductive cracks. With the same methodologies used for poled ferroelectric ceramics, we found the principle of fracture mechanics can also be used to measure the electrical fracture toughness for depoled PZT ceramics. The electrical fracture toughness G

_{C}^{E}= 263±35 N / m is about 9 times higher than the mechanical fracture toughness G

_{IC}^{M} = 30.4±3.9 N / m . The high electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under pure electric loading, which is impossible in the brittle depoled ceramics under pure mechanical loading. The energy release rate for combined mechanical and electric loadings, however, depends on the weighting of the electrical load in comparison with the mechanical load. When we normalized the critical intensity factor under combined loading by the critical stress intensity factor under purely mechanical loading and the critical electric intensity factor under combined loading by the critical electric intensity factor under purely electrical loading, we obtained a quadratic function to represent their relationship, which can be regarded as a failure criterion for depoled ferroelectric ceramics with conductive cracks.

We conducted a theoretical nonlinear analysis and computer simulations to understand the fracture behavior of a conductive crack in a dielectric material. A polarization saturation-free zone (SFZ) model is proposed to establish a failure criterion for conductive cracks in dielectric Theceramics under electric and/or mechanical loads. The SFZ model treats dielectric ceramics as mechanically brittle and electrically ductile material and allows the local intensity factors of electric field strength and electric displacement, as well as local stress and strain intensity factors, to have finite nonzero values. At failure we apply the Griffith criterion to balance the critical value of local energy release rate at the crack tip with the specific surface energy. Failure occurs when the local energy release rate exceeds the critical value. The experimental results in Chapter 5 agree with the predictions from the proposed SFZ model. The computer simulations are based on the results of the nonlinear analysis, which gives a polarization saturation zone, and a domain-switching model. In computations, we ignore the transformation strain in the depoled ceramics and use an electric dipole to represent the local net saturation polarization in an element such that a polydomain structure is simulated with a grid of points where each polarization is fixed at each grid point. Considering the interactions among the electric dipoles and the crack, we calculate the total electric field, which acts on a linear dielectric background medium. The entire material response is then described by the behavior of the background medium under the integrated loading from the electric dipoles and applied. To verify the algorithm, we simulated P~E curves under a remotely uniform loading for a finite medium with a single edge crack and obtained very satisfactory results, thereby ensuring the accuracy of the algorithm. We took the local energy release rate as the fracture criterion. Domain switching in the polarization saturation zone shields the conductive crack tip from the applied loads. That is why electrical fracture toughness is much higher than the mechanical fracture toughness. The simulation results illustrate that this combined polarization saturation zone and domain-switching model explain our experimental observations and facilitate the establishment of a failure criterion for conductive cracks in piezoelectric ceramics under combined mechanical and electrical loading.

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