Publisher Summary Piezoelectric ceramics can sense and actuate by rapidly converting mechanical and thermal signals into electrical ones, the reverse also being true. The piezoelectric properties and quick response characteristics have made piezoelectric ceramics one of the most commonly used smart materials. The intrinsic brittleness of piezoelectric ceramics and damageability of the materials under electric field — making the materials prone to fracture — are of major concern for product reliability. The fracture of piezoelectric ceramics under combined electrical and mechanical loading has been among the most prevalent research topics. The chapter describes piezoelectricity, ferroelectrics, spontaneous polarization, and electric domains; and discusses the poling process, the hysteresis loop of polarization versus the electric field strength, and the butterfly loop of strain versus the electric field. The chapter focuses on the basic equations commonly used in the study of the fracture behavior of piezoelectric ceramics within the thermodynamics framework, the general solution based on Stroh's formalism (a powerful tool for solving two-dimensional electroelastic problems), analysis of Green's functions for insulating elliptical cavities and cracks, study of conductive elliptical cavities and cracks, study of piezoelectric interface cracks, and three-dimensional electroelastic problems. The four types of nonlinear approaches considered are: electrostriction, domain switching, domain wall kinetics, and polarization saturation at a crack tip. The polarization saturation model that treats piezoelectric ceramics as mechanically brittle and electrically ductile materials is also discussed. The chapter provides an overview of experimental observations whose results show that microstructure and temperature have a profound influence on the fracture behaviors of piezoelectric ceramics under purely mechanical loads, and also discusses the commonly used failure criteria, the electric saturation model, the stress intensity factor criterion and the stress criterion.

Fracture of piezoelectric ceramics

Fracture behaviors of piezoelectric materials

Thermo-mechanical behavior of low-dimensional systems: The local bond average approach

Fracture mechanics of piezoelectric materials – Where are we right now?

We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack-face boundary conditions in sharp models) into the phase-field framework. The proposed models are verified through comparisons with the corresponding sharp-crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack-face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

Fracture of piezoelectric materials can be caused by either mechanical loads or by electric fields. It is shown in lead zirconate titanate ceramics that conductive cracks driven by electric fields can be described by the same fracture mechanics concepts used for mechanical loads, but with a much higher fracture toughness. The electrical fracture toughness GICE=223.7±17.0 N/m (95% confidence) is 25 times higher than the mechanical fracture toughness GICM=8.7±0.4 N/m (95% confidence). This is due to the greater energy dissipation that is possible under electric loading but not possible under mechanical loading in the brittle ceramics of lead zirconate titanate.

Electrical fracture toughness for conductive cracks driven by electric fields in piezoelectric materials

The effects of applied dc electric fields of ±10 kV/cm on the modulus of rupture of poled PZT-841 ceramics were studied using three-point bending tests. At each level of the applied electric field, 54 or 55 samples were tested and the data were statistically analyzed. The results showed that the measured moduli of rupture followed a Weibull distribution with a Weibull modulus of 10.6 when no electric field was applied. When the applied electric field was either parallel or antiparallel to the poling direction, the distribution of the modulus of rupture revealed two peaks and was fitted by a two-peak Weibull distribution. One peak occurred at about 95 MPa, approximately the same as that without the presence of the applied electric field, while the other peak occurred around 50 MPa under either a positive or a negative electric field. Obviously, either a positive or a negative electric field assisted the applied mechanical loading to fracture the samples.

Effects of an Applied Electric Field on the Modulus of Rupture of Poled Lead Zirconate Titanate Ceramics

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

Fracture behavior of conductive cracks in PZT-4 piezoelectric ceramics

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

Influences of temperature and electric field on the bending strength of lead zirconate titanate ceramics

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Papers

Electrical fracture toughness for conductive cracks driven by electric fields in piezoelectric materials

Effects of an Applied Electric Field on the Modulus of Rupture of Poled Lead Zirconate Titanate Ceramics

Fracture behavior of conductive cracks in PZT-4 piezoelectric ceramics

Fracture behavior of conductive cracks in PZT-4 piezoelectric ceramics

Influences of temperature and electric field on the bending strength of lead zirconate titanate ceramics