On the effect of remanent polarization on electro-mechanical fields near an elliptic cavity in poled or depolarized piezoelectric ceramics

In this paper the effect of remanent polarization on electric-mechanical fields near an elliptic cavity in piezoelectric ceramics is studied. The analysis is based on the application of exact electric boundary conditions at the rim of the elliptic cavity, thus avoiding the common assumption of electric impermeability. Expressions for electromechanical fields near the elliptic cavity are derived in a closed form in terms of complex potentials. The result shows that the problem of remanent polarization is similar to the problem of general strain mismatch and the effect of remanent polarization on fracture in poled or depolarized piezoelectric ceramics can not be omitted. When the permitivity of the medium in a cavity is small, the effect of remanent polarization is identical to the effect of a considerable strong positive electric field and the tangent stress at the major axial apex of the elliptical cavity is tensile. Such behavior explains why the positive electric field promotes the crack growth while the negative electric field retards the crack growth and accounts for the anisotropy of fracture toughness under mechanical loads. The results show that the effect of remanent polarization on electromechanical fields near an elliptic cavity depends not only on the geometry of the elliptic cavity, i.e. the ratio of the minor semi-axis to major semi-axis, but also on the ratio of permitivity of the medium in the cavity to permitivity of the piezoelectric ceramic.     

An approach for analysis of poled/depolarized piezoelectric materials with a crack

In this paper, the influence of dielectric medium inside a crack on crack growth, in an infinite poled or depolarized ceramic, has been studied by employing an electric boundary condition derived from the exact boundary conditions proposed by Sosa (1996). The effect of remanent polarization has also been examined. The results obtained show that electric displacement on crack surfaces is not always zero. Hence, for studying fracture problems of piezoelectric ceramics with cracks accurately, the exact boundary conditions should be implemented. In addition, the results indicate that the effect of remanent polarization is equivalent to that of a positive electric field and it cannot be neglected. It is also found that a positive electric field always has a tendency to open a crack, and a negative electric field tends to close a crack.     

Effects of electric field and poling on the mode I energy release rate in cracked piezoelectric ceramics at cryogenic temperatures

We discuss the mode I energy release rate of a rectangular piezoelectric material with a crack under electromechanical loading at cryogenic temperatures. A crack was created normal or parallel to the poling direction, and electric fields were applied parallel or normal to the poling. A plane strain finite element analysis was carried out, and the effects of electric field and localized polarization switching on the energy release rate were discussed for the piezoelectric ceramics at cryogenic temperatures.     

Electromechanical properties of lead zirconate titanate piezoceramics under the influence of mechanical stresses

In lead zirconate titanate piezoceramics, external stresses can cause substantial changes in the piezoelectric coefficients, dielectric constant, and elastic compliance due to nonlinear effects and stress depoling effects. In both soft and hard PZT piezoceramics, the aging can produce a memory effect that will facilitate the recovery of the poled state in the ceramics from momentary electric or stress depoling. In hard PZT ceramics, the local defect fields built up during the aging process can stabilize the ceramic against external stress depoling that results in a marked increase in the piezoelectric coefficient and electromechanical coupling factor in the ceramic under the stress. Although soft PZT ceramics can be easily stress depoled (losing piezoelectricity), a DC bias electric field, parallel to the original poling direction, can be employed to maintain the ceramic poling state so that the ceramic can be used at high stresses without depoling.     

热极化和电晕极化铁电PVDF薄膜的成分和结构

用高分辨率X-射线光电子能谱（XPS）研究了热极化和电晕极化的PVDF薄膜的成分和结构的变化。结果表明：PVDF薄膜的热极化和电晕极化反应过程和机理不同。在热极化过程中.高温强电场作用使PVDF薄膜产生了少量的F^-自由基,继而产生HF,形成了新C=C键：怛是,在电晕极化过程中荷能粒子使PVDF产生了H^＋自由基。热极...     

Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions

The purpose of the present work is to study the problem of two collinear unequal cracks in a piezoelectric plane under mode I electromechanical loadings via a new approach. For the first time, real fundamental solutions are derived for in-plane piezoelectric governing equations. The cracks are simulated by continuously distributed generalized dislocations and Cauchy singular integral equations are established from the solution of a generalized point dislocation. Both the theorectical derivation and numerical computations are validated by the exact solution in a special case. Parametric studies are conducted to reveal the effects of crack space, crack length, electric loading and remanent electric displacement on energy release rate. It is found that negative electric displacement loading can decrease both the total energy release rate (TERR) and the mechanical strain energy release rate (MSERR), implying that it has a shielding effect on cracks definitely. Positive electric displacement loading can enhance MSERR, but meanwhile it can enhance or reduce TERR depending on the magnitude of the electric loading factor. The effect of a remanent electric displacement along the poling direction is equivalent to that of a positive electric field loading and should be considered in engineering design.     

0．98Na0．5Bi0．5TiO3—0．02NaNbO3无铅压电陶瓷的极化研究

极化显著影响压电陶瓷的应变量和电畴转向率，从而影响其压电性能。本文研究了0．98Na0．5Bi0．5TiO3-0．02NaNbO3压电陶瓷的极化条件。研究表明极化电场为4kV／mm、极化温度为120℃、极化时间为20min时，其压电常数d33最大值为96pe·N^-1。     

Electric field dependence of the mode I energy release rate in single-edge cracked piezoelectric ceramics: effect due to polarization switching/dielectric breakdown

This study presents the results of the mode I energy release rate of a rectangular piezoelectric material with a single-edge crack under electromechanical loading. A crack was created normal or parallel to the poling direction, and electric fields were applied parallel and antiparallel to the poling. A nonlinear plane strain finite element analysis was carried out, and the effect of localized polarization switching on the energy release rate was discussed for the permeable, impermeable, open, and discharging cracks under a high-negative electric field. The effect of dielectric breakdown on the energy release rate was also examined under a high-positive electric field.     

The strip dielectric breakdown model

This paper reports on the analysis of the strip dielectric breakdown (DB) model for an electrically impermeable crack in a piezoelectric medium based on the general linear constitutive equations. The DB model assumes that the electric field in a strip ahead of the crack tip is equal to the dielectric breakdown strength, which is in analogy with the classical Dugdale model for plastic yielding. Using the Stroh formalism and the dislocation modeling of a crack, we derived the relationship between the DB strip size and applied mechanical and electrical loads, the intensity factors of stresses and electric displacement, and the local energy release rate. Based on the results, we discussed the effect of electric fields on fracture of a transversely isotropic piezoelectric ceramic by applying the local energy release rate as a failure criterion. It is shown that for an impermeable crack perpendicular to the poling direction, a positive electric field will assist an applied mechanical stress to propagate the crack, while a negative electric field will retard crack propagation. However, for an impermeable crack parallel to the poling direction, it is found that the applied electric field does not change the mode I stress intensity factor and the local energy release rate, i.e., the applied electric field has no effect on the crack growth.     

A pronounced manifestation of a new electric-to-mechanical coupling phenomenon in the ferroelectric ceramic PZT 65/35

Summary In this paper, we present experimental results to show a pronounced manifestation of a new electric-to-mechanical coupling phenomenon in the ferroelectric ceramic PZT 65/35. This phenomenon has been previously reported in the electro-optic ceramic PLZT 7/65/35. We believe that it is also present in other ferroelectric materials. In particular, experimental evidence indicates that this coupling phenomenon during the process of poling results in flexural mechanical displacements which are much larger than the combined changes in thickness due to domain switching and conventional piezoelectric coupling. Its influence also increases markedly with remanent polarization.With 1 FigureThis paper is dedicated to the memory of Professor Aris Phillips whom I have had the extreme privilege of knowing.     

Ferropiezoelectricity of calcium modified lead titanate ceramics

When a ceramic with grain Boundaries rich in OPb is poled Beyond 4O kV cm^–1 at ferroelectric phase, the highest anisotropy of electromechanical coupling factor is obtained. An attempt to explain this Behaviour is made in terms of domain switching and the strains and cracks generated during cooling down poling. Apart from composition, two more factors are revealed as contributing to the disappearance of radial coupling in Ca-modified lead titanate ceramics: microtexture and electric poling strategy.     

致密PZT95/5铁电陶瓷低温相结构与电性能研究

采用固相法制备了致密PZT95/5铁电陶瓷, 研究了低温下致密PZT95/5铁电陶瓷相结构和电性能的变化规律。变温X射线衍射(XRD)研究表明, 低温(-60℃)下极化和未极化致密PZT95/5铁电陶瓷相结构保持不变。电性能研究表明随着温度从30℃下降至-60℃, 致密PZT95/5铁电陶瓷的相对介电常数从278显著下降至173, 而电阻率和剩余极化强度基本保持不变。结合冲击波载荷下动态放电模拟分析, 发现相对介电常数的降低将引起动态电场增大至常温下的1.5倍, 这可能是导致致密PZT95/5铁电陶瓷低温下击穿概率显著增大的关键因素。     

On fracture testing of piezoelectric ceramics

Fracture tests carried out on unpoled and poled PZT-5H four-point bend specimens are presented in this paper. The crack faces were parallel to the poling direction. Both mechanical loads and electric fields were applied to the poled specimens. The experimental results were analyzed by means of the finite element method and a conservative M-integral including the crack face boundary conditions. Fracture tests on four-point bend PIC-151 specimens with the crack faces perpendicular to the poling directions were also analyzed here; the experimental results were taken from the literature. A mixed mode fracture criterion is proposed for piezoelectric ceramics. This criterion is based upon the energy release rate and two phase angles. This criterion was implemented with experimental results from the literature and from this investigation. Excellent agrement was found between the fracture curve and the experimental results of the specimens with the crack faces perpendicular to the poling direction. With some scatter, reasonable agreement was observed between the fracture curve and the experimental results of the specimens with crack faces parallel to the poling direction.     

The interface crack problem for bonded piezoelectric and orthotropic layers under antiplane shear loading

The primary objective of this paper is to study the influence of the electroelastic interactions on the stress intensity factor in bonded layers of piezoelectric and orthotropic materials containing a crack along the interface under antiplane shear. Attention is given to a two-layer hybrid laminate formed by adding a layer of piezoelectric ceramic to a unidirectional graphite/epoxy composite or an aluminum layer. Electric displacement or electric field is prescribed on the surfaces of the piezoelectric layer. The problem is formulated in terms of a singular integral equation which is solved by using a relatively simple and efficient technique. A number of examples are given for various material combinations. The results show that the effect of the electroelastic interactions on the stress intensity factor and the energy release rate can be highly significant. This revised version was published online in July 2006 with corrections to the Cover Date.     

A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics

A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.     

Impact response of a finite crack in an orthotropic piezoelectric ceramic

Summary The transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.     

PZN-PZT压电陶瓷及其PVDF压电复合材料的制备和性能

采用固相烧结法合成了PZN-PZT(铌锌锆钛酸铅)三元系压电陶瓷烧结块材和粉末,并采用XRD、SEM等测试方法对其结构和性能进行了分析。PZN-PZT常压烧结陶瓷具有优良的压电性能,PZN-PZT颗粒粒径在0.5~4 μm之间,颗粒形态不太规整。采用溶液共混法将PZN-PZT粒子均匀分散于PVDF基体中,制备了PZN-PZT/PVDF 0-3型压电复合材料。研究了PZN-PZT质量分数、极化电场等因素对该压电复合材料压电和介电性能的影响。实验结果表明,选用压电活性更高的压电陶瓷粉末进行复合,可有效提高压电复合材料的压电性能。增加PZN-PZT质量分数、提高极化电压均有利于复合材料压电性能的提高。     

Analysis of a circular arc-crack in piezoelectric materials

This paper is concerned with the development of a model for the treatment of a circular arc-crack in piezoelectric materials under antiplane shear and inplane electric field using the complex variable method. The problem is formulated in terms of the analytical continuation principle and complex series expansion, and as a result is reduced to two Riemann–Hilbert problems. The resulting closed form solution was then used to obtain the electroelastic field intensity factor and the energy release rate. Unlike the electric enthalpy release rate, the internal energy release rate is always positive and can thus be used as a more reliable fracture parameter in piezoelectric materials. It is also observed that the crack configuration has a significant influence upon the energy release rate. This revised version was published online in August 2006 with corrections to the Cover Date.     

The energy release rate for a Griffith crack in a piezoelectric material

The plane solution giving the stresses and electric fields in an infinite body around a cylindrical cavity with an elliptical cross-section is presented. The energy change in an infinite body due to the introduction of an elliptical cavity having an electric field within it is calculated. The electric field from the interior of the cavity is then used in conjunction with the energy change formula to calculate the total energy release rate per crack tip when a Griffith crack propagates. Due to a change of stored electrostatic energy within the crack, the total energy release rate is not equal to the energy release rate at the crack tips as the material separates. The implications for fracture and crack growth are discussed.