A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

掺杂压电陶瓷／铁电薄膜的制备和研究

PZT陶瓷粉体的制备和研究。用溶胶一凝胶法制备了错钦酸铅Pb(Zr_(0.52)Ti_(0.48))O_3（PZT），研究了溶剂乙二醇单甲醚和水的比例对PZT的晶化温度和晶粒尺寸的影响，结果表明，随溶剂比例的增大，PZT粉体的晶化温度升高晶粒尺寸增大，当V（C_3H_9O_2）／V（H_2O）＝4.47时，不仅缩短了溶胶-凝胶过程的时间，且得到的PZT粉体晶化温度低（443℃），晶粒的粒径分布集中（60-70nm）。PZT掺杂压电陶瓷的制备和研究。用同一主族元素对PZT进行掺杂改性实验，制备了Ca-PZT，Sr-PZT，Ba-PZT三个系列的压电陶瓷体系，其中每个体系中又包含1％、3％、5％、7％、9％（10％，11%）不同的掺杂量。经过压片，蒸镀电极，极化处理后测定其由，常数，结果表明，Ba离子的半径是最适合掺杂的离子半径。PZT和PbTIO。（PT）稳定溶胶的制备。在溶胶形成过程中，通过调整溶剂乙二醇单甲醚和水的比例，并加入适当量的乙酞丙酮作稳定剂，在有水体系下制备稳定的PZT和PT溶胶前驱体。该方法省略了制备中的蒸馏过程，简化了PZT和PT稳定溶胶的制备工艺。PZT铁电薄膜的制备。用自制的溶胶进行旋涂制膜，制备了膜层厚度不同的PZT和PT-PZT薄膜，在不同的锻烧温度，锻烧时间下处理为晶态膜，并对晶态膜进行表征，证明获得了钙钦矿结构的PZT晶态膜。

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Effective properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

Experimental Validation of Improving Aircraft Rolling Power Using Piezoelectric Actuators

Piezoelectric actuators are mounted on both sides of a rectangular wing model. Possibility of the improvement of aircraft rolling power is investigated. All experiment projects, including designing the wind tunnel model, checking the material constants, measuring the natural frequencies and checking the effects of actuators, guarantee the correctness and precision of the finite element model. The wind tunnel experiment results show that the calculations coincide with the experiments. The feasibility of fictitious control surface is validated.

Improvement of Aircraft Rolling Power by Use of Piezoelectric Actuators

Piezoelectric actuators are distributed on both side of a rectangular wing model,and the possibility of improvement of aircraft rolling power is investigated. The difference between the model with aileron deflection and the model without aileron (fictitious control surface, FCS) is studied. The analytical results show that these two cases are substantial different. In aileron deflection case, the aeroelastic effect is disadvantageous, so the structural stiffness should be high until the electrical voltage is not necessary. But in the case of FCS,the aeroelastic effect is advantageous and it means that lower structural stiffness can lead to lower voltage. Compared with aileron project, the FCS project can save structure weight.

Static shape control of repetitive structures integrated with piezoelectric actuators

In this paper, several simplification methods are presented for shape control of repetitive structures such as symmetrical, rotational periodic, linear periodic, chain and axisymmetrical structures. Some special features in the differential equations governing these repetitive structures are examined by considering the whole structures. Based on the special properties of the governing equations, several methods are presented for simplifying their solution process. Finally, the static shape control of a cantilever symmetrical plate with piezoelectric actuator patches is demonstrated using the present simplification method. The result shows that present methods can effectively be used to find the optimal control voltage for shape control.

Elastic Waves in a Hybrid Multilayered Piezoelectric Plate

An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a hybrid multilayered piezoelectric plate. In this method, the multilayered piezoelectric plate is divided into a number of layered elements with three-nodal-lines in the wall thickness, the coupling between the elastic field and the electric field is considered in each element. The associated frequency dispersion equation is developed and the phase velocity and slowness, as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. Examples provide a full understanding for the complex phenomena of elastic waves in hybrid multilayered piezoelectric media.

Crack problems of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials. A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric displacement D-2 induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For the bimaterials with real H, the normal electric displacement D-2 is constant along the crack faces and electric field E-2 has the singularity ahead of the crack tip and a jump across the interface.

Interacting multiple cracks in piezoelectric materials

In this paper, a method is presented to calculate the plane electro-elastic fields in piezoelectric materials with multiple cracks. The cracks may be distributed randomly in locations, orientations and sizes. In the method, each crack is treated as a continuous distributed dislocations with the density function to be determined according to the conditions of external loads and crack surfaces. Some numerical examples are given to show the interacting effect among multiple cracks.

Effect Of A Negative Poisson Ratio In The Tension Of Ceramics

The effect of a negative Poisson ratio is experimentally revealed in the tension deformation of a natural layered ceramic. This effect can increase the volume strain energy per unit volume by 1100% and, simultaneously, decrease the deformation strain energy per unit volume by about 44%, so that it effectively enhances the deformation capacity by about 1 order of magnitude in the tension of the material. The present study also shows that the physical mechanisms producing the effect are attributed to the climbing on one another of the nanostructures in the natural material, which provides a guide to the design of synthetic toughening composites.