Out-of-plane interface cracks in dissimilar piezoelectric materials

Summary This paper investigates the problem of an anti-plane interfacial crack between two dissimilar piezoelectric material layers. A single crack is first considered. The effect of interaction of two collinear cracks in the medium on the field intensity factors is investigated. The solutions of several particular cases, including an infinite piezoelectric bi-material and a piezoelectric material bonded to an elastic medium, are given. The bi-material constants governing the behavior of the crack tip fields are identified. By considering the crack as a notch of finite thickness, it is shown that the thickness of the notch has a pronounced influence on the crack tip field. The results for the assumption of a permeable crack represent the limit case where the notch thickness is reduced to zero.BLW would like to thank the National Science Foundation of China (#10102004) and the City University of Hong Kong (DAG #7100219) for the support of this work. YGS also thanks the Multidiscipline Scientific Research Foundation Project (HIT. MD 2001. 39) of the Harbin Institute of Technology and the SRF for ROCS, SEM.accepted for publication 3 April 2003     

Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate

The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration. Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China.     

Interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric material

The interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric medium is investigated. Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle. Based on the electroelastic fields derived, the stress and electric displacement intensity factors, the image force acting on the dislocation are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants. In the case where one of two phases is purely elastic, the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect, the position of the dislocation and the material properties on the interaction mechanism. The project supported by the Doctoral Foundation of Hebei Province (B2003113)     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

Laminated piezoelectric plate for active underwater acoustic control

The pressure reflected from a bi-laminated piezoelectric plate has been determined using the Thomson-Haskell matrix method. The plate is composed of a piezoelectric layer with grounded vacuum and an elastic layer in contact with the fluid. An incident plane wave in the fluid medium strikes the plate at different angles. The required electric potential across the piezoelectric layer to cancel the reflection from the fluid/elastic boundary has been determined for the piezoelectric material PZT-5 at various thicknes parameters and incident frequencies. Project supported by the National Natural Science Foundation of China (No. 10172039).     

Dynamic behavior of two parallel symmetric permeable cracks in a piezoelectric strip

The dynamic behavior of two parallel symmetric cracks in a piezoelectric strip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable crack surface conditions. The cracks are parallel to the edge of the strip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the schmidt method. The results show that the stress and the electric displacement intensity factors depend on the geometry of the cracks, the frequency of incident waves, the distance between cracks and the thickness of the strip. It is also found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. Project supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province, the National Science Foundation with the Excellent Young Investigator Award (No. 19725209) and the Scientific Research Foundation of Harbin Institute of Technology (HIT.2000.30).     

T -stress in piezoelectric solid

The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superpsition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants. Contributed by WANG Biao Foundation items: the Nature Science Foundation of Shandong of China (Q99F15); the Post Doctoral Science Foundation of Heilongjiang Provice of China Biography: MA Hao (1967≈), Professor, Doctor     

Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials

A permeable interface crack between elastic dielectric material and piezoelectric material is studied based on the extended Stroh’s formalism. Motivated by strong engineering demands to design new composite materials, the authors perform numerical analysis of interface crack tip singularities and the crack tip energy release rates for 35 types of dissimilar bimaterials, respectively, which are constructed by five kinds of elastic dielectric materials: Epoxy, Polymer, Al₂O₃, SiC, and Si₃N₄ and seven kinds of practical piezoelectric ceramics: PZT-4, BaTiO₃, PZT-5H, PZT-6B, PZT-7A, P-7, and PZT-PIC 151, respectively. The elastic dielectric material with much smaller permittivity than commercial piezoelectric ceramics is treated as a special transversely isotropic piezoelectric material with extremely small piezoelectricity. The present investigation shows that the structure of the singular field near the permeable interface crack tip consists of three singularities: and , which is quite different from that in the impermeable interface crack. It can be concluded that different far field loading cases have significant influence on the near-tip fracture behaviors of the permeable interface crack. Based on the present theoretical treatment and numerical analysis, the electric field induced crack growth is well explained, which provides a better understanding of the failure mechanism induced from interface crack growth in elastic dielectric/piezoelectric bimaterials. The project supported by the National Natural Science Foundation of China (10572110), Doctor Foundation of the Chinese Education Ministry and Doctorate Foundation of Xi’an Jiaotong University. The English text was polished by Yunming Chen.     

An internal crack problem for an infinite elastic layer

The elastostatic plane problem of an infinite elastic layer with an internal crack is considered. The elastic layer is subjected to two different loadings, (a) the elastic layer is loaded by a symmetric transverse pair of compressive concentrated forces P/2, (b) it is loaded by a symmetric transverse pair of tensile concentrated forces P/2. The crack is opened by an uniform internal pressure p ₀ along its surface and located halfway between and parallel to the surfaces of the elastic layer. It is assumed that the effect of the gravity force is neglected. Using an appropriate integral transform technique, the mixed boundary value problem is reduced to a singular integral equation. The singular integral equation is solved numerically by making use of an appropriate Gauss–Chebyshev integration formula and the stress-intensity factors and the crack opening displacements are determined according to two different loading cases for various dimensionless quantities.     

A crack in a piezoelectric layer bonded to a dissimilar elastic layer under transient load

Summary  A piezoelectric layer bonded to the surface of an elastic structure is considered. The piezoelectric and the elastic layers are infinite along the x-axis and have finite thickness in the y-direction. The polarization direction of the piezoelectric material is along the y-axis. By means of the method of singular integral equations, the solution in a Laplace transform plane is demonstrated. Laplace inversion yields the results in the time domain. Numerical values of the crack tip fields under in-plane transient electromechanical loading are obtained. The influence of layers thickness on stress and electric displacement intensity factors is investigated. Received 16 March 2000; accepted for publication 16 August 2000     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

Three-dimensional analysis of defects in a piezoelectric material

In this paper, the Green's function technique is used to develop a solution of an infinite, piezoelectric medium containing either an ellipsoidal cavity or a flat elliptical crack. The coupled elastic and electric fields both inside the cavity and on the boundary of the cavity are obtained, and the stress intensity factor and the electric field intensity factor are also obtained for an elliptical crack. It is found that; (1) the coupled elastic and electric fields inside the cavity keep uniform when the external elastic field and electric field are constant; (2) the behavior of the stress and electric field components in the neighborhood of the crack tip shows the classical type of singularity. The project supported by National Natural Science Foundation of China     

压电材料反平面裂纹自相似扩展分析

通过对耦合的波动方程和方程解耦,用自模拟方法研究了压电材料中反平面裂纹的自相似扩展问题。研究表明：对反平面问题,介质内的耦合场与裂纹扩展速度有关,在裂纹尖端有r^-1/2阶的奇异性;动态应力强度因子与电位称载荷有关,与静态结论不同;电位移强度因子与机械载 荷无关,与静态结果的表达形式一致。     

Antiplane internal crack normal to the edge of a functionally graded piezoelectric/piezomagnetic half plane

This paper deals with the antiplane magnetoelectroelastic problem of an internal crack normal to the edge of a functionally graded piezoelectric/piezomagnetic half plane. The properties of the material such as elastic modulus, piezoelectric constant, dielectric constant, piezomagnetic coefficient, magnetoelectric coefficient and magnetic permeability are assumed in exponential forms and vary along the crack direction. Fourier transforms are used to reduce the impermeable and permeable crack problems to a system of singular integral equations, which is solved numerically by using the Gauss-Chebyshev integration technique. The stress, electric displacement and magnetic induction intensity factors at the crack tips are determined numerically. The energy density theory is applied to study the effects of nonhomogeneous material parameter β, edge conditions, location of the crack and load ratios on the fracture behavior of the internal crack.     

A penny-shaped crack in a transversely isotropic piezoelectric layer

In this paper, we develop a model to treat penny-shaped crack configuration in a piezoelectric layer of finite thickness. The piezoelectric layer is subjected to axially symmetric mechanical and electrical loads. Hankel transform technique is used to reduce the problem to the solution of a system of integral equations. A numerical solution for the crack tip fields is obtained for different crack radius and crack position.     

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

Summary  The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems. Received 4 September 2001; accepted for publication 23 July 2002 The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation of Tsinghua University, and the Education Ministry of China.     

压电材料中裂纹面电边界条件的适用性

先分析理想裂纹面电边界条件(包括导通型裂纹和不导通型裂纹),然后分析缺陷的厚度及其对尖端场的影响,用封闭形式的解表示出了缺陷厚度的影响．结果指出,裂纹长厚比对计算结果是有影响的,除非裂纹极扁,不可通裂纹边界条件可以给出合理的结果,而可通边界条件只有在一些限制条件下才适用。     

Fracture analysis on a piezoelectric sensor with a viscoelastic interface

Fracture analysis is performed on a layered piezoelectric sensor possessing a Kelvin-type viscoelastic interface. An electrically permeable anti-plane crack is situated in the piezoelectric layer and perpendicular to the interface. The crack problem is solved by the methods of integral transform and Cauchy singular integral equation. The variations of the dynamic stress intensity factor (DSIF) vs. physical and geometrical parameters are investigated. At the beginning of creep and relaxation, larger viscosity coefficient always induces smaller DSIF. With time elapsing, the effect of viscosity coefficient becomes weaker and weaker. When time approaches infinity, the viscous effect disappears, and the DSIF converges to a value corresponding to the case of an elastic interface. The effect of the viscoelastic interface on the fracture behavior of the piezoelectric layer also depends on the substrate thickness. To some extent, thicker substrate may intensify the effect of the interface.     

The interaction between crack and electric dipole of piezoelectricity

Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are obtained. The function of piezoelectric anisotropic direction,p _a (θ)=cosθ+p _a sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip. Supported by National Natural Science Foundation of China(No. 10072033)