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1.
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 相似文献
2.
X.-F. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(10):745-758
Summary The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform
electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral
equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and
the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results
are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results
reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors
depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results
reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied
stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack
in a piezoelectric strip.
Received 14 August 2001; accepted for publication 24 September 2002
The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported
by the National Natural Science Foundation of China under Grant 70272043. 相似文献
3.
Summary The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered
under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to
the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral
equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement
and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are
obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary.
The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems.
Received 10 November 2000; accepted for publication 28 March 2001 相似文献
4.
Summary A finite crack propagating at constant speed in a functionally graded piezoelectric strip (FGPS) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPS vary exponentially across the thickness of the strip, and that the bimaterial strip is under combined anti-plane mechanical shear and in-plane electrical loads. The analysis is conducted for the electrically unified crack boundary condition, which includes both the traditional permeable and the impermeable ones. By using the Fourier transform, the problem is reduced to the solution of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and the crack sliding displacement are presented to show the influences of the crack propagation speed, electric loads, FGPS gradation, crack length, electromechanical coupling coefficient, properties of the bonded homogeneous piezoelectric strip and crack location. 相似文献
5.
Summary In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity
factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the
framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a
Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results
for the dynamic stress intensity factor show the influence of the geometry and electric field.
Received 29 June 2001; accepted for publication 3 December 2001 相似文献
6.
Hyung Jip Choi 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(4-5):342-362
Summary Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under
consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The
Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the
basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations
for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and
nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity
factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently,
the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated
in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim
of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation
of local homogeneity and brittleness of the crack-tip behavior.
Received 25 September 2001; accepted for publication 13 February 2002 相似文献
7.
Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts 总被引:1,自引:0,他引:1
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. 相似文献
8.
Propagation of an anti-plane moving crack in a functionally graded piezoelectric strip 总被引:4,自引:0,他引:4
Summary The propagation of an anti-plane moving crack in a functionally graded piezoelectric strip (FGPS) is studied in this paper. The governing equations for the proposed analysis are solved using Fourier cosine transform. The mixed boundary value problems of the anti-plane moving crack, which is assumed to be either impermeable or permeable, are formulated as dual integral equations. By appropriate transformations, the dual integral equations are reduced to Fredholm integral equations of the second kind. For the impermeable crack, the stress intensity factor (SIF) of the crack in the FGPS depends on both the mechanical and electric loading, whereas, the SIF for the permeable crack depends only on the mechanical loading. The results obtained show that the gradient parameter of the FGPS and the velocity of the crack have significant influence on the dynamic SIF.Support from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7081/00E) is acknowledged. Support from the National Natural Science Foundation of China (Project No. 10072041) is also acknowledged. 相似文献
9.
Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes 总被引:3,自引:0,他引:3
Summary In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through
a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular
integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution
and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of
the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of
applied electric impact.
Received 4 December 2001; accepted for publication 9 July 2002
This work is supported by the National Natural Science Foundation of China through Grant No. 10132010. 相似文献
10.
Summary Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent
or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic
coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem
of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier
transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved.
The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated.
Received 20 March 2001; accepted for publication 18 October 2001 相似文献
11.
Summary This paper is concerned with a semi-infinite interfacial crack between two bonded dissimilar elastic strips with equal thickness.
Solutions for the complex stress intensity factor (SIF) and energy release rate (ERR) are obtained in closed form under in-plane
deformations. During the procedure, the mixed boundary-value problem is reduced by means of the conformal mapping technique
to the standard Riemann–Hilbert problem. In some limiting cases, the present solutions can cover the results found in literature.
Received 21 February 2002; accepted for publication 2 July 2002
X.-F Wu's work was supported in part by the Milton E. Mohr Research Fellowship (2001, 2002) of the Engineering College at
University of Nebraska-Lincoln. 相似文献
12.
Summary In this paper, we study a two-dimensional electroelastic problem of an infinite piezoelectric body with two circular piezoelectric
inhomogeneities, one of which contains a crack. We formulate the stress intensity factor (SIF) analytically and investigate
it numerically. The problem is solved based on Bueckner's principle, and is reduced to a problem of a singular integral equation
of the first kind with respect to the distribution function of screw dislocation. The effect of interaction between the two
inhomogeneities and the crack on the electroelastic field as well as the control of the SIF by electrical loads is investigated.
Received 18 April 2000; accepted for publication 24 October 2000 相似文献
13.
Zhen-Gong Zhou Pei-Wei Zhang Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(12):861-882
The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the
generalized Almansi’s theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were
firstly considered. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations,
in which the unknown variables were jumps of displacements across crack surfaces, not the dislocation density functions or
the complex variable functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were
directly expanded in a series of Jacobi polynomials to obtain the relations among electric displacement intensity factors,
magnetic flux intensity factors and stress intensity factors at crack tips. 相似文献
14.
Electro-mechanical analysis of an interfacial crack between a piezoelectric and two orthotropic layers 总被引:1,自引:0,他引:1
Summary The problem of an interfacially cracked three-layered structure constructed of a piezoelectric and two orthotropic materials
is analyzed using the theory of linear piezoelectricity and fracture mechanics. Anti-plane shear loading is considered, and
the integral transform technique is used to determine the stress intensity factor. Numerical examples show the electro-mechanical
effects of various material combinations and layer thicknesses on the stress intensity factor. Interesting results are obtained
in comparison with earlier solutions for interfacially cracked piezoelectric structures.
Received 29 December 2000; accepted for publication 3 May 2001 相似文献
15.
Dynamic behavior of unequal parallel permeable interface multi-cracks in a piezoelectric layer bonded to two piezoelectric materials half planes 总被引:2,自引:0,他引:2
Jian-Liang Sun Zhen-Gong Zhou Biao Wang 《European Journal of Mechanics - A/Solids》2004,23(6):993-1005
This study is concerned with the treatment of the dynamic behavior of interacting cracks in a piezoelectric layer bonded to two dissimilar piezoelectric half planes subjected to harmonic anti-plane shear waves. The permeable electric boundary condition is considered. By use of the Fourier transform technique, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in two series of Jacobi polynomials. The electromechanical behavior of two pairs of unequal parallel cracks was determined. Numerical examples are provided to show the effects of the geometry of the cracks, the frequency of the incident waves and materials properties upon the dynamic stress intensity factors (DSIFs) and the electric displacement intensity factors. 相似文献
16.
Summary In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically.
Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones.
Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function
and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated.
It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of
the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent
of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case,
C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is.
Received 26 March 2002; accepted for publication 2 July 2002 相似文献
17.
We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing an eccentric Griffith crack off the centre line bonded to two elastic half planes under anti-plane shear loading using the continuous crack-face condition. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and energy release rate are obtained. 相似文献
18.
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. 相似文献
19.
Crack in functionally graded piezoelectric strip bonded to elastic surface layers under electromechanical loading 总被引:9,自引:0,他引:9
Solved is the problem of a crack in a functionally graded piezoelectric material (FGPM) bonded to two elastic surface layers. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric permittivity of the FGPM vary continuously along the thickness of the strip. The outside layers are under antiplane mechanical loading and in-plane electric loading. The solution involves solving singular integral equations by application of the Gauss–Jacobi integration formula. Numerical calculations are carried out to obtain the energy density factors. Their variations with the geometric, loading and material parameters are shown graphically. 相似文献
20.
The dynamic behavior of a limited-permeable rectangular crack in a transversely isotropic piezoelectric material is impinged by to a P-wave. The generalized Almansi theorem and the Schmidt method are used to determine the stress intensity factor and energy density factor as the primary fracture criterion of failure. The mixed boundary value problem entails the evaluation of the appropriate crack edge stress singularities that are characteristics of the fundamental functions. The stress and electric displacement intensity factors are also used to find the energy release rate that can be computed numerically and compared with the results corresponding to those of the stress intensity factor, and energy density factor. Graphical presentation shows that the energy release rate is always negative for the boundary conditions considered while the energy density factors always remain positive. Under certain conditions, the stress and electric displacement intensity factors can be negative and subject to physical limitations. Piezoelectric material boundary value problem solutions should therefore be qualified by the application of failure criteria by fracture of otherwise, particularly when the mechanical and electrical energy can release by creating free surface at the macroscopic and microscopic scales. Negative energy release rate found for the piezoelectric medium in this work can be a case in point.Positive definiteness of the energy density factor can be applied to mutliscale fracture. This is not true for the stress intensity factor nor the energy release rate. Hence, crack initiation behavior for the permittivity of a rectangular crack due to the wave propagation effects may be studied. In particular, the initiation of micro-cracks may be identified with certain critical stress wave frequency band. Negative stress intensity factor may not enhance macrocracking but it does not exclude microcrack initiation. 相似文献