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Summary The interface crack problem for a piezoelectric bimaterial based on permeable conditions is studied numerically. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical and electrical loads, the complex stress intensity factor for an interface crack is obtained. The influence of the applied loads on the electromechanical fields near the crack tip is also studied. For a particular case of a short crack with respect to the bimaterial size, the numerical results are compared with the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.One author (V.G.) gratefully acknowledges the support provided by the Alexander von Humboldt Foundation of Germany.accepted for publication 7 June 2004 相似文献
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Hou Mishan 《Acta Mechanica Solida Sinica》1999,12(1):83-90
The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed
by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric
field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the
electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release
rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity
and electric displacement inside electrically permeable cracks are all constants. 相似文献
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In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy. 相似文献
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The three-dimensional weight function method recently developed by the authors is used to determine stress intensity factors
for two symmetric quarter-elliptical corner cracks at a hole in a wide finite-thickness plate subjected to remote tensile
loading. The geometry parameters considered arer/t=0.5, 1, 2;a/c=0.2, 0.5, 1, 2;a/t=0.2, 0.5 withinc/r=2. The results are compared, where possible, with other solutions available in the literature. Generally good agreement is
observed. The effect of an approximation of the two-dimensional unflawed stress distribution on the accuracy of stress intensity
factors by the weight function method is discussed. 相似文献
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I.IntroductionItiswell'knownthatoneofthemostpowerfultoolsinlinearfieldtheoriesistheGreen'sfunction.Fore1asticity,considerableresearchcanbefoundintheliterature.However,theGreen'sfunctionforpiezoe1ectricityisratherlimitedduetotheanisotropyandelectromechanic… 相似文献
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Summary An interface crack with an artificial contact zone at the right-hand side crack tip between two piezoelectric semi-infinite
half-planes is considered under remote mixed-mode loading. Assuming the stresses, strains and displacements are independent
of the coordinate x
2, the expression for the displacement jumps and stresses along the interface are found via a sectionally holomorphic vector
function. For piezoceramics of the symmetry class 6 mm and for electrically permeable crack faces, the problem is reduced
to a combined Dirichlet-Riemann boundary value problem which can be solved analytically. Further, analytical expressions for
the stresses, electrical displacements, derivatives of elastic displacement jumps, stress and electrical intensity factors
are found at the interface. Real contact zone lengths and the well-known oscillating solution are derived from the obtained
solution as well. Analytical relationships between the fracture-mechanical parameters of various models are found, and recommendations
are suggested concerning the application of numerical methods to the problem of an interface crack in the discontinuity area
of a piezoelectric bimaterial.
Received 16 March 1999; accepted for publication 31 May 1999 相似文献
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Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact 总被引:1,自引:0,他引:1
By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around
a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress
intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric
field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric
load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the
width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response
of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation
of the crack depending on the time elapse since the application of the external electro-mechanical loads.
The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China 相似文献
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IntroductionItiswell_knownthatpiezoelectricmaterialsproduceanelectricfieldwhendeformedandundergodeformationwhensubjectedtoanelectricfield .Thecouplingnatureofpiezoelectricmaterialshasattractedwideapplicationsinelectric_mechanicalandelectricdevices,suc… 相似文献
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Chen Wei-qiu 《Archive of Applied Mechanics (Ingenieur Archiv)》1999,69(5):309-316
Summary The paper presents an exact and complete solution of the problem of a semi-infinite plane crack in an infinite transversely
isotropic piezoelectric body. The upper and lower crack faces are assumed to be loaded symmetrically by a couple of normal
point forces in opposite directions and a couple of point charges. The solution is derived through a limiting procedure from
the one of a penny-shaped crack. The expressions for the elastoelectric field are given in terms of elementary functions.
Received 10 August 1998; accepted for publication 18 November 1998 相似文献
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The transient response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric impacting
loads is investigated in the present paper. Laplace and Fourier transforms are used to reduce the mixed boundary value problems
to Cauchy-type singular integral equations in Laplace transform domain, which are solved numerically. The dynamic stress and
electric displacement factors are obtained as the functions of time and geometry parameters. The present study shows that
the presence of the dynamic electric field will impede or enhance the propagation of the crack in piezoelectric ceramics at
different stages of the dynamic electromechanical load. Moreover, the electromechanical response is greatly affected by the
ratio of the space of the cracks and the crack length. 相似文献
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Bao-Lin Wang Naotake Noda Jie-Cai Han Shan-Yi Du 《European Journal of Mechanics - A/Solids》2001,20(6):377
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. 相似文献
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Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading 总被引:5,自引:0,他引:5
E. Karapetian I. Sevostianov M. Kachanov 《Archive of Applied Mechanics (Ingenieur Archiv)》2000,70(1-3):201-229
Summary The problem of a penny-shaped crack in a transversely isotropic piezoelectric material loaded by both normal and tangential
tractions and by electric charges is analyzed. Closed-form solutions are obtained for the full electroelastic fields as well
as for the stress and electric displacement intensity factors. Solutions are also obtained for the (non-trivial) limiting
case of a half-plane crack. The results are illustrated on the example of piezoceramics PZT-6B.
Received 12 July 1999; accepted for publication 20 July 1999 相似文献
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首先,采用特征函数渐近展开法,推导了Reissner板弯曲界面裂纹尖端附近位移场渐近展开的前两阶显式表达式,并利用所获得的位移场渐近表达式构造了一种可用于Reissner板弯曲界面裂纹分析的奇异单元。然后,将该奇异单元与外部的常规有限单元相结合,开展了含界面裂纹Reissner板弯曲断裂问题的数值分析。奇异单元可以较好地描述裂纹尖端附近的内力场与位移场,其优势是它与常规单元进行连接时不需要使用过渡单元,并且可以直接给出应力强度因子等断裂参数的高精度数值结果。最后,通过两个数值算例验证了本文方法的有效性。 相似文献
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IntroductionDuetotheintrinsicelectro_mechanicalcouplingbehavior,piezoelectricmaterialsareveryusefulinelectronicdevices.However,mostpiezoelectricmaterialsarebrittlesuchasceramicsandcrystals.Therefore ,piezoelectricmaterialshaveatendencytodevelopcriticalcracksduringthemanufacturingandthepolingprocesses.So ,itisimportanttostudytheelectro_elasticinteractionandfracturebehaviorsofpiezoelectricmaterials.Theincreasingattentiontothestudyofcrackproblemsinpiezoelectricmaterialshasledtoalotofsignificantw… 相似文献
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Hong-Sen Lu 《Acta Mechanica Solida Sinica》1991,4(4):443-448
This paper proposes a new type of special element (sectorial singular element) for calculating the linear elastic stress intensity factor. The shape of element not only accords with the demands of finite element analysis, but also coincides with the theory of linear elastic fracture mechanics. The accuracy and economy of the result in this paper are satisfactory. 相似文献
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This paper presents a formulation for three-dimensional elastodynamics with an elliptic crack based on the Laplace and Fourier
transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm
integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral
equation method.
The project supported by the National Natural Science Foundation of China (K19672007) 相似文献
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基于有限元软件ANSYS数值模拟,计算了激光作用下的压电薄膜表面贯穿裂纹外场应力强度因子和电位移强度因子,并且研究了90°畴变所诱致的畴变增韧行为。首先,求解无裂纹压电薄膜在激光作用下的热-力-电响应,将求得的应力和电位移场反向作用于裂纹面,求解裂纹尖端处的外场应力和电位移强度因子,然后基于小范围畴变理论求解了90°畴变所致的屏蔽应力强度因子。讨论了薄膜表面裂纹的外场应力强度因子、电位移强度因子及屏蔽应力强度因子随激光作用时间和裂纹位置的变化关系,从而预测压电薄膜体系在加热工作状况下的裂纹扩展和断裂行为。 相似文献
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J. P. Shi 《Theoretical and Applied Fracture Mechanics》1998,28(3):223
A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack. 相似文献