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利用积分方程方法,本文研究了夹在两个均匀压电半空间的功能梯度压电带界面共线双裂纹的反平面问题。在电渗透型边界条件下,通过Fourier余弦变换将所考虑的问题化为一对偶积分方程,再用Copson方法将该对偶积分方程转化为Fredholm方程进行数值求解,从而给出了裂纹尖端的应力强度因子,电位移强度因子的表达式。分析了裂纹长度,功能梯度非均匀参数以及材料的几何尺寸等对应力强度因子的影响。 相似文献
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《工程数学学报》2016,(2)
本文利用复变函数方法和保角映射,研究一维六方压电准晶材料中带不对称三裂纹的圆形孔口的的断裂问题.根据准晶压电材料基本方程的基础上,利用点群的对称性和一维六方准晶的线性压电效应,导出了一维六方准晶压电材料反平面问题的控制方程,并结合Cauchy积分公式,得到电非渗透与电渗透边界条件下的裂纹尖端场强度因子的解析表达式.当改变裂纹长度和孔口半径时,所得结果可以模拟出一些新裂纹模型.在不考虑电载荷作用时,所得结果和原有结果是一致的.通过数值算例讨论了材料的几何参数对场强度因子的影响,得出水平裂纹长度和圆半径可以促进裂纹增长.本研究为工程中材料的制备与应用将提供可靠的理论价值. 相似文献
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研究了压电复合材料中圆孔边4个非对称裂纹在远处受面内电载荷和面外力载荷共同作用下的断裂行为。利用复变函数方法和新映射函数将问题转化为Cauchy积分方程组。通过求解Cauchy积分方程组,得到了电非渗透型和电渗透型两种边界条件下裂纹尖端电弹性场和场强度因子的解析解。所得结果不仅可退化为已有解,而且可模拟出若干新的缺陷构型,如压电复合材料中圆孔边三裂纹、半无限压电复合材料中半圆孔边单裂纹及半无限压电体中边界裂纹。将所得结果与有限元结果进行比较,吻合很好,证实了文中方法的正确性和有效性。数值算例分析了缺陷的几何参数对场强度因子的影响规律。 相似文献
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本文利用复变函数方法和保角映射,研究一维六方压电准晶材料中带不对称三裂纹的圆形孔口的的断裂问题。根据准晶压电材料基本方程的基础上,利用点群的对称性和一维六方准晶的线性压电效应,导出了一维六方准晶压电材料反平面问题的控制方程,并结合Cauchy积分公式,得到电非渗透与电渗透边界条件下的裂纹尖端场强度因子的解析表达式。当改变裂纹长度和孔口半径时,所得结果可以模拟出一些新裂纹模型。在不考虑电载荷作用时,所得结果和原有结果是一致的。通过数值算例讨论了材料的几何参数对场强度因子的影响,得出水平裂纹长度和圆半径可以促进裂纹增长。本研究为工程中材料的制备与应用将提供可靠的理论价值。 相似文献
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本文利用波函数法结合奇异积分方程技术分析了刚性半圆形基础与土体部分脱离时的出平面动力响应问题.将界面脱离区模拟为界面裂纹,根据问题的混合边值条件获得一组奇异积分方程,通过数值求解给出了基础和土体的位移场,并借助断裂力学中动应力强度因子的概念讨论了界面剪应力强度. 相似文献
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利用复变函数知识、半逆解法及待定系数法, 研究了压电复合材料的共线周期性裂纹问题, 给出了在电不可渗透边界条件下的应力、电位移、应力强度因子、电位移强度因子和机械应变能释放率的解析解。当裂纹间距趋于无穷时, 共线周期性裂纹退化为一条单裂纹, 得到了压电复合材料一条单裂纹的结果。通过数值算例讨论了共线周期性裂纹的裂纹长度、裂纹间距和机电载荷对机械应变能释放率的影响规律。结果表明, 机械应变能释放率随着共线周期性裂纹的裂纹长度、共线周期性裂纹的裂纹间距、机械载荷和正电场的增大而增大, 随着负电场的增大而减小。 相似文献
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The dynamic behavior of a piezoelectric-elastic laminate with a crack in the piezoelectric material under in-plane steady-state
electro-mechanical loads is considered. Based on the use of integral transform techniques, the problem is reduced to a set
of singular integral equations, which are solved using Chebyshev polynomial expansions. Numerical results are provided to
show the variation of both the dynamic stress intensity factors and electric displacement intensity factor with frequencies
of the applied electro-mechanical loads. A phenomenon similar to “resonance” is observed when the applied loads act in some
specific ranges of frequencies, and both the dynamic stress intensity factors and electric displacement intensity factor may
increase significantly, which will lead to the failure of piezoelectric material. The effects of applied electric fields,
crack geometry and elastic layer thickness on the phenomenon are also discussed. 相似文献
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Summary We consider an anti-plane edge moving crack problem with the constant velocity in a piezoelectric ceramic block. The far-field anti-plane shear mechanical and in-plane electrical loads are applied to the piezoelectric block. It is expressed to a Fredholm integral equation of the second kind. Expressions for the dynamic field intensity factors and the dynamic energy release rate are obtained. The dynamic stress intensity factor and the dynamic energy release rate depend on the crack propagation speed. Numerical results for several piezoelectric materials are also presented. 相似文献
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On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip 总被引:8,自引:0,他引:8
S. M. Kwon 《Acta Mechanica》2004,167(1-2):73-89
Summary. In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential gradients along the thickness of the strip, and that the strip is under anti-plane shear mechanical and in-plane electrical loads. The analysis is conducted on the electrically unified (natural) crack boundary condition, which is related to the ellipsoidal crack parameters. By using the Fourier transform, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, crack propagation speed, electric field, FGPM gradation, crack length, and electromechanical coupling coefficient. It reveals that there are considerable differences between traditional electric crack models and the present unified crack model. 相似文献
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The problem of a through permeable crack situated in the mid-plane of a piezoelectric strip is considered under anti-plane impact loads for two cases. The first is that the strip boundaries are free of stresses and of electric displacements, and the second is that the strip boundaries are clamped rigid electrodes. The method adopted is to reduce the mixed initial-boundary value problem, by using integral transform techniques, to dual integral equations, which are further transformed into a Fredholm integral equation of the second kind by introducing an auxiliary function. The dynamic stress intensity factor and energy release rate in the Laplace transform domain are obtained in explicit form in terms of the auxiliary function. Some numerical results for the dynamic stress intensity factor are presented graphically in the physical space by using numerical techniques for solving the resulting Fredholm integral equation and inverting Laplace transform. 相似文献
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Summary. The dynamic behavior of a crack in a functionally graded piezoelectric material (FGPM) strip bonded to two half dissimilar piezoelectric material planes subjected to combined harmonic anti-plane shear wave and in-plane electrical loading was studied under the limited permeable and permeable electric boundary conditions. It was assumed that the elastic stiffness, piezoelectric constant and dielectric permittivity of the functionally graded piezoelectric layer vary continuously along the thickness of the strip. By using the Fourier transform, the problem can be solved with a set of dual integral equations in which the unknown variables are the jumps of the displacements and the electric potentials across the crack surfaces. In solving the dual integral equations, the jumps of the displacements and the electric potentials across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical results illustrate the effects of the gradient parameter of FGPM, electric loading, wave number, thickness of FGPM strip and electric boundary conditions on the dynamic stress intensity factors (SIFs). 相似文献
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Effect of electromechanical coupling on the dynamic interaction of cracks in piezoelectric materials
Summary This article provides a comprehensive treatment of the dynamic interaction between two arbitrarily located and oriented cracks in a piezoelectric medium under steady-state inplane electrical and antiplane mechanical loads. Using an impermeable condition along the crack surfaces, a fundamental dynamic solution was developed for the single crack problem. In this fundamental solution, the single crack problem was treated using Fourier transform and the appropriate singular integral equations. The fundamental solution was then implemented into a pseudo-incident wave method to account for the interaction between the cracks. Numerical examples are provided to show the effect of the geometry of the cracks, the material constants, the frequency of the incident wave and the applied electrical field upon the dynamic stress intensity factors. The results show the significant effect of electromechanical coupling upon the stress intensity factor at the crack tip. 相似文献
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《International Journal of Engineering Science》2006,44(3-4):256-272
The strip dielectric breakdown (DB) model introduced by Zhang and Gao [T.Y. Zhang, C.F. Gao, Fracture behavior of piezoelectric materials, Thero. Appl. Fract. Mech. 41 (2004) 339–379] is used to study the generalized 2D problem of a conductive crack and an electrode in an infinite piezoelectric material. The energy release rate and stress intensity factors are derived based on the Stroh formalism, and then they are applied as failure criteria to predict the critical fracture loads. It is found that the DB strip may take the shielding effect on a conductive crack or electrode. For the case of an electrode, the local energy release rate and stress intensity factor become zero when DB happens ahead of the electrode tip. For the case of a mode-I conductive crack in a transversely isotropic piezoelectric solid, the results based on the DB model show that the critical stress intensity factor linearly increases as the applied electric field parallel to the poling direction increases, while it linearly decreases as the applied electric field anti-parallel to the poling direction increases. Finally, the upper and lower bounds of the actual critical fracture loads are proposed for a conductive crack in a piezoelectric material under combined mechanical–electrical loads. 相似文献
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In this paper, the Fourier integral transform–singular integral equation method is presented for the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a different functionally graded piezoelectric material. The properties of two materials, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The crack surface condition is assumed to be electrically impermeable or permeable. The mixed boundary value problem is reduced to a singular integral equation over crack by applying the Fourier transform and the singular integral equation is solved numerically by using the Lobatto–Chebyshev integration technique. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived. The effects of the loading parameter λ, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied. 相似文献
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Toshihisa Nishioka Shengping Shen Jiahuan Yu 《International Journal of Fracture》2003,122(3-4):101-130
First, the near-tip stress and electric displacement fields are analytically solved for a dynamically propagating interfacial crack in a piezoelectric bimaterial. Second, from the rate formulation of the energy balance in a piezoelectric material, the path independent dynamic J integral is derived, which has the physical significance of the energy release rate. Using the present near-tip analytical solutions, the relationships between the dynamic J integral and the stress and electric displacement intensity factors are also obtained. It is shown that the path independent dynamic J integral contains the static J integral and the dynamic J integral for elastic materials, and static J integral for piezoelectric materials as special cases. Third, for an interfacial crack in a piezoelectric bimaterial, the path independent separated dynamic J integrals are derived, which have the physical significance of energy flow rates into the propagating interfacial crack tip from the individual material sides or, equivalently, the separated dynamic energy release rates. Fourth, to accurately evaluate mixed-mode stress and electric displacement intensity factors, the component separation method of the dynamic J integral is developed. Finally, the finite element analyses of a static stationary interfacial crack in a piezoelectric bimaterial subject to mechanical, electrical and combined loading are carried out to demonstrate the applicability of the generalized (dynamic) J integral and the separated J integral, and the component separation method. 相似文献
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Summary. The elastostatic problem of an edge cracked orthotropic strip is considered. The crack possesses a semi-infinite length. The crack surfaces are subjected to opening mode I fracture, by a concentrated force action, while the strip surfaces are traction free. Fourier transforms and asymptotic analyses are employed to reduce the problem to a first kind singular integral equation. The stress intensity factor is determined in a closed form expression. The effects of geometric and elastic characteristics of the strip on the values of the stress intensity factor are explained. 相似文献