Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique,the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface.Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable.The results can be reduced to the well-known solutio...     

The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid

Based on the Stroh-type formalism, we present a concise analytic method to solve the problem of complicated defects in piezoelectric materials. Using this method and the technique of conformal mapping, the problem of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric solid is investigated under remotely uniform in-plane electric loading and anti-plane mechanical loading. The exact solutions of the field intensity factors and the energy release rate are presented in closed-form under the permeable electric boundary condition. With the variation of the geometrical parameters, the present results can be reduced to the well-known results of a mode-III crack in piezoelectric materials. Moreover, new special models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and single edge crack emanating from an elliptical hole or circular hole, T-shaped crack, cross-shaped crack, and semi-infinite plane with an edge crack. Numerical results are then presented to reveal the effects of geometrical parameters and the applied mechanical loading on the field intensity factors and the energy release rate.     

Closed form solution for two unequal collinear semi-permeable straight cracks in a piezoelectric media

The problem of two unequal collinear straight cracks weakening a poled transversely isotropic piezoelectric ceramic is addressed under semi-permeable electric boundary conditions on the crack faces. The plate has been subjected to combined in-plane normal(to the faces of the cracks) mechanical and electric loads. Problem is formulated employing Stroh formalism and solved using complex variable technique. The elastic field, electric field and energy release rate are obtained in closed analytic form. A case study is presented for poled PZT-5H cracked plate to study the effect of prescribed mechanical load, electric load, inter-crack distance and crack lengths on crack arrest parameters stress intensity factor (SIF), electric displacement intensity factor (EDIF) and mechanical and total energy release rates (ERR). Moreover a comparative study is done of impermeable and semi-permeable crack face boundary conditions on SIF, EDIF and ERR, and results obtained is presented graphically. It is observed that the effect of dielectric medium in the crack gap cannot be ignored.     

Anti-plane fracture analysis for the weak-discontinuous interface in a non-homogeneous piezoelectric bi-material structure

The concept of weak discontinuity is extended to functionally graded piezoelectric bi-material interface, and fracture analysis for the weak discontinuous interface is performed by the methods of Fourier integral transform and Cauchy singular integral equation. Numerical results of the total energy release rate (TERR) and the mechanical strain energy release rate (MSERR) are obtained to show the effects of non-homogeneity parameters, geometrical parameters and loads. Parametric studies yield three conclusions: (1) To reduce the weak-discontinuity of the interface is beneficial to resisting interfacial fracture. The effect of the weak-discontinuity of the interface on TERR and MSERR still depends on the strip width. The wider the strip, the more sensitive the TERR and MSERR will be to the weak-discontinuity of the interface. (2) To predict the effect of electric load on crack propagation, MSERR is more appropriate than TERR to be used as a fracture parameter. To predict the effect of mechanical load on crack propagation, both of them could be used as fracture parameters, and MSERR is more conservative. (3) Mechanical load and negative electric displacement load would promote crack propagation, but positive electric displacement load would retard it. For the structure applied by combined mechanical and positive electric displacement loads, crack propagation may be impeded by appropriately selecting the strip width and the ratio of non-homogeneity parameters.     

压电体中考虑表面效应时开裂孔洞的断裂特征

研究了反平面机械载荷和面内电载荷作用下压电体中考虑表面效应时孔边双裂纹问题的断裂特征。基于Gurtin-Murdoch表面理论模型，通过构造映射函数，利用复势电弹理论获得了应力场和电位移场的闭合解答。给出了裂纹尖端应力强度因子、电位移场强因子和能量释放率的解析解。讨论了开裂孔洞几何参数和施加力电载荷对电弹场强因子和能量释放率的影响。     

含中心裂纹压电体的二维精确解

解析地研究了含中心裂纹的压电体，它在无穷远处承受机电载荷，并在裂面上满足由Parton和Kudryavtsev以及Hao和Shen提出的绝对电边界条件。在平面应变假设下，给出其二维精确解，并提供了机械应变能释放率和裂尖能量释放率等数值结果。考虑工业应用范围之内常用的远场载荷时，由绝对电边界条件得出的能量释放率表现出明显的非线性特征及载荷相关性，而不是完全与电场无关，这一结论与Xu和Rajapakse在较小载荷下得到的规律不同。     

一维六方压电准晶对称条形体中共线双半无限快速传播裂纹的解析解

利用复变函数方法, 通过构造保角映射, 分析了一维六方压电准晶中对称条形体中共线双半无限快速传播裂纹的反平面问题, 给出了在电非渗透型与电渗透型两种情况下动态应力强度因子的解析解. 当速度趋于0时可退化为已有的对应的静力问题的解. 得到的解析解对准晶材料的工程应用中有一定的理论价值.     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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Electromechanical impact of an impermeable parallel crack in a functionally graded piezoelectric strip

The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under the in-plane mechanical and electric impact. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location, the material nonhomogeneity and the loading combination.     

An exact solution of crack problems in piezoelectric materials

IntroductionInrecentyearscrackproblemsinpiezoelectricmaterialhavereceivedmuchattention.Manytheoreticalanalyseshavebeengivenby[1～16].Itshouldbe,however,notedthatalltheaboveanalysesarebasedonaso-calledimpermeablecrackassumphon,i.e.thecrackfacesareassumedtobeimpermeabletoelectricfield,sotheelectricdisplacementvanishesinsidethecrack.Usingthisassumption,onewillobtainthefollowingresultS[2'3'5,6'9'16]=whentheelectricloadsaresolelyaPPliedatinLfinity,theelectricdisplacementissquare-rootsingularatthe…