压电材料平面问题的尖端场和应力强度因子的求解

利用Lekhnitskii理论和Stroh理论的相互联系,把已知的基于Lekhnitskii理论平面应变结果转化为Stroh理论形式的结果,直接获得Stroh公式中A,B的显式表达式,此方法可扩展到平面应力情况,然后导出压电材料平面应变问题的尖端场Williams形式的展开式,采用半权函数法计算有限大压电体平面问题应力和电位移强度因子。对无穷大板含中心裂纹的情况下本文结果和已有结果进行了比较,表明本文方法得到的结果精度可靠。本文方法的最大优点是可以求解有限压电体的应力强度因子,并且需要的单元少,精度高,实用性好。     

双压电体界面上的电偶极子和裂纹5

求得了压电体双材料界面上的孤立二维电偶极子的解析解，结果表明某点电偶极子激发的应力－电位移场与该点到电偶极子的距离的平方成反比。研究了压电体双材料界面上的电偶极子对裂纹的作用，得到了问题的闭合解。在电偶极子的作用下，界面裂纹裂尖近区应力－电位移仍具有r^-1/2 iεα的振荡奇异性，文中求得裂尖应力强度因子，当电偶极子距裂尖距离ρ很近时，裂尖应力强度因子与ρ^-3/2-iεα成比例。     

双周期裂纹压电材料反平面剪切问题断裂力学分析

研究压电材料双周期裂纹反平面剪切与平面电场作用的问题．运用复变函数方法，获得了该问题严格的闭合解，并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式．数值算例显示了裂纹分布特征对材料断裂行为的重要影响．叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用，相反行间小裂纹却起着放大作用，至于钻石形分布裂纹的影响规律则更为复杂．对于某些特殊情形给予了解答并导出一系列有意义的结果。     

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。     

功能梯度压电压磁材料粘结的Ⅲ型裂纹问题

利用奇异积分方程方法研究两个半无限大的功能梯度压电压磁材料粘结,在渗透和非 渗透边界条件下的III型裂纹问题. 首先通过积分变换构造出原问题的形式解，然 后利用边界条件通过积分变换与留数定理得到一组奇异积分方程， 最后利用Gauss-Chebyshev方法进行数值 求解，讨论材料参数、材料非均匀参数以及裂纹几何形状等对裂纹尖端应力 强度因子的影响. 从结果中可以看出，压电压磁复合材料中反平面问题的应力奇异性 形式与一般弹性材料中的反平面问题应力奇异形式相同，但材料梯度参数对功能梯度压电压 磁复合材料中的应力强度因子和电位移强度因子有很大的影响.     

压电体中裂纹与孤立电偶极子的相互作用

研究压电体裂纹与电偶极子的相互作用,得到问题的闭合解,包括应力-电位移场,裂纹张开位移和电势差,以及裂尖应力强度因子,结果表明,电偶极子的方向对裂纹场的影响可由压电体各向异性方向函数表示;当电偶极子位于裂尖附近时,在原点取在裂尖的局部极坐标系中电偶极子位置的极角对裂尖场的影响可由各向异性方向函数表示,电偶极子引起的裂尖应力强度因子与其距裂尖的距离的-3/2次幂成正比。     

功能梯度压电带中裂纹对SH波的散射

研究功能梯度压电带中裂纹对SH波的散射问题,为了便于分析,材料性质假定为指数模型,并假设裂纹面上的边界条件为电渗透型的.根据压电理论得到压电体的状态方程,利用Fourier积分变换,问题转化为对偶积分方程的求解.用Copson方法求解积分方程.求得了裂纹尖端动应力强度因子、电位移强度因子的解析表达式,最后数值结果显示了标准动应力强度因子与入射波数、材料参数、带宽、波数以及入射角之间的关系.     

用三维光弹法确定轴表面横向半椭圆裂纹应力强度因子及其修正系数

用三维光弹法测定了轴表面横向半椭圆裂纹的应力强度因子，并分析计算了应力强度因子修正系数，结果表明，应力强度因子的分布型式对加载条件和裂纹几何不敏感；修正系数对裂纹深度呈现对称分布趋势，仅取决于裂纹几何参数。     

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．     

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。     

压电薄膜表面贯穿裂纹的有限元分析

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。     

Coupled solution for anisotropic piezoelectric materials with cracks

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.     

各向异性压电材料平面裂纹的耦合场分析

用Stroh方法分析了各向异性压电材料电导通型裂纹问题的耦合场。结果表明,裂纹面上的切向电场强度和法向电位移均为常数,在裂纹尖端有由弹性场的耦事作用产生的奇异电导通裂纹模型中的静电场对裂纹尖端扩展的能量释放率不作贡献。     

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.     

Basic solution of two parallel non-symmetric permeable cracks in piezoelectric materials

The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations ip which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials.     

A penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer

The problem of a penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer is investigated. The surfaces of the composite structure are subjected to both mechanical and electrical loads. The crack surfaces are assumed to be electrically impermeable. Integral transform method is employed to reduce the problem to a Fredholm integral equation of the second kind. The stress intensity factor, electric displacement intensity factor and energy release rate are derived, some typical numerical results are plotted graphically. The effects of electrical loads, material nonhomogeneity and crack configuration on the fracture behaviors of the cracked composite structure are analyzed in detail.     

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)     

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)