弹性功能梯度材料板条中周期裂纹的反平面问题

讨论了弹性功能梯度材料板条中裂纹的反平面问题. 用Fourier 变换方法得到了一个基本解. 这个基本解表示了实轴上一点作用有点位错时引起的影响. 利 用此基本解可得单裂纹和周期裂纹问题的奇异积分方程. 在周期裂纹求解时, 远处裂纹对于中央裂纹的影响作了有效的近似处理. 最后, 给出了数值结果, 它表示了材料性质对于裂纹端应力强度因子的影响.     

反平面弹性中边缘内分叉裂纹的奇异积分方程解法

利用复变函数和奇异积分方程方法,求解反平面弹性中半平面边缘内分叉裂纹问题。提出了满足半平面边界自由的由分布位错密度表示的半平面中单裂纹的基本解,此基本解由主要部分和辅助部分组成。将半平面边缘内分叉裂纹问题看作是许多单裂纹问题的叠加,建立了以分布位错密度为未知函数的Cauchy型奇异积分方程组。然后,利用半开型积分法则求解奇异积分方程,得到了裂纹端处的应力强度因子。文中给出两个数值算例的计算结果。     

正交弹性材料中双周期裂纹反平面问题的封闭解

研究了无限大正交弹性材料中含双周期裂纹的反平面问题,其基本胞元含有三条裂纹,且三条裂纹的中心恰好位于一等腰三角形顶点。运用椭圆函数、保角变换理论、施瓦兹公式获得了该问题应力场的封闭解,并得到了裂纹尖端处的应力强度因子。该问题结果取特殊情形退化对应于单排共线周期裂纹的解答。通过数值算例,分析了双周期裂纹归一化的应力强度因子随双周期裂纹的横向间距和纵向间距之比/b a 分别取10、5、2、1时的变化曲线。结果表明：对于一定的横向间距,应力奇异因子随纵向间距的增大而减小,但随着纵向间距的增大,纵向间距对应力奇异因子的影响变得不明显;对于一定的纵向间距,应力奇异因子随横向间距的减小而减小,但随着横向间距的减小,横向间距对应力奇异因子的影响变得不明显。     

压电材料反平面运动裂纹的能量释放率与分叉角

用复变函数方法,研究了压电材料中反平面运动裂纹的动态断裂问题,研究表明：介质内的耦合场与裂纹运动速度有关,在裂纹尖端有奇异。应力强度因子与裂纹运动速度无关,与纯弹性结构一致,沿裂纹延长线扩展的动态能量释放率可用应力强度因子表示,而与电载荷无关,裂纹运动的高速度具有止裂作用,在一定条件下,裂纹有扩展成曲线裂纹或分叉的趋势。     

矩形压电体中反平面裂纹的电弹性场

基于线性压电理论,本文获得了含有中心反平面裂纹的矩形压电体中的奇异应力和电场。利用Fourier积分变换和Fourier正弦级数将电绝缘型裂纹问题化为对偶积分方程,并进一步归结为易于求解的第二类Fred-holm积分方程。获得了裂纹尖端应力、应变、电位移和电场的解析解,求得了裂纹尖端场的强度因子及能量释放率。分析了压电矩形体的几何尺寸对它们的影响。结果表明,对于电绝缘型裂纹,裂纹尖端附近的各个场变量都具有-1/2阶的奇异性,能量释放率与电荷载的方向及大小有关,并且有可能为负值。     

不同材料界面共圆弧裂纹的反平面问题

本文首次将不同弹性材料界面共圆弧裂纹版平面问题,化为解析函数边值问题,获得了一般解答,由此求出了几种典型情况的精确解,算出了应力强度因子。当两种材料相同时,本文结果与文[S]完全吻合。     

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。     

考虑表面弹性效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析

基于表面弹性理论和保角映射技术,研究了远场作用反平面剪切载荷作用下考虑表面弹性效应时正三角形孔边裂纹问题的断裂性能.给出了孔边应力场的精确解,获得了裂纹尖端应力强度因子的解析解答.数值算例中讨论了裂尖应力强度因子随三角形孔尺寸、裂纹长度和表面性能的变化规律.结果表明:当三角形孔的尺寸在纳米量级时,无量纲应力强度因子具有显著的尺寸效应;随着三角形孔尺寸的增大,论文结果趋近于经典断裂理论解答;无量纲应力强度因子随孔边裂纹长度的增加,先增大而后减小;当孔边裂纹长度较小时,表面效应影响较弱;应力强度因子的尺寸效应受表面性能影响显著.     

功能梯度材料涂层平面运动裂纹分析

研究粘结于均匀材料基底上功能梯度材料涂层平面运动裂纹问题,假设功能梯度材料剪切模量和密度为坐标的指数函数,而泊松比为常数.采用Fourier变换和传递矩阵法将该混合边值问题转化为一对奇异积分方程,通过数值求解奇异积分方程组获得功能梯度材料涂层平面运动裂纹的应力强度因子.考察了结构几何尺寸、裂纹运动速度以及材料梯度参数对运动裂纹的应力强度因子的影响,发现材料梯度参数、结构几何尺寸、裂纹长度以及运动速度均对功能梯度材料动态断裂行为有显著影响.     

Anti-plane crack moving along the interface of dissimilar piezoelectric materials

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result for the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials. Supported by the National Natural Science Foundation and the National Post-doctoral Science Foundation of China.     

Moving interfacial crack between piezoelectric ceramic and elastic layers

An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed.     

Study for 2D moving contact elastic body with closed crack using BEM

Using a sub-regional boundary element method, an algorithm for the two-dimensional elastic bodies with a closed crack loaded by a moving contact elastic body is proposed. Since the extent and status of the contact surface of two elastic bodies and the crack within the body are all not known in advance, a double iterative contact algorithm is used. The BEM program for solving the closed crack problems is developed, some numerical examples are calculated, and the results of the center crack cases are shown to be in good agreement with the analytical solution in the classical fracture mechanics. In the condition of friction and non-friction, some coupling computational results of the SIF for the closed crack, with different angles and loaded by a moving contact elastic body, are also obtained by a numerical computation. The project supported by the National Natural Science Foundation of China (10172053) and NJTU Foundation of China (PD-157)     

Interface crack between piezoelectric and elastic strips

Summary An interface crack between piezoelectric and elastic strips is analyzed using the theory of linear piezoelectricity. The combined out-of-plane mechanical and in-plane electrical loads are applied to the layered strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The stress intensity factor is determined, and numerical analysis is performed and discussed. Received 22 September 1999; accepted for publication 3 May 2000     

反平面断裂问题的无单元伽辽金比例边界法

将比例边界法与无单元伽辽金法相结合,建立了反平面断裂分析的无单元伽辽金比例边界法。这是一种边界型无网格法,在环向方向上采用无单元伽辽金法进行离散,因此计算时仅需要边界上的节点信息,不需要边界元所要求的基本解。为了便于施加本质边界条件,通过建立节点值和虚拟节点值之间的关系给出了修正的移动最小二乘形函数。在径向方向上,该方法利用解析的方法求解,因此是一种半解析的数值方法。最后,给出了数值算例,并验证了所提方法后处理简单和计算精度高的特点,适合于求解反平面断裂问题。     

Limiting velocity of crack propagation in elastic materials

A crack is represented as a continuous set of linear dislocations. Simple analytical expressions are obtained for the potential and kinetic energies of the environment of moving cracks and the attached mass of cracks for an arbitrary form of the stress applied to the crack P(x). It is shown that the indicated analytical expressions are bilinear integrals of the functions P(x) and ∂P(x)/∂x. These integrals are calculated in explicit form for a constant stress over the entire crack length and the stress due to the action of molecular adhesion forces in a narrow region near the crack openings. It is shown that the calculation results does not depend on the form of molecular adhesion forces. The proposed approach to describing cracks and calculations based on it has made it possible for the first time to obtain a complete analytical expression for the limiting crack propagation velocity in elastic materials as a function of the main mechanical characteristics of such materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 158–166, July–August, 2009.     

Electroelastic field for an impermeable anti-plane shear crack in a piezoelectric ceramics plate

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h → ∞. Biography: LI Xian-fang (1964-)     

Anti-plane wave motion in a cylindrically orthotropic elastic solid containing a stress-free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress-free crack. The resulting wave motion is anti-plane. An eigenfunction solution to the problem is obtained in the form of an infinite series. The series is summed into two parts. The first part contains the incident and reflected wave pulses while the second part gives the diffraction integral. Wave front patterns are presented with an application to wood.     

Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading

A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases.     

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…