垂直磁压电材料界面三维裂纹的超奇异积分法

应用有限部积分概念和广义位移基本解，垂直于磁压电双材料界面三维复合型裂纹问题被转 化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而，通过主部 分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后，通过将裂纹表面 位移间断未知函数表达为位移间断基本密度函数与多项式之积，使用有限部积分法对超奇异 积分方程组建立了数值方法. 最后，通过典型算例计算，讨论了广义应力强度因子的变化规 律.     

Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method

Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used for calculating transient responses of thermal and electromechanical fields respectively. The generalized dynamic intensity factors for the thermal stresses and electrical displacements are extracted by using the interaction integral. The accuracy of the developed approach is verified numerically by comparing the calculated results with reference solutions. Numerical examples with mixed-mode crack problems are analyzed. The effects of the crack-length, poling direction, material gradation, etc. on the dynamic intensity factors are investigated. It shows that the transient dynamic crack behaviors under the cooling shock differ from those under the heating shock. The influence of the thermal shock loading on the dynamic intensity factors is significant.     

A finite crack in a semi-infinite strip of a graded piezoelectric material under electric loading

In this paper, the mixed-mode crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electric loading. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

Functionally graded piezoelectric strip with a penny-shaped crack under electromechanical loadings

In this paper, the mixed-mode penny-shaped crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electromechanical loadings. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

压-剪混合型定常扩展裂纹尖端的弹黏塑性场

假定黏性系数与塑性等效应变率的幂次成反比，考虑其黏性和裂纹面摩擦接触效应 建立了压-剪混合型定常扩展裂纹尖端弹黏塑性场的渐近方程，求得了裂纹尖端场不含应力、应变间 断的数值解. 并讨论了压-剪混合型裂纹数值解随各个参数的变化规律，计算结果 和分析表明，压-剪混合型裂纹尖端场是满塑性的，不含有弹性卸载区，黏性效应是研究扩展裂纹尖端场时的一个重要因素. 无论混合裂纹趋近I型还是趋近II型，静水压力随摩擦系数的增加都是增加的,裂纹面摩擦 效应是阻止裂纹扩展速度的因素，且摩擦作用越强，裂纹尖端场的韧性越高.     

Inelastic material behavior and fracture mechanics: a variational approach

Summary A variational principle is presented, which relates the macroscopic fracture response of a mechanical component to its microscopic, inelastic material behavior. The principle allows a comparison between the crack driving force, expressed by the J-integral, and an integral expression of the fracture resistance. On this basis, the critical values of J are calculated for a Griffith crack under mixed-mode loading. The preliminary check with data available in literature shows a fairly good agreement. Received 18 July 1998; accepted for publication 9 February 1999     

The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin’s crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory’s expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.     

求解混合型裂纹应力强度因子的围线积分法

本文用复变函数理论推导出裂纹的辅助场，并用Betti功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法．此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子KⅠ和KⅡ的数值解．     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

Contact zone assessment for a fast growing interface crack in an anisotropic bimaterial

Summary A plane strain problem for a crack with a frictionless contact zone at the leading crack tip expanding stationary along the interface of two anisotropic half-spaces with a subsonic speed under the action of various loadings is considered. The cases of finite and infinite-length interface cracks under the action of a moving concentrated loading at its faces are considered. A finite-length crack for a uniform mixed-mode loading at infinity is considered as well. The associated combined Dirichlet-Riemann boundary value problems are formulated and solved exactly for all above-mentioned cases. The expressions for stresses and the derivatives of the displacement jumps at the interface are presented in a closed analytical form for an arbitrary contact zone length. Transcendental equations are obtained for the determination of the real contact zone length, and the associated closed form asymptotic formulas are found for small values of this parameter. It is found that independently of the types of the crack and loading, an increase of the crack tip speed leads to an increase of the real contact zone length and the correspondent stress intensity factor. The latter increase significantly for an interface crack tip speed approaching the Ragleigh wave speed.     

Driving forces and kinking of an oblique crack in bonded nonhomogeneous materials

Summary  Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently, the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation of local homogeneity and brittleness of the crack-tip behavior. Received 25 September 2001; accepted for publication 13 February 2002     

Plastic yielding on inclined slip-planes at a crack tip

Plastic yield at crack tips on singular slip-planes, inclined to the crack plane, has been studied under plane-strain conditions for combined tension, hydrostatic stress, and in-plane shear. The singular integral equation, which represents the equilibrium condition of edge dislocations on the slip-planes, is transformed into a Fredholm integral equation in order to avoid difficulties that occur with its numerical solution. Results are presented for the slip-band length, the plastic crack-tip opening displacement, stress fields, and crack-opening contours. A series expansion of the results obtained numerically confirms approximate analytical expressions given by J.R. Rice (1974), up to the third-order in the applied stresses. The results of finite element methods agree with values of the crack-tip opening displacement obtained here to within 10 per cent. Ahead of the crack tip, the principal tensile stresses exceed the principal shear stresses by a factor of 10, approximately.     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

Crack initiation behavior of functionally graded piezoelectric material: prediction by the strain energy density criterion

Transient response of a functionally graded piezoelectric medium is considered for a through crack under the mixed-mode in-plane mechanical and electric load. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor. This determines the direction of crack initiation. Numerical results display the effects of material constants, loading combination parameter, mechanical loading angle and material gradient parameter on the possible fracture behavior.     

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

A three-dimensional crack problem in electromagnetothermoelastic multiphase composites (EMTE-MCs) under extended loads is investigated in this paper. Using Green’s functions, the extended general displacement solutions are obtained by the boundary element method. This crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors (SIFs) and the extended energy release rate near the crack front in EMTE-MCs are provided. Also, a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended SIFs varying with the shape of the crack are presented. The results show that the present method accurately yields smooth variations of extended SIFs along the crack front.     

Fracture mechanics of a tension-shear macrocrack in rocks

Fracture in rocks is influenced by anisotropy and existence of faults. Fracture initiation and propagation is often under the combined presence of sliding and opening of preexisting cracks. Linear-elastic fracture-mechanics (LEFM) has been used as a model for describing the propagation of a main crack in materials such as rocks, concrete, ceramics, etc. However, the presence of the fracture process zone which includes interlocking of grains and ligament connections results in deviations from perfectly brittle behavior. These effects are more pronounced in mixed-mode fracture, which involves crack initiation under the combined presence of tension-shear or compression-shear stresses.Specimens of Indiana limestone with a preexisting inclined notch were studied to observe the fracture process under a mixed-mode state of stress. Experimental monitoring involved using the electronic speckle-pattern interferometry (ESPI) technique to monitor strains and crack-propagation paths with high sensitivity. A scanning electron microscope (SEM) was used to examine the specimen for the presence of microcracks. Experimental results were subsequently evaluated using a mixed-mode fracture theory and finite-element computations.It was possible to visually observe the pre-peak and post-peak development of the fracture process zone. Developments in the crack-tip strain concentration were observed at and beyong the peak load. While the experiments conducted involved tension-shear cracks, the possibility of extending the concepts to compression-shear cracks was also explored. The possibilities and limitations of using the fracture-mechanics approach to understanding fracture in rocks were subsequently discussed.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

界面超高速自相似动态分层分析：反平面情况

对材料界面超高速自相似动态分层的反平面问题进行了解析分析。分层模拟为界面裂纹由零长度自相似扩展，扩展速度为蹭音速或超音速。首先考虑运动集中载荷作用下界面动态分层的情况，利用界面裂纹自相似扩展的运动位错模型将问题归结为奇异积分方程，并求得解析解，分析了裂纹尖端的应力奇性，获得了动应力强度因子。最后，利用叠加原理给出了ｘ＾ｎ型载荷作用下界面动态分层的解。     

Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode deformations

An antisymmetric test fixture is employed to investigate interlaminar fracture behavior in graphite/epoxy composite material under mixed-mode deformations. Finite correction factors for the graphite/epoxy fracture specimen with various crack lengths are used to determine the interlaminar fracture toughness by finite-element stress analysis. Interlaminar fracture characteristics of graphite/epoxy composite material under mode-I, mode-II and mixed-mode deformations are evaluated experimentally. A mixed-mode fracture criterion is also investigated to obtain information on mixedmode interlaminar fracture behavior of graphite/epoxy composite material.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Crack spacing effect for a piezoelectric cylinder under electro-mechanical loading or transient heating

This paper investigates the fracture problem of a piezoelectric cylinder with a periodic array of embedded circular cracks. An electro-mechanical fracture mechanics model is established first. The model is further used to the thermal fracture analysis of a piezoelectric cylinder subjected to a sudden heating on its outer surface. The temperature field and the associated thermal stresses and electric displacements are obtained and are added to the crack surface to form a mixed-mode boundary value problem for the electro-mechanical coupling fracture. The stress and stress intensities are investigated for the effect of crack spacing. Strength evaluation of piezoelectric materials under the transient thermal environment is made and thermal shock resistance of the medium is given.     

三维体内含垂直于双材料界面混合型裂纹的超奇异积分解法

利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。