Stress Concentration Near an Elliptic Crack in the Interface Between Elastic Bodies under Steady-State Vibrations

The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body consisting of two perfectly joined dissimilar half-spaces with an elliptic mode I crack located in one of the half-spaces normally to the interface. The problem is reduced to a boundary integral equation for the crack opening function. The integration domain of the equation is bounded by the crack domain, and the interaction between the crack and the interface is described by a regular kernel. The equation is solved using the mapping method. Numerical results are obtained for the case where the surfaces of the elliptic crack are subjected to harmonic loading with constant amplitude. The dependences of the stress intensity factors on the wave number are presented for various relationships among the mechanical constants that ensure the absence of near-surface waves     

An Interface Crack for a Functionally Graded Strip Sandwiched Between Two Homogeneous Layers of Finite Thickness

In this paper, the behavior of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness subjected to an uniform tension is resolved using a somewhat different approach, named the Schmidt method. The Fourier transform technique is applied and a mixed boundary value problem is reduced to two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surface. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effects of the crack length, the thickness of the material layer and the materials constants upon the stress intensity factor of the cracks. It can be obtained that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.     

Initial Development of the Prefracture Zone Near the Tip of a Crack Reaching the Interface Between Dissimilar Media

The Wiener–Hopf method is used to analyze, within the framework of a plane static problem, the prefracture zone near the tip of a mode I crack reaching the interface separating two isotropic media and containing a corner point     

Three-Dimensional Dynamic Contact Problem for an Elliptic Crack Interacting with a Normally Incident Harmonic Compression–Expansion Wave

The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented     

General Spatial Dynamic Problem for an Elliptic Crack under the Action of a Normal Shear Wave,with Consideration for the Contact Interaction of the Crack Faces

Consideration is given to the contact interaction of the faces of a stationary plane elliptical crack under the action of a harmonic shear wave normally incident on the crack surface. The dependence of the mode II and III stress intensity factors on the wave number is studied for different values of the friction coefficient     

关于界面下裂纹对界面裂纹的屏蔽参数

讨论了界面下裂纹对界面裂干涉的合理屏蔽参数问题。对于一条在远场载荷作用下、受到附近界面下裂纹干涉的界面裂纹,采用伪力法计算不同长度单位时界面裂纹的G／G0、k1/k10和k11/k110以及K1／K10和K11／K110（G是能量释放率、k1 ik110是通常定义的应力强度因子、K10＋iK110是含标定长度的应力强度因子;G0、k10 ik110、K10＋iK110对应单一界面裂纹情况）。结果表明,G／G0、K1／K10和K11／K110是较为合理的描述界面下裂纹对界面裂纹屏蔽的参数。     

An Edge Crack Problem in a Semi-Infinite Plane Subjected to Concentrated Forces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｄｇｅｃｒａｃｋｐｒｏｂｌｅｍｉｎａｓｅｍｉ＿ｉｎｆｉｎｉｔｅｐｌａｎｅｗａｓｃｏｎｓｉｄｅｒｅｄｂｙｍａｎｙｉｎｖｅｓｔｉｇａｔｏｒｓ.ＵｓｉｎｇｔｈｅＦｒｅｄｈｏｌｍｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎａｎｄｔｈｅａｌｔｅｒｎａｔｉｎｇｍｅｔｈｏｄ ,ａｎｅｄｇｅｃｒａｃｋｐｒｏｂｌｅｍｉｎａｓｅｍｉ＿ｉｎｆｉｎｉｔｅｐｌａｎｅｗａｓｓｏｌｖｅｄ[1].Ｔｈｅｏｂｔａｉｎｅｄｒｅｓｕｌｔｓａｒｅｌｉｍｉｔｅｄｔｏｔｈｅｃａｓｅｔｈａｔｔｈｅｅｄｇｅｃｒａｃｋｉｓｎｏｒｍ…     

压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题

分析了压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题。利用傅立叶变换,使问题的求解转换为对一对以裂纹表面上的位移差为未知变量的对偶积分方程的求解。为了求解对偶积分方程,把裂纹面上的位移差展开为雅可比多项式形式,进而得到了裂纹长度、入射波波速及入射波频率对裂纹应力强度因子的影响。从数值结果可以看出,压电压磁复合材料中可导通裂纹的反平面问题的动应力奇异性与一般弹性材料中的反平面断裂问题动应力奇异性相同。     

弹性半平面中的斜边界裂纹问题

讨论了一群性半平面无限体中含有一斜烈纹的静力学问题,研究中以断裂力学原理为基础,采用了复变函数的方法,将原问题化为一组解析函数边值问题的求解。文中通过分析函数法以及应用Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ（Ｒ－Ｈ）边值问题的一般理论,给出了所研究问题的解析解,并且给出了此问题的应力强度因子Ｋ１,Ｋ１的显式形式,此外,裂纹上的位移发生的错动可以得以进一步的讨论,文中的结论对地学的研究有一定的应用价值。     

Solving the Contact Problem for a Rectangular Die on an Elastic Foundation

A method of orthogonal polynomials is proposed to solve the contact problem for a rectangular die on an elastic foundation. For the case of an elastic half-space, an exact formula is derived for the translation of the die under symmetric loading     

Determining Prefracture Zones at a Crack Tip Between Two Elastic Orthotropic Bodies

The model of prefracture zones is generalized to a crack between two anisotropic materials. An exact analytical solution is found on the assumptions that the prefracture zone is localized on the crack continuation and that only the normal displacements undergo discontinuity in the zone. From this solution, equations for determining the prefracture length and crack tip opening are derived     

幂硬化弹塑性-刚性界面Ⅲ型定常扩展裂纹尖端的渐近场

对幂硬化弹塑性材料－刚性材料界面上裂纹以定常方式扩展的Ⅲ型问题进行弹塑性渐近分析,给出裂纹尖端的应力,应变和位移场解。通过数值计算,考察了不同Mach数以及裂纹尖端混合参数对场解的构造以及应力,应变分布的影响,为给出合理的断裂准则提供理论依据。     

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。     

Crack kinking from an interface crack with initial contact between the crack lips

The authors recently theoretically studied crack kinking and opening from an initially closed crack (without friction) in some homogeneous medium. The same problem, but for an interface crack, is considered here. Comninou has shown that the asymptotic stress field prior to kinking is governed by a single, mode II stress intensity factor (SIF). Using this result, plus a homogeneity property of the problems of elastic fracture mechanics with unilateral contact envisaged, a change of scale, and two reasonable hypotheses, we establish the expression of the SIF at the tip of the small, open crack extension. It is shown that whatever the geometry of the external boundary and the crack and whatever the loading, these SIF depend solely upon the initial (mode II) SIF (in a linear way), the kink angle and Dundurs' parameters α and β. Using this result and Goldstein and Salganik's “principle of local symmetry” to predict the kink angle, one finds that it is independent of the loading but does depend upon Dundurs' parameters α and β. This contrasts with the case of an ordinary (initially closed) crack in some homogeneous medium, for which the kink angle was not only independent of the loading but an absolute constant. However, it is numerically found that the influence of the mismatch of elastic properties upon the kink angle is rather weak.     

Electroelastic Analysis of an Internal Interface Crack in a Half-Plane Consisting of Two Bonded Dissimilar Piezoelectric Quarter-Planes

The problem of an interface crack in a half-plane consisting of two bonded dissimilar piezoelectric quarters is considered under antiplane shear and inplane electric loading. The problem is solved under the electrically permeable assumption for a crack. The integral transform technique is employed to reduce the problem to triple integral equations, which is further converted to a hypersingular integral equation for the crack sliding displacement. By solving the resulting equation analytically, the electroelastic field along the interface and the energy release rate are obtained in explicit form, respectively. Several examples are given to illustrate the influence of the material properties and the crack position on the energy release rate.     

On unilateral contact of two plates aligned at an angle to each other

The contact problem for two elastic plates aligned at a prescribed angle to each other is considered. The set of contact points is assumed to be unknown in advance and to be determined only after the problem is solved. Various formulations of the problem are given, and their equivalence is proved. A complete set of boundary conditions fulfilled on the contact domain is found, and the character of satisfaction of these conditions is described. The asymptotic properties of solutions are studied for rigidity parameters of the contacting plates tending to infinity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 42–58, July–August, 2008.     

有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响

随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视.界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性.因此双材料界面附近的力学分析是比较复杂的.论文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响.运用弹性力学中的Goursat公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数.通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子.计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定.分析结果可以为预测双材料结构复合材料界面失效位置提供参考.     

功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载的响应分析

在忽略界面裂尖端裂纹面相互叠入的条件下,对功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载响应问题进行了分析。利用傅立叶变换,将问题的求解转换为对以裂纹面上位移差为未知函数的对偶积分方程的求解。为了求解对偶积分方程,将裂纹面上的位移差函数展开为雅可毕多项式的级数形式。最终给出了裂纹长度、入射波频率和材料性质对应力强度的影响。结果表明,当界面材料不连续时,获得了具有普通1/2奇异性的近似解。     

Scattering of harmonic elastic waves by a plane interface crack with linear adhesive tips in a layered half space

In this paper, the scattering of elastic waves by an interface crack with linear adhesive tips in a layered half space is considered. By use of integral transform and integral equation methods, the singular integral equations of this problem are derived, which are transformed into a set of algebraic equations by means of contour integration and Chebyshev polynomials expanding technique. The numerical results of the adhesive region and stress amplitudes are given in this paper.     

Analysis of the Interface Crack for Rubber-like Materials

The interface crack between two dissimilar rubber materials under mixed load is asymptotically analyzed in this paper. It is shown that the crack tip field is composed of one expanding sector and two shrinking sectors. For the case considered, the interface is located in the expanding sector. Analytical solutions are obtained for both the expanding sector and the shrinking sectors. The structures of the crack tip field obtained in this paper is compared with those in previous works for different constitutive equations.