纤维增强复合材料圆柱型界面裂纹分析

以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题．应用Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ的奇异积分方程理论，分析了圆柱型界面裂纹尖端应力场．针对裂纹尖端分别存在和不存在接触区两种情况，确定了裂纹尖端应力场的奇异性．利用数值方法计算了圆柱型界面裂纹尖端接触区尺寸对剪应力强度因子的影响．     

界面下主微裂纹间干涉的研究

涉及两相正交各向异性体界面干涉问题的研究,多裂纹问题被分解为只含单裂纹的子问题,利用位错理论和裂面应力自由条件,列出一组可数值求解位错密度函数的奇异积分方程,从耐 注得应力强度因子。     

Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface

The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak.     

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。     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

折线裂纹和两相材料界面的相互作用

利用螺位错基本解建立了和界面相交的折线裂纹的Cauchy型积分方程，根据奇异积分方程理论，得出了确定折线裂纹和界面交点处的奇性应力指数的特征方程，以及交点处各角形域内的奇性应力，利用所得的交点处的奇性应力定义了折线裂纹和界面交点处的应力强度因子，对所得积分方程进行数值求解，可得裂纹端点以及裂纹和界面交点处的应力强度因子。     

Analysis of stress intensity factors of a ring-shaped interface crack

In this paper, numerical solutions of singular integral equations are discussed in the analysis of axi-symmetric interface cracks under torsion and tension. The problems of a ring-shaped interface crack are formulated in terms of a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental densities are chosen to express a two-dimensional interface crack exactly. The accuracy of the present analysis is verified by comparing the present results with the results obtained by other researchers for the limiting cases of the geometries. The calculation shows that the present method gives rapidly converging numerical results for those problems as well as for ordinary crack problems in homogeneous material. The stress intensity factors of a ring-shaped interface crack are shown in tables and charts with varying the material combinations and also geometrical conditions.     

Mode III fracture problem of two arbitrarily oriented cracks located within two bonded functionally graded material strips

This paper shows the anti-plane crack problem of two bonded functionally graded material (FGM) strips. Each strip contains an arbitrarily oriented crack. The material properties of the strips are assumed in exponential forms varied in the direction normal to the interface. After employing the Fourier transforms, the unknowns are solved from the interface conditions, boundary conditions and the condition on the crack surfaces. The problem can then be reduced to a system of singular integral equations, which are solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. In the discussions, several degenerated problems are considered to demonstrate the influence of the non-homogeneous parameters, crack orientations, edge effects and the crack interactions on the normalized intensity factors. In general, the factors are larger when crack tips are located in stronger material. Also, the factors increase as the crack is oriented in the direction normal to the interface. The conclusions made in this research can be used to evaluate the safety of two bonded strips once the cracks exist inside the structure.     

折线型裂纹对SH波的动力响应

利用Fourier积分变换方法,得出了无限平面中用裂纹位错密度函数表示的单裂纹散射场．根据无穷积分的性质,把单裂纹的散射场分解为奇异部分和有界部分．利用单裂纹的散射场建立了折线裂纹在SH波作用下的Cauchy型奇异积分方程．根据折线裂纹散射场和所得的积分方程讨论了裂纹在折点处的奇性应力及折点处的奇性应力指数．利用所得的奇性应力定义了折点处的应力强度因子．对所得Cauchy型奇积分方程的数值求解,可得裂纹端点和折点处的动应力强度因子。     

Mode III crack problems for two bonded functionally graded piezoelectric materials

This paper investigates the singular electromechanical field near the crack tips of an internal crack. The crack is perpendicular to the interface formed by bonding two half planes of different functionally graded piezoelectric material. The properties of two materials, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The singular integral equations for impermeable and permeable cracks are derived and solved by using the Gauss–Chebyshev integration technique. It shows that the stresses and electrical displacements around the crack tips have the conventional square root singularity. The stress intensity and electric displacement intensity factors are highly affected by the material nonhomogeneity parameters β and γ. The solutions for some degenerated problems can also be obtained.     

A Self-Similar Crack Expansion method for three-dimensional cracks in an infinite or semi-infinite medium

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks are in good agreement with other analytical solutions.     

A new integral equation formulation of two-dimensional inclusion–crack problems

A new integral equation formulation of two-dimensional infinite isotropic medium (matrix) with various inclusions and cracks is presented in this paper. The proposed integral formulation only contains the unknown displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks. In order to solve the inclusion–crack problems, the displacement integral equation is used when the source points are acting on the inclusion–matrix interfaces, whilst the stress integral equation is adopted when the source points are being on the crack surfaces. Thus, the resulting system of equations can be formulated so that the displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks can be obtained. Based on one point formulation, the stress intensity factors at the crack tips can be achieved. Numerical results from the present method are in excellent agreement with those from the conventional boundary element method.     

Interaction between crack and elastic inclusion

ＩＮＴＥＲＡＣＴＩＯＮＢＥＴＷＥＥＮＣＲＡＣＫＡＮＤＥＬＡＳＴＩＣＩＮＣＬＵＳＩＯＮＺｈａｎｇＭｉｎｇ－ｈｕａｎ（张明焕）,ＴａｎｇＲｅｎ－ｊｉ（汤任基）（ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ,Ｓｈａｎｇｈａｉ,２０００３０,Ｐ．Ｒ．...     

NEW BOUNDARY ELEMENT METHOD FOR TORSION PROBLEMS OF CYLINDER WITH CURVILINEAR CRACKS

The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.     

SELF-SIMILAR CRACK EXPANSION METHOD FOR THE STRESS INTENSITY FACTOR ANALYSIS

The Self-Similar Crack Expansion (SSCE) method is proposed to evaluate stress intensi-ty factors at crack tips, whereby stress intensity factors of a crack can be determined by the crackopening displacement over the crack, not just by the local displacement around the crack tip. The crackexpansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy ofthe calculation is improved. The singular integrals on crack tip elements are also analyzed and are pre-cisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly in-creases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimen-sional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms ofthe self-similar expansion rate. Solutions are satisfied with errors less than 0.5% as compared with theanalytical solutions. Based on the calculations of the crack interactions, a theory for crack interactionsis proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tipsof cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod ofSelf-Similar Crack Expansion in this paper.     

Interaction between a circular inclusion and a symmetrically branched crack

The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated.     

Interaction of three interfacial Griffith cracks between bonded dissimilar orthotropic half planes

The paper deals with the interaction of a pair of outer cracks on a central crack situated at the interface of two dissimilar orthotropic half-planes. The mixed boundary value problem is reduced to solving a pair of simultaneous singular integral equations which have finally been solved numerically by using Jacobi polynomials. The analytical expressions for stress intensity factors at the central crack tip and the expression of the strain energy release rate have been derived for general loading. Numerical values of the interaction effects of the outer cracks on the central crack have been calculated through stress magnification factors. It is seen that the interaction effects are either shielding or amplification depending on the size of the outer cracks and their spacing from the central crack.     

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．     

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.     

基于修正权函数的多裂纹无网格模拟

本文采用了一种基于不连续场修正权函数的无网格方法来处理二维平面多裂纹问题。相较于传统的无网格断裂不连续场和奇异场模拟方法,修正权函数法算法简便易实现。采用修正权函数处理多裂纹时,只需要对每一段裂纹周围节点的权函数进行修正,就能同时模拟多裂纹不连续位移场和多裂尖奇异场。本文采用基于不连续场修正权函数的无单元Galerkin方法（EFGM）,对Y型裂纹板、十字型裂纹板和孔边双裂纹板进行了分析。数值结果表明,在不引入扩展基函数情况下,通过修正权函数法能够得到精度较高的应力强度因子解,能较好地拟合多裂纹的裂尖奇异场。