两种各向异性材料界面周期裂纹的反平面问题

研究两种各向异性材料界面含周期裂纹的反平面剪切问题，运用复变函数方法，获得了封闭形式解答，并给出了应力强度因子公式。从本文解签的特殊情形，可直接导出均匀各向异性材料共线裂纹，两种各向同性材料界面裂纹的相应问题公式。     

各向异性材料界面共线刚性线夹杂的反平面问题

研究两种各向异性材料焊接界面含共线刚性线夹杂的反平面问题,导出了一般问题的公式和几个典型问题的封闭形式解,求出了刚性线尖端的应力分布,从文中解答的特殊情况,直接导出各向性材料界面与均匀各向异性介质中相应问题的公式与结果,并与有关文献相一致。     

有限宽的粘接SANDWICH型正交各向异性板条具有界面裂纹或断裂的中间板条

本文研究了有限宽、粘接的对称SANDW(?)CH型正交各向异性板条的静裂纹问题.在中间板条有内部裂纹和完全断裂的两种情形,解法和应力奇异性分析的过程都和板条为各向同性时相似;但在界面裂纹时,却归结为解一组与各向同性粘接板条不同的二类柯西型奇异积分方程.此时,各向同性粘接板条界面裂纹的应力强度因子的定义已不再适用.本文提出一种广义的应力强度因子定义,并给出上述三种裂纹问题的算例,计算裂纹长度、板条宽度或弹性常数对应力强度因子的影响.     

L积分的显函数表达式

对均质各向同性材料,各向异性材料和两相各向同性材料中的裂纹问题各提出一种辅助的位移应力场,证明积分和Ｂｕｅｃｋｎｅｒ功共轭积分之间有一种固有的简单关系。这个关系在线弹性材料中与材料特征根无关,也不受界面裂纹尖端应力振荡奇性的影响。     

热释电材料问题的通解与界面裂纹

该文讨论了热释电材料中的热弹性问题的一般解，进而求解了共线界面裂纹问题．利用Ｓｔｒｏｈ方法，把热释电材料的热弹性界面裂纹问题化为一向量形式的Ｈｉｌｂｅｒｔ问题，求出这一Ｈｉｌｂｅｒｔ问题的通解，进而求得了热释电材料热弹性界面裂纹的闭合解，得到了温度、热流、位移、电势、应力和电位移的全场解，得到了裂纹张开位移及电势差的精确表达式．在此基础上，还求得了均匀热释电体中单个热弹性裂纹裂尖场，单个界面裂纹裂尖场以及点热源与界面裂纹的作用．此外，该文还对界面裂纹顶点附近的端部场作了渐近分析．     

带有扩展到和通过界面裂纹的各向同性/正交各向异性双层板条

本文分析了各向同性/正交各向异性双层板条的裂纹问题,由Fourier积分变换和问题的边界条件获得了一对奇异积分方程,确定了內部裂纹、边缘裂纹、到达和穿过界面裂纹的裂端及界面上的应力奇异性,利用Gauss-Jacobi和Gauss-Chebyshev积分公式求解奇异积分方程,得到了裂端和界面上的应力强度因子,并讨论了裂纹趋近于界面时进一步扩展的可能方式。     

含共线双半无限裂纹的正交异性复合材料板平面弹性问题的解析解

运用广义复变函数方法,通过构造适当的广义保角映射研究了含有共线双半无限裂纹的正交异性复合材料板的平面弹性问题,得出了部分裂纹面上受均匀面内载荷时应力场与两裂纹尖端处应力强度因子的解析解。结果表明:应力场的大小不仅与材料的几何构型及外载荷有关,还与材料的弹性常数有关,这是正交异性复合材料不同于各向同性材料的显著特征;两裂纹尖端处应力强度因子的大小只与材料的几何构型及外载荷有关;当两裂纹尖端的距离趋于无穷大时,所得到的解析解可退化为已有的正交异性复合材料板中半无限裂纹问题的解,通过将其与已有文献中的结果进行对比,验证了本文解析解的正确性。并通过数值算例分析了裂纹面上的受载长度、两裂纹尖端的距离对应力强度因子的影响规律以及两裂纹之间的相互作用。     

理想正交各向异性弹塑性材料平面应力条件下Ⅰ型静止裂纹尖端场

在本文中,以 Hill 的塑性理论为基础,详细地讨论了理想正交各向异性弹塑性材料,平面应力条件下Ⅰ型静止裂纹尖端场解。裂纹尖端应力场不包含应力间断线,但包含弹性区。分析的结果表明(i)对于平面应力静止裂纹问题,应力场解不是唯一的,场解中的自由参数必须由远场条件来确定。(ii)裂纹尖端的应力、应变的奇异性,无论是各向异性材料还是各向同性材料,都是相同的。但在各向异性材料中,各向异性参数影响着应力、应变的幅度和分布。     

理想正交各向异性弹塑性材料平面应力条件下Ⅰ型静止裂纹尖端场

在本文中,以 Hill 的塑性理论为基础,详细地讨论了理想正交各向异性弹塑性材料,平面应力条件下Ⅰ型静止裂纹尖端场解。裂纹尖端应力场不包含应力间断线,但包含弹性区。分析的结果表明(i)对于平面应力静止裂纹问题,应力场解不是唯一的,场解中的自由参数必须由远场条件来确定。(ii)裂纹尖端的应力、应变的奇异性,无论是各向异性材料还是各向同性材料,都是相同的。但在各向异性材料中,各向异性参数影响着应力、应变的幅度和分布。     

具有弹性对称面复合材料的Ⅲ型剪切缺陷或裂纹群应力强度因子的计算

本文应用lsida提出的复势罗朗展开法分析了具有弹性对称面复合材料的Ⅲ型剪切缺陷、裂纹群问题。在缺陷或裂纹平行分布情况下以级数形式给出了应力强度因子的计算公式。文中指出,对一般各向异性材料中的平行裂纹群问题,或正交各向异性复合材料中的平行缺陷或裂纹群问题,其解可简单地通过比拟由各向同性问题的解获得。     

Problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces

In this paper problems of cullinear cracks between bonded dissimilar materials underantiplane concentrated forces are dealt with.General solutions of the problems areformulated by applying extended Schwarz principle integrated with the analysis of thesingularity of complex stress functions.Closed-form solutions of several typical problemsare obtained and the stress intensity factors are given.These solutions include a series oforiginal results and some results of previous researches.It is found that under symmetricalloads the solutions for the dissimilar materials are the same as those for the homogeneousmaterials.     

LONGITUDINAL SHEAR PROBLEMS OF COLLINEAR RIGID LINE INCLUSIONS IN ANISOTROPIC MATERIALS

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Problems on collinear cracks between bonded dissimilar materials under concentrated loads

Following Ref. [6], this paper deals with the problem on collinear cracks between bonded dissimilar materials under a concentrated force and moment at an arbitrary point. Several typical solutions of complex stress functions in closed form are formulated and the stress intensity factors are given. These solutions include a series of results of previous researchers, and redress some errors in the researches of problems containing semi-infinite cracks^[3],[4].     

A unified definition for stress intensity factors of interface corners and cracks

Based upon linear fracture mechanics, it is well known that the singular order of stresses near the crack tip in homogeneous materials is a constant value −1/2, which is nothing to do with the material properties. For the interface cracks between two dissimilar materials, the near tip stresses are oscillatory due to the order of singularity being −1/2 ± iε and −1/2. The oscillation index ε is a constant related to the elastic properties of both materials. While for the general interface corners, their singular orders depend on the corner angle as well as the elastic properties of the materials. Owing to the difference of the singular orders of homogeneous cracks, interface cracks and interface corners, their associated stress intensity factors are usually defined separately and even not compatibly. Since homogenous cracks and interface cracks are just special cases of interface corners, in order to build a direct connection among them a unified definition for their stress intensity factors is proposed in this paper. Based upon the analytical solutions obtained previously for the multibonded anisotropic wedges, the near tip solutions for the general interface corners have been divided into five different categories depending on whether the singular order is distinct or repeated, real or complex. To provide a stable and efficient computing approach for the general mixed-mode stress intensity factors, the path-independent H-integral based on reciprocal theorem of Betti and Rayleigh is established in this paper. The complementary solutions needed for calculation of H-integral are also provided in this paper. To illustrate our results, several different kinds of examples are shown such as cracks in homogenous isotropic or anisotropic materials, central or edge notches in isotropic materials, interface cracks and interface corners between two dissimilar materials.     

Uniformly moving screw dislocation interacting with interface cracks in anisotropic bimaterials

This paper attempts to investigate the problem for the interaction between a uniformly subsonic moving screw dislocation and interface cracks in two dissimilar anisotropic materials. Using Riemann–Schwarz’s symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interface containing one and two cracks. The expressions of stress intensity factors at the crack tips and image force acting on moving dislocation are derived explicitly. The results show that the stress intensity factors at the crack tips decrease with increasing velocity of dislocation, and larger dislocation velocity leads to the equilibrium position of dislocation leaving from crack tips. The presented solutions contain previously known results as the special cases.     

复合材料承受剪切时双裂纹周围的应力强度因子

本文研究了由各向同性和各向异性半无限接合而成的复合材料中的应力强度因子问题，在复合材料的接合面附近处具有与接合面平行且共线的两个Ｇｒｉｆｆｉｔｈ裂纹，裂纹面上作用有剪应力，本文利用付利叶变换将混合边值问题归毕为求解奇异积分方程问题，为求解这些方程，将裂纹面上，下的位移差展成级数，并满足理解纹面外侧边界条件，级数中的待定系数利用裂纹面内的边界条件和施密特方法求得，本文对硼纤维塑料和铝板接合的复合材料     

The stress intensity factors near the tips of two collinear cracks in composite under in-plane shear

In this paper, the stress-intensity factors for two collinear cracks in a composite bonded by an isotropic and an anisotropic half-plane were calculated. The cracks are paralell to the interface, and the crack surfaces are loaded by uniform shear stresses. By using Fourier transform, the mixed boundary value problem is reduced to a set of singular integral equations. For solving the integral equations, the crack surface displacements are expanded in triangular series and the unknown coefficients in the series are determined by the Schmidt method. The stress intensity factors for the cracks in the boron-fibre plastics and aluminium joined composite and in carbon-fibre reinforced plastics were calculated numerically.     

Antiplane Problems of Periodical Rigid Line Inclusions between Dissimilar Anisotropic Materials

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