夹杂和裂纹相互影响时的界面应力分析

本文结合无限域上单根夹杂和单根裂纹的基本解,将裂纹与夹杂相互作用的问题归结为解一组柯西型奇异积分的积分方程组,使问题得到解决。本文还使用夹杂两侧的未知界面应力差,进一步推导了夹杂两侧的界面应力,并做了数值计算。有关这方面的计算可以作为研究与设计纤维与基体的联结强度的工程参考。     

线夹杂和线夹杂的相互作用

以短纤维复合材料为工程背景，本文利用线夹杂的工程计算模型以及无限平面中单夹杂的基本解，导出了线夹杂和线夹杂相互作用的平面问题的奇异积分方程。给出了夹杂端点的应力强度因子和夹杂界面应力的表达式，并作了具体的数值计算。     

多圆形刚性夹杂的反平面问题

构造任意分布且相互影响的多个圆形刚性夹杂模型的复应力函数，采用复变函数方法，达到满足各个夹杂的边界条件，利用坐标变换和围线积分将求解方程组化为线性代数方程组，推导出了圆形刚性夹杂任意分布的界面应力解析表达式，算例对多夹杂与单夹杂两种模型的界面应力最大值进行了对比，同时还给出了界面应力最大值随夹杂间距的变化规律，求出了刚性夹杂的合理间距。本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

圆形刚性夹杂双周期分布的反平面问题

研究含双周期分布的圆形刚性夹杂在无穷远受纵向剪切的弹性平面问题，遵循复合材料中各夹杂相互影响的重要条件。采用复变函数方法。构造相应模型的复应力函数。通过坐标变换，同时满足夹杂边界位移条件，再利用围线积分将求争方程组化为线性代数方程组。导出了圆形刚性夹杂双周期分布的界面应力解析表达式。算例给出了界面应力最大值与夹杂间距的变化规律。求出了刚性夹杂的合理间距问题，本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

考虑夹杂相互作用的复合陶瓷夹杂界面的断裂分析

复合材料中夹杂含量较高时,夹杂间的相互作用能显著改变材料细观应力应变场分布,基体和夹杂中的平均应力应变水平也会发生较大变化,导致复合材料强度等力学性能发生显著变化. 为修正单一夹杂模型运用在实际材料中的误差,基于相互作用直推估计法,建立一种考虑含夹杂相互作用的夹杂界面裂纹开裂模型. 首先根据相互作用直推估计法,得到残余应力和外载应力共同作用下夹杂中的平均应力,再计算无限大基体中相同的夹杂达到相同应力场时的等效加载应力,将此加载应力作为含界面裂纹夹杂的等效应力边界条件,在此边界条件下求得界面裂纹尖端的应力强度因子,进而得到界面裂纹开裂的极限加载条件,并分析了夹杂弹性性能、含量、热残余应力、夹杂尺寸等因素对界面裂纹开裂条件的影响. 结果表明,方法能够有效修正单夹杂模型运用在实际材料中的误差,较大的残余应力对界面裂纹开裂有重要的影响,夹杂刚度的影响并非单调且比较复杂;在残余应力较小时,降低柔性夹杂刚度或者增大刚性夹杂刚度都有利于提高材料强度;扩大夹杂尺寸将导致裂纹开裂极限应力显著降低,从而降低材料强度.      

穿过反平面圆形夹杂界面的曲线型刚性线

利用复变函数方法和叠加原理建立了求解刚性线夹杂问题的弱奇积分方程,利用Ｃａｕｃｈｙ型奇异积分方程主部分方法,研究了穿过反平面圆夹杂界面的曲线型刚性线夹杂在界面交点处点处的奇性应力指数以及交点处角形域内的奇性应力,并定义了交点处的应力奇性因子。利用所得的奇性应力指数,通过对弱奇异积分方程的数值求解,得出了刚性线端点和交点处的应力奇性因子。     

颗粒增强复合材料的椭圆形刚性夹杂呈双周期分布模型的反平面问题研究

在遵循复合材料中各夹杂相互影响的重要条件下，构造呈双周期分布且相互影响的椭圆形刚性夹杂模型的复应力函数，采用坐标变换和复变函数的依次保角映射方法，达到满足各个夹杂的边界条件，利用围线积分将求解方程化为线性代数方程，推导出了在无穷远双向均匀剪切，椭圆形刚性夹杂呈双周期分布的界面应力解析表达式，最后的算例分析给出了夹杂的形状对界面应力最大值(应力集中系数)的影响规律，并描绘出了曲线。     

应力诱发界面扩散下夹杂演化的有限元模拟

应力作用下内连导线中的夹杂等缺陷会迁移和变形,从而影响电子器件的可靠性.论文基于应力诱发表面扩散机制下的弱解描述,推导了固-固界面在界面扩散机制下的有限单元控制方程,并数值分析了应力诱发界面扩散下金属内连导线中夹杂的形貌演化.研究结果表明:在拉压应力下,夹杂会发生分节或者圆形化;在双向等值拉应力下,夹杂存在着沿长轴生长...     

夹杂对两相材料界面裂纹的影响

根据界面上应力和位移的连续条件,得到了单向拉伸状态下,含有椭圆夹杂的无限大双材料组合板的复势解。进一步通过求解Hilbert问题,得到了含有夹杂和半无限界面裂纹的无限大板的应力场,并由此给出了裂尖的应力强度因子K。计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响。计算结果表明夹杂到裂尖的距离和夹杂材料的性质对K影响较大,对于不同材料组合,该影响有较大差异。夹杂距裂尖较近时,会对K产生明显屏蔽作用,随着夹杂远离裂尖,对K的影响也逐渐减小。另外,软夹杂对K有屏蔽作用,硬夹杂对K有反屏蔽作用,而夹杂形状对K几乎没有影响。     

含椭圆夹杂正交各向异性体的界面应力研究

本文研究了远场作用反平面载荷时含椭圆夹杂正交各向异性体的界面应力分布规律．利用解析函数边值问题理论和共形映射技术,推导了反平面载荷下含椭圆夹杂正交异性体的精确解,获得了夹杂和基体内应力场的闭合解,并通过有限元结果验证了本文解析解的有效性．研究表明：基体材料主方向弹性模量比C55/C44和夹杂形状比 对界面应力影响显著;基体材料主方向模量比C55/C44对界面应力的影响受夹杂/基体模量比Cf/C44的限制．     

Analysis of a cracked concrete containing an inclusion with inhomogeneously imperfect interface

The distributed dislocation technique is applied to determine the behavior of a cracked concrete matrix containing an inclusion. The analysis of cracked concrete in the presence of inclusions such as steel expansions is a practical problem that needs special attention. The solution to the problem of interaction of an edge dislocation with a circular inclusion having circumferentially inhomogeneously imperfect interface is available in the literature. This analytical solution is used in the distributed dislocation technique to obtain the stress intensity factor for the cracked concrete in the presence of inclusion. The interface of the matrix and the inclusion is assumed inhomogeneously imperfect and the stress intensity factor is determined for the cracked concrete for a case of two identical cracks on diametrically opposite sides of the inclusion. Consideration of this general inhomogeneously imperfect interface is the contribution of this paper. The variation of the inhomogeneity parameters is studied and presented. Additionally, the general assumption for the interface is simplified to the special case of perfectly bonded interface. The observations for the perfect interface are coincident with the previously reported results.     

Interaction between crack and elastic inclusion

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THE INTERACTION PROBLEM BETWEEN THE ELASTIC LINE INCLUSIONS

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Scattering of SH-wave from interface cylindrical elastic inclusion with a semicircular disconnected curve

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green＇s function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green＇s function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed.     

Scattering of SH-wave from interface cylindrical elastic inclusion with a semicircular disconnected curve

Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated.The solution of dynamic stress concentration factor is given using the Gteen's function and the method of complex variable functions.First,the space is divided into upper and lower parts along the interface.In the lower half space,a suitable Green's function for the problem is constructed.It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface.Thus,the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces.Also,the expressions of displacement and stress fields are obtained in this situation.Finally,examples and results of dynamic stress concentration factor are given.Influences of the cylindrical inclusion and the difierence parameters of the two mediators are discussed.     

Uniform Stress Inside an Anisotropic Elliptic Inclusion with Imperfect Interface Bonding

In this paper we study the two-dimensional deformation of an anisotropic elliptic inclusion embedded in an infinite dissimilar anisotropic matrix subject to a uniform loading at infinity. The interface is assumed to be imperfectly bonded. The surface traction is continuous across the interface while the displacement is discontinuous. The interface function that relates the surface traction and the displacement discontinuity across the interface is a tensor function, not a scalar function as employed by most work in the literature. We choose the interface function such that the stress inside the elliptic inclusion is uniform. Explicit solution for the inclusion and the matrix is presented. The materials in the inclusion and in the matrix are general anisotropic elastic materials so that the antiplane and inplane displacements are coupled regardless of the applied loading at infinity. T.C.T. Ting is Professor Emeritus of University of Illinois at Chicago and Consulting Professor of Stanford University.     

Stress Analysis of an Elliptic Inclusion with Imperfect Interface in Plane Elasticity

In this paper, a semi-analytic solution of the problem associated with an elliptic inclusion embedded within an infinite matrix is developed for plane strain deformations. The bonding at the inclusion-matrix interface is assumed to be homogeneously imperfect. The interface is modeled as a spring (interphase) layer with vanishing thickness. The behavior of this interphase layer is based on the assumption that tractions are continuous but displacements are discontinuous across the interface.Complex variable techniques are used to obtain infinite series representations of the stresses which, when evaluated numerically, demonstrate how the peak stress along the inclusion-matrix interface and the average stress inside the inclusion vary with the aspect ratio of the inclusion and a representative parameter h (related to the two interface parameters describing the imperfect interface in two-dimensional elasticity) characterizing the imperfect interface. In addition, and perhaps most significantly, for different aspect ratios of the elliptic inclusion, we identify a specific value (h ^*) of the (representative) interface parameter h which corresponds to maximum peak stress along the inclusion-matrix interface. Similarly, for each aspect ratio, we identify a specific value of h (also referred to as h ^* in the paper) which corresponds to maximum peak strain energy density along the interface, as defined by Achenbach and Zhu (1990). In each case, we plot the relationship between the new parameter h ^*and the aspect ratio of the ellipse. This gives significant and valuable information regarding the failure of the interface using two established failure criteria.