压电螺型位错与含界面裂纹椭圆夹杂的干涉效应

运用求解复杂多连通域问题的复变函数方法，获得了压电螺型位错与含界面裂纹椭圆夹杂的干涉问题，复势函数的精确级数形式解。利用广义Peach-Koehler公式导出作用于螺型位错的位错力公式。分析结果表明，当裂纹的曲率或长度达到临界值，界面裂纹的存在会改变压电螺型位错与椭圆夹杂的干涉性质。     

集中载荷作用下含椭圆夹杂各向异性板的解法

应用复变函数方法研究了含椭圆夹杂各向异性板在集中载荷作用下的解法，首先将复应力函数在椭圆夹杂与板的接触边界上展开成幂级数，然后代入问题的边界条件，最后得到了幂级数形式的复应力函数的系数的线性方程组，进一步求解可获得板的应力分布。     

压电螺型位错与椭圆夹杂界面导电刚性线的干涉效应

研究了无限大压电基体材料中压电螺型位错与含界面导电刚性线椭圆夹杂的电弹耦合干涉问题。运用求解复杂多连通域问题的复变函数方法,获得了椭圆夹杂和基体区域复势函数以及电弹性场的精确级数形式解答。利用广义Peach-Koehler公式导出作用于压电螺型位错上的位错力公式。主要讨论了刚性线几何尺寸和椭圆曲率对位错力的影响规律。分析结果表明:界面刚性线排斥基体中的位错,对靠近椭圆夹杂界面的螺型位错的运动和平衡位置有重要的影响。当刚性线的长度达到临界值,界面刚性线的存在会改变螺型位错与压电椭圆夹杂的干涉规律。椭圆夹杂的压缩系数变大,刚性线尺寸对位错力的影响也越大。     

含界面层圆形夹杂的平面热弹性问题

研究了无穷远均匀拉伸条件下，含界面层圆形弹性夹杂的平面热弹性问题。运用Muskhelishvili复势理论的级数展开技术，将各区应力函数展开为合适的Taylor和Laurent级数，考虑边界上的力和位移连续性条件，将问题转化为线性方程组的求解，数值分析表明：总体上，软界面层可以有效的减小夹杂和基体的界面应力集中；硬界面层可以减小夹杂内的界面应力集中，但却增加了基体内的界面应力集中；此外，总体上，界面相热膨胀系数较基体相和夹杂相过高，不利于降低界面应力集中。     

含椭圆夹杂压电材料反平面问题的基本解

基于复变函数和级数展开方法，推导了闪杂压电材料反平面应变问题的基本解，从本文解答的特殊情形，可以直接得到圆形压电夹染，椭圆孔和裂纹问题的封闭形式的基本解，其中包括 些文献中已有有的结果。     

弹性模量比对界面迁移下夹杂演化的影响

集成电路的导线内不可避免存在夹杂等缺陷。在各种内在机制以及外界环境作用下夹杂会出现形态演化从而影响内连导线的各种性能。该文基于界面迁移机制下微结构演化理论,推导了应力诱发固-固界面迁移的单元控制方程,数值模拟了夹杂-基体弹性模量比对夹杂形态演化的影响。结果表明:不同模量比下夹杂的σ>σ_c、β>β_c或hc时,夹杂长大;反之收缩。随着模量比的增加,临界应力、临界形态比随之增大,而临界线宽会减小。并且,当夹杂与基体的弹性模量比α>0.6时,模量比对于临界应力和临界形态比的影响可忽略。     

含界面应力纳米尺度夹杂中刃型位错的稳定性分析

利用复变函数方法研究了刃型位错在含界面效应纳米尺寸夹杂中的稳定性问题.求解了作用在位错上的像力的精确表达式,给出了位错在纳米夹杂中稳定存在的夹杂临界半径条件.并且讨论了夹杂尺寸和界面效应等因素对夹杂临界半径的影响.研究表明:如果夹杂的半径保持不变,存在一个临界相对剪切模量或临界基体材料泊松比改变位错在夹杂中的稳定性.同...     

中空纳米夹杂填充复合材料的反平面问题

研究了中空纳米夹杂填充复合材料的反平面问题。基于Gurtin-Murdoch表/界面理论和广义自洽方法, 给出了考虑夹杂界面效应时空隙-夹杂-基体-等效介质模型的全场精确解, 并推导了中空纳米夹杂填充复合材料有效反平面剪切模量的闭合形式解。由本文结果的特殊情形, 可以得到一系列有意义的解。数值结果表明: 中空夹杂的尺寸在纳米量级时, 复合材料的有效反平面剪切模量受表/界面效应影响显著; 表/界面效应的影响随着夹杂尺寸的增大而逐渐减弱; 当中空纳米夹杂的体积分数和外半径一定时, 壁厚越薄其表/界面效应越大; 在相同的夹杂外半径下, 中空纳米夹杂填充复合材料的表/界面效应比实心纳米夹杂填充复合材料更加明显; 无量纲反平面剪切模量受夹杂的表/界面性能和刚度影响显著, 过高的夹杂刚度使得表/界面效应的影响变弱。      

集中载荷作用下弹性平面刚性夹杂的形状优化

当夹杂的弹性模量比基体的弹性模量大得多时,可将其看成刚性夹杂.对于这类硬夹杂与软基体的复合材料,采用复变函数方法中的保角映射技术和推广的Schwarz延拓原理,并结合对复应力函数的奇性主部分析,导出了焊接任意形状刚性夹杂的全场基本奇异解,求解了集中力与集中力偶作用下弹性平面刚性夹杂的形状优化问题,描绘出了夹杂界面应力最大值、界面主应力最大值随夹杂形状的变化规律,精确地定位出了界面应力最大值、界面主应力最大值的作用位置.通过对这些不同形状夹杂的界面主应力最大值的比较,确定了夹杂的最优形状.     

穿过界面的刚性线夹杂对SH波的散射

利用两个联结半平面中简谐集中力的格林函数,得出了穿过界面刚性线的散射场.刚性线的散射场可分解为有界部分和奇异部分.利用散射场的有界部分和奇异部分得出了刚性线的在SH波作用下的Cauchy型奇异积分方程.根据所得奇异积分方程和Cauchy型积分的端点性质,得出了确定刚性线和界面交点处奇异性阶数的特征方程.根据刚性线和界面交点处的奇性应力定义了交点处的应力奇异因子.对所得Cauchy型奇异积分方程的数值求解,可得刚性线端点和交点处的应力奇异因子.     

Surface/interface Energy Effect on Electromechanical Responses Around a Nanosized Elliptical Inclusion under Far-field Loading at an Arbitrary Angle

Electro-elastic surface/interface around nano-sized piezoelectric inclusions shows great effect on the response of piezoelectric nano-structures. In this paper, a theoretical model is proposed to examine the surface/interface effect on the electromechanical responses around a nano-sized elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix under far-field loading with an arbitrary angle, and the effect of loading angle is considered Combining the conformal mapping technique and electro-elastic surface/interface theory, a closed form solution of this problem is obtained and the interactive effect between the surface/interface and the aspect ratio of the elliptical inclusion is examined.     

Analysis of Interfacial Coating Effect on Thermal Stress in Composites

A preliminary model for the analysis of thermo-mechanical behaviour of interfacial coatings on thefibers in unidirectional composites have been developed on the solution of thermo-elastic mechan-ics. Thermal stress would be introduced into the composite during cooling because of the mismatchof thermo-mechanical properties among their components. The low modulus coating can effectivelyreduce the interracial stress caused by different thermal expansion coefficient between fibers and ma-trix, no matter how high or low the expansion coefficients of coatings are in CF/Al and SiC/Ticomposite systems, however, high modulus coating can decrease the interfacial compressive stress,only when the thermal expansion coefficient of coating is lower.     

Stress and Failure Analysis of Composite Laminates with an Inclusion under Multiaxial Compression-Tension Loading

The present paper investigates the failure of orthotropic laminates with a filled hole subjected to biaxial compression-tension loading. This is an idealised case that simulates a situation where the impact damaged laminate has been repaired by drilling a hole and then plugging the hole with a perfect-fit core made of a dissimilar material. The exact stress distribution in the laminate has been determined using the complex variable mapping method. These stresses are then employed in a fracture mechanics failure model to predict the failure load of a laminate with a filled hole under in-plane compression-dominated multi-axial loading. Failure strength predictions are compared to open hole results and experimental data.     

Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress

In the study of strength of particle reinforced composites, it is important to understand the energy release rate due to interfacial debonding between the particle and the matrix which is induced by manufacturing imperfection. This paper is aimed at the investigation of the critical condition for growth of the interfacial debonding and the corresponding volume increase due to void formation. The model used in the study is an isotropic elastic spherical inclusion embedded in an infinite isotropic elastic matrix under remote stress. Initial axisymmetrical interfacial debondings are assumed to exist in the vicinity of poles of the spherical inclusion. Axisymmetrical deformations of the matrix and the inclusion are analyzed based on the theory of three-dimensional elasticity in spherical coordinates. In order to avoid oscillatory stress singularity at the interfacial debonding front between two dissimilar materials, a condition of free slipping without friction at the interface is imposed. A Fredholm integral equation of the first kind is formulated based on the continuity conditions in the normal components of stress and displacement at the contact interface. The kernel function of the integral equation is expressed in terms of an infinite series of Legendre functions. Two types of remote stresses are considered in this study. The first type is the remote tension in the axial direction of the spherical inclusion and the second type is the remote compression in the transverse direction with respect to the axis of the spherical inclusion. Energy release rate is determined according to the rate of change of work done by remote stresses. In this paper, energy release rate and volume of the deformed void due to debonding are computed for any given size of initial interfacial debonding.     

Stress analysis for bonded materials with a graded interfacial layer under a rigid punch

It is well known that functionally graded materials can be used to eliminate the stress discontinuity that is often encountered in multilayer composites. In this article, the stress analysis for the coating-functionally graded interfacial layer-substrate structure under a rigid spherical punch is investigated. A linear multi-layer model is used to model the graded interfacial layer with arbitrary varying materials properties along the thickness direction. The spherical indentation problem is formulated in terms of a singular integrate equation with the method of transfer matrix and Hankel integral transform technique. The stress components in the coating-graded interfacial layer-substrate structure are calculated by solving the equation numerically. The results show that stiffens ratio and the gradient index of the graded interfacial layer has a significant effect on the distribution of stress components.     

复合材料泡沫夹层结构界面的温度-应变分布

复合材料泡沫夹层结构由于其比强度高、比刚度高、耐腐蚀等特点已广泛在土木工程领域中获得应用。然而,由于复合材料面板与夹芯材料在温度荷载作用下热膨胀系数显著不同,因此在面板与芯材之间的粘结层会产生温度应力,因此会降低界面的粘结性能。本文通过试验研究,系统地给出了复合材料泡沫夹层结构界面温度-应变分布规律,并通过理论建模,提出了界面温度-应变分布规律的计算模型,通过对比实验值与理论值,验证了理论分析模型的精确性。     

Thermal Mismatch Stress of a Spherical Inclusion in a Cubic Crystal

The thermal stress induced in a spherical inclusion by the difference of the thermal expansion coefficiences of the inclusion and its embedding matrix is considered. Both the inclusion and the matrix are assumed to be of cubic symmetry. Eshelby’s equivalent inclusion method is used to solve the problem. A smple expression for the determination of thermal mismatch stress is thus derived. Some numerical examples are provided.     

含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析

针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义 Liouville 定理、Riemann-Schwarz 解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明：随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。     

Weight Function Method for Stress Intensity Factor of Internal Surface Semi-elliptical Crack in Elliptical Holes

The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.