含界面相桥联矩阵

桥联模型能够有效分析复合材料的弹塑性性能,其在World-Wide Failure Exercise(WWFE)评比中被认定为精度最高的细观力学理论.桥联模型的核心是桥联矩阵,现有桥联模型是在两相复合材料理想界面条件下建立的,而对于实际的复合材料而言,纤维和基体之间总或多或少的出现界面非理想现象.学者们常用一个存在于基体和纤维之间的界面相来描述这种非理想界面情形,这时就需要建立含界面相的三相桥联矩阵.论文采用三相CCA模型,求得六种不同边界载荷下的应力场,再将各相体积平均后的应力场代入三相桥联模型方程,求解线性方程组即可得到三相桥联矩阵元素的精确表达式.进一步,将纤维相和界面相看作一个局部复合材料或等效横观各向同性纤维,其力学性能利用两相桥联模型确定,与外部的基体相构成的复合材料依然可以通过两相桥联模型分析.利用这种等效纤维的概念,论文将三相隐式桥联矩阵进行了有效简化,通过对复合材料等效弹性常数的数值计算,证明简化后的三相显式桥联矩阵与精确的三相隐式桥联矩阵有极高的近似度,从而给实际应用带来极大方便.     

面向剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数，各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场。讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件。所给出的数值算例显示出该结论的正确性。该方法为纤维增强复合材料的设计提供了一条新途径。     

面外剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数, 各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场. 讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件. 所给出的数值算例显示出该结论的正确性. 该方法为纤维增强复合材料的设计提供了一条新途径.     

考虑损伤界面的多相复合材料总体平均力学性能的预测

在广义自治有限元迭代法的基础上研究了损伤面对多相复合材料的总体平均横向力学性能的影响。给出了对于不同体分比和损伤界面性质的典型复合材料的数值结果。数值分析表明损伤界面的厚度及其损伤程度对复合材料总体平均横向平面应变体积模量和剪切模量有显著影响。本文还计算了损伤界面区域的局部应力场。     

考虑损伤界面的多相复合材料总体平均力学性能的预测

在广义自洽有限元迭代法￣［１］的基础上研究了损伤界面对多相复合材料的总体平均横向力学性能的影响。给出了对于不同体分比和损伤界面性质的典型复合材料的数值结果。数值分析表明损伤界面的厚度及其损伤程度对复合材料总体平均横向平面应变体积模量和剪切模量有显著影响。本文还计算了损伤界面区域的局部应力场。     

反平面剪切下电磁弹性纤维增强复合材料界面相效应研究

研究具有界面相电磁弹性纤维增强复合材料的反平面剪切问题,利用复变函数方法,获得了无穷域中带界面相纤维问题在远场力、电、磁多场作用下的闭合解,得到了复合材料内部各区域电磁弹性物理量的精确表达式.利用所得结果,考虑纤维和基体间的界面相效应,研究了界面相厚度及弹性模量对复合材料内部应力场、电场强度和磁场强度的影响,数值结果给出了复合材料电磁弹性物理量随界面相参数变化的规律,为该类复合材料的设计与计算提供了有价值的参考.     

用显微云纹干涉法研究SiC/Ti-15-3界面热残余应力场

SiC/Ti-15-3复合材料基体与增强体之间的热膨胀系数存在显著差异。在复合材料制造过程中经高温冷却后,在基体与增强体的界面会产生热残余应力场。此残余应力场对复合材料的力学性能会产生重要的影响。本文运用纤维推出法推出部分SiC纤维后,采用显微云纹干涉法在细观尺度研究了上述界面处的热残余应力,得到了分辨率较高的云纹图,并由此计算出了孔边处的残余应力。用有限元软件对界面热残余应力进行了数值模拟分析。实验结果表明,显微云纹干涉法可以用来测量直径为0.1 mm左右的纤维界面附近的残余应力场,在此尺度下,使用显微云纹干涉法比用电子束云纹法更方便。     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

兼具基体蠕变和轻度界面蠕变的复合材料的本构特性

金属基复合材料的基体蠕变特性在一定的温度与应力下表现明显，当界面为非理想并具有粘弹性性质时，其对复合材料的整体蠕变亦有重要影响．本文利用具有非理想界面的复合材料的Ｍｏｒｉ－Ｔａｎａｋａ方法，研究了既具有基体蠕变又具有界面轻度蠕变的复合材料的本构关系，给出了各微结构参量对复合材料整体蠕变特性的影响     

含共晶界面陶瓷复合材料的损伤应变场分析

研究了含共晶界面陶瓷复合材料的损伤应变场及其尺度效应。根据含共晶界面复合陶瓷的细观结构特性,利用含共晶界面陶瓷复合材料中三相胞元内的应力场分布规律,得出棒状共晶体内的无损应变场分布规律。针对棒状共晶体内存在损伤的现象,通过引入损伤变量,利用三相模型法得到了棒状共晶体内存在损伤时的应变场分布规律;根据应变和纤维状夹杂直径之间的关系,分析了棒状共晶体内的损伤应变场及其尺度效应。结果表明,含共晶界面陶瓷复合材料内三相胞元中基体、界面相和纤维夹杂内的损伤应变场对纤维夹杂直径具有明显的尺度效应。     

Interaction between edge dislocations and amorphous interphase in carbon nanotubes reinforced metal matrix nanocomposites incorporating interface effect

Dislocations mobility and stability in the carbon nanotubes (CNTs)-reinforced metal matrix nanocomposites (MMNCs) can significantly affect the mechanical properties of the composites. However, current processing techniques often lead to the formation of coated CNT (amorphous interphase exists between the reinforcement and metal matrix), which have large impact upon the image force exerting on dislocations. Even though the importance of the interphase zone formed in metal matrix composites has been demonstrated by many studies for elastic properties, the influence of interphase on the local elastoplastic behavior of CNT-reinforced MMNCs is still an open issue. This paper puts forward a three-phase composite cylinder model with new boundary conditions. In this model, the interaction between edge dislocations and a coated CNT incorporating interface effect is investigated. The explicit expressions for the stress fields and the image force acting on an edge dislocation are proposed. In addition, plastic flow occurring around the coated reinforcement is addressed. The influences of interface condition and the material properties of coated CNT on the glide/climb force are clearly analyzed. The results indicate that the interface effect becomes remarkable when the radius of the coated reinforcement is below 10 nm. In addition, different from the traditional particles, the coated CNT attracts the adjacent edge dislocations, causing pronounced local hardening at the interface between the interphase and the metal matrix under certain conditions. It is concluded that the presence of the interphase can have a profound effect on the local stress field in CNT-reinforced MMNCs. Finally, the condition of the dislocations stability and the equilibrium numbers of dislocations at a given size grain are evaluated for considering the interface effect.     

Neutrality in the case of N-phase elliptical inclusions with internal uniform hydrostatic stresses

A novel method is proposed to design neutral N-phase (N ? 3) elliptical inclusions with internal uniform hydrostatic stresses. We focus on the study of the internal and external stress states of an N-phase elliptical inclusion which is bonded to an infinite matrix through (N ? 2) interphase layers. The interfaces of the N-phase elliptical inclusion are (N ? 1) confocal ellipses. The design of the resulting overall composite material consists of four stages: (i) an inner perfectly bonded interphase/inclusion interface which is necessary to make the internal uniform stress state hydrostatic; (ii) outer imperfect interphase layers properly designed to make the coated inclusion harmonic (i.e., the uniform mean stress of the original field within the matrix is unperturbed); (iii) the aspect ratio of the elliptic inclusion uniquely chosen for a given material and thickness parameters to make the resulting coated inclusion neutral (i.e., the prescribed uniform stress field in the matrix remains undisturbed); and finally (iv) the derivation of a simple condition relating the remote uniform stresses and the thickness parameters of the (N ? 2) interphase layers for given material parameters which lead to internal uniform hydrostatic stresses. We note that another interesting feature of the present results is that the mean stress is found to be constant within each interphase layer, and the hoop stress in the innermost interphase layer is uniform along the entire interphase/inclusion interface.     

无限介质中单个纳米涂层夹杂反平面问题的两个模型

采用零厚度界面模型和界面层模型研究了无限介质中单个纳米涂层圆柱形夹杂的反平面问题,利用复变函数方法获得了两种模型夹杂、涂层和基体内应力场的封闭解析解．研究表明,当界面层模型中的界面相厚度趋于零时,界面层模型可以解析地退化为零厚度界面模型．数值算例分析了界面模量不同取值时应力场的分布和应力的尺度依赖性．本文结果丰富了对纳米夹杂力学行为的认识,并可为直接采用零厚度界面模型有困难的纳米夹杂问题的研究提供有价值的参考．     

A circular inclusion with a nonuniform interphase layer in anti-plane shear

An analytical solution is derived for the problem of a nonuniformly coated circular inclusion in an unbounded matrix under anti-plane deformations. The inclusion/interphase/matrix system is subject to (1) remote uniform shear and uniform eigenstrain imposed on the circular inclusion, and (2) a screw dislocation or a point force in the matrix. It is found that the varying interphase thickness will exert a significant influence on the nonuniform stress field within the circular inclusion, and on the direction and magnitude of the image force acting on a screw dislocation. In the course of development, it is found that the presence of certain coated inclusions, which are termed stealth, will not cause change of elastic energy in the body. The derived analytical solution for a screw dislocation is then employed as Green’s function to investigate a radial matrix crack interacting with the nonuniformly coated inclusion. The numerical results show that the varying interphase thickness will also affect the stress intensity factors.     

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.     

基于界面层模型的双周期纳米夹杂复合材料反平面问题研究

利用复变函数方法并结合双准周期Riemann边值问题理论,获得了含双周期分布非均匀相（夹杂/界面层）的复合材料在远场均匀反平面应力下弹性场的全场解答．该解答可用于对纳米夹杂复合材料的应力进行分析,结合平均场理论也用于预测纳米夹杂复合材料的有效性能．计算结果表明：当夹杂尺度在纳米量级时,应力和有效反平面剪切模量具有明显的尺度依赖性,并且随着夹杂尺寸的增加,趋近于不考虑界面效应时的结果;界面层厚度和性能对应力和有效反平面剪切模量明显变化时所对应的夹杂尺度范围和趋近于无界面效应结果的快慢有显著影响;当界面厚度足够薄时,界面层模型可用于模拟零厚度界面情况．     

Influences of imperfect interfaces on effective properties of multiferroic composites with coated inclusion

In order to predict the effective properties of multiferroic composite materials, the effective material constants of multiferroic composites with the coated inclusion and imperfect interface are investigated. Based on the generalized self-consistent theory, the closed-form solutions of the effective material constants are derived. For the composites with piezomagnetic inclusion, piezoelectric coating and polymer matrix, numerical calculations are performed to present the influences of the imperfect interface cooperating with the coating on the effective material constants. From the results, it can be observed that the effective constants can be enhanced by the coating but reduced by the imperfect interface. Moreover, the coating has the shielding effects on the imperfect interface for the composite structures with its higher filling ratio.     

A New Method for an Inhomogeneity with Stepwise Graded Interphase under Thermomechanical Loadings

The solution for a circular inhomogeneity embedded in an infinite elastic matrix with a multilayered interphase plays a fundamental role in many practical and theoretical problems. Therefore, improved analysis methods for this problem are of great interest. In this paper, a new procedure is presented to obtain the exact stress fields within the inhomogeneity and the matrix under thermomechanical loadings, without the need of solving the full multiphase composite problem. With this short-cut method, the problem is reduced to a single linear algebraic equation and two coupled linear algebraic equations which determine the only three real coefficients of the stress field within the inhomogeneity. In particular, the average stresses within the inhomogeneity can be calculated directly from the three real coefficients. Further, the other three unknown real coefficients associated with the stress field in the matrix can be determined subsequently. Hence, the influence of the stepwise graded interphase on the stress fields is manifested by its effect on the six real coefficients. All these results hold for stepwise graded interphase composed of any number of interphase layers. Several examples serve to illustrate the method and its advantages over other existing approaches. The explicit solutions are used to study the design of harmonic elastic inclusions, and the effect of a compliant interphase layer on thermal-mismatch induced residual stresses. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.     

Thin interphase/imperfect interface in elasticity with application to coated fiber composites

The imperfect interface conditions which are equivalent to the effect of a thin elastic interphase are derived by a Taylor expansion method in terms of interface displacement and traction jumps. Plane and cylindrical interfaces are analyzed as special cases. The effective elastic moduli of a unidirectional coated fiber composite are obtained on the basis of the derived imperfect interface conditions. High accuracy of the method is demonstrated by comparison of solutions of several problems in terms of the imperfect interface conditions or explicit presence of interphase as a third phase. The problems considered are transverse shear of a coated infinite fiber in infinite matrix and effective transverse bulk and shear moduli and effective axial shear modulus of a coated fiber composite. Unlike previous elastic imperfect interface conditions in the literature, the present ones are valid for the entire range of interphase stiffness, from very small to very large.