陶瓷颗粒增强金属基复合材料的细观强度分析

陶瓷颗粒增强金属基复合材料的失效主要有界面脱粘、增强粒子开裂等新的细观结构损伤机制。为了减小这些不足并对细观失效过程有一个清晰的了解,近来人们对金属基复合材料进行了大量研究,在此基础上,本文用细观力学的方法和损伤模型研究了陶瓷颗粒增强金属基复合材料的强度和损伤失效。为了计算方便,陶瓷颗粒简化为在复合材料中随机分布的椭球形粒子,然后以二相胞元模型计算分析了金属基体、颗粒中的应力应变分布情况,结果表明,基体中应力极不均匀,界面区存在应力集中,并计算了界面弧形裂纹扩展时的能量。最后分别提出了基体,颗粒和界面的失效强度准则,本文结果对于颗粒增强金属基复合材料具有普遍的实用性。     

含圆形夹杂的无穷大平面电致伸缩材料的应力分析

利用电致伸缩基本方程，采用伪总应力和复变函数解法，并利用级数展开方法得出了含圆形夹杂的无限大电致伸缩材料应力场，在一般情况下，与Eshelby夹杂理论不同，在电致伸缩材料圆形夹杂内部应力场是非均匀的．     

压电复合材料中的Eshelby夹杂问题

通过采用解析延拓和共形映射技术，获得了压电复合材料中有关Eshelby夹杂几个典型问题的精确弹性解答，即横观各向同性压电介质中任意形状的Eshelby夹杂与圆柱异相夹杂间相互作用；一般各向异性压电介质中任意形状的Eshelby夹杂与双压电材料所形成界面的相互作用．成功求解这些问题的关健在于构造一个辅助函数．与Ru所采用的方法不同，所引入的辅助函数在无穷远点不存在极点，从而使得所展开的分析更加自然合理．分析结果清楚地揭示出Eshelby夹杂的存在对压电复合材料机电耦合响应将产生不容被忽视的影响．很典型的一个例于是当一个Eshelby椭圆夹杂与圆柱异相夹杂相互作用时，每个夹杂体内部的应力场和电场都将是不均匀的；另一个例于是位于界面附近的Eshelby夹杂有可能是界面发生损伤的一个重要原因．     

含微裂纹和椭球颗粒介质的强度及本构关系

针对含随机分布微裂纹及椭球颗粒的复合材料，通过考虑椭球颗粒内的本征应变及其与微裂纹的相互作用，利用等效夹杂方法研究了微裂纹损伤对材料有效模量和强度的影响，推导了复合材料的细观应力场及本构关系，并导出了材料破坏的临界条件．     

三维立方准晶椭球夹杂的Eshelby张量

准晶体颗粒复合智能材料具有优异的物化性能和应用前景。不同于传统的各向同性材料,三维立方准晶体材料包含声子场,相位子场,及声子-相位子耦合场。为更好地研究准晶体颗粒夹杂问题,揭示准晶体材料夹杂问题的物理现象,本文利用本征应变公式和柯西留数定理,考虑椭球体夹杂,获得了三维立方准晶材料夹杂问题的Eshelby张量,并给出了统一的表达式。进而,当三维立方准晶夹杂形状为球形、棒状、扁平状和带状时,获得了封闭形式的三维立方准晶Eshelby张量表达式。同时,给出了椭球体长径比变化时Eshelby张量的变化规律,这对研究准晶体颗粒夹杂问题具有重要的理论意义。     

含非完好界面粒子增强复合材料对弹性波的散射

采用波函数展开的方法研究了非完好界面条件下圆球形夹杂对弹性波的散射。以非完好界面的弹簧模型为基础，通过适当选取弹簧常数，研究了法向和切向界面参数对纵波和横波不同的散射效果。考虑了单个圆球夹杂的散射和颗粒增强复合材料中弹性波的多重散射，研究了复合材料中的有效波速和动态有效弹性常数。并针对金属基颗粒增强复合材料SiC-Al...     

SMA短纤维复合材料的热胀系数和相变应变系数

基于Eshelby的等效夹杂模型、Mori和Tanaka的场平均法,考虑到形状记忆合金（SMA）的强物理非线性,发展了增量型的等效夹杂模型（Incremental Equivalent Inclusion Model)。讨论了SMA短纤维增强的铝基复合材料的热胀系数和相变应变系数。特别研究了SMA短纤维复合材料纤维几何尺寸和体积分数等参数对SMA复合材料的热胀系数和相变应变系数的影响。这些工作对于指导材料设计和了解SMA复合材料热机械特性是非常有意义的。     

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．     

横观各向同性介质中椭圆夹杂受非弹性剪切变形引起的弹性场的确定

本文求解了横观各向同性介质中椭圆夹杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法，结合保角变换，获得夹杂内应变能和基体内边界的应力分布和相应的应变能的表达式。进一步，根据最小应变能原理，获得表征夹杂平衡边界的两个特征剪切应变，从而得到了弹性场的解析解。通过应力转换关系，验证了应力解满足夹杂边界上法向正应力和剪应力的连续条件，表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。     

Eshelby问题中棱上各点位移梯度的跳跃

利用调和函数的积分方法,来研究各向同性材料非光滑界面Eshelby问题中,棱上各点位移梯度的跳跃,最终获得棱上各点应力张量的跳跃值.首先讨论Eshelby位移场的连续性,并将棱上各点位移梯度场的连续部分和跳跃部分分离开;再由各向同性的Green函数获得位移梯度场和应力场在核与基体间跳跃的显式表示.最后对应力场在界面上的跳跃进行讨论.     

An analysis of the modeling of stress and strain fields in a real microstructure using a hybrid method

The distribution of stress and strain fields in a micro-structural area of a particle reinforced composite is studied by a combination of experimental and numerical method (hybrid method). With the experimental values of displacements in a micro-region as the boundary loading condition, strain and stress fields inside the micro-region are calculated by the finite element method under two different kinds of modeling, namely, as plane stress and plane strain condition. The differences between the two kinds of modeling conditions as applied to micro-structural areas are discussed. Project Supported by the National Natural Science Foundation of China (19972046) and National Overseas Study Foundation.     

Effect of Maxwell stress on a moving crack with polarization saturation region in ferroelectric solid

The focus of this work is on a generalized two-dimensional problem of a crack moving in a piezoelectric solid subjected to uniform electrical load at infinity. The novel point includes that the electric field inside the crack is taken into account when polarization saturation region exists. Based on the extended Stroh formalism and complex function method, explicit expressions of both the stress fields in the solid and electric fields inside the crack are derived by using semi-permeable crack model, respectively. Effect of Maxwell stress along the crack surface is investigated and the results are illustrated graphically. It is shown that the moving speed of the crack cannot exceed the lowest bulk wave speed. It is also found that the medium properties inside the crack and surrounding the ferroelectric solid at infinity directly affect the Maxwell stress, and as a result the Maxwell stresses are remarkable and cannot be ignored under different electric load.     

On the anti-plane shear of an elliptic nano inhomogeneity

The elastic field of an elliptic nano inhomogeneity embedded in an infinite matrix under anti-plane shear is studied with the complex variable method. The interface stress effects of the nano inhomogeneity are accounted for with the Gurtin–Murdoch model. The conformal mapping method is then applied to solve the formulated boundary value problem. The obtained numerical results are compared with the existing closed form solutions for a circular nano inhomogeneity and a traditional elliptic inhomogeneity under anti-plane. It shows that the proposed semi-analytic method is effective and accurate. The stress fields inside the inhomogeneity and matrix are then systematically studied for different interfacial and geometrical parameters. It is found that the stress field inside the elliptic nano inhomogeneity is no longer uniform due to the interface effects. The shear stress distributions inside the inhomogeneity and matrix are size dependent when the size of the inhomogeneity is on the order of nanometers. The numerical results also show that the interface effects are highly influenced by the local curvature of the interface. The elastic field around an elliptic nano hole is also investigated in this paper. It is found that the traction free boundary condition breaks down at the elliptic nano hole surface. As the aspect ratio of the elliptic hole increases, it can be seen as a Mode-III blunt crack. Even for long blunt cracks, the surface effects can still be significant around the blunt crack tip. Finally, the equivalence between the uniform eigenstrain inside the inhomogeneity and the remote loading is discussed.     

Multi-grain analysis versus self-consistent estimates of ferroelectric polycrystals

Ferroelectrics are polycrystalline materials consisting of intragranular regions with different polarization directions, called domains. The domains can be switched into different states by the application of an electric field or mechanical stress. We study the influence of grain-to-grain interactions on the overall and local switching behavior. The behavior inside each grain is represented by the micromechanics model of Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47 (8), 1663-1697]. The predictions of a self-consistent model of the polycrystal response are compared with those of a multi-grain model in which grains are represented individually. In one flavor of the multi-grain model, each grain is represented by a single finite element, while in the other the fields inside each grain are captured in more detail through a fine discretization. Different electrical and mechanical loading situations are investigated. It is found that the overall response is only mildly dependent on the accuracy with which grain-to-grain interactions are captured, while the distribution of grain-average stresses is quite sensitive to the resolution of the intragranular fields.     

PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION

By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.     

Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression

This study investigates the elasto-plastic buckling behaviour of simply supported square and rectangular thin steel plates having elliptic cut-outs by means of finite element method. Plates with simply supported in the out-of-plane direction are applied uniform compression in long-edge direction. A50 steel was used in the analysis and the focus was on the effect of plate aspect ratio, elliptical hole size, elliptical hole angle, elliptical hole location and slenderness ratio on buckling behaviour. It was found in the study that as the plate slenderness ratio increases, the critical buckling stress decreases for all the perforated plates.     

A crystal plasticity analysis of length-scale dependent internal stresses with image effects

In this work, we present a stress functions approach to include image effects in continuum crystal plasticity arising from the long-range elastic interactions (LRI) between the GND density and free surfaces. The resulting length-scale dependent internal stresses augment those produced by the GND density variation. The formulation is applied to the case of a long, thin specimen subjected to uniform curvature. The analysis shows that under nominally uniform GND density distribution, internal stresses arise from two sources: (1) GND–GND LRI arising from the finite spatial extent of the uniform GND density field and (2) the LRI between the GND density and free surfaces appearing as image fields. A comparison with experimental results suggests that the length-scale for internal stresses, described as a correlation length-scale, should increase with decreasing specimen thickness. This observation is rationalized by associating the internal length-scale with the average slip-plane spacing, which may increase with decreasing specimen size due to paucity of dislocation sources. Finally, we also discuss the length-scale dependent image stress in terms of the Peach–Koehler force density proposed by Gurtin (2002).     

圆内旋轮线形状异质夹杂热弹性问题的解析解

论文研究具有圆内旋轮线型形状夹杂域的平面热弹性体在夹杂域内非均匀温度场作用下对弹性场所产生的影响，其中考虑的夹杂与基体的材料不同但是具有相同的剪切模量。借助黎曼映射理论，将平面光滑闭合曲线外部区域映射到单位圆外部区域，进而利用解析函数性质，结合柯西型积分与Faber多项式，求解得到夹杂域内外场势函数的显式解。通过得到的势函数求出内外场应力，并对应力分布进行分析，结果表明：一般形状异质夹杂时，内场应力值与有限元计算值相吻合；退化到椭圆同质夹杂时，与相关文献中的结果相同，但是更具一般性与实际可操作性。     

Three-dimensional analysis of defects in a piezoelectric material

In this paper, the Green's function technique is used to develop a solution of an infinite, piezoelectric medium containing either an ellipsoidal cavity or a flat elliptical crack. The coupled elastic and electric fields both inside the cavity and on the boundary of the cavity are obtained, and the stress intensity factor and the electric field intensity factor are also obtained for an elliptical crack. It is found that; (1) the coupled elastic and electric fields inside the cavity keep uniform when the external elastic field and electric field are constant; (2) the behavior of the stress and electric field components in the neighborhood of the crack tip shows the classical type of singularity. The project supported by National Natural Science Foundation of China     

Equivalent inclusion solution adapted to particle debonding with a non-linear cohesive law

Starting from Eshelby’s solution of the equivalent inclusion problem, an approximate solution is proposed in order to model interface debonding of a spherical inhomogeneity isolated in a uniform matrix. Both phases are linear elastic but the interface traction-separation law is non-linear. A semi-analytical incremental model is developed which is suitable for any type of loading. For computational efficiency, the model relies on two simplifying assumptions: (i) the eigenstrain is uniform inside the inhomogeneity and (ii) the interface compliance is averaged over inhomogeneity’s surface when computing the average strain within the inhomogeneity. An extensive parametric study is conducted for three loading modes and 144 combinations of non-dimensional parameters. The predictions are assessed against full-field finite element solutions based on two error measures of the mean stress field inside the inhomogeneity. The results show that the mean error value is acceptable in all cases and indicate the parameter ranges for which the model is most accurate.