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.      

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．     

任意形状热夹杂位移场的三角形单元离散算法

平面夹杂模型在纤维增强型复合材料中有广泛应用.复合材料内部通常含有不规则形状夹杂,而夹杂物的存在能严重影响材料的机械力学性能,往往导致应力集中及裂纹萌生等失效先兆.先前关于多边形夹杂的研究大多数关注受均匀本征应变下的应力/应变解,而对位移的分析较少. 基于格林函数方法和围道积分,本文给出了平面热夹杂边界线单元的封闭解析解,可方便应用于受任意分布本征应变的任意形状平面热夹杂位移场的数值计算.当夹杂受均匀本征应变时, 只需将该夹杂边界进行一维离散,因而本文方法可直接得出受均匀分布热本征应变的任意多边形夹杂位移场的封闭解析解.当夹杂区域存在非均匀分布本征应变时,可将该区域划分为足够小的三角形单元进行数值计算. 众所周知,应力应变场在多边形夹杂顶点处具有奇异性,容易导致数值计算上的处理困难及相应的数值稳定性问题; 然而本文工作表明,在多边形顶点处位移场是连续有界的, 因而数值稳定性较好.本文算法可以便捷高效地通过计算机编程实现. 文中给出的验证算例,均体现了本文离散方法的高精度、以及计算编程的鲁棒性.      

纳米夹杂复合材料的有效反平面剪切模量研究

基于Gurtin-Murdoch表面/界面理论模型,利用复变函数方法,获得了考虑夹杂界面应力时夹杂/基体/等效介质模型的全场精确解,发展了能够预测纳米夹杂复合材料有效反平面剪切模量的广义自洽方法,给出了复合材料有效反平面剪切模量的封闭形式解。数值结果显示：当夹杂尺寸在纳米量级时,复合材料的有效反平面剪切模量具有尺度相关性,随着夹杂尺寸的增大,本文结果趋近于经典弹性理论的预测值;夹杂尺寸对于有效反平面剪切模量(本文结果)的影响范围要小于其对有效体积模量与剪切模量(各向同性材料)的影响范围;有效反平面剪切模量受夹杂的界面性能和夹杂刚度影响显著。     

滑动界面的球形夹杂问题

滑动界面对多相介质力学性能的影响日益受到重视．但已有的解析结果往往假定界面是自由滑动的．即假设界面上的剪应力为零，这与大多数实际情况并不相符．本文假定界面上剪应力不为零并满足线弹簧型界面条件，在这一前提下，首次获得了球形夹杂本征应变问题的解析解．     

广义自洽Mori-Tanaka模型及涂层夹杂体复合材料的有效模量

经典广义自洽模型的最大不足是需要确定相材料的位移及应变场,这一过程十分繁杂,而且最后得到的有交剪切模量无法显式表达难以应用,该文摈弃这一经典做法,而从广义自洽模型的应变等价条件出发,在夹杂应变均匀的近似假定下,将Ｈｉｌｌ界面条件应用于整个二相体内,从而得到一种可以预报涂层夹杂体复合材料有效模量的广义自洽Ｍｏｒｉ－Ｔａｎａｋａ模型,与已有的实验及理论的比较表明,该模型准确可靠,而且有效体积和剪切模量     

双周期圆柱形压电夹杂反平面问题的精确解及其应用

研究无限压电介质中双周期圆柱形压电夹杂的反平面问题.借鉴Eshelby等效夹杂原理,通过引入双周期非均匀本征应变和本征电场,构造了一个与原问题等价的均匀介质双周期本征应变和本征电场问题.利用双准周期Riemann边值问题理论,获得了夹杂内外严格的电弹性解.作为压电纤维复合材料的一个重要模型,预测了压电纤维复合材料的有效电弹性模量.     

动载下复合材料基体裂纹与夹杂相互作用的数值模拟

采用ABAQUS软件及粘聚裂纹模型对动态拉伸载荷下复合材料中垂直于基体-夹杂界面的基体裂纹与夹杂的相互作用进行了数值模拟.结果表明:在给定的界面强度下,当加载率(或应变率)低于某一临界值(临界应变率)时裂纹将沿基体-夹杂界面扩展,当高于该临界值时裂纹可以穿过界面在夹杂中扩展.此外,随着界面强度的提高,临界应变率降低;当界面强度超过一定值后,裂纹扩展方向将不受外部载荷影响,裂纹将沿自相似方向扩展;当界面强度低于该临界值时,裂纹将沿界面扩展;并且临界应变率随夹杂尺寸的增大而降低,即小夹杂更难于破坏.上述结果可为前人的混凝土动态实验数据提供合理的细观理论解释.     

双周期分布圆环形截面夹杂反平面问题的解析方法

研究含双周期分布圆环形截面弹性夹杂的无限大介质在远场均匀反平面应力下的弹性响应。通过在双周期圆环形区域内引入非均匀本征应变,将双周期非均匀介质问题转化为带有双周期非均匀本征应变的均匀介质问题,结合双周期函数和双准周期Riemann边值问题理论,获得了该问题弹性场的级数形式解答。作为一个应用,利用该解答预测了含双周期圆环形截面夹杂复合材料的有效纵向剪切模量。数值结果表明,在相同夹杂体积分数下,含圆环形截面夹杂的复合材料比含圆形截面夹杂的复合材料拥有更高的有效纵向剪切模量。     

等参三角形热夹杂的构造及位移场数值计算

在材料制备和机械设计中,局部温升是造成材料失效和故障形成的重要因素之一.依照微观力学中,采用热夹杂模型可以定量深入地揭示与局部温升所关联的力学机理.在过往的研究中,受均匀热本征应变的夹杂模型广受关注;而相关非均匀分布的热本征应变问题,因其理论推导复杂而研究不多.论文首先给出在平面无限域中,受线性分布热本征应变作用的多边形夹杂的位移场解析解.基于格林函数法和围道积分,推导边界线单元的位移响应封闭解,该解通过叠加可直接给出线性热本征应变作用下的任意多边形夹杂的解析表达式.受到有限元分析中等参单元思想的启发,论文进一步将这种“等参元”方法扩展至求解Eshelby夹杂问题中.在该研究中,三角形单元的本征应变插值公式与位置坐标变换式均使用了相同的形函数与节点参数,因而所构建的单元模型称为等参三角形夹杂模型.论文方法可便捷地用于处理受任何分布热本征应变的任意形状二维Eshelby夹杂问题.相较于传统的有限元分析,论文所构建的数值求解方案实施方便且优势明显：只需在夹杂域上进行三角形网格剖分、而无需在无限的基体域上划分网格,因而可以极大地提高前处理便捷性及计算效率.此外,论文所给出的多边形夹杂解析解,...     

Elastoplastic modeling of circular fiber-reinforced ductile matrix composites considering a finite RVE

A micromechanical elastoplastic damage model considering a finite RVE is proposed to predict the overall elastoplastic damage behavior of circular fiber-reinforced ductile (matrix) composites. The constitutive damage model proposed in our preceding work (Kim and Lee, 2009) considering a finite Eshelby’s tensor (Li et al., 2005, Wang et al., 2005) is extended to accommodate the elastoplastic behavior of the composites. On the basis of the exterior-point Eshelby’s tensor for circular inclusions and the ensemble-averaged effective yield criterion, a micromechanical framework for predicting the effective elastoplastic damage behavior of ductile composites is derived. A series of numerical simulations are carried out to illustrate stress–strain response of the proposed micromechanical framework and to examine the influence of a Weibull parameter on the elastoplastic behavior of the composites. Furthermore, comparisons between the present predictions and experimental data available in the literature are made to further assess the predictive capability of the proposed model.     

A continuum micromechanical theory of overall plasticity for particulate composites including particle size effect

Classical continuum micromechanics cannot predict the particle size dependence of the overall plasticity for composite materials, a simple analytical micromechanical method is proposed in this paper to investigate this size dependence. The matrix material is idealized as a micropolar continuum, an average equivalent inclusion method is advanced and the Mori–Tanaka's method is extended to a micropolar medium to evaluate the effective elastic modulus tensor. The overall plasticity of composites is predicted by a new secant moduli method based on the second order moment of strain and torsion of the matrix in a framework of micropolar theory. The computed results show that the size dependence is more pronounced when the particle's size approaches to the matrix characteristic length, and for large particle sizes, the prediction coincides with that predicted by classical micromechanical models. The method is analytical in nature, and it can capture the particle size dependence on the overall plastic behavior for particulate composites, and the prediction agrees well with the experimental results presented in literature. The proposed model can be considered as a natural extension of the widely used secant moduli method from a heterogeneous Cauchy medium to a micropolar composite.     

Magneto-electro-elastic coated inclusion problem and its application to magnetic-piezoelectric composite materials

In this work, a micromechanical model for the estimate of the magneto-electro-elastic behavior of the magnetic-piezoelectric composites with coated reinforcements is proposed. The coating is considered as a thin layer with properties different from those of the inclusion and the matrix. The micromechanical approach based on the Green’s functions techniques and on the interfacial operators is designed for solving the magneto-electro-elastic inhomogeneous coated inclusion problem. The effective magneto-electro-elastic properties of the composite containing thinly coated inclusions are obtained through the Mori–Tanaka’s model. Numerical investigations into magneto-electro-elastic moduli responsible for the magneto-electric coupling are presented as functions of the volume fraction and characteristics of the coated inclusions. Comparisons with existing models are presented for various shape and orientation of the coated inclusions.     

On micromechanical modeling of particulate composites with inclusions of various shapes

The effective elastic properties of statistically homogeneous two-phase particulate composites are considered. Several first-order micromechanical models are re-written in terms of the inclusion compliance contribution tensor (H-tensor). This tensor is a convenient tool to evaluate contribution of arbitrarily shaped inclusions and cavities to the overall composite properties.For any inclusion shape, the procedure starts with calculation of the H-tensor for a single inclusion. The non-interaction approximation is obtained by direct summation. More advanced micromechanical schemes are derived by substituting the non-interaction inclusion compliance contribution tensor into the formulae provided in the paper. The proposed procedure is illustrated by considering several two-dimensional and three-dimensional examples.     

Electroelastic behavior of piezoelectric composites with coated reinforcements: Micromechanical approach and applications

In this work, a micromechanical model for the estimate of the electroelastic behavior of the piezoelectric composites with coated reinforcements is proposed. The piezoelectric coating is considered as a thin layer with active electroelastic properties different from those of the inclusion and the matrix. The micromechanical approach based on the Green’s functions technique and on the interfacial operators is designed for solving the electroelasticity inhomogeneous coated inclusion problem. The effective properties of a piezoelectric composite containing thinly coated inclusions are obtained through the Mori–Tanaka’s model. Numerical investigations into electroelastic moduli responsible for the electromechanical coupling are presented as functions of the volume fraction and characteristics of the coated inclusions. Comparisons with existing analytical and numerical results are presented for cylindrical and elliptic coated inclusions.     

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．     

Micromechanics-based elastic damage modeling of particulate composites with weakened interfaces

A micromechanical framework is proposed to predict the effective elastic behavior and weakened interface evolution of particulate composites. The Eshelby’s tensor for an ellipsoidal inclusion with slightly weakened interface [Qu, J., 1993a. Eshelby tensor for an elastic inclusion with slightly weakened interfaces. Journal of Applied Mechanics 60 (4), 1048–1050; Qu, J., 1993b. The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials 14, 269–281] is adopted to model spherical particles having imperfect interfaces in the composites and is incorporated into the micromechanical framework. Based on the Eshelby’s micromechanics, the effective elastic moduli of three-phase particulate composites are derived. A damage model is subsequently considered in accordance with the Weibull’s probabilistic function to characterize the varying probability of evolution of weakened interface between the inclusion and the matrix. The proposed micromechanical elastic damage model is applied to the uniaxial, biaxial and triaxial tensile loadings to predict the various stress–strain responses. Comparisons between the present predictions with other numerical and analytical predictions and available experimental data are conducted to assess the potential of the present framework.     

Inhomogeneity of the first and second statistical moments of stresses inside the heterogeneities of random structure matrix composites

In this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of heterogeneities. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the generalization of the “multiparticle effective field” method (MEFM, see for references Buryachenko, Appl. Mech. Rev. (2001), 54, 1–47), previously proposed for the estimation of stress field averages in the phases. The method exploits as a background the new general integral equation proposed by the author before and makes it possible to abandon the use of the central concept of classical micromechanics such as effective field hypothesis as well as their satellite hypothesis of “ellipsoidal symmetry”. The implicit recursion representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to the inhomogeneous effective fields evaluated from subsequent self-consistent estimations. One also estimates the inhomogeneous statistical moments of local stress fields which are extremely useful for understanding the evolution of nonlinear phenomena such as plasticity, creep, and damage. Just at some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green function, Eshelby tensor and external Eshelby tensor. These estimated inhomogeneities of effective fields lead to the detection of fundamentally new effects for the local stresses inside the heterogeneities.     

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of composites reinforced with solid spherical particles

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of particle reinforced polymers is developed. Particles are in the form of solid spheres having micro-scale diameters. The composite microstructures are idealized by periodically distributed cubic particles in a matrix medium. Each particle is assumed to be fully surrounded by polymeric matrix such that contact between particles can be avoided. A representative volume element (RVE) is then defined by a single particle embedded in the cubic matrix. A spatial periodicity boundary condition is imposed to the RVE. One eighth unit-cell model with four particle and polymer subcells is generated due to the three-plane symmetry of the RVE. The solid spherical particle is modeled as a linear elastic material. The polymeric matrix follows nonlinear viscoelastic behaviors of thermorheologically simple materials. The homogenized micromechanical relation is developed in terms of the average strains and stresses in the subcells and traction continuity and displacement compatibility at the subcells’ interfaces are imposed. A stress–strain correction scheme is also formulated to satisfy the linearized micromechanical and the nonlinear constitutive relations. The micromechanical model provides three-dimensional (3D) effective properties of homogeneous composite responses, while recognizing microstructural geometries and in situ material properties of the heterogeneous medium. The micromechanical formulation is designed to be compatible with general displacement based finite element (FE) analyses. Experimental data and analytical micromechanical models available in the literature are used to verify the capability of the above micromechanical model for predicting the overall composite behaviors. The proposed micromodel is also examined in terms of computational efficiency and accuracy.     

A micromechanical iterative approach for the behavior of polydispersed composites

In this paper, an iterative homogenization method is proposed in order to predict the behavior of polydispersed materials. Various families of heterogeneities according to their geometrical or mechanical properties are progressively introduced into a volume of matrix. At each step, the behavior of intermediate medium is obtained by any analytical homogenization method and is used as matrix of the following step. All homogenization methods, like dilute strain or stress approximations, Hashin’s bounds, three phases method, Mori–Tanaka’s approach or for example the N-layered inclusions method lead to the same effective behavior for the polydispersed material after convergence of the iterative process. Moreover, this convergence is obtained even for significant fractions of heterogeneities and for highly contrasted or polydispersed materials. This method is applied to various composites and validated by comparison with other modellings and experimental results.