含非均匀界面相粒子填充复合材料的有效比热

基于细观力学复合球模型研究了含非均匀界面相粒子填充复合材料的有效热弹性性质,重点讨论了界面相性质的径向分布对有效比热的影响. 首先,将非均匀界面相沿径向离散为多个同心球壳,每个球壳内的材料性质假设是均匀的. 基于上述离散模型,利用含界面相的复合球模型,推导了复合材料的有效体积模量、有效热膨胀系数及有效比热的数值求解表达式;进一步,假设界面相的性质沿径向连续变化,建立了一组微分方程,上述有效性质依赖于该微分方程组的解. 特别地,当界面相杨氏模量为幂次分布时,通过求解该微分方程组得到了有效比热等热弹性性质的解析解. 算例结果表明,应用此方法预测的有效热膨胀系数与实验结果吻合良好;界面相热膨胀系数的径向分布对有效比热和有效热膨胀系数均有显著的影响,而界面相弹性模量的径向分布对有效比热有显著的影响,对有效热膨胀系数的影响相对较小.      

Effective elastic moduli of composites reinforced by particle or fiber with an inhomogeneous interphase

The solution of the strain energy change of an infinite matrix due to the presence of one spherical particle or cylindrical fiber surrounded by an inhomogeneous interphase is the basis of solving effective elastic moduli of corresponding composites based on various micromechanics models. In order to find out the strain energy change, the composite sphere or cylinder, i.e., the spherical particle or cylindrical fiber together with its interphase, is replaced by an effective homogeneous particle or fiber. Independent governing differential equations for each modulus of the effective particle or fiber are derived by extending the replacement method [J. Mech. Phys. Solids 12 (1964) 199]. As far as the strain energy changes of the infinite matrix subjected to various far-field stress systems are concerned, the present model is simple. Meanwhile, FEM analysis is carried out for a verification, which shows that the model can lead to rather accurate results for most practical interphases. Besides, to check the validity of the model further when the interactions among composite cylinders exist, the two problems of an infinite matrix containing two composite cylinders and the effective moduli of composites with the equilateral triangular distribution of composite cylinders are analyzed using FEM. The FEM results show that the model is still rather accurate, especially for the case of interphase properties varying between those of fiber and matrix. Therefore, composite spheres or cylinders are assumed as the effective homogeneous particles or fibers and simple expressions of the effective moduli of composites containing the composite spheres or cylinders are obtained. Furthermore, the present model is compared with some existing models that are based on very complicated derivations.     

Influences of reinforcing particle and interface bonding strength on material properties of Mg/nano-particle composites

In the present study, an effective model is proposed to predict the effective elastic behavior of the three-phase composite containing spherical inclusions, each of which is surrounded by an interphase layer. The constitutive equations are derived for the stress and strain of each phase of the composite subjected to a far-field tension. Based on these constitutive laws, the effective bulk, shear and Young’s modulus are obtained. A statistical debonding criterion is adopted to characterize the varying probability of the evolution of interphase debonding. Influences of debonding damage, particle volume fraction, interphase properties and bonding strength on overall mechanical behavior of composites are also discussed. Numerical analyses are carried out on particle-reinforced composites and the predictions have a good agreement with the experimental results.     

Investigation on the effective conductivities of carbon/carbon fiber composites with inhomogeneous interphase

I.Intr0ducti0nThestudyofeffectivethermalconductivitiesofcompositesisaclassicaltopic.Theearlyresearcheswerec0ncernedmainIycompositesconsistingofisotropicphases,wheretheinterfacebetweentu'oconstituentswasassumedtobeperfect,i.e.,thetemperatureandheatfluxfiel…     

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.     

Effective mechanical properties of unidirectional composites in the presence of imperfect interface

In this paper, the equivalent inclusion method is implemented to estimate the effective mechanical properties of unidirectional composites in the presence of an imperfect interface. For this purpose, a representative volume element containing three constituents, a matrix, and interface layer, and a fiber component, is considered. A periodic eigenstrain defined in terms of Fourier series is then employed to homogenize non-dilute multi-phase composites. In order to take into account the interphase imperfection effects on mechanical properties of composites, a stiffness parameter in terms of a matrix and interphase elastic modulus is introduced. Consistency conditions are also modified accordingly in such a way that only the part of the fiber lateral stiffness is to be effective in estimating the equivalent composite mechanical properties. Employing the modified consistency equations together with the energy equivalence relation leads to a set of linear equations that are consequently used to estimate the average values of eigenstrain in non-homogeneous phases. It is shown that for composites with both soft and hard reinforcements, largest stiffness parameter that indicates complete fiber–matrix interfacial debonding causes the same equivalent lateral properties.     

ANALYTICAL SOLUTIONS FOR ELASTOSTATIC PROBLEMS OF PARTICLE-AND FIBER-REINFORCED COMPOSITES WITH INHOMOGENEOUS INTERPHASES

IntroductionRecently ,theinterphaseincompositeshasattractedtheattentionofmanyresearchers[1- 7].Someinterphasesareproducedbydesignandothersbychemicalreactionsinfabricatingcomposites.Fromtheviewpointofmechanicsofcompositematerials,oneofthefundamentalproblemsofcompositeswithinterphasesistopredicttheeffectivemoduli.Therearemanymethodsforpredictingeffectivemoduliofcomposites,suchasgeneralizedself_consistentmethod(GSCM) ,compositesphereandcompositecylindermodels (CCAandCSA)andIDDestimate ,etc …     

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．     

EFFECTIVE SPECIFIC HEATS OF MULTI-PHASE THERMOELASTIC COMPOSITES

This paper studies the effective properties of multi-phase thermoelastic composites. Based on the Helmholtz free energy and the Gibbs free energy of individual phases, the effective elastic tensor, thermal-expansion tensor, and specific heats of the multi-phase composites are derived by means of the volume average of free-energies of these phases. Particular emphasis is placed on the derivation of new analytical expressions of effective specific heats at constant-strain and constant-stress situations, in which a modified Eshelby’s micromechanics theory is developed and the interaction between inclusions is considered. As an illustrative example, the analytical expression of the effective specific heat for a three-phase thermoelastic composite is presented.     

Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites

The load transfer mechanisms and effective moduli of single-walled nanotube (SWNT) reinforced composites are studied using a continuum model. A “critical” fiber length is defined for full load transfer by numerically evaluating the strain-energy-changes for different fiber lengths. The effective longitudinal Young’s modulus and bulk modulus of the composite are derived. The effect of the interphase is also discussed. The results indicate the fiber length is critical both to the load transfer efficiency and effective moduli of the composite. The SWNT-matrix interphase plays an important role in load transfer efficiency but affects the effective moduli only slightly.     

基于等效特征应变原理的复合材料有效模量细观力学分析

基于等效特征应变原理,提出了一种新的复合材料有效模量细观力学分析方法。首先,在等效特征应变原理基础上提出平均等效特征应变原理,它可用于解决有限体下任意形状(无论是凸或凹形)的单个夹杂或多个夹杂的弹性变形问题。其次,将平均等效特征应变原理与细观力学直接均匀法相结合,来分析确定复合材料的有效模量。最后利用复合材料纤维与基体的力学性能参数及纤维的体分比,借助MATLAB编程方法,预测其有效模量。通过将理论预测值与已有的的试验值、其它理论预测值进行对比,验证了新分析方法的合理性和分析精度。     

界面特性对短纤维金属基复合材料蠕变行为的影响

基于短纤维增强金属基复合材料(MMC)的单纤维三维模型(三相)，利用粘弹性有限元分析方法对影响金属基复合材料的蠕变行为的因素进行了较为系统的分析。研究中主要讨论了界面特性和纤维取向角对金属基复合材料的蠕变性能的影响。研究结果发现，界面特性诸如厚度、模量和应力指数都对纤维最大轴应力和稳定蠕变率产生影响：稳态蠕变率随界面模量的增大而逐渐减小，当高于基体模量时基本保持不变；纤维轴应力的变化与蠕变率正好相反。稳态蠕变率随界面厚度、应力指数的增加而增大；而轴应力则随之减小。同时不同的纤维取向也影响金属基复合材料蠕变时的轴应力分布和稳态蠕变率。     

An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric–magnetic fiber composites

A three-phase cylindrical model for analyzing fiber composite subject to in-plane mechanical load under the coupling effects of multiple physical fields (thermo, electric, magnetic and elastic) is presented. By introducing an eigenstrain corresponding to the thermo-electro-magnetic-elastic effect, the complex multi-field coupling problem can be reduced to a formal in-plane elasticity problem for which an exact closed form solution is available. The present three-phase model can be applied to fiber/interphase/matrix composites, such that a lot of interesting thermo-electro-magnetism and stress coupling phenomena induced by the interphase layer are revealed. The present model can also be applied to fiber/matrix composites, in terms of which a generalized self-consistent method (GSCM) is developed for predicting the effective properties of piezoelectric–magnetic fiber reinforced composites. The effective piezoelectric, piezomagnetic, thermoelectric and magnetoelectric moduli can be expressed in compact explicit formulae for direct references and applications. A comparison of the predictions by the GSCM with available experimental data is presented, and interesting magnification effects and peculiar product properties are discussed. As a theoretical basis for the GSCM, the equivalence of the three sets of different average field equations in predicting the effective properties are proved, and this fact provides a strong evidence of mathematical rigor and physical realism in the formulation.     

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.     

Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites

The paper addresses the problem of modeling of fiber reinforced composites with imperfect bonding between the matrix and the inhomogeneities. The imperfections of different kinds are usually modeled as either layered inhomogeneities or by springs of certain stiffnesses distributed along the matrix/fiber interfaces. We compare the two approaches for the case of incompressible layer between the phases and calculate effective properties of fiber reinforced composites with periodic square arrays of fibers possessing imperfect contact with the surrounding material. We identify the interval of thickness at which the interphase does not influence the effective properties and show how the imperfection effects described by different models can be expressed in terms of each other.     

Influence of interphase and filler distribution on the elastic properties of nanoparticle filled polymers

The present work presents a preliminary study on the effect of the filler distribution on the elastic modulus of a nanoparticle filled polymer. To this end, two different theoretical approaches are implemented and compared. Both of them account for an interphase layer embedding the nanoparticle, with mechanical properties different from those of the matrix. Conversely, only one of them accounts for the variation of the interparticle distance. The comparison between these models allows to draw some conclusions on the effect of the filler distribution.     

A self-consistent statistical mechanics approach for determining effective elastic properties of composites

A self-consistent statistical mechanics approach for determining the effective elastic properties of composites with random structure is developed. The problem is reduced to the model of a single inclusion with a non-homogeneous elastic neighbourhood in a medium with effective elastic properties. The inhomogeneous elastic properties and size of neighbourhood are defined by randomness of the geometry, random size of inclusions and random elastic properties of the inclusions. Numerical results are given for the effective elastic properties of a composite with hollow spherical inclusions.     

混杂短纤维增强复合材料弹性模量预测

在现代工程结构中,纤维增强复合材料具有较高的刚度重量比、优异的耐久性和设计灵活性等优点,因此得到了广泛应用．本文结合细观力学中的Mori-Tanaka方法和Halpin-Tsai方法推导了混杂碳纤维和玻璃纤维增强复合材料有效弹性模量的解析表达式．通过引入参数λ,提出了计算随机方向混合纤维增强复合材料弹性模量的新模型,分析了纤维长径比和体积分数对复合材料弹性模量的影响．结果表明,复合材料的弹性性能对纤维长径比和体积分数非常敏感．根据提出的理论,混杂纤维增强复合材料的弹性模量处于单一纤维（纯碳纤维或纯玻璃纤维）增强复合材料弹性模量之间．对于单一纤维增强复合材料,采用Halpin-Tsai方法计算的复合材料弹性模量高于Mori-Tanaka方法计算结果．     

The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials

The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic Lamé problem for a pressurized homogeneous isotropic hollow circular cylinder or disk is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. It is shown that the stress response of the inhomogeneous cylinder (or disk) is significantly different from that of the homogeneous body. For example, the maximum hoop stress does not, in general, occur on the inner surface in contrast with the situation for the homogeneous material. The results are illustrated using a specific radially inhomogeneous material model for which explicit exact solutions are obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

含有随机夹杂的统计非均匀弹性介质参数的分析

本文提出了随机点场理论用于研究含有随机夹杂的统计非均匀介质。本文不同于其它作者,一般均将随机理论建立在Eshelby的等效夹杂原理之上,而这里是建立在Kunin的微结构理论基础之上。作为理论的一个应用,本文对复合材料的有效模量及夹杂内部及周围微观场进行了计算。