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．     

考虑碳纳米管非均匀分布的复合材料电导率计算

碳纳米管作为导电相在机敏复合材料中广泛应用,但碳纳米管为团簇材料,在基体中很难均匀分散。本文考虑碳纳米管的非均匀分布特性,提出了计算碳纳米管复合材料电导率的数值方法。通过引入随机谐和函数,建立了碳纳米管体积分数的三维随机场模型。基于细观力学的有效介质理论、Mori-Tanaka方法和H-S界限理论,考虑碳纳米管之间的隧穿效应,发展了复合材料微小体积单元的电导率计算方法。在此基础上,构建了考虑碳纳米管非均匀分布的复合材料等效电导率三维有限元计算模型。数值分析结果与试验值能够很好吻合,表明这一方法可以准确计算碳纳米管复合材料的电导率。本文进一步分析了碳纳米管非均匀分布对复合材料电导率的影响。     

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

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

SMA短纤维增强复合材料在热载下的相交特性

在形状记忆合金（ＳＭＡ）复合材料研究中,相变特性的研究是一个主要的工作．基于Ｅｓｈｅｌｂｙ的等效夹杂模型和Ｍｏｒｉ和Ｔａｎａｋａ的场平均法,考虑到ＳＭＡ材料的强物理非线性,发展了增量型的等效夹杂模型（ＩｎｃｒｅｍｅｎｔａｌＥｑｕｉｖａｌｅｎｔＩｎｃｌｕｓｉｏｎＭｏｄｅｌ）．考虑在某一温度循环条件下讨论形状记忆合金短纤维增强的铝基复合材料在热载下的相变行为．特别研究了ＳＭＡ短纤维复合材料在变温过程中纤维几何尺寸、体积分数等参数对ＳＭＡ复合材料的相变行为和ＳＭＡ内残余应力等的影响．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颇有意义的．     

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal (PQC) composites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective electroelastic constants of several different composites made up of PQC, quasicrystal (QC), and piezoelectric (PE) materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion (or fiber) on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized selfconsistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.     

三相多重铁性复合材料的有效磁电弹性模量预测

采用平均场Mori-Tanaka模型,计算了三相复合材料的有效磁电弹性模量,研究了复合材料磁电系数与微观结构之间关系;结果表明掺杂相的体积分数与颗粒形状系数对复合材料的有效磁电系数有很大的影响,这些结果可为复合材料的实验设计提供理论参考和指导.     

高体积含量非线性黏弹复合材料有效性质

提出了一个细观力学模型,可用于预测高体积含量非线性黏弹复合材料有效性质.该模型基于广义割线模量法、双球法以及Laplace-Carson变换技术.所提出的模型对玻璃微珠填充高密度聚乙烯(GB/HDPE)复合材料的应力应变关系进行了预测,结果与文献实验结果吻合;计算结果还表明在高体积百分比下文中所提出的方法比基于MT方法预测的粘性效应明显减弱;最后还将所提方法与线黏弹框架下的均质化模型做了比较,结果表明GB/HDPE表现出明显的非线性,线黏弹本构无法描述应变率对其力学行为的影响.     

界面及热残余应力对超磁致伸缩复合材料有效性能的影响

本文基于Mori-Tanaka理论，考虑了界面相对超磁致伸缩复合材料的有效性能的影响，得到了具有界面相的超磁致伸缩复合材料的有效性能的一般解析表达。考虑到固化过程中热残余应力对超磁致伸缩复合材料有效性能的影响，通过数值计算，给出超磁致伸缩复合材料有效弹性模量、有效磁致伸缩应变及有效热膨胀系数随夹杂物长径比、体分比、界面参数和固化热残余应力的变化特征曲线，数值结果表明：界面和固化热残余应力对于超磁致复合材料有效性能的影响是显著的。     

含夹杂和微裂纹复合材料的损伤演化和分析

利用细观力学的Ｅｓｈｅｌｂｙ和Ｍｏｒｉ－Ｔａｎａｋａ理论，考虑纤维和微裂纹之间的相互作用，研究了定向分布微裂纹的演化规律及其对材料力学性能的影响，分析了纤维体积份数，弹性系数、微裂纹密度，纤维不同取向与基体开裂强度之间的变化关系，并给出了许多有意义的结论。     

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     

纤维增强金属基复合材料整体蠕变性能的细观力学分析

高温下金属基复合材料的蠕变主要由基体蠕变和界面扩散蠕变两部分构成,以往的研究中常常只考虑其中一种蠕变机理,从而导致得到的规律具有较大的局限性．本文提出了一种可预测金属基复合材料整体蠕变性能的细观力学方法,同时考虑了基体蠕变和界面扩散蠕变两种蠕变机理,导出了具有张量形式并满足不可压缩性的界面扩散蠕变应变表达式．采用Mori-Tanaka法和自洽法二者结果的平均以便更准确地计算纤维中的应力,揭示了两种蠕变机理相互影响的竞争关系．研究了恒定双轴荷载下的总体蠕变和固定位移约束下的应力松弛这两种常见蠕变问题,探究了基体蠕变与界面扩散蠕变两种蠕变机理在总蠕变中发挥的作用,考察了不同加载条件和不同纤维体积分数对复合材料整体蠕变行为的影响．     

Effective multi-field properties of electro-magneto-thermoelastic composites estimated by finite element method approach

A finite element approach based on the micromechanics was performed to estimate the multi-field properties of electro-magneto-thermoelastic composites. The thermal field and the involved pyroelectric and pyromagnetic effect of the multi-phase composite materials were taken into account in the investigation and implemented in the finite element modeling. The multifields related to the electric field, magnetic field, deformation and temperature field, as well as their coupling effects of the smart composites under periodic boundary conditions were obtained numerically. Especially, by means of the homogenization approximation, the effective thermal expansion coefficients, pyroelectric coefficients, pyromagnetic coefficients and other elastic, electric,and magnetic properties for the piezoelectric material, piezomagnetic material and magnetoelectric material were calculated, respectively. Some results are compared to the theoretical predictions by the well-known Mori-Tanaka method to show good agreements.     

反平面剪切作用下双材料滑动界面的细观力学模型

非理想粘结界面对多相材料力学性能具有重要影响。对于双材料间含众多随机分布微裂纹的界面，宏观上可以等效为连续损伤的弱界面，其两侧的面力连续而位移有间断。只有切线方向的位移间断，而法线方向位移连续的弱界面称之为滑动界面。在反平面剪切的作用下，我们证明了对于含有随机分布微裂纹的弹性双材料界面在宏观上等效为线弹簧型滑动界面，并获得了滑动界面柔度的一般表达式。利用Mori—Tanaka方法和广义自洽方法，我们研究了滑动界面柔度系数和微裂纹密度的关系。对这两种方法所得的结果进行比较发现，Mori—Tanaka方法得到的界面柔度比广义自洽方法得到的界面柔度大。当裂纹密度比较小时，这两种方法求得的界面柔度很接近。两种方法的结果都表明，界面柔度随裂纹密度的增加而增加。Mori—Tanaka方法比广义自治方法求解更为简便。     

Modeling of anisotropic polydispersed composites by progressive micromechanical approach

A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly oriented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to obtain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the matrix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.     

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。     

基于细观力学方法的混凝土热膨胀系数预测

建立混凝土材料的有效性质与微结构参数之间的关系,是混凝土材料优化设计的基础。本文用细观力学方法对复合材料宏观有效热膨胀系数进行研究,得到了含有一球形夹杂物的无限大介质在均匀变温作用下的应力场。假定混凝土为由骨料和砂浆基质组成的二相复合材料,根据混凝土宏观体积热膨胀量与组成混凝土的各相介质细观体积热膨胀量相等的原则,采用基于Mori-Tanaka方法的混凝土宏观有效剪切模量,推导出混凝土有效热膨胀系数的解答。对稀疏解法、自洽方法和有限单元数值试验结果的比较说明,本文提出的基于自洽方法的混凝土宏观有效热膨胀系数的理论公式能够较好的描述混凝土的热学特性,该方法可以推广到多相复合材料宏观有效热膨胀系数的预测中。     

Meso-mechanical constitutive model for ratchetting of particle-reinforced metal matrix composites

Based on the Eshelby equivalent inclusion theory and Mori-Tanaka averaging method, a meso-mechanical cyclic elasto-plastic constitutive model is proposed to predict the ratchetting of particle-reinforced metal matrix composites. In the proposed model, a Hill-typed incremental formulation is used to simulate the elasto-plastic responses of the composites during cyclic loading with assumptions of elastic particle, elasto-plastic metal matrix and perfect interfacial bond between metal matrix and particles. A new nonlinear kinematic hardening rule extended from the Ohno-Abdel-Karim model [M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state, Int. J. Plasticity 16 (2000) 225-240] is employed to describe the ratchetting of metal matrix which dominates the ratchetting of the composites. With further assumption of spherical particles, the proposed meso-mechanical cyclic constitutive model is verified by comparing the predicted uniaxial ratchetting of SiC_P/6061Al composites with corresponding experiments obtained at room temperature [G.Z. Kang, Uniaxial time-dependent ratchetting of SiC_P/6061Al alloy composites at room and high temperature, Comp. Sci. Tech. 66 (2006) 1418-1430]. In the meantime, the effects of different tangent operators employed in the numerical implementation of the proposed model, i.e., continuum (or elasto-plastic) tangent operator C^ep and algorithmic (or consistent) one C^alg, on the predicted ratchetting are also discussed. It is concluded that the proposed model predicts the uniaxial ratchetting of SiC_P/6061Al composites at room temperature reasonably.     

点阵增强型复合材料夹层结构的力学性能实验与分析

采用真空导入成型工艺,制备出在面板与芯材界面上具有创新构型的点阵增强型复合材料夹层结构。对其面板拉伸性能、夹层结构剪切与平压性能进行了实验研究,得出点阵增强型复合材料夹层结构经树脂柱增强后,剪切与平压性能均得以提高的结论。对不同跨高比复合材料夹层结构开展了三点与四点弯曲实验,研究其典型受力破坏形态与机理。基于Eshelby等效夹杂原理,采用Mori-Tanaka方法求解了点阵增强型复合材料夹层结构经树脂柱增强后的剪切性能。利用经典夹层梁理论和非线性有限元模拟方法,预估了试件抗弯刚度与受弯极限承载力,理论分析与实验结果较吻合。     

A generalized self-consistent Mori-Tanaka model for predicting the effective moduli of the coated inclusion based composite materials

The weak point of the generalized self-consistent method (GSCM) is that its solution for the effective shear moduli involves determining the complicated displacement and strain fields in constitutents. Furthermore, the effective moduli estimated by GSCM cannot be expressed in an explicit form. Instead of following the procedure of GSCM, in this paper a generalized self-consistent Mori-Tanaka method (GSCMTM) is developed by means of Hill's interface condition and the assumption that the strain in the inclusion is uniform. A comparison with the existing theoretical and experimental results shows that the present GSCMTM is sufficiently accurate to predict the effective moduli of the coated inclusion-based composite materials. Moreover, it is interesting to find that the application of Hill's interface condition in volumetric domain is equivalent to the Mori-Tanaka average field approximation. This project was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation.