三维编织复合材料模量的双尺度有限元计算

针对三维编织复合材料的力学性能进行了双尺度有限元(TSA)数值计算,给出了计算模型和算法过程,并将数值结果与文献中的实验数据进行了比较,验证了算法的物理准确性。编织复合材料的力学性能不仅依赖于材料的基本组份,也与细观构造相关。双尺度有限元计算可以数值模拟出三维编织复合材料的整体力学性能,从而为材料的研发提供指导。本文的双尺度有限元三维数值计算方法可以推广到其他增强／孔隙等多相复合材料的数值模拟。     

复合材料中的渐近均匀化方法

本文将非均质弹性体的渐近均匀化方法应用于复合材料的宏观与细观分析之中。该方法基于平均化的思想，将复合材料视作由周期性的细观结构所构成，其场变量依赖于宏观和细观两个尺度的坐标变量而变化。通过建立位移和应力的渐近表达式，推导出关于周期性基元的细观平衡方程和细观本构关系，并与有限元数值方法相结合，得到材料的宏观等效性能和细观应力分布。对典型算例的分析，反映出该方法的有效性及准确性。     

加筋材料的格形模型和统计数值方法

本文采用格形化方法和统计技术建立加筋复合材料有限元力学模型，使用自动选取载荷步长方法和非平衡迭代技术，对加筋复合材料的宏观等效模量和破坏全过程进行了数值模拟，分析了材料分布的非均匀程度，相对体积比和横截面加筋分布方式对加筋复合材料整体宏观等效模量和承载力的影响。     

增强相形态对复合材料微区力学状态影响的有限元分析

采用三维有限元方法模拟了非连续增强金属基复合材料的应力场，得到了不同长径比的椭球形增强体周围的最大主应力场和应力球张量场的分布，分析了增强体长径比对非连续增强金属基复合材料的应力场、应力集中、界面应力过渡及材料内部最危险位置的影响。与仅适用于稀疏夹杂的Eshelby单夹杂模型相比，本文模型(体积分数约为20％—60％)与工程实际更加接近，所得的椭球状增强体内部应力分布并不均匀的计算结果与Eshelby的经典解析解有所不同。     

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．     

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。     

高温下编织复合材料热相关参数识别方法研究

为了获取高温下编织复合材料的准确弹性参数与热膨胀系数,提出一种基于均匀化理论的热相关参数识别方法. 首先,在编织复合材料单胞有限元模型基础上,基于均匀化理论和热弹性理论,施加周期性位移边界条件和温度边界条件,预测编织复合材 料的热弹性相关参数. 然后,考虑到等效过程中编织复合材料应力分布不均匀等因素引起的误差,将复合材料精细模型的热模态数据作为补 充信息,识别编织复合材料热相关参数,对预测的材料参数进行校准. 本文在二维编织结构单胞模型基础上,开展等效预测和识别方法研 究,验证所提出方法的有效性和准确性. 对比等效和识别后热模态的误差,结果表明:本文提出的基于等效预测的参数识别方法,能够 准确识别高温下编织复合材料宏观热相关参数.      

周期性复合材料湿热力耦合问题的二阶渐近分析

渐近均匀化方法是一种很好的分析复合材料力学性能的方法。通过建立考虑材料湿热效应的双尺度渐近展开模型,研究了周期性复合材料在湿、热、力耦合作用下的结构响应。将带有小参数的位移渐近展开式代入湿热力耦合控制方程,利用等效积分"弱"变换推导出复合材料等效参数的单胞控制方程以及均匀化方程。为了提高计算精度,本文对均匀化解进行了一阶和二阶修正,利用FreeFem++软件进行了数值模拟。结果显示:双尺度二阶渐近分析能够高效、准确地计算出一系列多场耦合问题,为研究周期性复合材料的力学性能提供了新的方法。     

混凝土受拉性能多尺度均匀化数值模拟研究

为研究混凝土的细观结构对其受拉性能的影响,本文首先采用蒙特卡罗方法生成了多组混凝土随机骨料模型;然后划分有限元网格并映射到所建立的混凝土随机骨料数值模型上,采用复合材料均匀化方法建立了混凝土多尺度均匀化数值模型。考虑骨料随机分布和骨料形状,通过数值分析得到了在单轴拉伸情况下混凝土损伤分布特性及宏观应力-应变关系,在考虑随机性与非均质性的同时得到了较为理想的结果。运用多尺度均匀化的建模方法不仅能反应混凝土细观结构的影响,而且等效化模型的模拟计算时间大大减少,节约计算资源,提高了计算效率,具有优越性。     

单向纤维复合材料粘弹性性能预测

建立了基于均匀化理论的单向纤维复合材料粘弹性性能预测方法。对单向纤维增强复合材料粘弹性问题的控制方程进行Laplace变换,在像空间中利用均匀化理论建立宏观松弛模量的Laplace变换与微结构描述参数以及变换参数间的关系。用Prony级数模拟松弛模量随变换参数的变化形式,并根据像空间中一系列变换参数对应的松弛模量的数值,采用函数拟合技术确定Prony级数的形式,从而确定用显示形式表示的松弛模量的Laplace变换随变换参数的变化规律。对显式表达式的逆变换获得时间域内的松弛模量。该方法利用拟合函数的逆变换避开了复杂的数值Laplace逆变换,使单向纤维增强复合材料的粘弹性性能的确定变得容易。文中给出了单向纤维复合材料松弛模量的数值预测结果并同有限元法模拟试验的结果对比,验证了预测结果的准确性以及本文方法的有效性。     

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.     

Metal matrix composite solidification in the presence of cooled fibers: numerical simulation and experimental observation

Attempts have been made to alter the solidification microstructures of fiber reinforced aluminum composites by cooling the ends of the fibers extending out of the mold. Experimental observations indicate that cooling the extended ends of the reinforcement results in finer microstructures in the matrix and changes the nature of the interface. In this paper, numerical simulation is performed on a two-dimensional axi-symmetric model to investigate the solidification process of metal matrix composite (MMC) with the extended ends of the fibers cooled by a heat sink. The numerical simulation is based on the source-based enthalpy method with finite volume discretization. The temperature profiles obtained by simulation are compared to the cooling curves measured experimentally in order to validate the current mathematical model. It is found that the simulation result matches the experimental data with reasonable agreement.     

A LOWER BOUND LIMIT ANALYSIS OF DUCTILE COMPOSITE MATERIALS

The plastic load-bearing capacity of ductile composites such as metal matrix composites is studied with an insight into the microstructures. The macroscopic strength of a composite is obtained by combining the homogenization theory with static limit analysis, where the temperature parameter method is used to construct the self-equilibrium stress field. An interface failure model is proposed to account for the effects of the interface on the failure of composites. The static limit analysis with the finite-element method is then formulated as a constrained nonlinear programming problem, which is solved by the Sequential Quadratic Programming （SQP） method. Finally, the macroscopic transverse strength of perforated materials, the macroscopic transverse and off-axis strength of fiber-reinforced composites are obtained through numerical calculation. The computational results are in good agreement with the experimental data.     

Computational studies on high-stiffness,high-damping SiC–InSn particulate reinforced composites

With the objective of achieving composite material systems that feature high stiffness and high mechanical damping, consideration is given here to unit cell analysis of particulate composites with high volume fraction of inclusions. Effective elastic properties of the composite are computed with computational homogenization based on unit cell analysis. The correspondence principle together with the viscoelastic properties of the indium–tin eutectic matrix are then used to compute the effective viscoelastic properties of the composite. Comparison is made with parallel experiments upon composites with an indium–tin eutectic matrix and high volume fractions of silicon-carbide reinforcement. The analytical techniques indicate that combinations of relatively high stiffness and high damping can be achieved in particulate composites with high SiC volume fractions. Based on analysis, the tradeoffs between stiffness and damping characteristics are assessed by changing the volume fraction, size, packing, and gradation of the particulate reinforcement phases. Practical considerations associated with realization of such composites based on the surface energy between the SiC and the InSn are discussed.     

一种预测颗粒增强复合材料界面力学性能的新方法

界面在颗粒增强复合材料中起到传递载荷的关键作用, 界面性能对复合材料整体力学行为产生重要影响. 然而由于复合材料内部结构较为复杂, 颗粒与基体间的界面强度和界面断裂韧性难以确定, 尤其是法向与切向界面强度的分别预测缺乏有效方法. 本文以氧化锆颗粒增强聚二甲基硅氧烷(PDMS)复合材料为研究对象, 提出一种预测颗粒增强复合材料界面力学性能的新方法. 首先, 实验获得纯PDMS基体材料及单颗粒填充PDMS试样的单轴拉伸应力$\!-\!$应变曲线, 标定出PDMS基体材料的单轴拉伸超弹性本构关系; 其次, 建立与单颗粒填充试样一致的有限元模型, 选择特定的黏结区模型描述界面力学行为, 通过样品不同阶段拉伸力学响应的实验与数值结果对比, 分别给出颗粒与基体界面的法向强度、切向强度及界面断裂韧性; 进一步应用标定的界面力学参数, 开展不同尺寸及不同数目颗粒填充试样的实验与数值结果比较, 验证界面性能预测结果的合理性. 本文提出的界面力学性能预测方法简便、易操作、精度高, 对定量预测颗粒增强复合材料的力学性能具有一定帮助, 亦对定量预测纤维增强复合材料的界面性能具有一定参考意义.      

Multiscale homogenization of n-component composites with semi-elliptical random interface defects

Effective elastic characteristics of periodic multicomponent composite materials with random interface defects are studied in the paper. The defects are assumed to be semi-elliptical and lying with major semi axes along the interfaces, where minor and major semi-axes as well as the defects number are given as input random variables. The homogenization approach has a multiscale character—some algebraic approximation is used first to calculate effective elastic parameters of the interphase including all defects located at the same interface. Equations for interphase random elastic parameters are obtained using MAPLE symbolic mathematics in conjunction with probabilistic generalized perturbation method. A different homogenization method is applied at the micro scale, where the cell problem is solved numerically using the Finite Element Method (FEM) program. Since the composites considered exhibit random variations of both elastic properties and the interface defects, the overall homogenized characteristics must be obtained as random quantities, which is realized on the micro scale by the Monte-Carlo simulation. The proposed interface defects model obeys the porosity effects resulting from the nature of some matrices in engineering composites as well as the interface cracks appearing as a result of composites ageing during static or fatigue fracture.     

The effect of interfacial properties on the cohesion of highly filled composite materials

It has long been recognized that the cohesion of composite materials, in low confinement, is strongly affected by the properties of the interfacial transition zone (ITZ) between inclusions and matrix. While the effect of the ITZ on the elasticity properties of composites has been studied by many authors in the context of linear homogenization methods, the upscaling of the cohesion strength of highly filled composite materials has not been addressed. This is the focus of the non-linear homogenization procedure developed in this paper, which is based on the separation of the heterogeneous material system in phases of constant strength properties, a non-linear elastic representation of the limit stress state in each phase, and the definition of appropriate effective strain quantities that capture the morphological features of the microstructure. Applied to a three phase composite model composed of rigid inclusion, interface zone and matrix, the model provides a quantitative means of studying the effect of the interface cohesion and the interface volume fraction on the composite cohesion. In particular, we identify a critical interface-to-matrix cohesion ratio, below which the composite cohesion is smaller than the one of the matrix. Furthermore, the model lends itself readily to the study of the degradation of the interfacial properties in composite materials. This is shown for non-degraded and chemically softened cement-based materials, for which we provide conclusive evidence (1) that the interface strength properties of mortar are far more affected by chemical degradation than the one of the cement paste matrix; and (2) that chemical degradation does affect the mechanical strength performance of the cement paste not only through a change of volume proportions (i.e. increase of porosity), but as well through a pure chemical softening of the solid’s cohesion.     

基于均匀化理论韧性复合材料塑性极限分析

运用细观力学中的均匀化方法分析了韧性复合材料的塑性极限承载能力.从反映复合材料细观结构的代表性胞元入手,将均匀化理论运用到塑性极限分析中,计算由理想刚塑性、Mises组分材料构成的复合材料的极限承载能力.运用机动极限方法和有限元技术,最终将上述问题归结为求解一组带等式约束的非线性数学规划问题,并采用一种无搜索直接迭代算法求解.为复合材料的强度分析提供了一个有效手段.     

Microstructure and fracture characteristic of Mg–Al–Zn–Si3N4 composites

Magnesium matrix composites reinforced by three dimensional (3-D) network structure were fabricated by pressure-less infiltration technology. The 3-D network structure reinforcement and its composites exhibited special topology structure and different fracture characteristic. Metal matrix fractured in a ductile mode is manifested by small dimples and craters on the fracture surface. When the volume fraction of reinforcement is not in excess of 6%, the composite had an improved fracture toughness. This is because of the relatively homogeneous Si₃N₄ particles distributed in the metal matrix and the occurrence of interface reaction product such as MgAlO₂ spinel phase. With the increases of volume fraction of reinforcement (>6%), the fracture toughness decreases slowly at the initial stages and then decreases rapidly towards the end. Therefore, the main fracture failure mechanisms consist of crack nucleation, growth, coalescence and crack propagation.     

非均匀微极介质的有效性质分析

首先讨论了不同尺度关系下宏细观过渡方法,然后重点介绍了尺度关系满足L>>l>>A ≈lm时(适用于金属基复合材料,泡沫基复合材料和纳米复合材料等),构元材料看作微极介质,而均质化后的材料仍可看作传统Cauchy介质时的解析弹塑性细观力学方法.在这样的理论框架下,细观结构的尺度影响可作为变量引入细观力学模型,并且当A>>lm 时,该方法自然退化成传统的细观力学方法.