Influence of fiber architecture on the inelastic response of metal matrix composites

This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).     

Plastic constitutive behavior of short-fiber/particle reinforced composites

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites.     

Finite element modelling of Al/SiCp metal matrix composites with particles aligned in stripes—a 2D–3D comparison

3D Finite element calculations comparing to axisymmetric calculations have been performed to predict quantitatively the tensile behaviour of composites reinforced with ceramic particles aligned in stripes. The analyses are based on a unit cell model, which assumes the periodic arrangement of reinforcements. The results are presented in such a manner that can be directly compared for all possible aspect ratios and inclusion volume fractions. It is indicated that varying the distance between the stripes when particle volume fraction is kept constant significantly influences the overall mechanical behaviour of composites. Whereas during elastic deformation 3D and axisymmetric formulations predict quantitatively similar results, the mechanical behaviour perpendicular to the stripe direction predicted by 3D and axisymmetric models may differ depending on the inclusion volume fraction. Nevertheless an appreciable strengthening in the stripe direction independent on the model and deformation stage is predicted.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.     

A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites

The effect of fiber arrangement on transverse tensile failure in unidirectional carbon fiber reinforced composites with a strong fiber-matrix interface was studied using a unit-cell model that includes a continuum damage mechanics model. The simulated results indicated that tensile strength is lower when neighboring fibers are arrayed parallel to the loading direction than with other fiber arrangements. A shear band occurs between neighboring fibers, and the damage in the matrix propagates around the shear band when the interfacial normal stress (INS) is sufficiently high. Moreover, based on the observation of Hobbiebrunken et al., we reproduced the damage process in actual composites with a nonuniform fiber arrangement. The simulated results clarified that the region where neighboring fibers are arrayed parallel to the loading direction becomes the origin of the transverse failure in the composites. The cracking sites observed in the simulation are consistent with experimental results. Therefore, the matrix damage in the region where the fiber is arrayed parallel to the loading direction is a key factor in understanding transverse failure in unidirectional carbon fiber reinforced composites with a strong fiber/matrix interface.     

复合材料动态粘弹性能的细观研究

利用细观力学的Eshelby等效夹杂方法研究了颗粒增强复合材料的动态粘弹性力学性能,分析了材料复模量随夹杂体积分数、载荷频率之间的变化规律,给出了许多有意义的结论,为复合材料结构的优化设计及应用提供了理论基础。     

Model for Elastic Modulus of Multi-Constituent Particulate Composites

In this paper, a methodology has been developed to accurately predict the elastic properties of multi-constituent particulate composites by accounting for irreversible effects, such as energy loss that arises due to internal friction. The complex dependence on loading density and particle properties (i.e., size, shape, morphology, etc.) is investigated in terms of their effects on the effective elastic modulus of the composite. Confirmed by experimental data from the compression loading of individual Ni and Al particles dispersed in an epoxy matrix, it is believed that this approach captures the effects of internal friction, consequently providing a more accurate and comprehensive representation for predicting and understanding the material behavior of multi-constituent particulate reinforced composites. The present methodology provides a model to directly compare the elastic modulus from an uncomplicated test, such as dual-cantilever beam loading in dynamic mechanical analysis (DMA), to the modulus obtained by other more complex experimental methods such as quasi-static compression. The model illustrates an efficient method to incorporate input data from DMA to represent realistic elastic moduli, hence promising for the characterization and design of particulate composites.     

Damage model of elastic rubber particulate composites

A discrete structural model is developed to simulate the behavior of randomly filled rubber particulate composites. Adopted is physical discretization approach for small linear deformations. It is expanded to systems for large elastic deformation that account for structure rearrangement and microdamage accumulation. The life cycle of the material is examined from its virgin state to multiple debonding of matrix from inclusions (primary damages) and growth of microcrack (secondary damages) corresponding to final macrofailure. Both macroscopic (tensile curves) and microscopic (primary and secondary damage accumulation) changes are evaluated for extensional loading. Effective strength characteristics scatter depending on filler concentration is calculated.     

A new formulation of the effective elastic–plastic response of two-phase particulate composite materials

In this paper the double-inclusion model, originally developed to determine effective linear elastic properties of composite materials, is reformulated and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The resulting problem of elastic–plastic deformation of a double-inclusion embedded in an infinite reference medium subjected to an incrementally applied far-field strain is solved by the finite element method. The proposed double-inclusion model is evaluated by comparison of the model predictions to the available exact results obtained by the direct approach using representative volume elements containing many particles. It is found that the double-inclusion formulation is capable of providing accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions.     

Analytical investigation of nonlinear interlaminar fracture in trilayered polymer composite beam under mode II crack loading conditions using the J -integral approach

The present study is concerned with a nonlinear fracture analysis of trilayered beam built up by two unidirectional fiber-reinforced polymer composites. It is assumed that two interlaminar cracks exist between the layers. A tensile force applied to the middle layer generates pure mode II crack loading conditions. The J -integral approach is used to investigate the nonlinear fracture behavior of the beam. The elastic-linearly hardening model is applied to describe the mechanical behavior of the two composites. Sixth expressions for J -integral are derived using a beam theory model. These expressions correspond to the characteristic magnitudes of the external force. The validity of the formulae obtained is proved by comparison with the J -integral solution in the case of linear-elastic behavior of the composite materials. A numerical example is presented in order to demonstrate the ability of the expressions obtained for the analysis of nonlinear fracture in polymer composites.     

Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells

This study introduces a non-linear finite element analysis approach to the procedure of modeling hybrid laminate composite shells with embedded shape memory alloy (SMA) wire subjected to coupled structural and thermal loading. Numerical analyses of SMA wire reinforced composite laminates were carried out by synergizing the non-linear laminate shell element with Brison's model of the SMA constitutive law. To verify the proposed procedure, the present illustrative applications involve rectangular laminated panels clamped along one side. Analysis results were compared with corresponding experimental results from a prior study. Several test cases that depend on the volume fraction of SMA, temperature, and ply angles are presented to illustrate the highly entangled thermo-mechanical behavior of shape memory alloy hybrid composites (SMAHCs). The results of the numerical analysis show the ability of the suggested procedure to compute the thermo-mechanical behavior of a SMAHC in accordance with the SMA's internal phase transformations induced by stress and temperature variation and demonstrate very good agreement with experimental results.     

增强颗粒对铝基复合材料摩擦学性能的影响

采用自制的摩擦磨损试验机考察了增强颗粒对铝基复合材料摩擦磨损性能的影响。结果表明：在基体合金、陶瓷颗粒尺寸和体积分数相同的条件下,SiC增强铝基复合材料的摩擦磨损性能优于Al2O3增强铝基复合材料;增大颗粒尺寸或增加颗粒体积分数均使得SiC颗粒增强铝基复合材料的平均摩擦系数略有降低,耐磨性能提高;在与半金属摩擦材料配副时,颗粒增强铝基复合材料的摩擦系数与基体合金的相近,耐磨性能提高了3个数量级。     

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.      

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．     

颗粒增强复合材料有效性能的三维数值分析

将细观力学和计算力学方法相结合用以确定复合材料中的局部和平均应力－应变场．对旋转体和非旋转体颗粒增强复合材料的有效模量进行了三维有限元数值计算，数值与实验结果对比表明，该方法是有效的、可靠的．分析了颗粒的排列分布、颗粒取向和颗粒的几何形状对有效模量的影响．数值结果表明，颗粒的排列对有效轴向弹性模量影响较大．颗粒的取向和颗粒的形状对有效性能的影响也是显著的     

Numerical simulation of thermo-mechanical fatigue properties for particulate reinforced composites

In this paper, a two dimensional Voronoi cell element, formulated with creep, thermal and plastic strain, is applied for the numerical simulation of thermo-mechanical fatigue behavior for particulate reinforced composites. The relation between mechanical fatigue phases and thermal fatigue phases influences the thermo-mechanical fatigue behavior and cyclic creep damage. The topological features of micro-structure in particulate reinforced composites, such as the orientation, depth-width ratio, distribution and volume fraction of inclusions, have a great influence on thermo-mechanical behavior. Some related conclusions are obtained by examples of numerical simulation.The project supported by the Special Funds for the National Major Fundamental Research Projects (2004CB619304), the National Natural Science Foundation of China (10276020 and 50371042), the Key Grant Project of Chinese Ministry of Education (0306)     

橡胶粘结颗粒材料粘弹性性能的试验研究与离散元模拟

制备了颗粒规则四方排列和六方排列的橡胶粘接颗粒材料试样,实验测试了所制备试样在单向拉伸载荷下的应力松弛曲线和不同应变率时的应力应变曲线。基于所测试的应力松弛曲线,采用曲线拟合方法得到了所测试材料的宏观Burger’s粘弹性本构模型参数。采用离散元模型中单元间连结模型代表颗粒间橡胶粘接剂的作用,并基于试样的宏观Burger’s模型参数与离散元模型中细观Burger’s连结模型参数间的关系,建立了橡胶粘接颗粒材料的无厚度胶结离散元分析模型。最后采用所建立的离散元模型计算了所测试试样的松弛和拉伸力学性能。离散元预测结果与实验结果的对比表明,采用无厚度胶结离散元模型能较好的计算颗粒规则排列的橡胶粘接颗粒材料松弛和拉伸力学性能,但基于应力松弛实验拟合而来参数不能准确反应橡胶粘接剂在高应变率条件下其力学性能的应变率相关性。