金属玻璃基复合材料的变形行为及本构关系研究综述

金属玻璃及其复合材料因其优良的力学性能而具有良好的应用前景,相关研究方兴未艾. 本文主要总结国内外的研究成果并结合本课题组的最新研究工作,针对块体金属玻璃基复合材料的变形行为、增韧机理和本构关系研究现状进行较为全面的综述. 首先,对近几十年来在块体金属玻璃基体材料的变形行为与失效机理以及本构关系研究方面的丰硕成果进行简要回顾. 其次,从实验研究和数值模拟两方面,重点对金属玻璃基复合材料的变形行为与失效机理研究成果进行介绍,总结了金属玻璃基复合材料的塑性变形、增韧机理及影响因素. 然后,对金属玻璃基复合材料的本构关系研究最新进展进行评述,重点介绍了均匀化方法在该领域的应用. 作为代表,较为详细地介绍了作者新近提出的一个二次均匀化的方法,并在此基础上,结合纳米孔洞作为自变量的失效判据而建立了本构模型,该模型对金属玻璃基复合材料的变形和失效行为进行了合理预测. 最后,对该领域的研究现状进行简单的总结,并对未来的研究问题进行展望.      

Constitutive relation of discontinuous reinforced metal-matrix composites

A micromechanical model is developed to simulate the mechanical behaviors of discontinuous reinforced composites. The analysis for a representative unit cell is based on the assumption of a periodic array of aligned reinforcements. The minimum energy principle is used to determine the unknown coefficients of the displacement field of the unit cell. The constitutive behavior of composites is studied to obtain the relationship between the main variables of matrix and reinforcements. It is concluded that the flow strength of composites is strongly influenced by volume fraction, aspect ratio of reinforcement, and the strain hardening exponent of matrix. An analytical constitutive relation of composites is obtained. The predicted results are in agreement with the existing experimental and numerical results. The project supported by the National Natural Science Foundation of China (19704100) and National Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

含旋转椭球形夹杂复合材料的弹塑性本构关系

在体胞模型的基础之上应用解析方法分析了颗粒或短纤维增强复合材料的本构行为，结合数值计算给出了表征材料本构关系的解析表达式，提出了一种新的正交椭球坐标变换以简化推导过程，在计算中，将真实位移场分为两部分：基本场的扰动场，然后通过摄动方法将原来的非线性问题转化为一组线性方程组的求解，计算了当基体材料和夹杂的特征参数取不同值时的应力应变曲线，并与已有的实验和分析结果进行了比较，符合得较好，通过对数值计算结果的拟合，提出了一个颗粒或短纤维增强复合材料的弹塑性本构关系的解析表达式。     

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.      

On constitutive modelling of porous neo-Hookean composites

In this paper a hyperelastic constitutive model is developed for neo-Hookean composites with aligned continuous cylindrical pores in the finite elasticity regime. Although the matrix is incompressible, the composite itself is compressible because of the existence of voids. For this compressible transversely isotropic material, the deformation gradient can be decomposed multiplicatively into three parts: an isochoric uniaxial deformation along the preferred direction of the material (which is identical to the direction of the cylindrical pores here); an equi-biaxial deformation on the transverse plane (the plane perpendicular to the preferred direction); and subsequent shear deformation (which includes “along-fibre” shear and transverse shear). Compared to the multiplicative decomposition used in our previous model for incompressible fibre reinforced composites [Guo, Z., Peng, X.Q., Moran, B., 2006, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971], the equi-biaxial deformation is introduced to achieve the desired volume change. To estimate the strain energy function for this composite, a cylindrical composite element model is developed. Analytically exact strain distributions in the composite element model are derived for the isochoric uniaxial deformation along the preferred direction, the equi-biaxial deformation on the transverse plane, as well as the “along-fibre” shear deformation. The effective shear modulus from conventional composites theory based on the infinitesimal strain linear elasticity is extended to the present finite deformation regime to estimate the strain energy related to the transverse shear deformation, which leads to an explicit formula for the strain energy function of the composite under a general finite deformation state.     

Thermomechanical properties of smart composites

The smart composite materials reinforced by SMA show a high performance and special deformation behavior. The thermomechanical constitutive formulas of the composites are derived by means of Eshelby's equivalent inclusion method and Mori-Tanaka's mean field concept. The interaction between the inclusion and crack and toughening mechanism are considered and the energy release rate of a crack in the smart composite is calculated. This work shows that there are the multiple mechanisms contributing to the toughening of the smart composite materials reinforced by SMA.This project is supported by the National Natural Science Foundation of China.     

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp.     

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.     

A homogenization theory for time-dependentnonlinear composites with periodic internal structures

A homogenization theory for time-dependent deformation such as creep andviscoplasticity of nonlinear composites with periodic internal structures is developed. To beginwith, in the macroscopically uniform case, a rate-type macroscopic constitutive relation betweenstress and strain and an evolution equation of microscopic stress are derived by introducing twokinds of Y-periodic functions, which are determined by solving two unit cell problems.Then, the macroscopically nonuniform case is discussed in an incremental form using thetwo-scale asymptotic expansion of field variables. The resulting equations are shown to beeffective for computing incrementally the time-dependent deformation for which the history ofeither macroscopic stress or macroscopic strain is prescribed. As an application of the theory,transverse creep of metal matrix composites reinforced undirectionally with continuous fibers isanalyzed numerically to discuss the effect of fiber arrays on the anisotropy in such creep.     

Elastic-plastic constitutive relation of particle reinforced composites

In this paper, a systematic approach is proposed to obtain the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC). The strain energy density of PRC is analyzed based on the cell model, and the analytical formula for the macro-constitutive relation of PRC is obtained. The strength effects of volume fraction of the particle and the strain hardening exponent of matrix material on the macro-constitutive relation are investigated, the relation curve of strain versus stress of PRC is calculated in detail. The present results are consistent with the results given in the existing references. The project supported by the National Natural Science Foundation of China (No. 19704100) and National Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20).     

Micromechanics-based constitutive modeling for unidirectional laminated composites

A micromechanics-based constitutive model is developed to predict the effective mechanical behavior of unidirectional laminated composites. A newly developed Eshelby’s tensor for an infinite circular cylindrical inclusion [Cheng, Z.Q., Batra, R.C., 1999. Exact Eshelby tensor for a dynamic circular cylindrical inclusion. J. Appl. Mech. 66, 563–565] is adopted to model the unidirectional fibers and is incorporated into the micromechanical framework. The progressive loss of strength resulting from the partial fiber debonding and the nucleation of microcracks is incorporated into the constitutive model. To validate the proposed model, the predicted effective stiffness of transversely isotropic composites under far field loading conditions is compared with analytical solutions. The constitutive model incorporating the damage models is then implemented into a finite element code to numerically characterize the elastic behavior of laminated composites. Finally, the present predictions on the stress–strain behavior of laminated composite plate containing an open hole is compared with experimental data to verify the predictive capability of the model.     

Homogenization estimates for fiber-reinforced elastomers with periodic microstructures

This work presents a homogenization-based constitutive model for the mechanical behavior of elastomers reinforced with aligned cylindrical fibers subjected to finite deformations. The proposed model is derived by making use of the second-order homogenization method [Lopez-Pamies, O., Ponte Castañeda, P., 2006a. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I—theory. J. Mech. Phys. Solids 54, 807–830], which is based on suitably designed variational principles utilizing the idea of a “linear comparison composite.” Specific results are generated for the case when the matrix and fiber materials are characterized by generalized Neo-Hookean solids, and the distribution of fibers is periodic. In particular, model predictions are provided and analyzed for fiber-reinforced elastomers with Gent phases and square and hexagonal fiber distributions, subjected to a wide variety of three-dimensional loading conditions. It is found that for compressive loadings in the fiber direction, the derived constitutive model may lose strong ellipticity, indicating the possible development of macroscopic instabilities that may lead to kink band formation. The onset of shear band-type instabilities is also detected for certain in-plane modes of deformation. Furthermore, the subtle influence of the distribution, volume fraction, and stiffness of the fibers on the effective behavior and onset of macroscopic instabilities in these materials is investigated thoroughly.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

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.     

Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al–SiC composite cylinder

The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.     

An approach for prediction of the elasto-plastic behavior of particulate reinforced composites

A numerical approach is presented in this paper for the calculation of the elasto-plastic deformation behavior of particulate reinforced composites. The effect of shape and arrangement of particulate on the elastic modulus and tensile deformation behavior were estimated. The approach presented can consider the shape and arrangement effect of reinforcement particulate via a simple parameter called the geometrical factor (Gf). Elastic moduli and tensile deformation estimations for the particulate reinforced composites were studied. The results of proposed approach were in very good agreement with the results of finite element analysis.     

2124 Al/SiC_p复合材料的动态变形行为及微结构效应

研究了在动态压缩时２１２４Ａｌ／ＳｉＣｐ复合材料的变形行为与微结构效应．分析结果表明，对于给定材料，复合材料的流动应力主要取决于微结构尺度效应．若增强相尺寸，基体晶粒尺寸以及增强相间距三者大小相当，则复合材料的流动应力取决于增强相的分散程度和位错密度；若增强相尺寸及其间距大小相当，但比基体晶粒大得多，那复合材料的流动应力主要取决于增强相的分散度．微观观测发现在同样加载条件下，变形局部化更容易在含较小碳化硅颗粒的复合材料内形成；变形区内的微损伤几乎都是基体与粒子界面脱粘和粒子角点邻近的微裂纹．对于所研究的这类复合材料，弹性模量及应变硬化几乎不受增强颗粒尺寸影响．     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations(BIE)and solved with the newly developed boundary point method(BPM).The model is closely derived from the concept of the equivalent inclusion of Eshelby tensors.Eigenstrains are iteratively determined for each short.fiber embedded in the matrix with various properties via the Eshelby tensors,which can be readily obtained beforehand either through analytical or numerical means.As unknown variables appear only on the boundary of the solution domain,the solution scale of the inhomogeneity problem with the model is greatly reduced.This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM.The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element(RVE),showing the validity and the effectiveness of the proposed computational modal and the solution procedure.