冲击作用下含孔洞纤维增强复合材料平板的动力学实验与数值研究

作为复合材料动力学实验与数值研究的应用实例 ,实验研究采用正交异性动态光弹性方法 ,数值分析运用各向异性介质的时域边界元方法。纤维增强光弹性复合材料平板被用来模拟含孔洞的正交异性半无限域 ,用小口径步枪施加与纤维方向成 0及 90两个方向的冲击载荷 ,在正交异性动态光弹性实验中记录了应力波在孔洞周围的传播、反射与绕射过程 ,此过程被进一步转换成应力分量的变化时程 ,并与相应的时域边界元方法的数值分析结果进行了比较。     

缺陷岩体中弹性波传播的多次散射效应分析

弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响,建立了双椭圆缺陷模型,基于Green函数基本解,采用边界积分的计算方法,得到了反映缺陷界面条件的刚度矩阵,分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明：与单椭圆缺陷模型相比,双缺陷的相互作用使得弹性波频散和衰减效应增强,定量给出了缺陷的影响区域,从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应,结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关,存在明确的定量关系。相应的数值模拟结果表明,弹性波和缺陷相互作用在缺陷界面上诱发界面波,该界面波也存在频率相关性,影响了弹性波宏观传播的频散和衰减特征。     

考虑界面行为的SMA纤维复合材料模型

构造了一个考虑部分界面开脱情况下SMA长纤维复合材料的双圆柱模型.在理想界面区域SMA纤维所受的轴力恒定,而在开脱区域则考虑为受线性变化轴力.计算结果表明,开脱区长度及临界界面剪应力只对SMA纤维的相变区有很明显的影响,而对母相及马氏体相的弹性变形区没有影响.这对进一步研究SMA纤维增强复合材料的性能提供理论帮助.     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

纤维排列方式对单向纤维加强复合材料弹性常数的影响

本文应用GMC方法计算了纤维在规则排列和随机排列时单向纤维加强复合材料的总体弹性系数，结果表明，在一定纤维体积比范围内，虽然纵向弹性模量不受纤维排列方式的影响，但是复合材料的横向弹性模量和横向剪切模量受纤维排列方式的影响较大，所以，在考察复合材料的横向弹性常数时，应该考虑纤维排列方式的影响，在相同纤维比的情况下，正方形排列和正方形对角排列所得的弹性常数是上下界，而六角形排列和随机排列的结果位于以上两者之间，当纤维比较小时（小于20％），纤维的排列方式对各弹性常数均无明显影响，本文的结果在工程应用中有指导意义。     

含有多个涂层压电纤维复合材料的平面问题研究

压电纤维在未来的复合材料结构健康监测中具有重要作用．本文基于横观各向同性压电材料位移和应力连续条件以及经典的复势函数理论,讨论了同时受到平面内机械载荷和出平面电载荷作用时含有多个带涂层压电纤维的无限大线弹性基体的平面力学问题．首先将线弹性基体、涂层和压电纤维的应力场、位移场表示成复势函数,然后通过横观各向同性压电材料和线弹性材料的位移和应力连续条件确定复势函数表达式．将得到的复势函数表达式代入线弹性基体、涂层和压电纤维的的应力场、位移场公式可确定其应力场和位移场．最后,通过定量的案例讨论了涂层的材料属性对线弹性基体应力场的影响．案例分析表明涂层的材料属性对压电复合材料的应力场有重要的影响．     

舰用轻型复合装甲结构及其抗弹实验研究

采用纤维增强复合材料(简称FRC)板前置船体结构钢(简称C型钢)板模拟舰用轻型复合装甲结构,对有间隙和无间隙复合装甲结构以及不同纤维增强复合材料防弹板进行了打靶实验研究,实验测试了不同纤维增强复合材料防弹板以及有间隙和无间隙复合装甲结构抗弹丸穿甲的吸能量。结果表明:FRC板较C型钢板有明显的抗弹优势;弹丸速度和形状对FRC板的抗弹性能有较大影响;基体种类和基体含量对FRC板的抗弹性能有一定影响;FRC板与C型钢板之间间距的增大将有利于组合靶板综合抗弹能力的提高。     

纤维增强复合材料的轴对称横向裂纹分析

从弹性力学解出发,借助积分变换将纤维和基体内的位移场和应力表示成以裂纹面上位错函数为未知量的积分形式。由边界条件纤维增强复合材料三维轴对称裂纹问题化成求解一组奇异积分方程的问题。     

玄武岩中裂隙分布形式对声波传播的影响

复杂岩体含有大量的裂隙,这些裂隙尺寸及其分布形式等对弹性波传播都有很大的影响.本文加工了含单个裂隙、双裂隙和三个裂隙的玄武岩岩样单元对其进行组合,进行了25kHz、 50kHz、 400kHz、 600kHz和1000kHz 等5种频率的声波测试.通过考虑垂直或平行波传播方向的裂隙长度,来探索裂隙分布形式和不同裂隙长度对弹性波传播的影响,研究玄武岩的频散效应和波的衰减.结果表明:裂隙方向与波传播方向夹角对弹性波传播有很大的影响.当裂隙方向与波传播方向垂直时,散射效应最大;而当裂隙方向与波传播方向平行时,影响最小.上述结果可为理论模型和数值分析提供依据.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

MULTIPLE SCATTERING AND DYNAMIC STRESS ANALYSIS OF ELASTIC WAVES IN A FIBER—REINFORCED COMPOSITE WITH INTERFACES

Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber-reinforced composite are studied. The analytical expressions of elastic waves in different regions are presented. The mode coefficients of elastic waves are determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi-interfaces. By using the addition theorem of Hankel functions, the formula of scattered wave fields in different local coordinates are transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors (DSCFs). The influences of the distance between two inclusions, material properties and structural size on the DSCFs near the interfaces are analyzed. As examples, the numerical results of DSCFs near the interfaces for two kinds of fiber-reinforced composites are presented and discussed. The project supported by the National Natural Science Foundation of China (19972018)     

Intensity of singular stress at the fiber end in a hexagonal array of fibers

To evaluate the mechanical strength of fiber-reinforced composites it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. The singular stress field is controlled by generalized stress intensity factor (GSIF) defined at the fiber end. In this study, periodic and zigzag arrays of cylindrical inclusions under longitudinal tension are considered in comparison with the results for a single fiber. The unit cell region is approximated as an axi-symmetric cell; then, the body force method is applied, which requires the stress and displacement fields due to ring forces in infinite bodies having the same elastic constants as those of the matrix and inclusions. The given problem is solved on the superposition of two auxiliary problems under different boundary conditions. To obtain the GSIF accurately, the unknown body force densities are expressed as piecewise smooth functions using fundamental densities and power series. Here, the fundamental densities are chosen to represent the symmetric stress singularity, and the skew-symmetric stress singularity. The GSIFs are systematically calculated with varying the elastic modulus ratio and spacing of fibers. The effects of volume fraction and spacing of fibers are discussed in fiber-reinforced plastics.     

Propagation of one-dimensional elastoviscoplastic waves in composite materials

We consider the problems of propagation of elastic and elastoviscoplastic waves in laminated and fiber composites on the basis of the two-velocity model proposed in [1]. We study plane waves propagating parallel to the fibers and waves propagating in the perpendicular direction. We compare our solutions with the experimental results presented in the literature [2, 3] for several specific composites (carbon-filled plastics, boron plastics, and wolfram fibers in aluminum matrix). The coincidence between the theoretical results and experimental data is shown to be good. To understand the typical features of propagation of nonstationary waves in composites, we solved several one-dimensional problems about the propagation of both elastic and elastoviscoplastic waves in laminated and fiber composites. We compare the solutions obtained using the one-velocity and two-velocity models [1, 4] with the results of experiments and the results obtained in the literature using different models, which permits estimating the accuracy of both models and the numerical method in question. We use the numerical method of characteristics to improve the accuracy of calculations in the solution of the resulting systems of hyperbolic equations.     

Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Many composite materials, including biological tissues, are modeled as non-linear elastic materials reinforced with elastic fibers. In the current paper, the full set of dynamic equations for finite deformations of incompressible hyperelastic solids containing a single fiber family are considered. Finite-amplitude wave propagation ansätze compatible with the incompressibility condition are employed for a generic fiber family orientation. Corresponding non-linear and linear wave equations are derived. It is shown that for a certain class of constitutive relations, the fiber contribution vanishes when the displacement is independent of the fiber direction.Point symmetries of the derived wave models are classified with respect to the material parameters and the angle between the fibers and the wave propagation direction. For planar shear waves in materials with a strong fiber contribution, a special wave propagation direction is found for which the non-linear wave equations admit an additional symmetry group. Examples of exact time-dependent solutions are provided in several physical situations, including the evolution of pre-strained configurations and traveling waves.     

含大量随机分布细小纤维的单向纤维增强复合材料横向弹性性能参数计算的内嵌区域模型法

利用有限元方法求取单向纤维增强复合材料的横向弹性性能参数的计算模型包括三维模型、两维平面应变模型、单胞模型等等.由于单胞模型仅仅适用于纤维规则排列情况.在纤维随机分布且纤维大小亦为随机时,单向纤维增强复合材料横向弹性性能参数必须通过对于复合材料块体的计算才能获得.同时在随机分布纤维的数量增大时,三维模型和二维平面应变模型的计算量急剧增加,模型的处理能力不强.该文提出一种利用内嵌区域模型来计算含大量随机大小、随机分布细小纤维的单向纤维增强复合材料块体的横向弹性性能参数的方法,有效降低了计算量.在较低的计算费用下,能够快速获得单向纤维增强复合材料的横向弹性性能参数.     

Elastic waves in a fiber-reinforced composite

The propagation of time-harmonic elastic waves in a fiber-reinforced composite is studied. The circular fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. The direction of propagation and the associated particle motion are considered to be normal to the fibers. It is shown that the average waves in the composite separate into compressional and shear types. General formulae for the complex wave number giving the phase velocity and the damping are obtained. It is shown that these formulae lead to the Hashin-Rosen expressions for the transverse bulk modulus and the lower bound for the transverse rigidity, if the correlation in the positions of the fibers can be ignored. The correlation terms, for exponential correlation, are shown to have a significant effect on the damping property of the composite, especially at high frequencies and concentrations.     

Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

The propagation of oscillatory waves through periodic elastic composites has been analysed on the basis of the Floquet theory. This leads to self-adjoint differential equation systems which it was proved convenient to solve by variational methods. Many composites, such as the light-weight high-strength boron-epoxy material, consist of strong reinforcing components in a plastic matrix. The latter can exhibit viscoelastic properties which can have a significant influence on wave propagation characteristics. Replacement of the elastic constant by the viscoelastic complex modulus changes the mathematical structure so that the differential equation system is no longer self-adjoint. However, a modification of the variational principles is suggested which retains formal self-adjointness, and yields variational principles which contain additional boundary terms. These are applied to the determination of wave speeds and mode shapes for a laminated composite made of homogeneous elastic reinforcing plates in a homogeneous viscoelastic matrix for plane waves propagating normally to the reinforcing plates. These results agree well with the exact solution which can be evaluated in this simple case. The variational principles permit solutions for periodic, but otherwise arbitrary variation of material properties.     

Simulation of crack propagation in fiber-reinforced bulk metallic glasses

Based on a phase-field model for deformation in bulk metallic glasses (BMGs), shear band formation and crack propagation in the fiber-reinforced BMG are investigated. Ideal unbroken fibers embedded in the BMG matrix are found to significantly influence the shear banding and crack propagation in the matrix. The crack propagation affected by fibers’ length and orientation is quantitatively characterized and is described by micromechanics models for composite materials. Furthermore, fractures in some practical fiber-reinforced BMG composites such as tungsten-reinforced Zr-based BMG are simulated. The relation between the enhanced fracture toughness and the mechanical properties of fiber reinforcements is determined. Different fracture modes of BMG-matrix composites are identified from the systematic simulation studies, which are found to be consistent with experiments. The simulation results suggest that the phase-field modeling approach could be a useful tool to assist the fabrication and design of BMG composites with high fracture toughness and ductility.     

Effect of negative permeability on elastic wave propagation in magnetoelastic multilayered composites

With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wave propagation in magnetoelastic multilayered composites with negative permeability as comparecd to those in counterpart structures with positlve permeability. These novel properties of elastic waves are discerned from the diversified dispersion curves, which represent the propagation and attenuation characteristics of elastic waves. To compute these dispersion curves, the method of reverberation-ray matrix is extended for the analysis of elastic waves in magnctoelastic multilayered composites. Although only the results of a single piezomagnetic and a binary magnetoelastic layers with mechanically free and magnetically short surfaces as well as pelrfect interface are illustrated in the numerical examples, the analysis is applicable lo magnetoelastic multilayered structures with other kinds of boundaries/interfaces.     

Harmonic waves in one-, two- and three-dimensional composites: Bounds for eigenfrequencies

Harmonic waves in one-, two- and three-dimensional elastic composites with periodic structure are considered. Based on a new quotient recently proposed by Nemat-Nasser, lower and upper bounds for the eigenfrequencies are developed. For illustration waves propagating normal to the layers in layered composites, and normal to the fibers in fiber-reinforced composites, are considered. These examples show that the new quotient is very effective and yields very accurate results for the considered class of problems. While these results are of interest in their own right, they can be used to check the effectiveness of various approximate theories which recently have been proposed by various authors.