Effect of Magnetic Inclusions on the Effective Magnetostriction of Bulk Superconductors

A simple model is presented based on the Kim–Anderson model to further investigate the dependence of the effective magnetostriction of magnetic inclusion-superconducting matrix system on both the elastic and magnetic parameters including the elastic modulus, permeability, and volume fraction. The effect of the permeability on the magnetostriction is also obtained by implementing the continuity conditions of displacement and strain at the interface between the inclusion and the matrix through the magnetostriction loop. The results indicate that a stiffer inclusion can decrease the effective magnetostriction no matter whether the inclusion is magnetic or not and a larger effective magnetostriction can be obtained by choosing the matrix with a higher permeability, which gives an explanation about why the composite made from a matrix with a high permeability but a negligibly small magnetostriction yields unexpectedly low magnetostriction. Of particular interest is that in a certain range the effective magnetostriction of composites can be enhanced until it is saturated by increasing the permeability of matrix.     

Variations of the Effective Magnetostriction with Annealing Conditions for Nanocrystalline Magnetic Alloys

A theoretical model of effective magnetostriction for nanocrystalline magnetic alloys was proposed considering the effects of impurity phases. The dependence of effective magnetostriction on the volume fraction of different components determined by annealing conditions was analyzed. Moreover, the phenomenon that the effective magnetostriction has a valley value which can??t be explained previously was interpreted perfectly by using this model. The results of theoretical analysis are in excellent agreement with existing experimental data.     

Mechanical Behaviors of a Cylindrical Superconducting Composite with Transport Current

The stress, displacement, and magnetostriction induced by flux pinning for a superconducting composite cylinder, which is consisted of two concentric shells with different critical current densities, are calculated analytically in the presence of transport current. Firstly, both the flux and current distributions are given for increasing and decreasing transport current cases by adopting the Bean model. Then the elastic solutions to stress, displacement and magnetostriction are obtained by using plane strain approach. Finally, lots of numerical results on these mechanical behaviors (including the cases of inner superconducting shell being replaced by an elastomer and/or by a hole) are displayed graphically and analyzed in detail. Numerical results show that, among others, during the transport current reduction, tensile stress especially radial tensile stress will occur in the outer region of the composite, and that in general, displacement is always negative in the superconducting composite with transport current. In addition, different to homogeneous superconducting cylinder, as the applied maximal transport current exceeds outer-cylinder critical current, the hysteresis loop of the magnetostriction exists for the full cycle of the transport current. Moreover, different to superconducting composite (including the case of the inner shell being an elastomer), the inner hole has significant effects on both the stress and displacement distributions of the outer superconducting shell, and for a hollow superconductor, the magnetostriction loop still exists even if the maximal transport current does not exceeds the its critical current.     

C/C复合材料液相浸渍制备工艺及其力学性能模拟

针对酚醛先驱体C/C复合材料液相浸渍制备工艺各组分相的化学转化特性, 基于Arrhenius方程建立了C/C复合材料液相浸渍制备工艺力学模型, 详细分析了固化-炭化和石墨化两个重要的工艺阶段各组分相的体积变化规律, 得到的气孔体积分数与Micro-CT系统扫描处理的细编穿刺C/C复合材料微结构图像中气孔体积分数相吻合, 并结合均匀化方法对制备过程材料基体有效弹性模量进行了预测。结果表明: 材料基体的有效弹性模量随着致密化次数的增加而增大, 在每一次致密化过程中材料基体的有效弹性模量先增大后减小, 石墨化工艺过程中材料基体的有效弹性模量达到某一值后保持平稳。      

考虑界面影响的混凝土弹性模量的数值预测

提出了一种考虑界面过渡层影响的混凝土弹性模量的数值预测方法。将球形骨料与包裹它的界面过渡层作为二相复合球结构的等效颗粒,由广义自洽方法计算不同粒径骨料与界面过渡层组成复合球的有效模量。然后由等效颗粒生成的随机骨料模型建立体积表征单元,施加均匀位移边界条件,通过数值方法计算该体积表征单元中的应力和应变场,由细观力学数值均匀化方法预测体积表征单元的有效弹性模量。计算结果表明:对于不同骨料含量的混凝土,有效弹性模量的预测值与试验值非常接近,界面过渡层的厚度对混凝土的整体弹性性质有较大影响。     

二维二轴编织复合材料几何模型及弹性性能预测

提出了二维二轴1×1和2×2编织复合材料的几何模型,模型考虑了纤维束的相互挤压及横截面的变化。基于细观分析和体积平均法,建立了预测二维二轴编织复合材料弹性性能的理论分析方法。数值结果与试验结果吻合,表明该方法行之有效,且具有运算快、精度高、适合工程分析等优点。分析了编织角、纤维体积含量和纤维束横截面形状对材料弹性常数的影响。研究表明,编织角对弹性常数的影响具有互补性,材料弹性模量与纤维体积含量成正比,纤维束截面形状变化对材料弹性常数影响不大。     

树脂基稀土-铁系超磁致伸缩复合材料的磁致伸缩及其高频磁性能

以粉末粘结、模压成型方法,研制了0-3型的E-44环氧树脂基稀土-铁系超磁致伸缩复合材料。采用电阻应变片技术与Agilent 4294A型动态阻抗分析仪,研究了超磁致伸缩合金/环氧树脂复合材料的磁致伸缩性能及高频磁性能,并对所制备的磁致伸缩复合材料的磁导率、截止使用频率等随频率和树脂体积分数的变化规律进行了系统研究。结果表明:树脂的添加,不仅可以提高复合材料的截止频率和高频磁性能,使其具有良好的高频响应特性,其截止频率达30 MHz以上;而且通过适当选择树脂的体积分数,复合材料仍能保持良好的磁致伸缩性能,当树脂体积分数分别为20%、30%时,磁致伸缩系数分别达808×10-6、821×10-6,而当复合材料中树脂的体积分数为50%时,其磁致伸缩系数仍高达592×10-6。探讨了树脂/磁致伸缩复合材料的磁电耦合机制。      

结晶聚合物基纳米复合材料多层次结构及有效性能预测

根据结晶聚合物基纳米复合材料实验分析．将结晶聚合物基纳米复合材料内部结构分别用宏观、细观和纳观三个层次来描述。利用数学上的渐近均匀化理论,结合有限元方法,经二次纳观层次的均匀化和一次细观层次的均匀化,预测了聚合物基纳米复合材料的有效性能。并用FORTRAN语言编写了计算程序。具体分析了聚合物的结晶度、聚合物结晶相的弹性模量、纳米颗粒的弹性模量和纳米颗粒的体积分数等参数对结晶聚合物基纳米复合材料有效性能的影响,得到了一些有意义的结论,对指导结晶聚合物基纳米复合材料的制备有一定的指导作用。     

基于周期性边界条件的炭黑填充橡胶复合材料力学行为的预测

在分析炭黑填充橡胶复合材料的宏观与细观特征之间联系的基础上,提出了具有随机分布形态的代表性体积单元,推导并应用了周期性细观结构的边界约束条件,建立了三维多颗粒夹杂代表性体积单元的数值模型,对炭黑填充橡胶复合材料的宏观力学行为进行了模拟仿真。研究表明,该模型通过周期性边界条件的约束保证了宏观结构变形场和应力场的协调性;计算得到的炭黑填充橡胶复合材料的弹性模量明显高于未填充橡胶材料,并随着炭黑颗粒所占体积分数的增加而增大;该模型对复合材料有效弹性模量的预测结果与实验结果吻合较好,而且比Bergstrom三维模型的预测结果更好,证实了该模型能够用于炭黑颗粒增强橡胶基复合材料有效性能的模拟分析。     

中空纳米夹杂填充复合材料的反平面问题

研究了中空纳米夹杂填充复合材料的反平面问题。基于Gurtin-Murdoch表/界面理论和广义自洽方法, 给出了考虑夹杂界面效应时空隙-夹杂-基体-等效介质模型的全场精确解, 并推导了中空纳米夹杂填充复合材料有效反平面剪切模量的闭合形式解。由本文结果的特殊情形, 可以得到一系列有意义的解。数值结果表明: 中空夹杂的尺寸在纳米量级时, 复合材料的有效反平面剪切模量受表/界面效应影响显著; 表/界面效应的影响随着夹杂尺寸的增大而逐渐减弱; 当中空纳米夹杂的体积分数和外半径一定时, 壁厚越薄其表/界面效应越大; 在相同的夹杂外半径下, 中空纳米夹杂填充复合材料的表/界面效应比实心纳米夹杂填充复合材料更加明显; 无量纲反平面剪切模量受夹杂的表/界面性能和刚度影响显著, 过高的夹杂刚度使得表/界面效应的影响变弱。      

数值模拟碳纳米管增强铝基复合材料的力学性能

本文根据连续介质理论,采用代表性体积元的方法计算了碳纳米管增强铝基复合材料的力学性能。使用有限元软件ABAQUS对代表性体积元模型进行分析,研究了不同碳纳米管体积分数对复合材料弹性模量、屈服强度、泊松比及剪切模量的影响。结果表明碳纳米管体积分数对复合材料力学性能有显著影响,随着碳纳米管体积分数的增加,复合材料的弹性模量、屈服强度及剪切强度都明显提高,泊松比略有下降。     

Calculating the elastic moduli of steel-fiber reinforced concrete using a dedicated empirical formula

The equivalent inclusion method (EIM) is adopted to study the characteristics of the equivalent material properties of steel-fiber reinforced concrete as a function of the volume fraction and the length to diameter ratio of the fibers. It is found that the equivalent material moduli of concrete reinforce with randomly orientated and distributed fibers are insensitive to the length to diameter ratio of the steel fibers. A set of empirical formulae is then proposed for the purposes of engineering applications. The proposed empirical model can simplify the calculation of the equivalent material moduli. Verifications of the proposed empirical formulae with the EIM model and with experimental data are performed with two examples. The first is a compression test. The second is 4 point bending test. The empirical formulae, based on the equivalent inclusion method proposed in this study, represent an alternative means of quickly calculating the effective elastic modulus of steel-fiber reinforced concrete materials.     

Effective elastic modulus and micro-structure damage of particle-reinforced composites

A new analysis method of effective elastic modulus for composites has been developed by combining Eshelby’s equivalent inclusion method and self-consistent method. The equations obtained can describe the evolution of debonding damage of the composites with multi-phase particles and single-phase particles. Based on the incremental relation between particles and the matrix, the incremental constitutive relations of composite, matrix, particles and voids have been developed. Numerical analysis has been conducted for Ramburg–Qsgood function incorporating with equivalent elastic modulus obtained. The constitutive equation curves for different particle volume fractions can describe the influence of debonding damage on effective elastic modulus of the composites. Numerical results of the present study have a better agreement with the experimental results.     

炭黑填充型导电复合材料的压阻计算模型及实验验证

为研究新型传感器材料,在通用有效介质理论的基础上,提出了炭黑填充型导电复合材料的压阻特性数学计算模型,定量地得出炭黑颗粒的基本特征参数、体积分数和聚合物基体的弹性模量在复合材料压阻规律中的影响。分别以硅橡胶和高密度聚乙烯为基体相,三种不同粒径的炭黑为导电相,制备了炭黑填充型复合材料,对计算模型进行了实验验证。在炭黑颗粒分布均匀、炭黑体积分数在渗流阈值附近和外加压力≤2 MPa等三个边界条件下,数学计算模型与实验结果基本吻合,且压力-电阻变化规律一致。      

Temperature dependence of the elastic constants of niobium and lead in the normal and superconducting states

The temperature dependence of the elastic constants of niobium and lead was measured in the normal and superconducting states. Both a continuous wave and a coherent gated-carrier technique were used to measure the velocity changes associated with the superconducting transition. The elastic constants were found to exhibit the same temperature dependence as the free energy in either state. The discontinuity in the modulus associated with longitudinal strains and the slope discontinuities at the transition temperature were used to calculate the strain dependence of the transition temperature. The strain dependence in all cases is mainly quadratic.Research supported by a NSF Grant and in part by the Office of Naval Research.     

Successive iteration method applied to composites containing sliding inclusions: effective modulus and anelasticity

The effective shear modulus and Poisson's ratio of a body containing spherical sliding inclusions are calculated. First, the amount of sliding on the surface of a single spherical sliding inclusion is determined so that the tangential traction of the stresses due to the sliding, the Somigliana dislocations, cancels that of the external stresses on the surface of the inclusion. Next, the influence of other inclusions is accounted for by using a successive iteration method based on the average field theory. The successive iteration converges into closed forms, leading to analytical forms of the effective elastic constants. It is shown that the sliding occurs in a first order kinetics, the relaxation time of which is proportional to the radius of the inclusions with a constant depending on the volume fraction of the inclusions. The two-dimensional problem of a body containing aligned cylindrical fibers is also solved.     

An n-layered spherical inclusion model for predicting the elastic moduli of concrete with inhomogeneous ITZ

An n-layered spherical inclusion model is presented in this paper for predicting the elastic moduli of concrete with inhomogeneous interfacial transition zone (ITZ). In this model, concrete is represented as a three-phase composite material, composed of the aggregate, bulk paste, and an inhomogeneous ITZ. An analytical solution for the ITZ volume fraction is derived for the general aggregate gradation. By constituting a semi-empirical initial cement gradient model, the local water/cement ratio, degree of hydration, and porosity at the ITZ are estimated. The inhomogeneous ITZ is then divided into a series of homogenous concentric shell elements of equal thickness. The elastic moduli of concrete are determined by solving the n-layered spherical inclusion problem. Finally, the validity of the model is verified with three independent sets of experimental data and the effects of the maximum aggregate diameter, aggregate gradation, and ITZ thickness on the Young’s modulus of concrete are evaluated in a quantitative manner. The paper concludes that the proposed n-layered spherical inclusion model can be used to predict the elastic moduli of concrete.     

具有开孔泡沫骨架的双连续相复合材料弹性模量的理论预测

基于具有开孔泡沫骨架的双连续相复合材料(IPC)的细观结构,提出了一种十四面体弹性地基梁力学模型,结合最小势能原理推导了该IPC的弹性模量预测公式。根据文献给出的实验材料参数进行算例分析,结果表明,理论估算结果与实验值吻合良好,证明了该模型的有效性。在此基础上,进一步讨论了不同骨架材料体积含量和支柱截面形状对IPC弹性模量的影响。本文给出的半经验理论模型为表征具有开孔泡沫骨架的IPC的弹性性能提供了新思路,也为进一步预测IPC的强度性能和热物理性能奠定了基础。     

Laguerre tessellations for elastic stiffness simulations of closed foams with strongly varying cell sizes

The dependency of the elastic stiffness, i.e., Young’s modulus, of isotropic closed-cell foams on the cell size variation is studied by microstructural simulation. For this purpose, we use random Laguerre tessellations which, unlike classical Voronoi models, allow to generate model foams with strongly varying cell sizes. The elastic stiffness of the model realizations is computed by micro finite element analysis using shell elements. The main result is a moderate decrease of the effective elastic stiffness for increasing cell size variations if the solid volume fraction is assumed to be constant.     

Some Further Considerations about the Theory of Elastic Stress Transfer from Partially Embedded Axially Loaded Fiber to Matrix

In this paper the elastic stress transfer from the fiber to the matrix is analysed for fiber-reinforcedcomposites when the fiber is loaded axially.The dependence of the elastic stress transfer on the as-pect ratio of the fiber,the volume fraction of the fiber,the fiber-to-matrix elastic modulus ratio andthe Poisson's ratio of the fiber and the matrix has been shown in detail.