有限厚度模型校准二维MoS2的Bimodal-AFM杨氏模量测量

二维材料因其独特的晶体结构、新奇的物理特性和优异的力学性能, 在微纳机电系统、柔性电子器件等诸多领域有着广阔的应用前景. 弹性模量是二维材料的基本力学特性参量之一, 对其器件应用及应变调控有重要影响. 受限于二维结构和原子级厚度特征, 难以实现二维材料弹性模量的精确测量. 双模原子力显微镜的振幅调制-频率调制模式是一种高效测量二维材料杨氏模量的方法, 但刚性衬底对测量结果的影响不可忽视. 本工作通过双模原子力显微镜直接测得衬底与二维硫化钼的杨氏模量分布图, 并基于有限厚度模型对衬底效应进行修正, 得到了样品的本征杨氏模量值. 利用第一性原理计算得到了二维二硫化钼的弹性系数和杨氏模量, 对比发现实验和计算结果相当. 这说明双模原子力显微镜测量是一种可靠的二维材料杨氏模量直接测试方法, 且该方法无需制备悬空二维材料等繁琐步骤, 避免了常规测试中的不足. 本工作为大面积二维材料薄膜力学性能的程序化测试分析以及高通量力学实验数据的统计分析提供了可靠的实验基础.      

基于三相球模型确定泡沫塑料有效模量

通过复合材料三相球模型确定泡沫塑料的体积模量、剪切模量、杨氏模量和泊松比等材料等参数与材料孔隙比的关系，并将该文结果同微分法得到的结果进行了对比；结果表明：三相球模型确定的材料参数在相同孔隙比情况下，一般都高于微分法确定的结果，两种方法得到的有效剪切模量和杨氏模量差异较小，而体积模量和泊松比则差异较大，然而，由三相球模型确定的泡沫塑料杨氏模量仍可与实验较好地符合。此外，该文结果也同现有的理论及实验     

DETERMINATION OF EFFECTIVE MODULI FOR FOAM PLASTICS BASED ON THREE PHASE SPHEROIDAL MODEL

The relations of bulk modulus,shear modulus,Young's modulus and the Poisson's ra-tio with porosity of foam plastics are determined by a three phase spheroidal model commonly used inComposite Mechanics.The results are compared with those using differential scheme.It is shownthat the material properties derived from the present model normally are larger than those obtained bydifferential scheme for foam plastics with identical porosity.The differences in shear moduli andYoung's moduli obtained by the two methods are small,but they are larger for bulk moduli of incom-pressible matrix and Poisson's ratios.The Young's moduli of high density foam plastics derived by thepresent model agree better with experimental ones.     

非晶材料弛豫过程加杨氏模量的唯象研究

从晶态材料弛豫过程中模量的唯象描述的基本思想出发，同时考虑到近年来对非晶材料弛豫规律的种种研究，将传统的构造力学参数模型作为弛豫单元的作法与现在流行的双能级模型统一起来，对非晶材料弛豫过程中的杨氏模量进行了唯象处理，得到了与以往不同的弛豫规律。     

胞体椭球比对泡沫塑料力学性能的影响

本文通过数值法研究了胞体椭球比对材料模量及泊松比的影响；在单向受力情况下，研究了变形对材料孔隙度、椭球比、杨氏模量和泊松比等材料参数的影响。     

基于光纤传感器的固体杨氏模量与泊松比测量方法研究

提出了一种基于光纤传感器的测量固体材料杨氏模量与泊松比的方法,给出了Sagnac光纤干涉仪的环形光纤作为点传感器检测声波及用于声速测量的原理,推导出固体中声波速度与材料的杨氏模量及泊松比的关系式.以光纤Sagnac干涉仪作为传感器贴附于三角铸铁导轨表面,分别测出声表面波与纵波的速度,根据理论推导,得到了铸铁的杨氏模量与泊松比.实验结果与理论数值基本吻合,表明了此测量方法的可行性,为固体材料性能评估提供了一种新的方法.     

岩石时频效应的实验研究

对饱和泵油南京砂岩和饱水大理岩在MTS上进行了单轴压缩实验和正弦波加载实验,求得两种饱和岩石的单轴抗压强度和屈服强度,并获得随正弦波频率的提高,饱和泵油南京砂岩的杨氏模量、纵横波速度增大,具有较明显的频散效应.饱和岩石中的微细观缺陷在正弦波加载中引起滞后,导致瞬时杨氏模量与应力成不对称"X"形,获得随正弦波频率增高,"X"交点在模量轴上的位置增高,杨氏模量增大,模量的频散增强.本文揭示了岩石的非线性时频响应的一些物理机理,对于岩石介质中的非线性波动研究以及地震、工程等理论研究和应用都具有重要意义.     

Modeling and prediction of bulk properties of open-cell carbon foam

The emerging ultralightweight material, carbon foam, was modeled with three-dimensional microstructures to develop a basic understanding in correlating microstructural configuration with bulk performance of open-cell foam materials. Because of the randomness and complexity of the microstructure of the carbon foam, representative cell ligaments were first characterized in detail at the microstructural level. The salient microstructural characteristics (or properties) were then correlated with the bulk properties through the present model. In order to implement the varying anisotropic nature of material properties in the foam ligaments, we made an attempt to use a finite element method to implement such variation along the ligaments as well as at a nodal point where the ligaments meet. The model was expected to provide a basis for establishing a process-property relationship and optimizing foam properties.The present model yielded a fairly reasonable prediction of the effective bulk properties of the foams. We observed that the effective elastic properties of the foams were dominated by the bending mode associated with shear deformation. The effective Young's modulus of the foam was strongly influenced by the ligament moduli, but was not influenced by the ligament Poisson's ratio. The effective Poisson's ratio of the foam was practically independent of the ligament Young's modulus, but dependent on the ligament Poisson's ratio. The effective Young's modulus of the carbon foam was dependent more on the transverse Young's modulus and the shear moduli of the foam ligaments, but less significantly on the ligament longitudinal Young's modulus. A parametric study indicated that the effective Young's modulus was significantly improved by increasing the solid modulus in the middle of the foam ligaments, but nearly invariant with that at the nodal point where the ligaments meet. Therefore, appropriate processing schemes toward improving the transverse and shear properties of the foam ligaments in the middle section of the ligaments rather than at the nodal points are highly desirable for enhancing the bulk moduli of the carbon foam.     

多晶石墨烯拉伸力学性能及其影响因素的灵敏度分析

晶粒尺寸、温度和应变率等对纳米材料的力学性能有重要影响。本文通过分子动力学（MD）数值模拟,分析了不同晶粒尺寸多晶石墨烯在不同温度、拉伸应变率下的杨氏弹性模量、极限应力、极限应变等拉伸力学性能。结果表明,晶粒尺寸、温度和拉伸应变率对拉伸力学性能有较大影响。利用正交实验法,分别分析了杨氏弹性模量、极限应力和极限应变对晶粒尺寸、温度和拉伸应变率的敏感程度。结果表明,杨氏弹性模量和极限应力对影响因素的敏感程度由大到小依次为晶粒尺寸、温度和拉伸应变率;极限应变对影响因素的敏感程度由大到小依次为晶粒尺寸、拉伸应变率和温度。研究结果可为多晶石墨烯的理论研究和工程应用提供参考。     

Constitutive model for high speed tillage using narrow tools

Dynamic effects on soil–tool cutting forces are important when operating at elevated speeds. The rate-dependent behavior of narrow tillage tools was investigated in this study. A hypoelastic soil constitutive relationship with variable Young's modulus and Poisson's ratio was developed to describe the dynamic soil-tool cutting problem. An initial finite element formulation with viscous components incorporated in the stiffness matrix resulted in severe numerical oscillations. A modified model that incorporated lumped viscous components in the equation of motion (independent of the stiffness matrix) was proposed. Numerical oscillations still occurred, but at sufficiently high tool displacements (1–10 mm) to enable the determination of peak draft forces. Experimental data for flat and triangular edged narrow tools were obtained using a 9-m long linear monorail system designed to accelerate narrow tools through a linear soil bin to high speeds. Steady-state speeds from 0.5 to 10.0 m/s over a distance of 1 to 3 m were attained using this system. A reference-tool inverse procedure was used to estimate the dynamic soil parameter in the soil model using draft data obtained for the flat tool. Predictions of triangular tool draft produced correct trends but overestimated experimental data. Draft was overpredicted by less than 1% at a tool speed of 2.8 m/s and by 25% at 8.4 m/s.     

具有梯度界面层的双材料悬臂梁解析解

采用应力函数法,求得了具有弹性模量沿高度线性变化的梯度界面层的双材料悬臂梁在均布载荷作用下的应力和位移解析解。该解可退化为双材料梁、弹性模量沿整个梁高线性变化的梯度梁以及均质材料梁的情况,退化为均质材料梁时与已有结果一致。通过一具体算例将得到的解析解与有限元解进行了比较,两者吻合较好。并讨论了梯度界面层的高度变化对梁中的应力和梁端挠度的影响。结果表明,在梁的总高度不变的情况下,增加梯度界面层的高度可减小弯曲应力和梁端挠度,而对挤压应力和切应力的影响很小。     

Connexions between the moduli for anistropic elastic materials

Summary For homogeneous isotropic elastic materials there are simple interrelations connecting Young's modulus, Poisson's ratio, the rigidity modulus and the modulus of compression. However for anisotropic materials the situation is quite different. Young's modulus is a function of direction and Poisson's ratio and the rigidity modulus are functions of pairs of orthogonal directions. Here some simple universal connexions between the moduli for various directions are simply derived for general anisotropic materials. No particular symmetry is assumed in the material.     

梯度弹性基础上正交异性薄板的屈曲分析

基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K₁ 与K₂的计算式;进而,通过将位移函数采用三角函数展开的方法,给出了单向压缩载荷作用下、四边简支正交异性弹性基础板屈曲载荷的计算式;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.     

Predicting the elastic properties of single-walled carbon nanotubes

Advances in the prediction of the mechanical properties of single-walled carbon nanotubes (SWNTs) are reviewed in this paper. Based on the classical Cauchy-Born rule, a new computational method for the prediction of Young's modulus of SWNTs is investigated. Compared with the existing approaches, the developed method circumvents the difficulties of high computational efforts by taking into consideration of the microstructure of nanotube and the atomic potential of hydrocarbons. Numerical results of Young's modulus and its variation with respect to the deformation gradient tensor are given and discussed. The results obtained are in good agreement with those obtained by laboratory experiments and other numerical methods.     

基于近场动力学的单晶冰弹性各向异性数值模拟方法

天然冰材料在变形与破坏行为上的各向异性特征是冰与结构相互作用中产生复杂载荷过程的关键诱因, 而天然冰各向异性的根源则在于单晶冰的各向异性. 目前, 学术界针对单晶冰各向异性的数值模拟方法研究仍较为缺乏. 为了准确再现天然冰材料的特殊力学性质, 本文基于近场动力学理论, 提出了一种单晶冰弹性各向异性的数值模拟方法. 该方法的核心思想是将单晶冰杨氏模量沿不同加载方向的变化规律引入到近场动力学力密度向量的影响函数中. 以前人实验测试得到的杨氏模量值为参考, 通过开展与C轴呈0°, 45°和90°三个加载方向的单晶冰单轴压缩数值模拟实验, 提出了针对该影响函数的修正和辅助参数标定方法, 最终在15°, 30°, 60°和75°等其他四个加载方向进行了验证. 结果表明: 本文提出的针对影响函数的修正与参数标定方法, 能够较为便捷地找到数值模型杨氏模量与参考杨氏模量相一致的影响函数最优解, 即本文提出的基于影响函数的近场动力学数值模拟方法, 能够合理、准确地模拟单晶冰的弹性各向异性行为. 本文研究成果可为后续多晶冰各向异性数值模拟方法的建立提供基础性参考.      

Effect of Oxidation-Induced Material Parameter Variation on the High Temperature Oxidation Behavior of Nickel

In high temperature oxidation environment, the oxidation reaction will induce variations in material parameters, such as Young's modulus, thermal expansion coefficient(CTE),coefficient of oxygen diffusion(COD), etc. The oxidation-induced material parameter variations should be considered in high temperature mechanical analysis. In this paper, high temperature oxidation behavior of an oxide film/metal substrate system was investigated through a modified phase field approach. The oxidative stress and oxidation weight gain induced by high temperature oxidation were studied. Effects of Young's modulus, COD and CTE on oxidative stress in the oxide film were studied particularly. The simulation results showed that a better agreement with the experimental results could be obtained when considering the oxidation-induced material parameter variations in the high temperature mechanical analysis of oxide film/metal substrate system. The simulation results demonstrated that oxidative stress and oxidation weight gain were more sensitive to the variation of Young's modulus than to the variations of COD and CTE.     

Elastic constant measurement by using line-focus-beam acoustic microscope

The purpose of this study is to develop a method for measuring elastic constants using a LFB acoustic microscope. For this purpose, a theoretical procedure for the estimation of Young's modulus and Poisson's ratio is introduced based on elastic theory. According to this procedure, experimental velocity measurement and elastic constants estimation are made by use of a LFB acoustic microscope. For the confirmation of the availability of this method, the estimated elastic constant is compared to measurements of elastic constants by other methods. The resulting estimated values of Young's modulus and Poisson's ratio obtained by the LFB acoustic microscope are highly accurate which confirms the usefulness of the elastic constant measurement system. T. Mihara is Research Associate, and M. Obata (former SEM Member), deceased, was Professor, Department of Materials Processing, Faculty of Engineering, Tohoku University, Aramaki Aoba, Sendai, 980, Japan.     

Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force

A realistic beam structure often exhibits material and geometrical non-linearity, in particular for those made of metals. The mechanical behaviors of a non-linear functionally graded-material (FGM) cantilever beam subjected to an end force are investigated by using large and small deformation theories. Young's modulus is assumed to be depth-dependent. For an FGM beam of power-law hardening, the location of the neutral axis is determined. The effects of depth-dependent Young's modulus and non-linearity parameter on the deflections and rotations of the FGM beams are analyzed. Our results show that different gradient indexes may change the bending stiffness of the beam so that an FGM beam may bear larger applied load than a homogeneous beam when choosing appropriate gradients. Moreover, the bending stress distribution in an FGM beam is completely different from that in a homogeneous beam. The bending stress arrives at the maximum tensile stress at an internal position rather than at the surface. Obtained results are useful in safety design of linear and non-linear beams.     

COMP．B复合炸药动态力学性能和塑性流动本构关系的研究

利用自制的含能材料动态变温三轴压缩实验装置，采用准静态应变速率（１０－４／ｓ）和中等应变速率（３／ｓ），对国产复合炸药Ｃｏｍｐ．Ｂ进行了三轴压缩实验．测试了Ｃｏｍｐ．Ｂ在不同温度、不同应变速率条件下的杨氏模量Ｅ，泊松比ν和屈服强度Ｙ．实验结果表明，Ｃｏｍｐ．Ｂ具有明显的应变率相关和热软化效应．基于热激活模型，作了适当的改进，根据实验数据建立了含能材料塑性流动模型，分析表明该模型能合理地描述率相关材料的塑性流动，同时考虑了应变率和温度对塑性流动的影响．这些基础研究为含能材料动态力学性能的研究和炸药早爆机理的理论分析提供了依据     

NANOINDENTATION OF THIN-FILM-SUBSTRATE SYSTEM： DETERMINATION OF FILM HARDNESS AND YOUNG’S MODULUS

In the present paper, the hardness and Young‘s modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates, i.e. glass and silicon, are studied. Nanoindentation XP Ⅱ and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young‘s modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young‘s modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, φ, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.