Predictions of Young's Modulus of Polymer Composites Reinforced with Short Natural Fibers

Polymers reinforced with natural fibers are beneficial to prepare biodegradable composite materials. A new expression for the Young's modulus of short, natural fiber (SNF) reinforced polymer composites was derived based on a micro-mechanical model. The Young's moduli of poly(lactic acid) reinforced with reed fibers and low-density polyethylene (LDPE) reinforced with sisal fibers, from literature data, were estimated in the fiber weight fraction range from 0 to 50% using the equation and both the compounding rule and the Halpin–Tsai equation, and the estimations were compared with the reported measured data. The results showed that the predictions of the Young's moduli by means of the new Young's modulus equation were close to the measured data from the low density polyethylene/sisal fiber composites, as well as the poly(lactic acid)/reed composites at high fiber concentration. Comparing with other Young's modulus equations, the new Young's modulus equation would be more convenient to use owing to the parameters in the equation being easily determined.     

The influence of grain size and texture on the Young's modulus of nanocrystalline nickel and nickel–iron alloys

Hardness and Young's modulus were measured by nanoindentation on a series of electrodeposited nanocrystalline nickel and nickel–iron alloys. Hardness values showed a transition from regular to inverse Hall–Petch behaviour, consistent with previous studies. There was no significant influence of grain size on the Young's modulus of nanocrystalline nickel and nickel–iron alloys with grain sizes greater than 20?nm. The Young's modulus values for nanocrystalline nickel and nickel–iron alloys for grain sizes less than 20?nm were slightly reduced when compared to their conventional (randomly oriented) polycrystalline counterparts. The observed trend with decreasing grain size was found to be consistent with composite model predictions that consider the influence of intercrystalline defects. However, there was some notable variability of the measured values when compared to the model predictions. Three theoretical relationships were used to characterise the anisotropic elastic behaviour of these materials. As a result, texture was also considered to have an influence on the measured Young's modulus and used to explain some of the observed variability for the entire grain size range (9.8–81?nm).     

Temperature-dependent elastic moduli of lead telluride-based thermoelectric materials

In the open literature, reports of mechanical properties are limited for semiconducting thermoelectric materials, including the temperature dependence of elastic moduli. In this study, for both cast ingots and hot-pressed billets of Ag-, Sb-, Sn- and S-doped PbTe thermoelectric materials, resonant ultrasound spectroscopy (RUS) was utilized to determine the temperature dependence of elastic moduli, including Young's modulus, shear modulus and Poisson's ratio. This study is the first to determine the temperature-dependent elastic moduli for these PbTe-based thermoelectrics, and among the few determinations of elasticity of any thermoelectric material for temperatures above 300 K. The Young's modulus and Poisson's ratio, measured from room temperature to 773 K during heating and cooling, agreed well. Also, the observed Young's modulus, E, versus temperature, T, relationship, E(T) = E ₀(1–bT), is consistent with predictions for materials in the range well above the Debye temperature. A nanoindentation study of Young's modulus on the specimen faces showed that both the cast and hot-pressed specimens were approximately elastically isotropic.     

单层石墨烯杨氏模量的理论模型

石墨烯力学性能的研究对其在半导体技术中的应用是十分重要的,本文基于半连续体模型并结合石墨烯纳米结构特性,通过对原子的描述构建了石墨烯形变分量和位移分量的新关系,从而给出了单层石墨烯结构形变能,并计算了不同尺寸单层石墨烯的杨氏模量值.通过对不同方向杨氏模量的分析,讨论了单层石墨烯的手性行为.结果表明:随着尺寸的增加,单层石墨烯两个方向的杨氏模量分别趋于0.746 TPa和0.743 TPa,当尺寸相同时,两方向杨氏模量的最大差值不超过0.003 TPa,此结果与文献报道结果相符.在小应变情况下,单层石墨烯薄膜呈各向同性,且薄膜尺寸变化对该特性影响不大.该计算结果对研究石墨烯的其它力学特性提供一定的参考价值.     

Nanoindentation of gold nanoparticles functionalized with proteins

The hardness and Young's modulus of 10 and 20 nm gold nanoparticles (Au NPs) modified with bovine serum albumin and streptavidin were measured using a nanoindenter. The Au NPs were immobilized on a semiconductor surface through organic self-assembled monolayers. Changes in mechanical properties occurred when the Au NPs were immobilized on the surface. The hardness and Young's modulus were dependent on the size of the NPs, and the proteins on the particles showed highly plastic and elastic behavior compared to flat surfaces modified with self-assembled monolayers.     

Reverse analysis in depth-sensing indentation for evaluation of the Young's modulus of thin films

This paper presents an approach to reverse analysis in depth-sensing indentation of composite film/substrate materials, which makes use of numerical simulation. This methodology allows the results of experimental hardness tests, acquired with pyramidal indenter geometry, to be used to determine the Young's modulus of thin film materials. Forward and reverse analyses were performing using three-dimensional numerical simulations of pyramidal and flat punch indentation tests to determine the Young's modulus of the thin films. The pyramidal indenter used in the numerical simulations takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses fictitious composite materials with different relationships between the values of the Young's modulus of the film and substrate. The proposed reverse analysis procedure provides a unique value for the film's Young's modulus. Depending on material properties, the value of the Young's modulus of the film can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment. The validity of the proposed reverse analysis method is checked using four real cases of composite materials.     

Surface Tension and Shear Strain Contributions to the Mechanical Behavior of Individual Mg-Ni-Phyllosilicate Nanoscrolls

Some phyllosilicate compounds have the ability of spontaneous scrolling because of the size mismatch between the covalently bounded metal oxide and silica sheets. Their unique structure and high theoretically predicted Young's modulus (around 210–230 GPa) induce phyllosilicates’ application as reinforcing fillers. However, previous nanomechanical experiments with individual phyllosilicate nanoscrolls are in poor agreement with theory. The main reason for this is the low accuracy of experiments, which leads to large measurement errors compared to measured average values. Here, the study of the mechanical properties of synthetic (Mg_1–xNi_x)₃Si₂O₅(OH)₄ phyllosilicates is reported by testing a suspended nanoobject (a nanobridge) with an atomic force microscope (AFM). The Young's modulus of corresponding phyllosilicate model layers is also calculated by means of the density functional theory (DFT). The original AFM approach makes it possible to account for the probe slipping off the nanobridge and determine its boundary conditions. The measured Young's modulus values are considered within the models of surface tension and shear strain contributions. The shear strain appears to have a decisive impact on the measured Young's modulus (from 150 ± 70 GPa to 200 ± 210 GPa) and its spread.     

The composition-dependent mechanical properties of Ge/Si core–shell nanowires

The Stillinger–Weber potential is used to study the composition-dependent Young's modulus for Ge-core/Si-shell and Si-core/Ge-shell nanowires. Here, the composition is defined as a ratio of the number of atoms of the core to the number of atoms of a core–shell nanowire. For each concerned Ge-core/Si-shell nanowire with a specified diameter, we find that its Young's modulus increases to a maximal value and then decreases as the composition increases. Whereas Young's modulus of the Si-core/Ge-shell nanowires increase nonlinearly in a wide compositional range. Our calculations reveal that these observed trends of Young's modulus of core–shell nanowires are essentially attributed to the different components of the cores and the shells, as well as the different strains in the interfaces between the cores and the shells.     

Young's Modulus Characterization of Nano-Level Silicon Nanomembrane

Silicon nanomembrane (SiNM) has drawn great attention for the application in nanoelectrical devices as it shows excellent flexibility and is compatible with the integrated circuit process. The mechanical property measurement of the SiNM with nanoscale thickness is critical. A suspended SiNM (40 nm thick) for mechanical measurements is fabricated by transferring a chemically etched ultrathin monocrystalline silicon film from silicon on insulator wafer to a substrate with a multi-hole array. And then, the atomic force probe is utilized to load force on the free-standing SiNM to obtain a force deflection curve, and then the Young's modulus of such floating SiNM can be directly calculated based on the large deflection plane model. It shows that the Young's modulus of such SiNM is basically consistent with that of the bulk silicon. However, the SiNMs’ floating area significantly affects the results, i.e., the Young's modulus varies with the ratio of the suspended area diameter (i.e., hole diameter) to the film thickness. The Young's modulus is independent of hole diameter when the ratio is greater than 425. According to this relationship, the variation of Young's modulus can be predicted for arbitrary thick SiNMs and any transferable nanofilms.     

分子动力学研究表面缺陷对硅纳米线杨氏模量的影响

硅纳米线因受量子尺寸效应与表面效应的影响而具有奇特的力、电及其耦合特性,成为了纳米电子器件的核心构件.然而在硅纳米线的制备过程中,表面产生缺陷不可避免.因此本文采用分子动力学方法着重研究了表面缺陷浓度对不同横截面形状(正方形、六角形和三角形)的[110]晶向和[111]晶向硅纳米线杨氏模量的影响.研究结果表明,当硅纳米线仅有单一表面缺陷时,不同晶向硅纳米线的杨氏模量均随表面缺陷浓度增加而迅速单调减小.当表面缺陷浓度为10%时,杨氏模量的减小幅度在10%-20%之间,减小幅度的差异与硅纳米线的晶向以及横截面形状密切相关.当存在多个表面缺陷时,杨氏模量随着缺陷浓度的增加表现出了不同程度的波动趋势.三角形截面硅纳米线的杨氏模量波动幅度最大,正方形截面的波动较小,即表面缺陷分布的不同对正方形截面硅纳米线的杨氏模量影响较小,这表明表面缺陷的影响与其分布及硅纳米线的横截面形状密切相关.通过与实验结果对比,本文的研究结果揭示了表面缺陷是导致硅纳米线杨氏模量实验值变小的重要因素,因此在表征硅纳米线的力学性能时,需要考虑表面缺陷的影响.     

Measuring the aspect ratios of ZnO nanobelts

Nanobelts are new materials that have a rectangular cross-section and are characterized by widths and width-to-thickness aspect ratios. In this paper, the thickness and aspect ratios of ZnO nanobelts are measured by a conjunction application of convergent beam electron diffraction (CBED) and electron energy-loss spectroscopy (EELS). The thicknesses of thicker nanobelts are first determined by CBED under two-beam diffracting condition, then they are used to determine the electron inelastic mean-free-path (MFP) length, which is 161±15 nm for ZnO at 200 kV. The thicknesses of the thinner nanobelts are then determined by EELS using the calibrated MFP. The results show that the aspect ratio depends on conditions under which the sample was synthesized.     

First-principles study of elastic properties of high hydrogenated single-walled carbon nanotube

Using the first-principles calculations based on the density functional theory (DFT), we have investigated the mechanical properties of three typical patterns of the highly hydrogenated SWCNTs. For the stable parallel polyacetylene-like chains pattern (pattern III), Young's modulus of the type A configuration, which is one of the stable configurations of pattern III, has larger Young's modulus than that of the others with the same coverage on the same pristine tube, i.e. the vertical chain pattern (pattern I) and the dimer pattern (pattern II) ones. On the other hand, Young's modulus of type B configuration also belonged to pattern III changes slightly. We also verified that Young's modulus decreases enormously as the coverage increases above 50% and reduces to about one-third of that of the pristine carbon nanotubes at 100% coverage.     

Surface waves and mode conversion at a surface coated with an elastic heavy layer

A surface wave of frequency lying within bulk band of transverse waves is found in an elastic medium coated with a thin layer endowed with a surface mass density, surface Young's modulus and surface bending modulus. The wave is a particular case of surface resonance with infinite lifetime. In materials with negative Poisson's ratio (auxetics) the wave exists even for coating material with zero bending modulus, whereas with positive Poisson's ratio it requires the surface bending modulus to be larger than the surface Young's modulus. The manifestation of this wave in the reflection coefficient seems promising for fabrication of devices showing monochromator properties.     

Elastic properties of SWCNTs with curved morphology: Density functional tight binding based treatment

The self-consistent charge density functional based tight-binding method is used to calculate the effect of curvature on the structure, average energy of atoms and Young's modulus of armchair single-wall carbon nanotubes (SWCNTs) under axial strains. We found that as the amount of curvature increases, the average energy of atoms and the Young's modulus decrease and the equilibrium CC distance increases for (7,7) SWCNTs. However, we also found that the average energy of atoms and Young's modulus of (5,5) SWCNTs are weakly affected by increasing the amount of curvature. Our results also show that the average energy of atoms and Young's modulus of smaller diameter armchair nanotubes are smaller than that of the larger diameter ones.     

Fabrication of MgO nanobelts using a halide source and their structural characterization

MgO nanobelts have been fabricated by chemical vapor deposition using MgCl₃ as starting material. The products consist of a large quantity of belt-like nanostructures with typical lengths in the range of several tens to several hundreds of micrometers; some of them even have lengths on the order of a millimeter. The typical thickness and width-to-thickness ratio of the MgO nanobelts are in the range of 20 to 100 nm and about 5 to 10, respectively. The size and morphology of the MgO nanobelts were measured by transmission electron microscopy. Investigations of X-ray diffraction patterns and using high-resolution transmission electron microscopy indicate that the nanobelts have a cubic structure and are single-crystalline. Received: 23 August 2001 / Accepted: 27 August 2001 / Published online: 2 October 2001     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.     

Study of the bending modulus of individual silicon nitride nanobelts via atomic force microscopy

Analysis of the bending modulus of individual silicon nitride nanobelts in elastic regime is reported here. The nanobelts have the size between 200∼800 nm in width, and thickness 20∼50 nm. Atomic force microscopy was used to image and to perform measurements of force versus bending displacement on individual nanobelts suspending over strips. The bending modulus E_b is deduced by comparison of the measured force curves on the substrate and on the suspending nanobelts. It is shown that the elastic modulus of the silicon nitride nanobelts is about 570 GPa, which is much larger than that of bulk and film of the silicon nitride material. The larger elastic modulus is ascribed to the fact there are less structural defects in the silicon nitride nanobelts. PACS 81.70.Bt; 81.40.Lm; 61.80.+g     

FeCrNiCoCu纳米压痕性能的分子动力学研究

纳米压痕是研究金属特性最广泛的方法之一.因此,本文采用分子动力学方法研究了晶粒数、压痕半径和压痕速度对FeCrNiCoCu压痕性能的影响.结果表明,晶粒数从4增加到16,杨氏模量和硬度值逐渐减小,呈现反Hall-Petch现象;随着压头半径的增加,杨氏模量增大,硬度受接触面积的影响较大而减小,较大的压头半径有利于模型内部位错的产生和扩展;压入速度对杨氏模量和硬度的影响微弱,压入速度越快,位错密度越低,位错传播速度越慢.本工作以期为FeCrNiCoCu的研究提供理论指导.     

Mechanical properties of Co-Si-B amorphous alloys

The ternary amorphous systems Co_xSi₅B_95?x with 7070Si _y B_30?y with 5<y<18 were studied for their mechanical properties at room temperature. Structure sensitive parameters as density, Young's modulus, micro-hardness and crystallization temperature were investigated as a function of Co and Si contents. The value of density increases with higher Co content but not linearly as for Co-B. Young's modulus, micro-hardness and crystallization temperature decrease with increasing Co concentration. The packing fractionη was calculated using 12-coordinated Goldschmidt atomic radii. It is shown that changes in the proportions of metalloids contents in the alloys have more significant influence on the atomic structure and therefore on the mechanical properties than changes of Co content. The maximum tensile elastic strain for the Co-Si-B system was estimated. Influence of magnetic moment on Young's modulus is discussed.