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.     

The effect of temperature,defect and strain rate on the mechanical property of multi-layer graphene: Coarse-grained molecular dynamics study

In this work, we investigate the effect of temperature, defect, and strain rate on the mechanical properties of multi-layer graphene using coarse-grained molecular dynamics (CGMD) simulations. The simulation results reveal that the mechanical properties of multi-layer graphene tend to be less sensitive to temperature as the layer increases, but they are sensitive to the distribution and coverage of Stone-Wales (SW) defects. For the same number of defect, there is less decline in the fracture stress and Young's modulus of graphene when the defects have a regular distribution, in contrast to random distribution. In addition, Young's modulus is less influenced by temperature and defect, compared to fracture stress. Both the fracture stress and Young's modulus have little dependence on strain rate.     

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.     

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.     

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.     

Dynamic ball hardness tests on polymers

The present work demonstrates the possibility of determining and differentiating the elastic and plastic material properties (like the Young's modulus, the ball hardness under load, and the plastic hardness) by applying the dynamic ball hardness indentation test. In Ref. 1, the elastic properties are neglected. Nevertheless, the obtained hardness number includes both elastic and plastic parts. Now, the continuous data acquisition allows the determination of the elastic modulus of the polymer and also its dynamic and thermal dependence. Furthermore, a way of specifying a plastic hardness number is shown. Using the approach of Oliver and Pharr [2] enables the separation of the real material property of plastic hardness. Topographic measurements allowed taking the wall formation during a hardness test into account while analyzing the impression. It turned out that the elastic modulus determined in the manner described is independent of the penetration rate, but decreases with increasing temperature or caoutchouc mass content. Also, the dynamic and thermal dependence of the hardness are discussed.     

Influence of temperature on tensile and fatigue behavior of nanoscale copper using molecular dynamics simulation

The tensile and fatigue behavior of nanoscale copper at various temperatures has been analyzed using molecular dynamics simulation. The stress–strain curve for nanoscale copper was obtained first and then the Young's modulus of the material was determined. The modulus was larger than that obtained by previous studies and decreased with increasing temperature. From the fatigue test, the cyclic stress–number of cycles curve was obtained and the stress increased with increasing temperature. Furthermore, the ductile fracture configuration was observed in the fatigue testing process under the lower applied stress. It was also observed that nanoscale copper appears to have a fatigue limit of 10⁵ cycles.     

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.     

Mechanical Characterization of Protein Crystals

The mechanical properties (critical stress intensity factor, hardness and Young's modulus) of 4 crystalline materials (two proteins, lysozyme and glucose isomerase and two non‐proteins, glutamic acid and potassium sulphate) were measured with an indentation technique. It was found that the mechanical properties of lysozyme crystals depend on their state – dried, partly dried and moisture saturated – and their surroundings. The hardness, Young's modulus and the critical stress intensity factor of lysozyme crystals were observed to be much lower than those for the tested non‐proteins, leading to the conclusion that crystalline lysozyme is comparatively more fragile and softer. In combination the mechanical properties of lysozyme and the non‐proteins indicated that these materials were fairly brittle. Mechanical properties for crystals of the other protein, glucose isomerase, could not be quantified by indentation. However, qualitatively crystalline glucose isomerase was found to be more ductile and less fragile than crystalline lysozyme. The experimental findings were interpreted in terms of relative susceptibility to attrition and secondary nucleation in stirred industrial crystallizers.     

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.     

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.     

Pressure‐induced incompressibility and point singularity of mechanical properties of TaC in NiAs‐type structure

The structural and elastic properties of TaC in NiAs‐type structure under high pressure have been investigated using first principles calculations based on density functional theory. Results indicate that the incompressibility along the c‐axis of TaC exceeds that of diamond under higher pressure. Particularly, an interesting point singularity exists in its mechanical properties as the pressure increases from 20 GPa to 40 GPa. The minimal shear modulus, Young's modulus, Debye temperature, and maximum Poisson ratio of TaC are simultaneously obtained at 28 GPa. The calculations of hardness indicate that the NiAs‐type TaC crystal possesses excellent mechanical properties. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanical properties,anisotropy and hardness of group IVA ternary spinel nitrides

In this work, new ternary cubic spinel structures are designed by the substitutional method. The structures, elasticity properties, intrinsic hardness and Debye temperature of the cubic ternary spinel nitrides are studied by first principles based on the density-functional theory. The results show that γ-CSn₂N₄, γ-SiC₂N₄, γ-GeC₂N₄ and γ-SnC₂N₄ are not mechanically stable. The elastic constants C_ij of these cubic spinel structures are obtained using the stress–strain method. Derived elastic constants, such as bulk modulus, shear modulus, Young's modulus, Poisson coefficient and brittle/ductile behaviour are estimated using Voigt–Reuss–Hill theories. The B/G value, the Poisson's ratio and anisotropic factor are calculated for eight ternary stable crystals. Based on the microscopic hardness model, we further estimate the Vickers hardness of all the stable crystals. From the calculated hardness of the stable group IVA ternary spinel nitrides by Gao's and Jiang's methods, it is observed that the stable group IVA ternary spinel nitrides are not superhard materials except for γ-CSi₂N₄. Furthermore, the Debye temperature for the eight stable crystals is also estimated.     

Effect of the conditions of dynamic nanoindentation on the strain-rate sensitivity of hardness for solids with different structures

A technique for the determination of the strain-rate sensitivity of hardness during dynamic nanoindentation is proposed. The strain-rate sensitivities of the dynamic hardnesses of a wide class of materials (fcc metals, carbon steels, bulk amorphous metallic alloys, ionic and covalent crystals, polymers, and ceramics) are determined. The variation of these strain-rate sensitivities with the relative-strain rate (in the [(e)\dot]\dot \varepsilon range from 3 × 10⁻³ to 5 × 10³ s⁻¹) and the indentation depth (in the range from 30 nm to 2μm) is studied.     

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).     

利用分子动力学方法铁素体-渗碳体相界面效应探究

珠光体是十分重要的组织结构,因此本文构建了含铁素体-渗碳体相界面的模型,并采用分子动力学模拟方法模拟纳米压入的过程。通过对模拟结果的力学性能和组织结构分析,探究了铁素体-渗碳体相界面效应。研究发现,距铁素体-渗碳体晶界不同距离（位置压入）,在压入最初阶段,压头载荷随着压头与晶界距离的增大而增大,当压入深度达到一定深度后,载荷随着距离的增大而减小。杨氏模量和最大剪切模量受压头尖端下方原子结构的直接影响,硬度受到结构完整性和类型的共同影响。铁素体-渗碳体相界面影响了纳米压入过程中位错形核、增殖和扩展,宏观表现为在相同压入深度下,不同压入位置压头载荷的差异。     

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.     

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.