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Showing papers on "Young's modulus published in 2009"


Journal ArticleDOI
TL;DR: This work investigates the mechanical strength and properties of graphene under uniaxial tensile test as a function of size and chirality using the orthogonal tight-binding method and molecular dynamics simulations with the AIREBO potential.
Abstract: We investigate the mechanical strength and properties of graphene under uniaxial tensile test as a function of size and chirality using the orthogonal tight-binding method and molecular dynamics simulations with the AIREBO potential. Our results on Young's modulus, fracture strain, and fracture strength of bulk graphene are in reasonable agreement with the recently published experimental data. Our results indicate that fracture strain and fracture strength of bulk graphene under uniaxial tension can have a significant dependence on the chirality. Mechanical properties such as Young's modulus and Poisson's ratio can depend strongly on the size and chirality of the graphene nanoribbon.

789 citations


Journal ArticleDOI
TL;DR: In this paper, a modified form of the Stoney equation, well known for elastic isotropic substrates, is derived for Si(001) and Si(111) wafers, using the elastic stiffness constants of silicon, cij, instead of the orientation averaged values E and ν, which do not have a meaning for elastically anisotropic single crystal materials.

563 citations


Journal ArticleDOI
TL;DR: The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading.
Abstract: The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

481 citations


Journal ArticleDOI
TL;DR: In this article, the Young's modulus of graphene is investigated through the intrinsic thermal vibration in graphene which is observed by molecular dynamics and the results agree very well with the recent experiment [Lee et al., Science 321, 385 (2008)].
Abstract: The Young's modulus of graphene is investigated through the intrinsic thermal vibration in graphene which is ``observed'' by molecular dynamics and the results agree very well with the recent experiment [Lee et al., Science 321, 385 (2008)]. This method is further applied to show that the Young's modulus of graphene (1) increases with increasing size and saturates after a threshold value of the size; (2) increases from 0.95 to 1.1 TPa as temperature increases in the region [100, 500] K; (3) is insensitive to the isotopic disorder in the low disorder region $(l5%)$ and decreases gradually after further increasing the disorder percentage.

393 citations


Journal ArticleDOI
TL;DR: In this paper, the results obtained from laboratory tests carried out on different types of clay-bearing rock collected from various parts of Turkey, to quantify the effects of water content on mechanical properties of the rocks, and to develop a method for estimating the rock strength and deformability at any water content based on physical properties.

372 citations


Journal ArticleDOI
Yong Zhu1, Feng Xu1, Qingquan Qin1, Wayne Y. Fung1, Wei Lu1 
TL;DR: Repeated loading and unloading during tensile tests demonstrated that the nanowires are linear elastic until fracture without appreciable plasticity.
Abstract: The Young’s modulus and fracture strength of silicon nanowires with diameters between 15 and 60 nm and lengths between 1.5 and 4.3 μm were measured. The nanowires, grown by the vapor−liquid−solid process, were subjected to tensile tests in situ inside a scanning electron microscope. The Young’s modulus decreased while the fracture strength increased up to 12.2 GPa, as the nanowire diameter decreased. The fracture strength also increased with the decrease of the side surface area; the increase rate for the chemically synthesized silicon nanowires was found to be much higher than that for the microfabricated silicon thin films. Repeated loading and unloading during tensile tests demonstrated that the nanowires are linear elastic until fracture without appreciable plasticity.

334 citations


Journal ArticleDOI
TL;DR: In this article, the authors demonstrate that both the mechanical strength and the Young's modulus of polydimethylsiloxane (PDMS) membranes are thickness dependent and the transition from bulk behavior to dimension dependent is predicted to occur at a membrane thickness of about 200 µm.
Abstract: Polydimethylsiloxane (PDMS) has cross-linked network structures and its properties have been regarded as dimensionally independent. Here we demonstrate that both the mechanical strength and the Young's modulus of the PDMS membranes are thickness dependent and the transition from bulk behavior to dimension dependent is predicted to occur at a membrane thickness of about 200 µm. The thickness-dependent phenomenon is attributed to shear stress during fabrication, which is proportional to the thickness-induced reorder of polymer chain coils to form stronger cross-linked networks.

306 citations


Journal ArticleDOI
TL;DR: In this article, an atomistic simulation method is adopted to investigate the elastic characteristics of defect-free single-layered graphene sheet (SLGS), and the equivalent structural beam is employed to model interatomic forces of the covalently bonded carbon atoms.

245 citations


Journal ArticleDOI
TL;DR: The results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate, and for various mixing ratios and strain rates.
Abstract: Tensile tests on Polydimethylsiloxane (PDMS) materials were conducted to illustrate the effects of mixing ratio, definition of the stress-strain curve, and the strain rate on the elastic modulus and stress-strain curve. PDMS specimens were prepared according to the ASTM standards for elastic materials. Our results indicate that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio, and the strain rate. For various mixing ratios and strain rates, true stress-strain definition results in higher stress and elastic modulus compared with engineering stress-strain and true stress-engineering strain definitions. The elastic modulus increases as the mixing ratio increases up-to 9:1 ratio after which the elastic modulus begins to decrease even as the mixing ratio continues to increase. The results presented in this study will be helpful to assist the design of in vitro experiments to mimic blood flow in arteries and to understand the complex interaction between blood flow and the walls of arteries using PDMS elastomer.

224 citations


Journal ArticleDOI
TL;DR: In this paper, a comprehensive study on the mechanical behavior of plasma enhanced chemical vapor deposited silicon oxide, oxynitride and nitride thin films is provided, and the results are compared with standard nanoindentation measurements.

220 citations


Journal ArticleDOI
TL;DR: In this article, a servo-hydraulic test jig and a fixture were designed and manufactured for testing composites under uni-axial loading at quasi-static and intermediate strain rates of 0.001−100−1.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the relationship between the mechanical properties and the relative density of porous Ti and found that the strength of the porous Ti is mainly affected by the density.
Abstract: To satisfy the mechanical requirement of porous bone substitutes, the porous Ti with the porosity in the range of 55–75% was fabricated using the space-holder sintering process. The pore size is in the range of 200–500 μm, and the mean value is 410 μm. The mechanical properties were investigated by the compressive test. Results show that the plateau stress and Young's modulus are in the range of 10–35 MPa and 3–6.4 GPa, respectively. The relationship between the mechanical properties and the relative density of porous Ti is found to obey a power law relation. The strength of the porous Ti is mainly affected by the density. The typical rupture section of compressed samples has the V-shape.

Journal ArticleDOI
TL;DR: In this paper, the structural, electronic and mechanical properties of zigzag graphene nanoribbons were investigated by applying density functional theory within the generalized gradient approximation-Perdew-Burke-Ernzerhof (GGA-PBE) approximation.
Abstract: Herein, we investigate the structural, electronic and mechanical properties of zigzag graphene nanoribbons in the presence of stress by applying density functional theory within the GGA-PBE (generalized gradient approximation-Perdew–Burke–Ernzerhof) approximation. The uniaxial stress is applied along the periodic direction, allowing a unitary deformation in the range of ± 0.02%. The mechanical properties show a linear response within that range while a nonlinear dependence is found for higher strain. The most relevant results indicate that Young's modulus is considerable higher than those determined for graphene and carbon nanotubes. The geometrical reconstruction of the C–C bonds at the edges hardens the nanostructure. The features of the electronic structure are not sensitive to strain in this linear elastic regime, suggesting the potential for using carbon nanostructures in nano-electronic devices in the near future.

Journal ArticleDOI
TL;DR: Results indicate that vapor-liquid-solid grown wires are relatively free of extended volume defects and that fracture strength is likely controlled by twinning and interfacial effects at the wire foot.
Abstract: Elastic modulus and fracture strength of vertically aligned Si [111] nanowires (o ) 100-700 nm) in an as-grown state have been measured using a new, multipoint bending protocol in an atomic force microscope. All wires showed linear elastic behavior, spring constants which scale with (length) 3 , and brittle failure at the wire-substrate junction. The “effective” Young’s modulus increased slightly (100 f 160-180 GPa) as wire diameter decreased, but fracture strength increased by 2-3 orders of magnitude (MPa f GPa). These results indicate that vapor-liquid-solid grown wires are relatively free of extended volume defects and that fracture strength is likely controlled by twinning and interfacial effects at the wire foot. Small wires (100 nm) grown with a colloidal catalyst were the best performers with high modulus (∼180 GPa) and fracture stress >1 GPa. One-dimensional nano-objects (nanowires, tubes, rods, springs, etc.) have attracted considerable interest lately as building blocks for electromechanical systems (oscillators, sensors, actuators), circuit interconnects, and composite materials of the future. Manipulation and exploitation of these new structures for technological applications requires detailed knowledge of material properties at the single nanostructure level. Previous studies have shown that the “effective” elasticity, strength, and plasticity of materials can all be influenced by size, shape, and “surface effects” (surface stress, oxide layers, roughness, and defects) when nanometer dimensions are involved. 1-5 Given the importance of such issues, it is no surprise that many interrogation techniques have been used to explore these effects: nanoindentation, tensile/bending (static and dynamic) tests, and resonant excitation. 1-16 In particular, atomic force microscope (AFM)based bending experiments on nanobeams and nanowires (NW) are very popular. These approaches typically measure the force required to deform a “beam” fabricated via topdown techniques, 6,7 NWs that have been artificially “fixed” to a surface with metallic pads, 8 or NWs positioned across a gap 9-12 (with and without surface pinning of the wire ends).

Journal ArticleDOI
TL;DR: A series of Steered Molecular Dynamics simulations in explicit solvent is used to elucidate the influence of the pulling rate on the Young's modulus of individual tropocollagen molecules, and enables for the first time to predict the elastic properties of a single tropocollsagen molecule at physiologically and experimentally relevant pulling rates, directly from atomistic-level calculations.
Abstract: Collagen is an important structural protein in vertebrates and is responsible for the integrity of many tissues like bone, teeth, cartilage and tendon. The mechanical properties of these tissues are primarily determined by their hierarchical arrangement and the role of the collagen matrix in their structures. Here we report a series of Steered Molecular Dynamics (SMD) simulations in explicit solvent, used to elucidate the influence of the pulling rate on the Young's modulus of individual tropocollagen molecules. We stretch a collagen peptide model sequence [(Gly-Pro-Hyp)(10)](3) with pulling rates ranging from 0.01 to 100 m/s, reaching much smaller deformation rates than reported in earlier SMD studies. Our results clearly demonstrate a strong influence of the loading velocity on the observed mechanical properties. Most notably, we find that Young's modulus converges to a constant value of approximately 4 GPa tangent modulus at 8% tensile strain when the initially crimped molecule is straightened out, for pulling rates below 0.5 m/s. This enables us for the first time to predict the elastic properties of a single tropocollagen molecule at physiologically and experimentally relevant pulling rates, directly from atomistic-level calculations. At deformation rates larger than 0.5 m/s, Young's modulus increases continuously and approaches values in excess of 15 GPa for deformation rates larger than 100 m/s. The analyses of the molecular deformation mechanisms show that the tropocollagen molecule unfolds in distinctly different ways, depending on the loading rate, which explains the observation of different values of Young's modulus at different loading rates. For low pulling rates, the triple helix first uncoils completely at 10%-20% strain, then undergoes some recoiling in the opposite direction, and finally straightens for strains larger than 30%. At intermediate rates, the molecule uncoils linearly with increasing strain up to 35% strain. Finally, at higher velocities the triple helix does not uncoil during stretching.

Journal ArticleDOI
TL;DR: In this article, best fit equations for predicting the uniaxial compressive strength and static Young's modulus of sedimentary rocks are proposed, which have larger value of accuracy and correlation coefficient (R2 ).
Abstract: The uniaxial compressive strength and static Young’s modulus ( Es ) of intact rocks are the most important geotechnical parameters for stability analysis of surface and underground structures. These parameters are obtained by the uniaxial compressive test. Although this test is simple, the preparation of the samples, especially of soft rocks, is a hard and time consuming task. By using a nondestructive method such as the ultrasonic test, one can indirectly predict the mentioned parameters. The uniaxial compressive and the ultrasonic tests were carried out on 64 samples of sedimentary rocks and, after regression analysis of the test results; best fit equations for predicting the uniaxial compressive strength and static Young’s modulus of these samples are proposed. Thus, in comparison with other proposed equations, these equations have larger value of accuracy and correlation coefficient ( R2 ) . The equations are practical, simple, and accurate enough to apply and can be used in practice for the predictio...

Journal ArticleDOI
TL;DR: In this paper, the tensile elastic modulus of a rock is calculated by measuring tensile strain on the center part of a Brazilian disc's two side faces along the direction perpendicular to the line load, and then the force sensor is used to record the force applied; finally the E t can be calculated according to those related formulas which are derived on the basis of elasticity theory.

Journal ArticleDOI
TL;DR: In this article, the influence of expanded clay and shale aggregates on the mechanical performances of concrete is studied through their volume fractions and aggregate qualities, and a reverse determination of the elastic modulus of LWA is carried out based to the experimental data.

Journal ArticleDOI
TL;DR: In this article, composite resonators with zero linear temperature coefficient of frequency were fabricated and characterized, and the resulting resonators have a quadratic temperature coefficient for Young's modulus of approximately -20 ppb/degC2 and a tunable turnover temperature in the -55degC to 125degC range.
Abstract: Utilizing silicon and silicon dioxide's opposing temperature coefficients of Young's modulus, composite resonators with zero linear temperature coefficient of frequency are fabricated and characterized. The resulting resonators have a quadratic temperature coefficient of frequency of approximately -20 ppb/degC2 and a tunable turnover temperature in the -55degC to 125degC range. Reduction of the temperature dependence of frequency is shown in flexural-mode resonators (700 kHz-1.3 MHz) and extensional-mode ring resonators (20 MHz). The linear temperature coefficient of Young's modulus of silicon dioxide is extracted from measurements to be +179 ppm/degC. The composite resonators are fabricated and packaged in a CMOS-compatible wafer-scale hermetic encapsulation process. The long-term stability of the resonators is monitored for longer than six months. Although most devices exhibit less than 2 ppm frequency drift, there is evidence of dielectric charging in the silicon dioxide.

Journal ArticleDOI
TL;DR: Bourmaud et al. as discussed by the authors investigated the relationship between the mechanical properties of the fibres and those of the composites by taking the influence of the recycling into account, and obtained results that the tensile modulus of these polypropylene/vegetal fibre composites is well conserved with the number of reprocessing cycles.

Journal ArticleDOI
27 Apr 2009-ACS Nano
TL;DR: The results indicated that FWNTs are practically the optimum reinforcing filler for the next generation of carbon nanotube-based composite materials.
Abstract: Compared to single-walled carbon nanotubes (SWNTs) and more defective multiwalled carbon nanotubes (MWNTs), the thin few-walled carbon nanotubes (FWNTs) are believed to have extraordinary mechanical properties. However, the enhancement of mechanical properties in FWNTs-polymer composites has remained elusive. In this study, free-standing carbon nanotubes (CNTs)/polymer composite films were fabricated with three types (SWNTs, FWNTs, MWNTs) of functionalized CNTs. The mechanical properties of composite films have been investigated. It is observed that the Young’s modulus of composite films with only 0.2 wt % functionalized FWNTs shows a remarkable reinforcement value of dY/dVf = 1658 GPa, which is ∼400 GPa higher than the highest value (dY/dVf = 1244 GPa) that was previously reported. In addition, the Young’s modulus increased steadily with the increased concentration of FWNTs. The results indicated that FWNTs are practically the optimum reinforcing filler for the next generation of carbon nanotube-based co...

Journal ArticleDOI
TL;DR: In this article, the authors presented the application of electrostatic pull-in instability to study the size-dependent effective Young's Modulus of [110] silicon nanocantilevers (thickness ~1019-40nm).
Abstract: This letter presents the application of electrostatic pull-in instability to study the size-dependent effective Young’s Modulus ? ( ~170–70?GPa) of [110] silicon nanocantilevers (thickness ~1019–40?nm). The presented approach shows substantial advantages over the previous methods used for characterization of nanoelectromechanical systems behaviors. The ? is retrieved from the pull-in voltage of the structure via the electromechanical coupled equation, with a typical error of ? 12%, much less than previous work in the field. Measurement results show a strong size-dependence of ?. The approach is simple and reproducible for various dimensions and can be extended to the characterization of nanobeams and nanowires.

Journal ArticleDOI
TL;DR: In this paper, the mechanical behavior of graphene nanoribbons (GNRs) was investigated by molecular dynamics simulations and it was shown that GNRs behave nonlinear elastically under tensile loads.

Journal ArticleDOI
TL;DR: In this article, the effects of organically modified clay on the physical, mechanical, thermal and morphological properties of the prepared polypropylene/surface modified clay nanocomposites were studied.

Journal ArticleDOI
TL;DR: In this paper, the effective Young's modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20-684 nm by measuring resonance frequencies from thermal noise spectra.
Abstract: The effective Young’s modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20–684 nm by measuring resonance frequencies from thermal noise spectra. A significant deviation from the bulk value is observed for cantilevers thinner than 150 nm. To explain the observations we have compared the thickness dependence of the effective Young’s modulus for the first and second flexural resonance mode and measured the static curvature profiles of the cantilevers. We conclude that surface stress cannot explain the observed behavior. A surface elasticity model fits the experimental data consistently.

Journal ArticleDOI
TL;DR: In this paper, the effect of high-pressures on the structural and elastic properties of XP zinc-blende compounds, with X = B, Al, Ga and In, has been investigated using the full-potential augmented plane wave plus local orbitals method within density functional theory.

Journal ArticleDOI
TL;DR: In this article, more than 3000 data sets obtained by many investigators using various materials have been collected and analyzed statistically in order to develop a reliable new equation for elastic modulus of concrete.
Abstract: The mechanical properties of concrete are highly dependent on the types and proportions of binders and aggregates. Because existing equations for predicting the modulus of elasticity as a function of compressive strength are obtained from experiments performed on a restricted number of concrete specimens subjected to uniaxial compression, the existing equations cannot cover the entire experimental data. In this study, more than 3000 data sets obtained by many investigators using various materials have been collected and analyzed statistically in order to develop a reliable new equation for elastic modulus of concrete. The compressive strengths of the considered concretes range from 40 to 160 MPa (5.8 to 23.2 ksi). The new equation also takes into consideration the types of coarse aggregates and mineral admixtures. The proposed formula should be effective in the design of both normal strength concrete and high strength concrete structures.

Journal ArticleDOI
Hai Yan Yu1
TL;DR: In this paper, an empirical expression describing the relation of elastic modulus with plastic deformation has been proposed and implemented into LS-DYNA software to simulate U-channel springback.

Journal ArticleDOI
TL;DR: In this paper, a 3D analytical model is developed to characterize the axial stiffness behavior of a single F 2MC tube, and the test results show good agreement with the model predictions.
Abstract: In this research, the capability of utilizing fluidic flexible matrix composites (F2MC) for autonomous structural tailoring is investigated. By taking advantage of the high anisotropy of flexible matrix composite (FMC) tubes and the high bulk modulus of the pressurizing fluid, significant changes in the effective modulus of elasticity can be achieved by controlling the inlet valve to the fluid-filled F2MC structure. The variable modulus F2MC structure has the flexibility to easily deform when desired (open-valve), possesses the high modulus required during loading conditions when deformation is not desired (closed-valve — locked state), and has the adaptability to vary the modulus between the flexible/stiff states through control of the valve. In the current study, a 3D analytical model is developed to characterize the axial stiffness behavior of a single F 2MC tube. Experiments are conducted to validate the proposed model, and the test results show good agreement with the model predictions. A closed/open...

Journal ArticleDOI
TL;DR: Values of tensile strength, compressive strength, bending strength, hardness and modulus of elasticity are reported for the shell material of various species of bivalve, gastropod and cephalopod mollusc.
Abstract: Values of tensile strength, compressive strength, bending strength, hardness and modulus of elasticity are reported for the shell material of various species of bivalve, gastropod and cephalopod mollusc. Nacre is the strongest structural type, but crossed lamellar structure is the hardest. Possible selective reasons for these differences are discussed but no firm conclusions are drawn.