Showing papers on "Elastic modulus published in 2011"

Stretching and Breaking of Ultrathin MoS2

Abstract: We report on measurements of the stiffness and breaking strength of monolayer MoS2, a new semiconducting analogue of graphene. Single and bilayer MoS2 is exfoliated from bulk and transferred to a substrate containing an array of microfabricated circular holes. The resulting suspended, free-standing membranes are deformed and eventually broken using an atomic force microscope. We find that the in-plane stiffness of monolayer MoS2 is 180 ± 60 Nm–1, corresponding to an effective Young’s modulus of 270 ± 100 GPa, which is comparable to that of steel. Breaking occurs at an effective strain between 6 and 11% with the average breaking strength of 15 ± 3 Nm–1 (23 GPa). The strength of strongest monolayer membranes is 11% of its Young’s modulus, corresponding to the upper theoretical limit which indicates that the material can be highly crystalline and almost defect-free. Our results show that monolayer MoS2 could be suitable for a variety of applications such as reinforcing elements in composites and for fabricat...

Mechanical properties of hybrid inorganic–organic framework materials: establishing fundamental structure–property relationships

Abstract: The mechanical properties of hybrid framework materials, including both nanoporous metal–organic frameworks (MOFs) and dense inorganic–organic frameworks, are discussed in this critical review. Although there are relatively few studies of this kind in the literature, major recent advances in this area are beginning to shed light on the fundamental structure–mechanical property relationships. Indeed research into the mechanical behavior of this important new class of solid-state materials is central to the design and optimal performance of a multitude of technological applications envisaged. In this review, we examine the elasticity of hybrid frameworks by considering their Young's modulus, Poisson's ratio, bulk modulus and shear modulus. This is followed by discussions of their hardness, plasticity, yield strength and fracture behavior. Our focus is on both experimental and computational approaches. Experimental work on single crystals and amorphized monoliths involved primarily the application of nanoindentation and atomic force microscopy to determine the elastic moduli and hardness properties. The compressibility and bulk moduli of single crystals and polycrystalline powders were studied by high-pressure X-ray crystallography in the diamond anvil cell, while in one instance spectroscopic ellipsometry has also been used to estimate the elastic moduli of MOF nanoparticles and deposited films. Theoretical studies, on the other hand, encompassed the application of first principles density-functional calculations and finite-temperature molecular dynamics simulations. Finally, by virtue of the diverse mechanical properties achievable in hybrid framework materials, we propose that a new domain be established in the materials selection map to define this emerging class of materials (137 references).

Indentation versus tensile measurements of Young's modulus for soft biological tissues.

Abstract: In this review, we compare the reported values of Young's modulus (YM) obtained from indentation and tensile deformations of soft biological tissues. When the method of deformation is ignored, YM values for any given tissue typically span several orders of magnitude. If the method of deformation is considered, then a consistent and less ambiguous result emerges. On average, YM values for soft tissues are consistently lower when obtained by indentation deformations. We discuss the implications and potential impact of this finding.

An elastic metamaterial with simultaneously negative mass density and bulk modulus

Abstract: In this letter, an elasticmetamaterial which exhibits simultaneously negative effective mass density and bulk modulus is presented with a single unit structure made of solid materials. The double-negative properties are achieved through a chiralmicrostructure that is capable of producing simultaneous translational and rotational resonances. The negative effective mass density and effective bulk modulus are numerically determined and confirmed by the analysis of wave propagation. The left-handed wave propagation property of this metamaterial is demonstrated by the negative refraction of acoustic waves.

Local elastic properties of a metallic glass

Abstract: In contrast to the long-range order of crystalline materials, non-crystalline compounds, such as metallic glasses, have a more inhomogeneous distribution of atoms on a local scale. Atomic force acoustic microscopy now demonstrates how these local variations translate into much stronger variations in local elastic properties of a metallic glass compared with its crystalline counterpart.

Mechanical properties of graphene under shear deformation

Abstract: In this letter, we investigate the mechanical properties of graphene under shear deformation. Specifically, using molecular dynamics simulations, we compute the shear modulus, shear fracture strength, and shear fracture strain of zigzag and armchair graphene structures at various temperatures. To predict shear strength and fracture shear strain, we also present an analytical theory based on the kinetic analysis. We show that wrinkling behavior of graphene under shear deformation can be significant. We compute the amplitude to wavelength ratio of wrinkles using molecular dynamics and compare it with existing theory. Our results indicate that graphene can be a promising mechanical material under shear deformation.

Mechanical Properties of Fly-Ash-Based Geopolymer Concrete

Abstract: The mechanical properties of fly-ash-based geopolymer concrete (GPC) were studied. Experimentally measured values of the static elastic modulus, Poisson’s ratio, compressive strength, and flexural strength of GPC specimens made from 25 fly ash (FA) stockpiles from different sources were recorded and analyzed. The results were studied using regression analysis to identify tendencies and correlations within the mechanical properties of GPC. It was found that the mechanical behavior of GPC is similar to that of ordinary portland cement (OPC) concrete, suggesting that equations, akin to those given by ACI 318-08, could be applied for GPC to determine its flexural strength and static elastic modulus. The validity of an equation to determine the density of GPC as a function of FA fineness was also put forward.

Elastic metamaterials with simultaneously negative effective shear modulus and mass density.

Abstract: We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess a negative shear modulus and negative mass density over a large frequency region. Such a material has the unique property that only transverse waves can propagate with a negative dispersion while longitudinal waves are forbidden. This leads to many interesting phenomena such as negative refraction, which is demonstrated by using a wedge sample and a significant amount of mode conversion from transverse waves to longitudinal waves that cannot occur on the interface of two natural solids.

Deformation of an elastic substrate by a three-phase contact line.

Abstract: Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it is expected that this unresolved force is balanced by the elastic response of the solid, a definitive analysis has remained elusive because of an apparent divergence of stress at the contact line. While a number of theories have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the solid substrate. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.

Measuring substrate-independent modulus of thin films

Abstract: Substrate influence is a common problem when using instrumented indentation (also known as nano-indentation) to evaluate the elastic modulus of thin films. Many have proposed models to be able to extract the film modulus (Ef) from the measured substrate-affected modulus, assuming that the film thickness (t) and substrate modulus (Es) are known. Existing analytic models work well if the film is more compliant than the substrate. However, no analytic model accurately predicts response when the modulus of the film is more than double the modulus of the substrate. In this work, a new analytic model is proposed. This new model is shown by finite-element analysis to be able to accurately predict composite response over the domain 0.1 < Ef/Es < 10. Finally, the new model is used to analyze experimental data for compliant films on stiff substrates and stiff films on compliant substrates.

Correlation between relaxations and plastic deformation, and elastic model of flow in metallic glasses and glass-forming liquids

Abstract: We study the similarity and correlations between relaxations and plastic deformation in metallic glasses (MGs) and MG-forming liquids. It is shown that the microscope plastic events, the initiation and formation of shear bands, and the mechanical yield in MGs where the atomic sites are topologically unstable induced by applied stress, can be treated as the glass to supercooled liquid state transition induced by external shear stress. On the other hand, the glass transition, the primary and secondary relaxations, plastic deformation and yield can be attributed to the free volume increase induced flow, and the flow can be modeled as the activated hopping between the inherent states in the potential energy landscape. We then propose an extended elastic model to describe the flow based on the energy landscape theory. That is, the flow activation energy density is linear proportional to the instantaneous elastic moduli, and the activation energy density ρE is determined to be a simple expression of ρ E = 10 11 G + 1 11 K . The model indicates that both shear and bulk moduli are critical parameters accounting for both the homogeneous and inhomogeneous flows in MGs and MG-forming liquids. The elastic model is experimentally certified. We show that the elastic perspectives offers a simple scenario for the flow in MGs and MG-forming liquids and are suggestive for understanding the glass transition,plastic deformation, and nature and characteristics of MGs

Curvature-dependent surface energy and implications for nanostructures

Abstract: At small length scales, several size-effects in both physical phenomena and properties can be rationalized by invoking the concept of surface energy. Conventional theoretical frameworks of surface energy, in both the mechanics and physics communities, assume curvature independence. In this work we adopt a simplified and linearized version of a theory proposed by Steigmann–Ogden to capture curvature-dependence of surface energy. Connecting the theory to atomistic calculations and the solution to an illustrative paradigmatical problem of a bent cantilever beam, we catalog the influence of curvature-dependence of surface energy on the effective elastic modulus of nanostructures. The observation in atomistic calculations that the elastic modulus of bent nanostructures is dramatically different than under tension – sometimes softer, sometimes stiffer – has been a source of puzzlement to the scientific community. We show that the corrected surface mechanics framework provides a resolution to this issue. Finally, we propose an unambiguous definition of the thickness of a crystalline surface.

Atomistic simulation and continuum modeling of graphene nanoribbons under uniaxial tension

Abstract: Atomistic simulations are performed to study the nonlinear mechanical behavior of graphene nanoribbons under quasistatic uniaxial tension, emphasizing the effects of edge structures (armchair and zigzag, without and with hydrogen passivation) on elastic modulus and fracture strength. The numerical results are analyzed within a theoretical model of thermodynamics, which enables determination of the bulk strain energy density, the edge energy density and the hydrogen adsorption energy density as nonlinear functions of the applied strain based on static molecular mechanics simulations. These functions can be used to describe mechanical behavior of graphene nanoribbons from the initial linear elasticity to fracture. It is found that the initial Young's modulus of a graphene nanoribbon depends on the ribbon width and the edge chirality. Furthermore, it is found that the nominal strain to fracture is considerably lower for graphene nanoribbons with armchair edges than for ribbons with zigzag edges. Molecular dynamics simulations reveal two distinct fracture nucleation mechanisms: homogeneous nucleation for the zigzag-edged graphene nanoribbons and edge-controlled heterogeneous nucleation for the armchair-edged ribbons. The modeling and simulations in this study highlight the atomistic mechanisms for the nonlinear mechanical behavior of graphene nanoribbons with the edge effects, which is potentially important for developing integrated graphene-based devices.