Showing papers on "Elastic modulus published in 2004"

A buckling-based metrology for measuring the elastic moduli of polymeric thin films

Abstract: As technology continues towards smaller, thinner and lighter devices, more stringent demands are placed on thin polymer films as diffusion barriers, dielectric coatings, electronic packaging and so on. Therefore, there is a growing need for testing platforms to rapidly determine the mechanical properties of thin polymer films and coatings. We introduce here an elegant, efficient measurement method that yields the elastic moduli of nanoscale polymer films in a rapid and quantitative manner without the need for expensive equipment or material-specific modelling. The technique exploits a buckling instability that occurs in bilayers consisting of a stiff, thin film coated onto a relatively soft, thick substrate. Using the spacing of these highly periodic wrinkles, we calculate the film's elastic modulus by applying well-established buckling mechanics. We successfully apply this new measurement platform to several systems displaying a wide range of thicknessess (nanometre to micrometre) and moduli (MPa to GPa).

Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy

Abstract: The effect of reduced size on the elastic properties measured on silver and lead nanowires and on polypyrrole nanotubes with an outer diameter ranging between 30 and 250 nm is presented and discussed. Resonant-contact atomic force microscopy (AFM) is used to measure their apparent elastic modulus. The measured modulus of the nanomaterials with smaller diameters is significantly higher than that of the larger ones. The latter is comparable to the macroscopic modulus of the materials. The increase of the apparent elastic modulus for the smaller diameters is attributed to surface tension effects. The surface tension of the probed material may be experimentally determined from these AFM measurements.

High-Strength Zirconium Diboride-Based Ceramics

Abstract: Zirconium diboride (ZrB 2 ) and ZrB 2 ceramics containing 10, 20, and 30 vol% SiC particulates were prepared from commercially available powders by hot pressing. Four-point bend strength, fracture toughness, elastic modulus, and hardness were measured. Modulus and hardness did not vary significantly with SiC content. In contrast, strength and toughness increased as SiC content increased. Strength increased from 565 MPa for ZrB 2 to >1000 MPa for samples containing 20 or 30 vol% SiC. The increase in strength was attributed to a decrease in grain size and the presence of WC.

Reinforcement of single-walled carbon nanotube bundles by intertube bridging

Abstract: During their production, single-walled carbon nanotubes form bundles. Owing to the weak van der Waals interaction that holds them together in the bundle, the tubes can easily slide on each other, resulting in a shear modulus comparable to that of graphite. This low shear modulus is also a major obstacle in the fabrication of macroscopic fibres composed of carbon nanotubes. Here, we have introduced stable links between neighbouring carbon nanotubes within bundles, using moderate electron-beam irradiation inside a transmission electron microscope. Concurrent measurements of the mechanical properties using an atomic force microscope show a 30-fold increase of the bending modulus, due to the formation of stable crosslinks that effectively eliminate sliding between the nanotubes. Crosslinks were modelled using first-principles calculations, showing that interstitial carbon atoms formed during irradiation in addition to carboxyl groups, can independently lead to bridge formation between neighbouring nanotubes.

Mechanical properties of continuous natural fibre-reinforced polymer composites

Abstract: The mechanical behaviour high density polyethylene (HDPE) reinforced with continuous henequen fibres (Agave fourcroydes) was studied. Fibre-matrix adhesion was promoted by fibre surface modifications using an alkaline treatment and a matrix preimpregnation together with a silane coupling agent. The use of the silane coupling agent to promote a chemical interaction, improved the degree of fibre-matrix adhesion. However, it was found that the resulting strength and stiffness of the composite depended on the amount of silane deposited on the fibre. A maximum value for the tensile strength was obtained for a certain silane concentration but when using higher concentrations, the tensile strength did not increase. Using the silane concentration that resulted in higher tensile strength values, the flexural and shear properties were also studied. The elastic modulus of the composite did not improve with the fibre surface modification. The elastic modulus, in the longitudinal fibre direction obtained from the tensile and flexural measurements was compared with values calculated using the rule of mixtures. It was observed that the increase in stiffness from the use of henequen fibres was approximately 80% of the calculated values. The increase in the mechanical properties ranged between 3 and 43%, for the longitudinal tensile and flexural properties, whereas in the transverse direction to the fibre, the increase was greater than 50% with respect to the properties of the composite made with untreated fibre composite. In the case of the shear strength, the increase was of the order of 50%. From the failure surfaces it was observed that with increasing fibre-matrix interaction the failure mode changed from interfacial failure to matrix failure.

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

Abstract: A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.

Design criteria for wear-resistant nanostructured and glassy-metal coatings

Abstract: There is increasing scientific and commercial interest in the development of nanostructured coatings, particularly those based on low-miscibility ‘ceramic–ceramic’ or ‘ceramic–metal’ crystalline/amorphous nanocomposite phase mixtures deposited by plasma-assisted PVD or CVD. In laboratory mechanical testing, extreme values of hardness (which may be in excess of 70 GPa) are often found for such films, similar to those claimed for intrinsically hard materials such as c-BN and diamond. High hardness is, however, often accompanied by an associated high elastic modulus, which although desirable in principle for cutting tool materials and/or coatings, may in practice limit coating durability, on low-strength, low-modulus substrates (e.g. low-alloy steels and the light alloys) and in many wear applications other than metal cutting. In this paper, we discuss the benefits of using the ratio of hardness to elastic modulus ( H / E ) as an indicator of coating durability since this parameter essentially describes the elastic strain to failure capability (and resilience ) of a candidate material. Furthermore, we consider the likely need for tribological coatings to accommodate some degree of substrate deformation; in this respect film toughness , i.e. ‘engineering toughness’ in the sense of an ability to absorb deformation energy (both elastic and plastic) needs to be considered. The concept of predominantly metallic films with a nanograined and/or glassy microstructure (containing little or no high-modulus ceramic constituents) is introduced, through which we point to the importance of retaining ‘sufficient’ coating hardness, whilst reducing coating elastic moduli to more closely match those of candidate substrate materials. With regard to the implications of H / E for practical tribological coating applications, we propose that closer matching of the coating/substrate interfacial elastic properties and thus an improved ability for the coating to accommodate substrate strain, where necessary, is often a more important factor in wear resistance than is extremely high hardness.

Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension

Abstract: The membrane deflection experiment developed by Espinosa and co-workers was used to examine size effects on mechanical properties of free-standing polycrystalline FCC thin films. We present stress–strain curves obtained on films 0.2, 0.3, 0.5 and 1.0 μm thick including specimen widths of 2.5, 5.0, 10.0 and 20.0 μm for each thickness. Elastic modulus was consistently measured in the range of 53– 55 GPa for Au, 125– 129 GPa for Cu and 65– 70 GPa for Al. Several size effects were observed including yield stress variations with membrane width and film thickness in pure tension. The yield stress of the membranes was found to increase as membrane width and thickness decreased. It was also observed that thickness plays a major role in deformation behavior and fracture of polycrystalline FCC metals. A strengthening size scale of one over film thickness was identified. In the case of Au free-standing films, a major transition in the material inelastic response occurs when thickness is changed from 1 to 0.5 μm . In this transition, the yield stress more than doubled when film thickness was decreased, with the 0.5 μm thick specimen exhibiting a more brittle-like failure and the 1 μm thick specimen exhibiting a strain softening behavior. Similar plasticity size effects were observed in Cu and Al. Scanning electron microscopy performed on Au films revealed that the number of grains through the thickness essentially halved, from approximately 5 to 2, as thickness decreased. It is postulated that this feature affects the number of dislocations sources, active slip systems, and dislocation motion paths leading to the observed strengthening. This statistical effect is corroborated by the stress–strain data in the sense that data scatter increases with increase in thickness, i.e., plasticity activity. The size effects here reported are the first of their kind in the sense that the measurements were performed on free-standing polycrystalline FCC thin films subjected to macroscopic homogeneous axial deformation, i.e., in the absence of deformation gradients, in contrast to nanoindentation, beam deflection, and torsion, where deformation gradients occur. To the best of our understanding, continuum plasticity models in their current form cannot capture the observed size scale effects.

Elastic modulus and resonance behavior of boron nitride nanotubes

Abstract: The effective elastic modulus (E) of boron nitride nanotubes (BNNTs) was measured using the electric-field-induced resonance method inside a transmission electron microscope. The average value of E from the measurements of 18 individually cantilevered BNNTs was 722 GPa, comparable to the theoretical estimate of ∼850 GPa. No strong variation of E with the diameter of the BNNTs, which spanned from 34 to 94 nm, was observed. Low quality factors (<680) obtained from the mechanical resonance is attributed to the layered structural nature of BNNT.

Are surfaces elastically softer or stiffer

Abstract: This letter addresses the issue of surface softening versus stiffening during elastic deformation. Using a combination of molecular statics and ab initio calculations, we show that a solid surface can be either softer or stiffer elastically than the corresponding bulk. Whether a particular surface is softer or stiffer depends on the competition between atomic coordination and electron redistribution (which sometimes is referred as bond saturation) on the surface. Taking Cu as an example, we demonstrate that the Young’s modulus along 〈110〉 direction on {100} surface is larger than its bulk counterpart; meanwhile, it is smaller along 〈100〉 direction on {100} surface.

Atomistic simulation of the structure and elastic properties of gold nanowires

Abstract: We performed atomistic simulations to study the effect of free surfaces on the structure and elastic properties of gold nanowires aligned in the 〈1 0 0〉 and 〈1 1 1〉 crystallographic directions. Computationally, we formed a nanowire by assembling gold atoms into a long wire with free sides by putting them in their bulk fcc lattice positions. We then performed a static relaxation on the assemblage. The tensile surface stresses on the sides of the wire cause the wire to contract along the length with respect to the original fcc lattice, and we characterize this deformation in terms of an equilibrium strain versus the cross-sectional area. While the surface stress causes wires of both orientations and all sizes to increasingly contract with decreasing cross-sectional area, when the cross-sectional area of a 〈1 0 0〉 nanowire is less than 1.83 nm ×1.83 nm , the wire undergoes a phase transformation from fcc to bct, and the equilibrium strain increases by an order of magnitude. We then applied a uniform uniaxial strain incrementally to 1.2% to the relaxed nanowires in a molecular statics framework. From the simulation results we computed the effective axial Young's modulus and Poisson's ratios of the nanowire as a function of cross-sectional area. We used two approaches to compute the effective elastic moduli, one based on a definition in terms of the strain derivative of the total energy and another in terms of the virial stress often used in atomistic simulations. Both give quantitatively similar results, showing an increase in Young's modulus with a decrease of cross-sectional area in the nanowires that do not undergo a phase transformation. Those that undergo a phase transformation experience an increase of about a factor of three of Young's modulus. The Poisson's ratio of the 〈1 0 0〉 wires that do not undergo a phase transformation show little change with the cross-sectional area. Those wires that undergo a phase transformation experience an increase of about 10% in Poisson's ratio. The 〈1 1 1〉 wires show, with a decrease of cross-sectional area, an increase in one of Poisson's ratios and small change in the other.

Enhanced Dielectric and Electromechanical Responses in High Dielectric Constant All-Polymer Percolative Composites

Abstract: A type of all-polymer percolative composite is introduced which exhibits a very high dielectric constant (> 7000). The experimental results also show that the dielectric behavior of this new class of percolative composites follows the predictions of the percolation theory and the analysis of conductive percolation phenomena. The very high dielectric constant of the all-polymer composites, which are also very flexible and possesses an elastic modulus close to that of the insulation polymer matrix, makes it possible to induce a high electromechanical response under a very reduced electric field (a strain of 2.65 % with an elastic energy density of 0.18 J cm–3 can be achieved under a field of 16 MV m–1). Data analysis also suggests that within the composites, the non-uniform local field distribution as well as interface effects can significantly enhance the strain responses. Furthermore, the experimental data as well as the data analysis indicate that conduction loss in the composites will not affect the strain hysteresis.

Transversely isotropic elastic properties of single-walled carbon nanotubes

Abstract: While it is known that the elastic properties of a single-walled carbon nanotube (SWNT) are transversely isotropic, the closed-form solutions for all five independent elastic moduli have not been solved completely. In this paper, an energy approach in the framework of molecular mechanics is used to evaluate the local and global deformations of a SWNT in a unified manner. This is carried out under four loading conditions: axial tension, torsional moment, in-plane biaxial tension, and in-plane pure shear, respectively, from which the closed-form expressions for the longitudinal Young's modulus, major Poisson's ratio, longitudinal shear, plane strain bulk, and in-plane shear moduli are obtained. It is shown that as the tube diameter increases, the major Poisson's ratio approaches a constant, the longitudinal Young's and shear moduli and the plane strain bulk modulus are inversely proportional to the tube diameter, and the in-plane shear modulus is inversely proportional to the third power of the tube diameter. The dependence of the elastic moduli of a SWNT on the tube diameter and helicity is displayed and discussed.

Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics.

Abstract: Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the $1∕3$ power law predicted by Hertz-Mindlin effective medium theories of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a long-standing question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations, and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.