Showing papers on "Elastic modulus published in 2005"

Intrinsic plasticity or brittleness of metallic glasses

Abstract: The intrinsic plasticity or brittleness of crystalline metals correlates with the ratio of the elastic shear modulus μ to the bulk modulus B; when the ratio μ/B exceeds a critical value, the metal is brittle. Sufficient data on elastic moduli and toughness are now available to permit an assessment for metallic glasses. We find a similar correlation, with the critical value of μ/B for metallic glasses (0.41–0.43) more sharply defined than for crystalline metals. This critical value applies also for annealing-induced embrittlement of metallic glasses. The clear correlation between mechanical behaviour (plasticity or brittleness) and μ/B assists in understanding flow and fracture mechanisms, and in guiding alloy design to alleviate brittleness of metallic glasses.

First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives

Abstract: The structural, dynamical, and thermodynamic properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory total-energy calculations and density-functional perturbation theory lattice dynamics in the generalized gradient approximation. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the associated elastic constants and phonon dispersions. Both the C-33 elastic constant and the F to A phonon dispersions are brought to close agreement with available data once the experimental c/a is chosen for the calculations. The vibrational free energy and the thermal expansion, the temperature dependence of the elastic moduli and the specific heat are calculated using the quasiharmonic approximation. Graphite shows a distinctive in-plane negative thermal-expansion coefficient that reaches its lowest value around room temperature, in very good agreement with experiments. Thermal contraction in graphene is found to be three times as large; in both cases, bending acoustic modes are shown to be responsible for the contraction, in a direct manifestation of the membrane effect predicted by Lifshitz over 50 years ago. Stacking directly affects the bending modes, explaining the large numerical difference between the thermal-contraction coefficients in graphite and graphene, notwithstanding their common physical origin.

Role of material microstructure in plate stiffness with relevance to microcantilever sensors

Abstract: This work examines the effect of microstructure upon microcantilever bending stiffness. An existing beam theory model, based upon an isotropic Hooke's law constitutive relationship, is compared to a model based upon a micropolar elasticity constitutive model. The micropolar approach introduces a bending stiffness relation which is a function of any two independent elastic constants of the Hooke's law model (e.g., the elastic modulus and the Poisson's ratio), and an additional material constant (called γ). A consequence of the additional material constant is the prediction of an increased bending stiffness as the cantilever thickness decreases—a stiffening due to the material microstructure which becomes measurable at micron-order thicknesses. Polypropylene microcantilevers, which have a non-homogeneous microstructure due to their semi-crystalline nature, were fabricated via injection molding. A nanoindenter was used to measure their stiffness. The nanoindenter-determined stiffness values, which include the effect of the additional micropolar material constant, are compared to stiffness values obtained from beam theory. The nanoindenter stiffness values are seen to be at least four times larger than the beam theory stiffness predictions. This stiffening effect has relevance in future MEMS applications which employ materials with non-homogeneous microstructures instead of the conventional MEMS materials (e.g., silicon, silicon nitride), which have a very uniform microstructure.

Evaluated Material Properties for a Sintered alpha-Alumina

Abstract: Results of a data evaluation exercise are presented for a particular specification of sintered alpha-alumina (mass fraction of Al2O3, ≥0995; relative density (rho/rhotheoretical), ≥098; and nominal grain size, 5 μm) A comprehensive set of material property data is established based on published physical, mechanical, and thermal properties of alumina specimens that conform to the constraints of the material specification The criteria imposed on the properties are that the values should be derived from independent experimental studies, that the values for physically related properties should be mutually self-consistent, and that the sets of values should be compatible with established material property relations The properties assessed in this manner include crystallography, thermal expansion, density, sound velocity, elastic modulus, shear modulus, Poisson's ratio, bulk modulus, compressive strength, flexural strength, Weibull characteristic strength, Weibull modulus, tensile strength, hardness, fracture toughness, creep rate, creep rate stress exponent, creep activation energy, friction coefficient, wear coefficient, melting point, specific heat, thermal conductivity, and thermal diffusivity

Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress

Abstract: The fundamental framework of micromechanical procedure is generalized to take into account the surface/interface stress effect at the nano-scale. This framework is applied to the derivation of the effective moduli of solids containing nano-inhomogeneities in conjunction with the composite spheres assemblage model, the Mori–Tanaka method and the generalized self-consistent method. Closed-form expressions are given for the bulk and shear moduli, which are shown to be functions of the interface properties and the size of the inhomogeneities. The dependence of the elastic moduli on the size of the inhomogeneities highlights the importance of the surface/interface in analysing the deformation of nano-scale structures. The present results are applicable to analysis of the properties of nano-composites and foam structures.

Finite element modeling of single-walled carbon nanotubes

Abstract: A three-dimensional finite element (FE) model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) is proposed. The model development is based on the assumption that carbon nanotubes, when subjected to loading, behave like space-frame structures. The bonds between carbon atoms are considered as connecting load-carrying members, while the carbon atoms as joints of the members. To create the FE models, nodes are placed at the locations of carbon atoms and the bonds between them are modeled using three-dimensional elastic beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. In order to evaluate the FE model and demonstrate its performance, the influence of tube wall thickness, diameter and chirality on the elastic moduli (Young's modulus and shear modulus) of SWCNTs is investigated. The investigation includes armchair, zigzag and chiral SWCNTs. It is found that the choice of wall thickness significantly affects the calculation of Young's modulus. For the values of wall thickness used in the literature, the obtained values of Young's modulus agree very well with the corresponding theoretical results and many experimental measurements. Dependence of elastic moduli to diameter and chirality of the nanotubes is also obtained. With increased tube diameter, the elastic moduli of the SWCNTs increase. The Young's modulus of chiral SWCNTs is found to be larger than that of armchair and zigzag SWCNTs. The presented results demonstrate that the proposed FE model may provide a valuable tool for studying the mechanical behavior of carbon nanotubes and their integration in nano-composites.

Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites

Abstract: The thermo-mechanical properties of epoxy-based nanocomposites based on low weight fractions (from 0.01 to 0.5 wt%) of randomly oriented single- and multi-walled carbon nanotubes were examined. Preparation methods for the nanocomposites, using two types of epoxy resins, were developed and good dispersion was generally achieved. The mechanical properties examined were the tensile Young's modulus by Dynamic Mechanical Thermal Analysis and the toughness under tensile impact using notched specimens. Moderate Young's modulus improvements of nanocomposites were observed with respect to the pure matrix material. A particularly significant enhancement of the tensile impact toughness was obtained for specific nanocomposites, using only minute nanotube weight fractions. No significant change in the glass transition temperature of SWCNT/epoxy nanocomposites was observed, compared to that of the epoxy matrix. The elastic modulus of the SWNT-based nanocomposites was found to be slightly higher than the value predicted by the Krenchel model for short-fiber composites with random orientation.

Measurement of the Elastic Modulus of Single Bacterial Cellulose Fibers Using Atomic Force Microscopy

Abstract: The ability of the atomic force microscope to measure forces with subnanonewton sensitivity at nanometer-scale lateral resolutions has led to its use in the mechanical characterization of nanomaterials. Recent studies have shown that the atomic force microscope can be used to measure the elastic moduli of suspended fibers by performing a nanoscale three-point bending test, in which the center of the fiber is deflected by a known force. We extend this technique by modeling the deflection measured at several points along a suspended fiber, allowing us to obtain more accurate data, as well as to justify the mechanical model used. As a demonstration, we have measured a value of 78 ± 17 GPa for Young's modulus of bacterial cellulose fibers with diameters ranging from 35 to 90 nm. This value is considerably higher than previous estimates, obtained by less direct means, of the mechanical strength of individual cellulose fibers.

Large amplitude light-induced motion in high elastic modulus polymer actuators

Abstract: Well-defined gradients in molecular alignment have been used as tools to generate large amplitude, light-induced deformations in stiff polymer networks. These systems are reversible, monolithic and based on a simple one-step self-assembly process. To fabricate the actuators, diacrylate dopants containing azobenzene moieties were blended with liquid crystalline diacrylate hosts and photopolymerized in a twisted configuration. The resulting twisted networks were heavily crosslinked with room temperature elastic moduli on the order of 1 GPa. Regardless of the temperature with respect to the glass transitions, subsequent exposure to UV radiation induced anisotropic expansion/contraction, and simple variations in geometry were used to generate uniaxial bending or helical coiling deformation modes. Because mechanical energy is directly related to elastic modulus, these systems are expected to provide significantly greater work output than contemporary polymer actuator materials.

On the rigidity of amorphous solids

Abstract: We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the "boson peak" in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.

Characterizing the viscoelastic properties of thin hydrogel-based constructs for tissue engineering applications.

Abstract: We present a novel indentation method for characterizing the viscoelastic properties of alginate and agarose hydrogel based constructs, which are often used as a model system of soft biological tissues. A sensitive long working distance microscope was used for measuring the time-dependent deformation of the thin circular hydrogel membranes under a constant load. The deformation of the constructs was measured laterally. The elastic modulus as a function of time can be determined by a large deformation theory based on Mooney–Rivlin elasticity. A viscoelastic theory, Zener model, was applied to correlate the time-dependent deformation of the constructs with various gel concentrations, and the creep parameters can therefore be quantitatively estimated. The value of Young's modulus was shown to increase in proportion with gel concentration. This finding is consistent with other publications. Our results also showed the great capability of using the technique to measure gels with incorporated corneal stromal cells. This study demonstrates a novel and convenient technique to measure mechanical properties of hydrogel in a non-destructive, online and real-time fashion. Thus this novel technique can become a valuable tool for soft tissue engineering.

Elastic property of vertically aligned nanowires.

Abstract: An atomic force microscopy (AFM) based technique is demonstrated for measuring the elastic modulus of individual nanowires/nanotubes aligned on a solid substrate without destructing or manipulating the sample. By simultaneously acquiring the topography and lateral force image of the aligned nanowires in the AFM contacting mode, the elastic modulus of the individual nanowires in the image has been derived. The measurement is based on quantifying the lateral force required to induce the maximal deflection of the nanowire where the AFM tip was scanning over the surface in contact mode. For the [0001] ZnO nanowires/nanorods grown on a sapphire surface with an average diameter of 45 nm, the elastic modulus is measured to be 29 ± 8 GPa.

Improvement of electromechanical actuating performances of a silicone dielectric elastomer by dispersion of titanium dioxide powder

Abstract: This paper presents the first reported data on the embedding of highly dielectric ceramic inclusions in a rubbery host medium as a means to increase the electromechanical material response for dielectric elastomer actuation. The studied polymer/ceramic composite, consisting of a silicone matrix in which titanium dioxide powder was dispersed, exhibited, in comparison with pure silicone, a decreased elastic modulus, as well as an increased dielectric constant. The measured low frequency permittivity resulted in accordance with several classical dielectric mixing rules. The use of this material as elastomeric dielectric for planar actuators enabled a reduction of the driving electric fields, so that a transverse strain of 11% at 10 V//spl mu/m and a transverse stress of 16.5 kPa at 9 V//spl mu/m were obtained. These levels of strain and stress were respectively more than eight and four times higher than the corresponding values generated with the pure polymer matrix for analogous electrical stimuli.

Hard superconducting nitrides.

Abstract: Detailed study of the equation of state, elasticity, and hardness of selected superconducting transition-metal nitrides reveals interesting correlations among their physical properties. Both the bulk modulus and Vickers hardness are found to decrease with increasing zero-pressure volume in NbN, HfN, and ZrN. The computed elastic constants from first principles satisfy c(11) > c(12) > c(44) for NbN, but c(11) > c(44) > c(12) for HfN and ZrN, which are in good agreement with the neutron scattering data. The cubic delta-NbN superconducting phase possesses a bulk modulus of 348 GPa, comparable to that of cubic boron nitride, and a Vickers hardness of 20 GPa, which is close to sapphire. Theoretical calculations for NbN show that all elastic moduli increase monotonically with increasing pressure. These results suggest technological applications of such materials in extreme environments.

Orientation and size dependence of the elastic properties of zinc oxide nanobelts

Abstract: Molecular dynamics simulations are performed to characterize the response of zinc oxide (ZnO) nanobelts to tensile loading. The ultimate tensile strength (UTS) and Young's modulus are obtained as functions of size and growth orientation. Nanobelts in three growth orientations are generated by assembling the unit wurtzite cell along the [0001], , and crystalline axes. Following the geometric construction, dynamic relaxation is carried out to yield free-standing nanobelts at 300 K. Two distinct configurations are observed in the [0001] and orientations. When the lateral dimensions are above 10 A, nanobelts with rectangular cross-sections are seen. Below this critical size, tubular structures involving two concentric shells similar to double-walled carbon nanotubes are obtained. Quasi-static deformations of belts with and orientations consist of three stages, including initial elastic stretching, wurtzite-ZnO to graphitic-ZnO structural transformation, and cleavage fracture. On the other hand, [0001] belts do not undergo any structural transformation and fail through cleavage along (0001) planes. Calculations show that the UTS and Young's modulus of the belts are size dependent and are higher than the corresponding values for bulk ZnO. Specifically, as the lateral dimensions increase from 10 to 40 A, decreases between 38–76% and 24–63% are observed for the UTS and Young's modulus, respectively. This effect is attributed to the size-dependent compressive stress induced by tensile surface stress in the nanobelts. and nanobelts with multi-walled tubular structures are seen to have higher values of elastic moduli (~340 GPa) and UTS (~36 GPa) compared to their wurtzite counterparts, echoing a similar trend in multi-walled carbon nanotubes.

Investigating linear and nonlinear viscoelastic behavior using model silica-particle-filled polybutadiene

Abstract: We explore filler reinforcement (i.e., increase of elastic modulus G‘ due to incorporation of fillers) and Payne effect (i.e., decrease of G‘ at large strain amplitudes) in terms of the matrix molecular weight, filler loading, and time scales used to probe the viscoelasticity of filled melts. Use of monodisperse non-cross-linked 1,4-polybutadiene (PBD) along with a silica filler allows illustration of different mechanisms of filler reinforcement in the elastic and liquid regimes. The greater filler reinforcement for matrices of higher molecular weight indicates the filler association through chain adsorption and bridging. The role of matrix-mediated filler−filler interactions is explicitly illustrated in terms of the increased elastic modulus in the terminal region due to replacement a fraction of the matrix chains with longer chains of the same kind. The Payne effect is seen to be time-dependent and comprised of an instantly recoverable and a slowly recovering component. Measuring G‘ at both high and low...

On the thermodynamics of particle-stabilized emulsions: curvature effects and catastrophic phase inversion.

Abstract: The flexural properties of a particle adsorption monolayer are investigated theoretically. If the particles are not densely packed, the interfacial bending moment and the spontaneous curvature (due to the particles) are equal to zero. The situation changes if the particles are closely packed. Then the particle adsorption monolayer possesses a significant bending moment, and the interfacial energies of bending and dilatation become comparable. In this case, the bending energy can either stabilize or destabilize the Pickering emulsion, depending on whether the particle contact angle is smaller or greater than 90 degrees . Theoretical expressions are derived for the bending moment, for the curvature elastic modulus, and for the work of interfacial deformation and emulsification. The latter is dominated by the work for creation of a new oil-water interface and by the work for particle adsorption. The curvature effects give a contribution of second order, which is significant only for emulsification at 50:50 water/oil volume fractions. A thermodynamic criterion for the type of the formed emulsion is proposed. It predicts the existence of a catastrophic phase inversion in particle-stabilized emulsions, in agreement with the experimental observations. The derived theoretical expressions could find application for interpretation of experimental data on production and stability of Pickering emulsions.

Nanoindentation of polydimethylsiloxane elastomers: Effect of crosslinking, work of adhesion, and fluid environment on elastic modulus

Abstract: With the potential to map mechanical properties of heterogeneous materials on a micrometer scale, there is growing interest in nanoindentation as a materials characterization technique. However, nanoindentation has been developed primarily for characterization of hard, elasto-plastic materials, and the technique has not been validated for very soft materials with moduli less than 5 MPa. The current study attempted to use nanoindentation to characterize the elastic moduli of soft, elastomeric polydimethylsiloxane (PDMS) samples (with different degrees of crosslinking) and determine the effects of adhesion on these measurements using adhesion contact mechanics models. Results indicate that nanoindentation was able to differentiate between elastic moduli on the order of hundreds of kilo-Pascals. Moreover, calculations using the classical Hertz contact model for dry and aqueous environment gave higher elastic modulus values when compared to those obtained from unconfined compression testing. These data seem to suggest that consideration of the adhesion energy at the tip-sample interface is a significantly important parameter and needs to be taken into account for consistent elastic modulus determination of soft materials by nanoindentation.

Three-Dimensional Probabilistic Foundation Settlement

Abstract: By modeling soil as a three-dimensional spatially random medium, the reliability of shallow foundations against serviceability limit state failure, in the form of excessive settlement and/or differential settlement, can be estimated. The soil’s elastic modulus, E , is represented as a lognormally distributed random field with an isotropic correlation structure. The settlements of individual and pairs of square footings placed on the surface of the soil are computed using the finite element method. A probabilistic model for total and differential settlement is presented and compared to results obtained using Monte Carlo simulation. The distributions of total and differential settlement are found to be closely predicted using the distributions of geometric averages of the underlying soil elastic modulus field.