Shear waves in a resonator with cubic nonlinearity

Shear waves with finite amplitude in a one-dimensional resonator in the form of a layer of a rubber-like medium with a rigid plate of finite mass at the upper surface of the layer are investigated. The lower boundary of the layer oscillates according to a harmonic law with a preset acceleration. The equation of motion for particles in a resonator is determined using a model of a medium with a single relaxation time and cubical dependence of the shear modulus on deformation. The amplitude and form of shear waves in a resonator are calculated numerically by the finite difference method at shifted grids. Resonance curves are obtained at different acceleration amplitudes at the lower boundary of a layer. It is demonstrated that, as the oscillation amplitude in the resonator grows, the value of the resonance frequency increases and the shape of the resonance curve becomes asymmetrical. At sufficiently large amplitudes, a bistability region is observed. Measurements were conducted with a resonator, where a layer with the thickness of 15 mm was manufactured of a rubber-like polymer called plastisol. The shear modulus of the polymer at small deformations and the nonlinearity coefficient were determined according to the experimental dependence of mechanical stress on shear deformation. Oscillation amplitudes in the resonator attained values when the maximum shear deformations in the layer were 0.4–0.6, which provided an opportunity to observe nonlinear effects. Measured dependences of the resonance frequency on the oscillation amplitude corresponded to the calculated ones that were obtained at a smaller value of the nonlinear coefficient.     

The synergetic theory of the glass transition in liquids

The glass transition is treated as a spontaneous emergence of the shear components of strain and stress elastic fields upon cooling a liquid at a rate exceeding the critical value. The stationary elastic strains and stresses and the effective relaxation time are determined within the adiabatic approximation. It is shown that the glass transition process occurs through the mechanism of a first-order kinetic transition with allowance made for the strain dependence of the shear modulus. The critical cooling rate turns out to be proportional to the thermal diffusivity and unrelaxed shear modulus and inversely proportional to the temperature derivative of the relaxed shear modulus and the square of the heat conductivity length of the sample.     

Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

提出了一种纳米尺度的有限元方法,碳纳米管中的碳-碳化学键被模拟为键单元．按照平衡关系,根据有限元理论,作用于每个碳原子上的作用力可以写成键单元的刚度矩阵与每个碳原子位移的乘积．在分子力学的基本假设下,键单元刚度矩阵的每个元素可以写为分子力学中力场常数的函数,这样建立起了宏观力学方法(有限元)与纳米尺度力学方法(分子力学)之间的联系．应用该方法模拟了扶椅型与锯齿型单壁碳纳米管的力学行为从而验证了该方法的有效性．分析结果说明单壁碳纳米管的弹性模量与管厚度的选取直接相关．此外,弹性模量对所选取的分子力学中的力场常数非常敏感,管的弹性模量显示出对半径的尺度依赖性,但是管长度对弹性模量的影响小到可以被忽略．     

Elastic phase transitions in plutonium

The rich phase diagram of plutonium with a large number of different transitions in a narrow temperature interval has been puzzling scientists for decades. We offer a theoretical proof that most of the structural transformations in plutonium at temperatures exceeding the Debye temperature are the elastic phase transitions. The proof is given in the framework of the Landau theory of phase transitions and space group theory taking into account the anomalously small value of the elastic shear constants related to tetragonal and orthorhombic lattice deformations.     

Shear elasticity of fluids at low-frequent shear influence

The visco-elastic properties of liquids have been investigated using acoustical resonance method. Piezoquatrz performed tangential oscillations on the main resonance frequency of 74 kHz contacts by the one end of horizontal surface with the studied liquid layer covered by quartz cover-plate. So the stagnant shear waves are installed in layer. The solution of interaction of piezoquartz-liquid layer-cover-plate gives three methods of determination of the real shear modulus (G) and the tangent of mechanical loss angle (tan theta) of liquid. The first method is realized at smaller thickness of liquid layer then the length of shear wave. Liquids of different classes have been studied using this method: polymer liquids, oils, glycols and alcohols. The second method is connected with the propagation of shear wave in liquid layer, parameters of which are determined the G and tan theta. And the third method is based on the determination of limit shift of resonance frequencies at completes damping of shear wave in thick layer of liquid. All these three methods give satisfactory agreement of results.     

Oscillations of polymeric microbubbles: effect of the encapsulating shell

A model for the oscillation of gas bubbles encapsulated in a thin shell has been developed. The model depends on viscous and elastic properties of the shell, described by thickness, shear modulus, and shear viscosity. This theory was used to describe an experimental ultrasound contrast agent from Nycomed, composed of air bubbles encapsulated in a polymer shell. Theoretical calculations were compared with measurements of acoustic attenuation at amplitudes where bubble oscillations are linear. A good fit between measured and calculated results was obtained. The results were used to estimate the viscoelastic properties of the shell material. The shell shear modulus was estimated to between 10.6 and 12.9 MPa, the shell viscosity was estimated to between 0.39 and 0.49 Pas. The shell thickness was 5% of the particle radius. These results imply that the particles are around 20 times more rigid than free air bubbles, and that the oscillations are heavily damped, corresponding to Q-values around 1. We conclude that the shell strongly alters the acoustic behavior of the bubbles: The stiffness and viscosity of the particles are mainly determined by the encapsulating shell, not by the air inside.     

Dislocation motion in anisotropic multilayer materials

Line integral forms for the elastic field of dislocations in anisotropic, multilayer materials are developed and utilized in Parametric Dislocation Dynamics (PDD) computer simulations. Developed equations account for interface image forces on dislocations as a result of elastic modulus mismatch between adjacent layers. The method is applied to study dislocation motion in multilayer thin films. The operation of dislocation sources, dislocation pileups, confined layer slip (CLS), and the loss of layer confinement are demonstrated for a duplex Cu/Ni system. The strength of a thin film of alternating nanolayers is shown to increase with decreasing layer thickness, and that the maximum strength is determined by the Koehler barrier in the absence of coherency strains. For alternating Cu/Ni nanolayers, the dependence of the strength on the duplex layer thickness is found to be consistent with experimental results, down to a layer thickness of ≈10nm.     

Determination of elastic constants of Na0.5Bi0.5TiO3 from ab initio calculations

Elastic constants and bulk modulus for the tetragonal, rhombohedral, and cubic phase of Na_0.5Bi_0.5TiO₃ crystal were calculated from the first principles. From the calculated elastic constants, other structural properties such as bulk modulus, shear modulus, Young's modulus, and Poisson's ratio can be derived using respective relationships from Voight–Reuss–Hill approximation; bulk modulus was calculated as an example in this article. It was shown that elastic constants show different behavior for compression and elongation. The different values of elastic constants have been calculated for the direction parallel to the bismuth layer (crystallographic a(b)-axis) and the perpendicular direction (crystallographic c-axis). It seems to be caused by bismuth layer structure oxides of Na_0.5Bi_0.5TiO₃ crystal.     

Shock-wave compression of x-cut quartz as determined by electrical response measurements

The mechanical response of x-cut quartz in the vicinity of the Hugoniot elastic limit is determined from measurements of the piezoelectric current from samples impact loaded from 26 to 130 kbar. The Hugoniot elastic limit is determined to be 60_?1·5⁺³ kbar at a compression of 0·066_?0·002^+0·004 This Hugoniot elastic limit corresponds to a shear strength of 5·5 per cent of the C₄₄ shear modulus. For stresses well above the Hugoniot elastic limit the electrical current measurements show that the material exhibits a substantial reduction of shear strength. The pressure derivative of the bulk modulus is determined to be 4·5, substantially less than the ultrasonic value. The experimental records show evidence for a time delay for reduction of shear strength which varies from about 10^?7 sec immediately above the 60 kbar Hugoniot elastic limit to about 10^?8 sec for stresses well above the Hugoniot elastic limit. The measurements also show stress relaxation below the Hugoniot elastic limit between 40 and 60 kbar.     

On a simple impact test method for accurate measurement of material properties

A simple impact test method is presented to accurately measure the elastic and shear moduli and Poisson's ratio of a uniform Aluminum 6061-T651 cylindrical specimen with free boundary conditions. The elastic modulus is determined from the longitudinal vibration of the specimen and the shear modulus is determined from its torsional vibration. A new technique is developed to mount an accelerometer on the specimen to measure its torsional vibration. The Poisson's ratio determined for the specimen matches exactly with its known value.     

Viscoelastic phase separation in polymer blends

In this paper, the dynamics and morphology of viscoelastic phase separation in polymer blends is investigated based on the two-fluid model in two dimensions. At critical composition, we have carefully checked the role of shear modulus, without taking account of bulk modulus. The results show that the higher shear modulus component tends to form a dispersed phase in the intermediate stage of phase separation, if the difference between the shear moduli of the components is large enough. This is opposite to the role of bulk modulus, that the higher bulk modulus component forms a networklike pattern without taking account of the shear modulus even if it is the minority phase. The morphological formation is determined by the competition of opposite effects of shear modulus and bulk modulus. For polymer blends at critical composition, the bulk modulus difference leads to a networklike pattern formed by the higher modulus component in the intermediate stage of phase separation. But if the difference between the shear moduli of the components is large enough, a co-continuous structure is observed, resulting from the competition between shear and bulk moduli. For off-critical composition, difference in bulk modulus also leads to a networklike pattern of the component with higher bulk modulus in the intermediate stage of phase separation, but phase inversion is observed rapidly. A small difference between the shear moduli of the components can support the networklike pattern to continue for longer time. But the networklike pattern does not occur for large difference between shear moduli.Received: 9 September 2004, Published online: 10 November 2004PACS: 64.75. + g Solubility, segregation, and mixing; phase separation - 83.80.Tc Polymer blends     

Existence of Perturbed Equilibrium States in Some Two-Layer Systems with Density Inversion

In the system formed by a heavy elastic layer (lithosphere) and a half-space filled by an ideal incompressible fluid (asthenosphere), the possibility of the existence of equilibrium states with curved boundaries near an equilibrium of a system with rectilinear boundaries is investigated. Using an analysis of the characteristic equation, we obtain a relationship between the wave number of the desired static perturbation and the dimensionless parameters of the problem, namely, the dimensionless shear modulus, Poisson’s ratio, and the decompression. The assumption that the deformations are small imposes conditions on the ranges of modification of the quantities. For example, for a moderately compressible elastic material, the equilibrium which is called tectonic waves in geophysical applications is possible only in the long-wavelength range in the presence of the inversion of density and very strong decompression. The stability problem with respect to small dynamical perturbations of an (obtained) equilibrium with curved boundaries is stated. A wave dispersion relation connecting the complex frequency of oscillations with the wave number of perturbations and with the above dimensionless parameters of the system is derived.     

Structures and elastic properties of paraelectric and ferroelectric KTa0.5Nb0.5O3 from first-principles calculation

The structures, elastic properties and intrinsic hardness of B-O bonds of KTa_0.5Nb_0.5O₃ crystal in paraelectric and ferroelectric phase structures have been investigated by means of the density functional theory. Both structures are found to be elastically stable and in good agreement with available results. The elastic properties including the bulk modulus, shear modulus and Young’s modulus change largely during phase transition. The paraelectric KTa_0.5Nb_0.5O₃ crystal is more incompressible and harder than ferroelectric phase. The hardness of KTa_0.5Nb_0.5O₃ crystal is mostly determined by Nb-O bonds and the modifications of the bond strength affect the hardness of the crystal. Charge density contours indicate that the electronic distributions between B-O bonds play an important role in the formation of elastic properties.     

Toughening through multilayering in TiN–AlTiN films

The damage response of columnar multilayers of TiN and AlTiN to Vickers indentation is studied through focused ion beam machining and elastic modelling. Multilayers display an enhanced resistance, which increases with layer refinement, to the multiple fracture modes that appear at high loads in these materials, including edge (nested) cracks and inclined shear cracks. Measurements of layer thickness reveal that multilayers display additional modes of plastic deformation that lead to permanent compression and bending of the film. An elastic model of contact deformation in a bilayer where plasticity is mimicked by greatly enhanced elastic compliance of the film is used to rationalize the trends in crack resistance. It is shown that the enhanced toughness is not due to any increase in the strain capacity (hardness/modulus) of the film material, brought about by multilayering.     

Measurement of the shear strength of a charge density wave

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Influence of Adhesive Characteristics on the Interfacial Stress Concentrations in Externally FRP Plated Steel Beams

This paper deals with the influence of adhesive properties on the interlaminar stress in externally FRP plated steel beams. The analysis provides efficient calculations for both shear and normal interfacial stresses in steel beams strengthened with composite plates, and accounts for various effects of Poisson's ratio and Young's modulus of adhesive. Such interfacial stresses play a fundamental role in the mechanics of plated beams, because they can produce a sudden and premature failure. The analysis is based on equilibrium and deformations compatibility approach developed by Tounsi [1]. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the steel beam and bonded plate. The paper concludes with a summary and recommendations for the design of the strengthened beam.     

Tensile strength of aluminium nitride films

Two-layered aluminium nitride (AlN)/silicon nitride microbridges were fabricated for microbridge tests to evaluate the elastic modulus, residual stress and tensile strength of the AlN films. The silicon nitride layer was added to increase the robustness of the structure. In a microbridge test, load was applied to the centre of a microbridge and was gradually increased by a nano-indenter equipped with a wedge tip until the sample was broken, while displacement was recorded coherently. Measurements were performed on single-layered silicon nitride microbridges and two-layered AlN/silicon nitride microbridges respectively. The data were fitted to a theory to derive the elastic modulus, residual stress and tensile strength of the silicon nitride films and AlN films. For the AlN films, the three parameters were determined to be 200, 0.06 and 0.3?GPa, respectively. The values of elastic modulus obtained were consistent with those measured by conventional nano-indentation method. The tensile strength value can be used as a reference to reflect the maximum tolerable tensile stress of AlN films when they are used in micro-electromechanical devices.     

Reinforcement of Carbon Nanotube/Polydimethylsiloxane True Nanocomposite

Russian Physics Journal - The paper shows that the elastic modulus of carbon nanotubes in a polymer matrix nanocomposite is lower not only than its nominal value, but also the elastic modulus of...     

Prestressed FRP and interface slip effect on interfacial stresses analysis: the new FRP sheets rigidity model

This paper presents an improved bi-material beam theory with adhesive interface and the new prestressed-fiber reinforced polymer (FRP) – model, which has been applied to the study the problem of interfacial stresses. This work explicitly considers the interfacial slip effect on the structural performance by including both the effect of adherend shear deformations and the fiber volume fraction of the prestressed laminates. This new method needs only one differential equation to determine both shear and normal interfacial stress, which is one aspect that has not been taken into account by the previous studies in the literature. A parametrical study is carried out to show the effects of some design variables, e.g., stiffness and thickness of adhesive layer and FRP plate.