Elastic self-healing during shear accommodation in crystalline nanotube ropes

Rigid-tube computations of simple (transverse) shear in crystalline nanotube ropes (CNTRs) reveal that shear modulus and strength increase and decrease with the tube radius, respectively. High modulus to strength ratios suggest that dislocations play a minor role during their plasticity. The computed shear moduli are in agreement with previous studies, although shape change and rolling-based shear may modify low strain and temperature behavior. The instability past the shear strength is due to shear localization via interlayer sliding, wherein stress relief results in significant elastic energy dissipation. Large-tube radius CNTRs accommodate large strains at minimal energetic cost during sliding, due to the increasingly cohesive and short range nature of the intertube potential. Fascinatingly, the crystal aids its recovery, implying that CNTRs may be promising materials for energy absorption and tribology.     

Standing shear waves in rubberlike layered media

Standing shear waves arising in layered media the shear modulus of which varies in a stepwise manner at the plain boundaries between the layers are considered. A general solution is obtained for the shear wave amplitudes in a resonator with an N-layer structure the lower boundary of which performs harmonic vibrations while a finite-mass plate is attached to the upper boundary. Results of calculations and measurements are presented for a resonator with a structure in which nondeformable metal layers alternate with elastic rubberlike polymer layers. It is shown that the resonance frequencies of such a resonator can be controlled by changing the number of layers and their thicknesses. It is demonstrated, both experimentally and theoretically, that, from the resonance curve of a resonator with a two-layer structure, it is possible to determine the shear modulus of one of the layers under the condition that the elasticity of the other layer is known. The method of separation into a finite number of layers is used to analyze the resonance characteristics of a one-dimensional resonator filled with a rubberlike medium the properties of which continuously vary in the direction perpendicular to the shear displacements. The choice of the number of layers depending on the type of inhomogeneity is analyzed.     

Two-layer tubes from cubic crystals

Effective Young’s moduli and Poisson’s ratios of two-layer tubes from cubic crystals have been analyzed theoretically. It is shown (using derived formulas for numerical estimates) that the mechanical properties of two-layer tube composites from auxetics and nonauxetics are not described by the mixture rule. It is demonstrated that the deviation of the effective modulus from the mixture rule predictions rapidly increases with an increase in Young’s modulus of the nonauxetic components of a composite. It is established that, combining auxetics and nonauxetics in layered tubes, one can obtain, depending on the packing order in layers, either a strong increase or a decrease in auxeticity.     

Possible nature of oscillations in the time dependences of the internal friction and effective shear modulus in Al-Cu alloys

The conditions of the appearance of in-phase oscillations in the time dependences of the low-frequency internal friction and effective shear modulus G _eff in Al-0.01 wt% Cu and Al-0.001 wt % Cu alloys are studied. The in-phase oscillations are shown to appear in the alloys only when their dislocation-impurity structure is disturbed from equilibrium and the impurity concentration near a dislocation is optimum. This fact suggests that the in-phase oscillations are due to a collective character of dislocation-impurity interactions, which leads to a transfer of energy of translational dislocation motion to transverse dislocation vibrations in the main slip plane.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

Estimation of the state vector and identification of the complex modulus of a beam

A non-uniform viscoelastic beam traversed by flexural waves was considered. Methods based on Timoshenko's model were established for (i) estimation of its state (shear force, transverse velocity, bending moment and angular velocity) at an arbitrary section on the basis of at least four independent measurements, and (ii) identification of its complex modulus, parametric as well as non-parametric, on the basis of at least five independent measurements. From the estimated state, related useful quantities such as strain, stress and power transmission can be obtained. Experimental tests were carried out with beams made of polymethyl methacrylate and polypropylene and instrumented with pairs of strain gauges at eight non-uniformly distributed sections. Estimation of strain at one instrumented section was based on measured strains at five to seven surrounding sections, while identification of the complex modulus was based on measured strains at five to eight sections. Generally, the identified complex moduli showed fair agreement with previous results from tests involving extensional waves, while the estimated strains were in good accord with measured strains. No significant improvement in the quality of results was achieved when the number of measured strains was increased to more than five for the identification of the complex modulus and six for the estimation of state.     

Free vibrations of a laminated beam by a microstructure theory

The free vibrations of a laminated beam are considered within the framework of a theory that models the composite beam as a macrohomogeneous beam with microstructure. The beams are assumed to consist of several parallel alternating layers of two homogeneous, isotropic elastic materials. The system of three coupled partial differential equations is solved exactly, and attention is devoted to the determination of natural frequencies of vibration of laminated beams with (i) hinged-hinged ends and (ii) clamped-clamped ends. For the sake of comparison, the same boundary value problems are also solved within the framework of the so-called effective modulus theory, which treats the composite as a transversely isotropic and “fictitiously” homogeneous Timoshenko beam, with effective moduli and density. For relatively long beams, i.e., in the low frequency range, the natural frequencies obtained from the two theories are in excellent agreement, but as the depth-to-length ratio, ζ, increases the microstructure frequencies are observed to be much lower than the effective modulus frequencies, the magnitude of the effect becoming more pronounced with increasing mode number n.     

Universal elasticity and fluctuations of nematic gels

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.     

Elastic properties of mono- and poly-crystalline PbO-type FeSe1−xTex (x = 0–1.0): A first-principles study

The structural parameters of the alloys are obtained as non-magnetic cases for which justification is provided. The elastic coefficients and various moduli of the monocrystalline FeSe_1−xTe_x system as a function of doping are predicted for the first time using density functional method. The bulk moduli, shear moduli, Young’s moduli, Poisson’s ratios, velocities of sound and Debye temperature of the corresponding poly-crystalline aggregates have been calculated and the results discussed.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.     

Elastic moduli of nc-TiN/a-Si3N4 nanocomposites: Compressible, yet superhard

Earlier measurements of elastic moduli of nc-TiN/a-Si₃N₄ nanocomposites of different composition and hardness by means of vibrating reed and surface Brillouing scattering, that yield Young’s and shear modulus, as well as the Poisson’s ratio, have been confirmed by high-pressure X-ray diffraction measurements, that yield bulk modulus. It is found that elastic moduli of all measured samples are essentially the same within relatively small error of measurements, and only slightly lower than that of pure TiN. The nanocomposites are superhard thanks to their unique nanostructure with strengthened SiN_x interface.     

Strength statistics and the distribution of earthquake interevent times

The Weibull distribution is often used to model the earthquake interevent times distribution (ITD). We propose a link between the earthquake ITD on single faults with the Earth’s crustal shear strength distribution by means of a phenomenological stick–slip model. For single faults or fault systems with homogeneous strength statistics and power-law stress accumulation we obtain the Weibull ITD. We prove that the moduli of the interevent times and crustal shear strength are linearly related, while the time scale is an algebraic function of the scale of crustal shear strength. We also show that logarithmic stress accumulation leads to the log-Weibull ITD. We investigate deviations of the ITD tails from the Weibull model due to sampling bias, magnitude cutoff thresholds, and non-homogeneous strength parameters. Assuming the Gutenberg–Richter law and independence of the Weibull modulus on the magnitude threshold, we deduce that the interevent time scale drops exponentially with the magnitude threshold. We demonstrate that a microearthquake sequence from the island of Crete and a seismic sequence from Southern California conform reasonably well to the Weibull model.     

Second virial coefficient and mechanical moduli of metallic glasses

The relationship between the bulk, shear moduli and second virial coefficient of amorphous materials is derived according to their dependences with the radial distribution function. Lennard-Jones–Gaussian potential is used to investigate the relationship between second virial coefficient and temperature, where Lennard-Jones potential represents interactions with the nearest neighbor atoms, and Gaussian potential is responsible for the multi-atom interactions including the next nearest neighbor atoms and heterogeneous structures for a metallic glass. The results show that deep potential well formed by Gaussian potential causes a large second virial coefficient at low temperatures, which is very obvious for the larger fragility glasses. The quadratic form relationship of shear modulus and compositions is proposed, and confirmed by the experimental results of Pd_xNi_100−x−20P₂₀ alloy.     

Determination of Poisson's ratio and Young's modulus of low-density polyethylene

The extensional moduli and Poisson's ratios of cold-drawn low-density polyethylene sheets have been determined by direct observation of the changes in dimensions under load of electron microscope grids printed on the surfaces of the sheets.

The highly drawn sheets show incompressible behavior only for vanishingly small strains. It is proposed that the departure from incompressibility is associated with the departure from linear deformation. It is suggested that the anisotropic behavior can be analyzed in terms of three deformation mechanisms: (a) the c-shear mechanism; (b) incompressible elastic deformation associated with the amorphous regions; and (c) a slip mechanism which produces the departure from linear deformation.     

Elastic interaction between adatoms near a distortive phase transition

The indirect elastic interaction between two adatoms on substrates with a very small shear modulus such as V₃Si and Nb₃Sn near the transformation temperature T_M is calculated. As the temperature decreases towards T_M, the shear moduli of these materials go to zero, and the strength of the interaction increases dramatically. The interaction is strongly attractive if the adatoms are aligned along a cube axis and repulsive if they are at 45° to the axis.     

A first-principles study of the properties of P-43m-Si3×2 (X = N,P and As)

The new P-43m-Si₃P₂ and P-43m-Si₃As₂ structures are predicted using the first-principles approach based density functional theory (DFT). The elastic constants, structural stability, phonon dispersion spectra, band structures, density of states, and optical properties of P-43m-Si₃×₂ (X=N, P and As) have been analyzed. The values of the elastic constants indicate that their structures are mechanically stable. Each elastic constant of the Si₃N₂ is greater than the corresponding elastic constants of Si₃P₂ and Si₃As₂. The Young's moduli, shear moduli, bulk moduli, Pugh ratios and Poisson's ratios of P-43m-Si₃×₂ are calculated at 0 GPa. Si₃N₂ has a larger Young's modulus, so it has higher hardness and good resistance to deformation. The bulk moduli of P-43m-Si₃×₂ are isotropic. The shear modulus of Si₃As₂ is anisotropic. The Pugh ratios of P-43m-Si₃×₂ are 0.50, 0.49 and 0.39, respectively. Their Poisson's ratios are 0.28, 0.29 and 0.33, respectively. The results show that they are brittle materials at zero pressure. The calculated phonon spectra confirm that they are dynamically stable. The calculated enthalpy of formation indicates their thermodynamic stability. The energy band gaps of P-43m-Si₃×₂ calculated by HSE06 hybrid function are 0.786, 0.955 and 0.343 eV, respectively. Si₃N₂ has a direct bandgap, Si₃P₂ and Si₃As₂ have indirect bandgaps. The dielectric functions, refractive indices, optical reflectance spectra, absorption coefficients, conductivities and loss functions of P-43m-Si₃×₂ are calculated. The calculated static dielectric constants of P-43m-Si₃×₂ are 5.207, 9.237 and 10.072, respectively. The maximum values of the loss functions of P-43m-Si₃×₂ are 6.408, 5.672 and 5.276 eV, respectively.     

Dynamic compliance of multilayer coatings

The algorithm for calculation of dynamic compliance of multilayer coatings was developed. The compliance modulus and phase lag of coating surface motion vs. the current pressure depend on viscoelastic properties of materials, ratio of wavelength to layer thickness λ/H, and ratio of wave velocity to propagation velocity of shear vibrations in the base layer V / C _t,2 ⁰ Dynamic compliance of the two-layer coating consisting of a thick base layer and thin durable outer layer was calculated. The elasticity modulus of the outer layer ranged up to eight values of elastic modulus of the inner layer; the density of the outer layer either remained equal to the density of the inner layer or increased proportionally to the elastic modulus. Depending on V / C _t,2 ⁰ two scenarios of compliant coating interaction with the turbulent flow were distinguished: resonant and broadband ones. It is shown that the vibration properties of two-layer coatings can be significantly better than the properties of the monolayer coatings. This makes it possible either to increase the coating strength or to work efficiently at lower velocities.     

Boron–Carbon Nanocomposites Fabricated at High Pressures and Temperatures

Interaction of amorphous boron and C₆₀ fullerite is analyzed at pressures of 2.0 and 7.7. GPa and temperatures of 600–1800°C. Effect of pressure and temperature on the material structure is studied, temperatures for synthesis of boron carbide and diamond are found, and the sequence of transformations of the carbon component is determined. Ultrasonic method is used to measure elastic moduli of the samples, and the dependences of the moduli on the structure are analyzed. It is demonstrated that the boron–carbon nanocomposite synthesized at relatively low pressure (2.0 GPa) and temperature (about 1000°C) exhibits high elastic parameters (bulk modulus, B ≈ 75.3–84.0 GPa; Young modulus, E ≈ 108–119 GPa; and shear modulus, G ≈ 43–47 GPa at a density of about 2.2 g/cm³). The results can be used for development of novel nanocomposite materials.     

Low-frequency shear parameters of liquid viscoelastic materials

An experimental study of the shear parameters of viscoelastic liquids is carried out by the acoustic resonance method based on the changes in the natural frequency and Q factor of a piezoelectric quartz resonator. The liquid to be studied is placed between a stationary quartz strap and the piezoelectric quartz crystal vibrating at the resonance frequency. For a set of drilling muds, the values of the real and imaginary shear moduli are obtained at a frequency of 74 kHz. The measurements are performed with a liquid layer thickness much smaller than the shear wavelength. It is shown that the shear modulus decreases with increasing strain amplitude. A cluster model based on the Isakovich-Chaban nonlocal diffusion theory is proposed for explaining the low-frequency viscoelastic relaxation process.     

Mechanical anisotropy and thermoacoustic properties of SnO2 under high pressures: an ab initio approach

The effects of hydrostatic pressures on the electronic, thermoacoustic and elastic anisotropies of SnO₂ in the rutile structure is analyzed up to 18 GPa. It is found that the polycrystalline bulk modulus B increases from 227 to 312 GPa between 0 and 18 GPa while the Young and shear moduli slightly decrease with pressures. The resulting polycrystalline ductility increases with pressures. The speed of the sound for longitudinal waves increases with pressure, while the transverse polarizations and the Debye temperature decrease. Large crystal anisotropy for the shear planes {001} between ? 110? and ? 010? directions under pressures, associated with the phase transition to the Cl₂Ca, is found.