Numerical Simulation Of Ultrasonic Wave Propagation In Elastically Anisotropic Media

The ultrasonic non-destructive testing of components may encounter considerable difficulties to interpret some inspections results mainly in anisotropic crystalline structures. A numerical method for the simulation of elastic wave propagation in homogeneous elastically anisotropic media, based on the general finite element approach, is used to help this interpretation. The successful modeling of elastic field associated with NDE is based on the generation of a realistic pulsed ultrasonic wave, which is launched from a piezoelectric transducer into the material under inspection. The values of elastic constants are great interest information that provide the application of equations analytical models, until small and medium complexity problems through programs of numerical analysis as finite elements and/or boundary elements. The aim of this work is the comparison between the results of numerical solution of an ultrasonic wave, which is obtained from transient excitation pulse that can be specified by either force or displacement variation across the aperture of the transducer, and the results obtained from a experiment that was realized in an aluminum block in the IEN Ultrasonic Laboratory. The wave propagation can be simulated using all the characteristics of the material used in the experiment evaluation associated to boundary conditions and from these results, the comparison can be made.

Anharmonicity in NaCl and beta brass

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A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

A symmetric solution for a cylindrical shell enclosed in an elastic casing

The problem of a long, thin circular cylindrical shell enclosed in an elastic casing and subjected to a ring of radial load on the inner rim is solved using the Love function for the casing in conjunction with Flügge shell theory. Numerical work has been done with a digital computer and the results for stress and displacement fields are given for various values of the shell geometry parameters and material constants.

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders. (C) 2009 Elsevier B.V. All rights reserved.

Restricted rotation dynamics and far-infrared spectra of liquid water governed by elastic interactions

A semi-phenomenological model describing wideband dielectric and far-infrared spectra of liquid water was proposed recently by the same authors [J. Mol. Struct. 606 (2002) 9], where a small dipole-moment component changing harmonically with time determines a weak absorption band (termed here the R-band) centred at the wavenumber v similar to 200 cm(-1). In the present work, a rough molecular theory of the R-band based on the concept of elastic interactions is given. Stretching and bending of hydrogen bonds cause restricted rotation (RR) of a polar water molecule in terms of a dimer comprising the H- bonded molecules. Analytical expression for the RR frequency nu(str) is derived as a function of the RR amplitude, geometrical parameters and force constants. The density g(nu(str)) of frequency distribution is shown to be centred in the R-band. The spectrum of the dipolar auto-correlation function calculated for this structural-dynamical model is found. A composite model comprising two intermolecular potentials is proposed, which yields for water a good description of the experimental wideband (from 0 to 1000 cm(- 1)) spectra of complex permittivity and of absorption coefficient. The presented interpretation of these spectra is based on a concept that water presents a two-component solution, with components differing by the types of molecular rotation. (C) 2003 Elsevier B.V. All rights reserved.

Adsorption of Ni(SO4) on Malaysian rubber-wood ash

The possible use of wood ash as an adsorbent of nickel sulphate from dilute solutions and the effect of operating parameters were investigated in this study. The rate constants of adsorption were determined at different concentrations and temperatures. The applicability of the first-order reversible equation and an empirical kinetic model were tested to understand the kinetics of nickel sulphate removal at different concentrations. Pore diffusion was found as the rate-controlling step. The Langmuir and Freundlich isotherms were applied to find out the adsorption parameters. The activation energy of adsorption was -11.54 kJ mol-1. The value of the enthalpy change was ?H=-10.35 kcal mol-1.

Anisotropy in elastic properties of lithium sodium sulphate hexahydrate single crystal—An ultrasonic study

The double sulfate family (ABSO4), where A and B are alkali metal cations, is the object of great interest owing to the complexity and richness of its sequence of phase transition induced by temperature variation. A new sulfate salt characterized by the presence of water molecule in the unit cell with the chemical formula, Li2Na3(SO4)2⋅6H2O (LSSW), was obtained. The ultrasonic velocity measurement was done with pulse echo overlap technique [PEO]. All the six second order elastic stiffness constants, C11 = C22, C33, C44 = C55, C12, C14 and C13 = C23 are reported for the first time. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the polar plots of phase velocity, slowness, Young’s modulus and linear compressibility in a–b and a–c planes.