Ultrasonic leaky interface waves for composite-metal adhesive bond characterization

Highly stressed or damaged regions in aircraft structures are increasingly being reinforced by adhesively bonding an overlay of a unidirectional boron fiber-epoxy composite to the aircraft metallic substrate. While conventional C-scan ultrasonics can be used to detect disbonding of the overlay, nondestructive methods are also required to detect weak adhesive bonding. This paper describes a preliminary experimental investigation of the existence of ultrasonic leaky interface waves between overlays and 2024-T351 aluminum alloy and D6ac steel substrates, and their possible use for detection of weak bonds. The approach used was to excite these leaky waves using Rayleigh waves generated by a laser line-source on the substrate. The existence of the leaky waves, traveling normal to the composite fibers, between boron-epoxy overlays and either an aluminum or steel substrate, was confirmed by observations of the quasishear pulses leaked to the top of the overlay, and of the Rayleigh wave transmitted to the free surface beyond the overlay. When quantitative measurements were possible, measured values of the complex interface wave speed agreed satisfactorily with predicted values. This paper also demonstrates one case for which leaky interface waves are sensitive to weak bonding caused by the presence of a contaminant on the substrate surface prior to bonding: application of a low-concentration aqueous solution of hydraulic oil to the aluminum substrate prior to bonding of the overlay caused a marked increase, over that for the well-bonded case, in the observed amplitude of the quasi-shear pulses leaked to the top of the overlay by decay of the interface wave. More experiments are needed to establish whether leaky interface waves are sensitive to bond condition for various other combinations of substrate, overlay and contaminant.     

Acoustic microscopy and dispersion of leaky Rayleigh waves onrandomly rough surfaces: a theoretical study

A theoretical investigation of the dispersion of leaky Rayleigh waves propagating along one-dimensional (1-D) rough fluid-solid interfaces was carried out by simulating the measurement process of a line-focus beam acoustic microscope. The interface profiles were described in terms of their rms, also known as the roughness of the profile, autocorrelation length, and autocorrelation function. The reflectivity of the interfaces was calculated by using a second-order perturbation approach in the profile roughness. Theoretical V(z) curves were generated and analyzed to yield values of the phase velocity of the Rayleigh waves. The dependence of the Rayleigh wave velocity on the profile and material parameters was examined. Significant variations of the phase velocity were found for values of the roughness which are small compared to the shortest of the wavelengths involved in the scattering. The dispersion relations also showed considerable sensitivity to changes in mechanical properties typical of materials of engineering interest. In the low-frequency range, simulations indicated the dispersion of Rayleigh waves to be rather insensitive to the spectral content of the profile     

Response of acoustic imaging systems using convergent leaky waves to cylindrical flaws

A theoretical study of imaging systems utilizing focused leaky surface acoustic waves (SAWs), and their response to certain kind of defects is presented. In particular, circular cylindrical inhomogeneities with axes perpendicular to the surface are considered. The scattering of the SAW from this cylinder is formulated with some approximations. The surface wave incident on the inhomogeneity is initially found as an angular spectrum of plane waves. However, to apply the boundary conditions at the cylindrical surface, the incident field has to be transformed into a superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAWs, is converted back to a plane wave spectrum. A formula is obtained for the transducer output voltage in terms of the position and the radius of the cylinder, and it is suitable for computer evaluation. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. By comparing the output voltages for cylinders of different radii, the sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are in agreement with the experimental observations.     

Finite element simulation and visualization of leaky Rayleigh wavesfor ultrasonic NDE

The generation and propagation properties of transient leaky Rayleigh waves are characterized by a two-dimensional finite element model. The displacement vector is used as the primary variable for the solid medium and a potential scalar, which is a replacement for the pressure, is taken as the fundamental variable for the fluid medium. The coupled system of finite element equations are solved in the time domain by direct integration through the central difference scheme. Three configurations are considered: the conversion of a Rayleigh surface wave into a leaky Rayleigh wave, a focused beam probing a fluid/solid interface at the Rayleigh angle, and the interaction of a defocused wave with the interface. The wave velocity in the fluid (water) is lower than the Rayleigh wave velocity in the solid (aluminum). The wave propagation profile in each case is predicted by the model. The finite element model proves to be an effective tool for surface acoustic device design and ultrasonic NDE     

Rayleigh waves in magneto-electro-elastic half planes

This paper investigates Rayleigh waves in magneto-electro-elastic half planes. The magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry. Sixteen sets of boundary conditions are considered and the corresponding frequency equations are derived. It is found that for any of the 16 sets of boundary conditions, the Rayleigh waves, if exist, are always non-dispersive. Numerical results show that both the material coefficients and boundary conditions can significantly influence the Rayleigh wave properties in magneto-electro-elastic half planes.     

Rayleigh waves in electrostrictive dielectric solids

Summary The possibility of the propagation of Rayleigh waves in an electrostrictive dielectric medium is investigated. It is shown that such waves can propagate, but they induce some body forces and surface tractions.     

Rayleigh waves in Cosserat elastic materials

The present paper gives explicit solutions for surface waves propagation in a homogeneous half space filled with an isotropic Cosserat elastic material. Such solutions are important in the study of seismic waves in an earthquake, supposing that the bottom land is modeled as having a microstructure. To construct explicit expressions for the possible surface waves under consideration, we use the Stroh formalism. These solutions are further used to study the Rayleigh waves and to give the explicit equation for the Rayleigh surface wave speed (secular equation). Numerical calculations and graphics corresponding to the analytical solution are given for aluminium-epoxy composite.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Analysis of guided and leaky waves excited by an infinite line source in metamaterial substrates

The properties of electromagnetic modes having real and complex propagation constants are thoroughly examined in this article by considering the excitation of a metamaterial slab having both negative values of dielectric permittivity and magnetic permeability. The conditions of existence of modes are investigated and the excited corresponding modes are analysed. Several types of waves are examined and their corresponding dispersion properties are derived     

Ultrasonic guided waves in bone

Recent progress in quantitative ultrasound (QUS) has shown increasing interest toward measuring long bones by ultrasonic guided waves. This technology is widely used in the field of nondestructive testing and evaluation of different waveguide structures. Cortical bone provides such an elastic waveguide and its ability to sustain loading and resist fractures is known to be related to its mechanical properties at different length scales. Because guided waves could yield diverse characterizations of the bone's mechanical properties at the macroscopic level, the method of guided waves has a strong potential over the standardized bone densitometry as a tool for bone assessment. Despite this, development of guided wave methods is challenging, e.g., due to interferences and rnultiparametric inversion problems. This paper discusses the promises and challenges related to bone characterization by ultrasonic guided waves.     

Focusing of Rayleigh waves: simulation and experiments

A linear array of surface wave transducers has been developed to generate focused surface wave motion. A novel theoretical approach, whereby time-harmonic surface wave motion is represented by a carrier wave that satisfies a reduced wave equation on the surface of the body and supports the subsurface motion, is used to model the beam generated by a single element of the array. Comparison of theoretical and experimental results show that, for a single element, the opening angle of the beam is about 20 degrees and its cross-section can be represented by a Gaussian distribution of the normal displacements. For an eight-element array, the focused beam is subsequently obtained by superposition considerations. For the focused beam comparisons of theoretical and experimental results, in which the latter have been obtained by the use of a laser interferometer, show excellent agreement both for the normal displacements along a radial line and across the width of the beam. The array can be used for self-focusing of surface waves on a surface defect.     

SAW device applications of longitudinal leaky surface waves on lithium tetraborate

The possibility of high frequency SAW device applications of longitudinal leaky surface waves (LLSW) on lithium tetraborate (Li₂ B₄O₇; LBO) is investigated in this paper. An electrical equivalent circuit model (ECM) is extended in order to consider effects of bulk wave scattering for the LLSWs. The equivalent circuit parameters used in the extended ECM for designing the LLSW devices are directly determined from numerically calculated dispersion curves. For applications of the LLSW, high frequency SAW filters on LBO with the Euler angles (0°, 47.3°, 90°) are demonstrated. As examples of the high frequency devices, 1.5 GHz and 1.2 GHz SAW filters using the mode are designed by using the extended ECM, and fabricated by using conventional patterning processes. One is for the filter of the global positioning system (GPS), another is for the 1.2 GHz band data transmission radio system in Japan. As a result, low loss SAW filters can be obtained easily without submicron fabrication techniques by using the LLSWs on LBO. Furthermore, the frequency response calculated by the extended ECM are in a good agreement with the experiments     

Rayleigh waves in magneto-thermoelastic solids with thermal relaxation

Following a linear theory of magneto-thermo-elasticity with thermal relaxation, the propagation of Rayleigh waves in a semi-infinite body permeated by an uniform magnetostatic field parallel to the boundary surface is investigated. It is assumed that the elastic medium under consideration is a homogeneous, isotropic, electrically and thermally conducting one. The roots of the frequency equation are calculated numerically. The approximate solution for small thermoelastic and magnetoelastic coupling is obtained and compared with the exact solution.     

Rayleigh surface waves problem in linear thermoviscoelasticity with voids

In this paper, we study the propagation of the Rayleigh surface waves in a half-space filled by an exponentially functionally graded thermoviscoelastic material with voids. We take into consideration the dissipative character of the porous thermoviscoelastic models upon the propagation waves and study the damped in time wave solutions. The propagation condition is established in the form of an algebraic equation of tenth degree whose coefficients are complex numbers. The eigensolutions of the dynamical system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is expressed as a linear combination of the five analytical solutions, while the secular equation is established in an implicit form. The explicit secular equation is obtained for an isotropic and homogeneous thermoviscoelastic porous half-space, and some numerical simulations are given for a specific material.     

Side radiation of Rayleigh waves from synchronous SAW resonators

Surface acoustic wave (SAW) resonators on lithium tantalate (LiTaO3) and lithium niobate (LiNbO3) are investigated. The amplitude of the acoustic fields in the resonators are measured using a scanning laser interferometer. The amplitude profiles of the surface vibrations reveal the presence of distinct acoustic beams radiated from the transducer region of the SAW resonators and propagating with low attenuation. We suggest that this radiation is generated by the charges accumulating at the tips of the finger electrodes. The periodic system of sources, namely oscillating charges at the fingertips, generates Rayleigh-wave beams in the perpendicular and oblique directions. Green's function theory is used to calculate the coupling strength and slowness of the Rayleigh waves on 42 degrees Y-cut LiTaO3 and Y-cut LiNbO3 substrates as a function of the propagation direction. Furthermore, the propagation angles of the Rayleigh-wave beams as a function of frequency are calculated. The computed angles are compared with the measured ones for both the LiTaO3 and LiNbO3 substrates.     

Rayleigh imaging of graphene and graphene layers

We investigate graphene and graphene layers on different substrates by monochromatic and white-light confocal Rayleigh scattering microscopy. The image contrast depends sensitively on the dielectric properties of the sample as well as the substrate geometry and can be described quantitatively using the complex refractive index of bulk graphite. For a few layers (<6), the monochromatic contrast increases linearly with thickness. The data can be adequately understood by considering the samples behaving as a superposition of single sheets that act as independent two-dimensional electron gases. Thus, Rayleigh imaging is a general, simple, and quick tool to identify graphene layers, which is readily combined with Raman scattering, that provides structural identification.     

Ultrasonic imaging by local shape function method with CGFFT

A numerical algorithm for the reconstruction of the density and the compressibility of a biological body from ultrasonic scattering data is presented. The reconstruction algorithm is based on the local shape function method (LSF) combined with the conjugate gradient method with fast Fourier transform (CGFFT). The nonlinearity due to the multiple scattering has been accounted for in an iterative minimization scheme. Numerical examples of simulation data and real experimental data are given showing the capability of this algorithm     

Temperature imaging in nonpremixed flames by joint filtered Rayleigh and Raman scattering

Joint fuel Raman and filtered Rayleigh-scattering (FRS) imaging is demonstrated in a laminar methane-air diffusion flame. These experiments are, to our knowledge, the first reported extension of the FRS technique to nonpremixed combustion. This joint imaging approach allows for correction of the FRS images for the large variations in Rayleigh cross section that occur in diffusion flames and for a secondary measurement of fuel mole fraction. The temperature-dependent filtered Rayleigh cross sections are computed with a six-moment kinetic model for calculation of major-species Rayleigh-Brillouin line shapes and a flamelet-based model for physically judicious estimates of gas-phase chemical composition. Shot-averaged temperatures, fuel mole fractions, and fuel number densities from steady and vortex-strained diffusion flames stabilized on a Wolfhard-Parker slot burner are presented, and a detailed uncertainty analysis reveals that the FRS-measured temperatures are accurate to within +/- 4.5 to 6% of the local absolute temperature.