Leaky Lamb Waves Research Articles

Nondestructive evaluation of composite laminates by leaky Lamb waves

Nondestructive evaluation of composite laminates by leaky Lamb waves

漏えいラム波用すだれ状トランスジューサの動作特性と漏えい表面波速度測定システム

漏えいラム波用すだれ状トランスジューサの動作特性と漏えい表面波速度測定システム

Anomalies in the ray synthesis of backscattering from hollow elastic spherical shells

When the form function for backscattering f(θ = πka) from a hollow spherical shell is described by a ray synthesis based on a generalized surface ray theory [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)], two anomalies occur in the vicinity of the first axial longitudinal resonance within the shell. The first anomaly is the manifestation of the longitudinal resonance and a ray synthesis of the specular reflection contribution fsp, which includes a novel curvature correction fcc, seems to properly describe one effect of longitudinal resonances on f [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 88, 1114–1122 (1990)]. The fundamental longitudinal resonance occurs at ka = πcL/[c(1 − b/a)], where k is the wave number of the incident wave, b/a is the inner‐to‐outer radii ratio of the shell, and cL and c are the longitudinal sound speed of the elastic material and speed of sound in water, respectively. The present ray synthesis contains leaky Lamb wave contributions that account for the circumnaviga...

Ray synthesis of Lamb wave contributions to the total scattering cross section for an elastic spherical shell

The optical theorem relates the extinction cross section σe(ka) to the forward-scattering amplitude f (θ=0,ka). Here, θ denotes the scattering angle, k is the wavenumber of the incident sound, and a is the radius of the scatterer. If the absorption by the scatterer is negligible so that the scatterer is elastic, σe is equal to the total scattering cross section σt. By applying this theorem to the partial wave series for f (0,ka), an expression can be obtained for σt for an elastic spherical shell in water. However, the series representation of σt does not facilitate a direct understanding of the rich structure caused by the shell’s elastic response. In particular, the elastic response is attributable to leaky Lamb waves. A generalization of the geometrical theory of diffraction [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)] is employed to synthesize f (0,ka). This simple ray acoustic synthesis contains a component for ordinary diffraction by the shell and distinct contributions for the individual Lamb waves that can be excited on the shell. A comparison of numerical computations for σt utilizing the exact partial wave series and the ray synthesis shows good agreement in the description of the resonance structure. The relevant range of ka for this comparison is 7<ka<100. The elastic material of the shell is 440c stainless steel and the inner-to-outer radius ratio is b/a=0.838. Dispersion curves and radiation damping for Lamb waves were calculated by Watson transform methods. The structure in σt(ka) due to Lamb waves may also be depicted as a manifestation of forward glory scattering and experimental evidence for the forward glory is noted.

Inversion of leaky Lamb wave data by simplex algorithm

A numerical procedure is presented for the inversion of leaky Lamb wave (LLW) data to determine certain material properties of a waveguide, using a modified version of the simplex algorithm. The technique is capable of computing the parameter values that best fit a particular set of data, given an analytical model of the associated phenomenon containing any number of variables and parameters. The basic theoretical concepts involved are reviewed, and the versatility and simplicity of the method are illustrated by examples. The inversion scheme is used to estimate the elastic properties and thickness of an adhesive layer between two aluminum plates and the elastic constants of a unidirectional graphite/epoxy composite laminate. The limitations of the LLW data in the determination of the elastic constants of a composite are discussed.

Determination of the properties of composite interfaces by an ultrasonic method

The feasibility of using a recently developed ultrasonic technique to determine certain macroscopic properties of the interface zones of composite laminates is studied. The strong influence of the elastic properties and the thickness of the interface zone on the phase velocity of guided waves is demonstrated by means of a simple model of a single fiber embedded in a layer of the matrix material. The overall dynamic elastic moduli of a unidirectional graphite-epoxy composite laminate are determined through inversion of guided wave dispersion data obtained by the leaky Lamb wave experiment. The thickness and elastic properties of the interlaminar interface zone in a cross-ply graphite-epoxy laminate are also estimated by the same approach.

Ray synthesis of the form function for backscattering from hollow elastic spherical shells including leaky Lamb waves and longitudinal axial resonances

A ray synthesis [P. L. Marston, J. Acoust. Soc. Am. 88, 25–37 (1988)] is employed for describing the form function f (θ = π,ka) for backscattering from a hollow, elastic spherical shell. The synthesis of f contains a component associated with a specular reflection fsp and contributions from leaky Lamb waves. The contribution fl, of the l th leaky Lamb wave is expressed in a Fabry‐Perot form. The present synthesis differs from previous results by including the effects of longitudinal axial resonances on fsp. A novel ray synthesis of fsp, which sums amplitudes associated with multiply reflected rays within the shell, indicates a significant resonance effect near the condition kt/h = nπ (n = 1,2,…,), where kL is the longitudinal wavenumber of the shell's material and h is the thickness of the shell. The ray synthesis shows that the curvature of the shell is essential to the modeling of longitudinal resonances. The ray synthesis of f is compared with the exact partial‐wave series representation for a 440c sta...

Applications to radiation and scattering of a wave front construction using the involute of circular virtual caustics

From the classical theory of plane curves applied to two-dimensional wave propagation in uniform media, it is known that the wave fronts are involutes of caustics or virtual caustics. (The involute of a curve C is constructed by the unwinding of a taut thread tangent to C.) in the present research, the involute construction is applied to wave fronts radiated into water by surface guided elastic waves (SEW) on scatterers having a uniform circular profile. Examples of SEW include circumferential leaky Rayleigh or Lamb waves on solid or hollow circular cylinders, respectively, with an outer radius = a. The outgoing wave appears to radiate from a virtual caustic that is a circle of radius sl = ac/cl, where cl is the phase velocity along the surface of the SEW and c is the sound speed in water. Consequently, the radiated wave fronts are the portion with r > a of the involute of a circle of radius sl. When the SEW are only weakly dispersive, radiated bursts imaged by schlieren photograph [W. G. Neubauer, J. Acoust. Soc. Am. 45, 1134–1144 (1969)] approximate the location of wave fronts. In the present research such images are found to be involutes of circles of radius sl. Applications to scattering from spherical shells and to the localization principle were also investigated. [Work supported by ONR.]

Propagation Characteristics of A0 Mode Leaky Lamb Wave Having Phase Velocity Close to Liquid Sound Velocity

Characteristics of A0 mode leaky Lamb waves propagating along a liquid-solid interface are numerically analyzed. In the phase velocity region close to the liquid sound velocity, the dependences of the phase velocity deviation and the damping ratio on the liquid state variables of density, volume elasticity and viscosity are investigated. The leaky wave radiation becomes the maximum at the critical frequency where the phase velocity of the A0 mode Lamb wave is equal to that of the liquid sound. The phase velocity deviation takes the peak value in the vicinity of the critical frequency.

Ultrasonic Evaluation of Adhesive Bonding

Abstract The capabilities of existing ultrasonic nondestructive evaluation (NDE) methods for the strength-related properties of bonds in structural components is reviewed. The severe limitations of conventional NDE methods in yielding quantitative results are indicated. Some recent results of a joint theoretical and experimental program of research using leaky Lamb waves (LLW) in laboratory specimens are presented. The LLW technique is shown to have several advantages over conventional techniques. Potential applications of the technique to determine non-destructively the quality of bonds in a variety of models are discussed.

Leaky Lamb waves in an anisotropic plate. I: An exact solution and experiments

The propagation of leaky Lamb waves in a plate consisting of a general balanced symmetric composite material is considered. The problem has been examined both analytically as well as experimentally. An exact solution for the dispersion equation was obtained. Numerical results for complex-valued wavenumber were obtained for an isotropic material (aluminum) and a (0/903)s graphite/epoxy laminate. Excellent agreement for the isotropic case and a satisfactory agreement for the anisotropic case between the theory and experiment were observed.

On the topology of the complex wave spectrum in a fluid-coupled elastic layer

The behavior of the complex leaky Lamb wave (LLW) spectrum of a plate immersed in a fluid has been studied as a function of the ratio of fluid-to-solid densities. It has been shown that widely accepted assumptions concerning the similarities between the classical Lamb wave spectrum and the LLW spectrum are not valid as the fluid density approaches that of the solid. Recent experimental and theoretical results demonstrate that there is a strong anomaly in the reflectance of composite plates in water. This anomaly is related to the details of the complex LLW spectrum. The spectrum is composed of both the familiar propagating Lamb wave branches and the mostly imaginary, nonpropagating branches. From the character of the complex spectrum, it is demonstrated that topological changes in the fundamental symmetric mode are related to its nearness to the first complex branch of the spectrum. Increasing the fluid–solid density ratio leads to interaction between these modes and to mutual interchange between portions of their branches. As the density ratio increases from zero to infinity, the complex spectrum is gradually transformed from a classical Lamb wave spectrum to one appropriate for a plate with zero normal surface displacements.

Recent Advances in the Application of Leaky Lamb Waves to the Nondestructive Evaluation of Adhesive Bonds

Abstract In earlier work, the feasibility of applying the Leaky Lamb Wave (LLW) method to the nondestructive evaluation (NDE) of bonded rubber/metal structures was demonstrated. The capability of LLWs to detect and delineate flaws at the bond line was proven, even when the adherends remain in intimate contact. However, variations in adherend properties, surface orientation and thickness can adversely affect detection of bond flaws and assessment of bond quality. In this paper, parameters which degrade both LLW sensitivity and resolution to bond flaws are discussed. Examples of the effects of cold work, thickness change and specimen tilt are presented along with bond flaw detection and characterization results. Also, advances in the theory of bond flaw NDE by LLWs are presented.

Measurement of the Liquid Surface Level Using a Leaky Lamb Wave Transducer

A technique for liquid surface level measuring is described by using a leaky Lamb wave device. An interdigital transducer on a piezoelectric thin plate operating in a liquid excites a leaky Lamb wave along the liquid-solid interface. The wave is mode-converted to a longitudinal wave into the liquid. Near the critical value of the product of the frequency and the plate thickness, an ultrasonic beam is radiated in the direction normal to the plate surface. The frequency is 3.4 times higher than that of the thickness mode vibration. This is essential for high resolution in the liquid level measurement system. The average error of the measured level is 200 µm for a depth of 100 mm and the deviation is within 0.1% for a temperature change of 30°C.

Analysis of leaky Lamb waves in bonded plates

The feasibility of using ultrasonic nondestructive evaluation (NDE) methods to determine the quality of bonds in structural components is considered. The severe limitations of conventional NDE method in yielding quantitative results are indicated. Some recent results of a joint theoretical and experimental program of research using leaky Lamb waves (LLW) in laboratory specimens are presented. The LLW technique is shown to have several advantages over conventional techniques. Potential applications of the technique to nondestructively determine the elastic properties of bonds in several models are discussed.

Analysis of the Liquid State Variables Dependence of Leaky Lamb Wave Characteristics at Liquid-Solid Interface

Propagation characteristics of leaky Lamb waves propagating along a piezoelectric plate under the influence of liquid loading are numerically analyzed. Dependence of the phase velocity of the leaky Lamb waves on the liquid state variables such as density, viscosity, and liquid sound velocity is examined. More than three modes which have different phase velocities dependent on the liquid state variables are excited on a piezoelectric plate by an interdigital transducer. On the basis of the results of the numerical analysis, a method of estimating these liquid state variables is discussed.

A study of the mechanical property of materials using acoustic microscopy

The interpretation of the general features of acoustic microscopy images is discussed in conjunction with its application to materials science under the following topics. (1) Interference fringes have been discovered around surface breaking cracks, and a model based on the leaky Rayleigh wave has been proposed. It has attracted a considerable amount of interest because these fringes might give new information on the elastic properties of microscopic discontinuity such as cracks, grain boundaries, and steps that are almost normal in sample surfaces. (2) When subsurface cracks are close to parallel to the sample surface, they can be analyzed by a simple plate model with water or air below. Either the V(z) curve measurement or the resonance method is useful depending on whether the frequency-depth product is much smaller or close to the first cutoff of the higher-order modes of the leaky Lamb waves. This analysis was successfully applied to a study of indentation fractures of steel ball bearings in use. (3) Image observation and the leaky SSCW velocity measurement at 775 MHz have been applied to individual spherulites in semicrystalline polypropylene. Through the signal processing of the V(x,z) image, it has been found that the difference in velocity between spherulites with different thermal histories can be larger than 30%.

Leaky Lamb wave inspection of thin plates

A single‐transducer immersion technique is introduced to study dispersion of leaky Lamb waves in different plates, such as fiber‐reinforced composite laminates and adhesive lap joints. The plate under study is interrogated by a broadband pulse from both sides when placed between the transmitting‐receiving transducer and a perpendicularly aligned mirror. The transmitted peaks in the spectrum of the received echo from this mirror correspond to double mode‐converted leaky Lamb wave resonances. These peaks are measured at different angles of incidence, i.e., at given phase velocities to get velocity dispersion curves. Experimental results are presented to demonstrate the accuracy and versatility of this very simple measuring technique

Modification of Lamb wave spectrum in fluid coupled plate

It has been accepted previously that for most practical eases when a plate is immersed in a liquid the Lamb wave spectrum is only slightly perturbed due to energy loss related to leakage of the wave from the plate to the liquid. In contrast it was recently discovered by D. E. Chimenti and A. H. Nayfeh [Appl. Phys. Lett. 49 (9) (1986)] that for leaky Lamb waves in a graphite epoxy composite plate in water a strong anomaly appears in the topology of the S0 mode as a function of frequency. Although it was caused by the fluid, the reason for this anomaly was still not clear. The nature of the anomalous behavior of leaky Lamb waves is discussed in this paper. It is shown that for an understanding of the spectrum topology, the full complex spectrum of propagating and nonpropagating modes should be considered. It is demonstrated that the topological changes in the S0 mode are related to its nearness to the first complex branch of the spectrum. Increasing liquid density leads to interaction between these modes and mutual interchange between their branches in the complex plane. It is shown that, in general, as the density of the immersion liquid increases from zero to infinity the complex spectrum of plate modes gradually transforms from a spectrum of Lamb waves in a free plate to a spectrum of waves in a plate clamped on its surfaces with slip (boundary conditions σxy = 0, Uy = 0).

Another look at the Rayleigh angle backscattering

The increased backscattering from a liquid‐solid interface at the Rayleigh angle is a well‐known indication of leaky surface wave generation (similar phenomena were observed from thin plates immersed in liquid due to leaky Lamb wave generation, too). This simple technique has proved to be very useful in material evaluation via measuring both surface and Lamb wave velocities. On the other hand, a comprehensive experimental study [M. de Billy, L. Adler, and G. Quentin, J. Acoust. Soc. Am. 72, 1018 (1982)] showed much stronger backscattered signals than predicted later by theoretical works based on back reflection. New experimental results are presented demonstrating that this back reflection is negligible in the backward signal, which is simply backscattering from inevitable material inhomogeneities greatly enhanced by surface or Lamb wave generation. Therefore, beside measuring macroscopic elastic properties in the previously suggested way, the backscattered signal can be used to characterize surface and near‐surface material inhomogeneities as well. [This work was supported by the U.S. Department of Energy, Basic Energy Sciences, Grant DE‐FG02‐84ER45057A.004.]