Ultrasonic evaluation of interlayer interfacial stiffness of multilayered structures

A procedure for the ultrasonic evaluation of the interlayer interfacial stiffness of multilayered structures is proposed. As a theoretical background to this proposal, the elastic wave propagation in a multilayered structure, in which the layers are bonded with spring-type interfaces, is analyzed theoretically based on the transfer-matrix method. Using the notion of the Bloch phase which characterizes wave transmission in the corresponding infinite periodic structure, some explicit relations are derived for the reflection coefficient of the multilayered structure. Based on the features clarified theoretically, the interlayer interfacial stiffness of the multilayered structure can be evaluated from the locations of local minima and maxima of the amplitude reflection spectrum. By numerical analysis, the proposed procedure is shown to apply even when the viscous property of the layers is not known precisely, and when a transient waveform of a limited length is used. Using the proposed procedure, the stiffness of interlayer resin-rich regions in a carbon-epoxy cross-ply composite laminate is identified from the experimental reflection spectrum. The identified stiffness is shown to lie within the range as expected from the micrographic observation and a simple estimate for a thin resin layer

Ultrasonic characterization of alumina/silicone-rubber composites for acoustical applications

ICSV28 Local Committee in Singapore, July 24-28, 2022Silicone rubber has been used commonly as a material for an acoustic lens in medical ultrasonic probes. In order to achieve the desired properties for an acoustic lens, i.e., acoustic impedance close that of, and wave velocity lower than that of, human body, different materials have been considered as fillers or dopants to be dispersed in silicone rubber. A micromechanics-based analysis has revealed that silicone-rubber composites can have the desired acoustical properties with a certainamount of dispersed alumina particles. In this study, the ultrasonic wave propagation characteristics of alumina-particle-dispersed silicone-rubber composites fabricated with different particle concentrations and average particle radii were investigated experimentally. Namely, the velocity and attenuation coefficient of longitudinal wave in the alumina/silicone-rubber composites were evaluated at the frequency of 5 MHz by the spectral analysis of the reflected waves obtained in the immersion measurement. The experimental results have shown that the acoustic impedance and the wave velocity desired for an acoustic lens can be achieved by the alumina particle concentration as predicted by the micromechanics-based analysis. The influence of the particle radius on the acoustical properties of the composite has also been examined

Frequency Dependence of Second-Harmonic Generation in Lamb Waves

The frequency dependence of the second-harmonic generation in Lamb waves is studied theoretically and numerically in order to examine the role of phase matching for sensitive evaluation of material nonlinearity. Nonlinear Lamb wave propagation in an isotropic plate is analyzed using the perturbation technique and the modal decomposition in the neighborhood of a typical frequency satisfying the phase matching. The results show that the ratio of the amplitude of second-harmonic Lamb mode to the squared amplitude of fundamental Lamb mode grows cumulatively in a certain range of fundamental frequency for a finite propagation distance. It is also shown that the frequency for which this ratio reaches maximum is close but not equal to the phase-matching frequency when the propagation distance is finite. This feature is confirmed numerically using the finite-difference time-domain method incorporating material and geometrical nonlinearities. The fact that the amplitude of second-harmonic mode becomes high in a finite range of fundamental frequency proves robustness of the material evaluation method using second harmonics in Lamb waves

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components

Multiple scattering of flexural waves on Mindlin plates with circular scatterers

The multiple scattering of flexural waves on an elastic plate with circular scatterers is analyzed in the frequency domain based on the Mindlin plate theory accounting for the rotary inertia and shear deformation of the plate. To this purpose, a semi-analytical numerical method is formulated as an extension of the previous study based on the Kirchhoff plate theory. It consists of expressing the flexural wave field in terms of the superposition of the wave function expansion, and determining the expansion coefficients by a collocation technique. As demonstrative examples, the transmission of a plane flexural wave across a square array of circular through-thickness holes or thin-plate inclusions is analyzed using the proposed method. The comparison between the results based on the Mindlin and Kirchhoff theories is shown for the case of multiple holes. The analysis shows that the transmission amplitude of the flexural wave is reduced at certain frequencies due to the Bragg reflection by the inclusions. In the case of thin-plate inclusions, the resonance of the inclusions also brings about a sharp decrease of the transmission amplitude

Harmonic generation at a nonlinear imperfect joint of plates by the S0 Lamb wave incidence

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity

Ultrasonic wave transmission and bandgap in multidirectional composite laminates with spring-type interlayer interfaces

The ultrasonic wave transmission through multidirectional composite laminates is studied theoretically by accounting for the effect of thin interlayer resin-rich regions based on the spring-type interface model. Using the stiffness-matrix method, the energy transmission spectrum of the longitudinal wave impinging obliquely on cross-ply and quasi-isotropic laminates immersed in water is calculated. The location and bandwidth of the frequency ranges where the transmissivity becomes vanishingly small are shown to be significantly influenced by the incident angle, the laminate lay-up, and the interlayer interfacial stiffnesses. By examining the energy flux density of partial waves inside the laminate, these frequency ranges are shown to be the bandgaps due to the constructive interference of scattered waves from the interlayer interfaces. The mode combination causing the interference is found to vary remarkably with the bandgap location. Furthermore, the interference in the finite laminate structure is shown to occur in almost the same manner as the Floquet wave does in the infinitely extended laminate structure. The energy transmission spectrum is experimentally measured for 16-ply carbon/epoxy cross-ply and quasi-isotropic composite laminates using the through-transmission technique. The transmission and bandgap characteristics observed in the experimental results are reasonably reproduced by the present theory incorporating the interlayer resin-rich regions

ハイブリッド キョウカイ ヨウソ ホウ ヲ モチイタ ダイリョウイキ ラムハ シミュレーション

The simulation of Lamb wave propagation is an efficient tool to improve the accuracy of nondestructive inspection of metallic plates by ultrasonic methods. However the widely used modeling techniques such as FDM, FEM and BEM require too much computation time. Since the Lamb wave technique is often used for large structures relative to the ultrasonic wavelength (e.g. fluid pipes, storage tanks etc.), its computing requires a huge number of nodes or elements which are nearly proportional to computation time. This study is therefore focused on the Hybrid BEM (HBEM), which is the combination of exact Lamb wave theory and BEM for two-dimensional elastodynamics. In HBEM much less nodes should be considered in the calculations, and it results in much shorter calculation time. A description of HBEM used for Lamb wave simulation is given in this paper. The parameters for the exact solution of Lamb wave propagation were optimized to achieve the shortest calculation time. Finally, an effective simulation of a large structure is presented under pre-determined conditions

Influence of axle-wheel interface on ultrasonic testing of fatigue cracks in wheelset.

For the ultrasonic testing at the wheel seat of railway axles, quantitative investigation of the reflection and transmission phenomena at the axle-wheel interface is important. This paper describes the influence of the axle-wheel interface on the ultrasonic testing of a fatigue crack in a wheelset by applying the spring interface model. The normal and tangential stiffnesses were identified experimentally for an as-manufactured wheelset at the normal incidence, and the reflection coefficient for the shear-wave oblique incidence was calculated. A parametric study was performed to clarify the influence of these interfacial stiffnesses on the incident-angle dependence of the reflection coefficient. The calculated reflection coefficient at the incident angle of 45° qualitatively explained the relative echo-height decrease due to the presence of a wheel observed experimentally for a wheelset in fatigue loading by rotating bending. The quantitative difference between the experimental and calculated results was considered to be due to the reduction of the effective interference of shrink fit by the wear at the axle-wheel interface during the fatigue loading as well as by the applied bending moment. For the estimated relative echo-height decrease to agree with the experimental results, the interfacial stiffnesses were found to be smaller than the values identified for the as-manufactured wheelset by a factor of 0.5-0.7

The SH0 wave manipulation in graded stubbed plates and its application to wave focusing and frequency separation

In this study, a methodology to artificially control the propagation of fundamental shear horizontal (SH0) waves in elastic plates is proposed using stubs with spatially graded height, and two novel phenomena, wave focusing and low-pass wave filtering, are realized. As a basis for this, the band structure analysis is carried out for an aluminum plate with hexagonally arranged stubs, and the relationships between the wave velocity, the band gap and the stub height are established. Based on these results, omni-directional SH0 wave-based Luneburg and Maxwell fish-eye lenses, as well as low-pass wave filter, are designed artificially using multiple stubs with spatially graded heights. It is demonstrated that both of the lenses exhibit good focusing ability, with the focusing size smaller than the wavelength. Additionally, they can work with a finite bandwidth around the design frequency. It has also been revealed both in time and frequency domain simulations that the SH0 wave with a lower frequency can travel over a longer distance when it enters the low-pass wave filter, which demonstrates its frequency separation capability