Ultrasonic evaluation of ply and interleaf layer properties of interleaved composite laminates.

An ultrasonic nondestructive evaluation procedure is presented for the ply and interleaf layer properties of carbon/epoxy composite laminates having interleaf resin layers at their interlaminar interfaces. It is shown that the material properties of plies (density, thickness, and transversely isotropic complex elastic moduli) and elastic interleaf layers (density, thickness, Young's modulus, and Poisson's ratio) can be identified by best fitting the theoretical energy transmission spectra of longitudinal waves through the laminate immersed in water to those obtained in ultrasonic measurement. It is also demonstrated that compared to the mass-less and null-thickness spring-type interlaminar interface model employed in the previous works, the present finite-thickness interleaf layer model can better reproduce the experimental transmission spectra of a unidirectional interleaved composite laminate containing ultrasonic bandgaps. Furthermore, the property characterization in the case where the plies and interleaf layers are assumed to be elastic and viscoelastic, respectively, is also examined. It is also shown that the ply and interleaf layer properties determined for the unidirectional laminate can be used to reproduce the transmission spectra measured for a quasi-isotropic laminate consisting of the same plies and interleaf layers.

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.

Analytical modeling of the interaction of an ultrasonic wave with a rough bone-implant interface.

Quantitative ultrasound can be used to characterize the evolution of the bone-implant interface (BII), which is a complex system due to the implant surface roughness and to partial contact between bone and the implant. The determination of the constitutive law of the BII would be of interest in the context of implant acoustical modeling in order to take into account the imperfect characteristics of the BII. The aim of the present study is to propose an analytical effective model describing the interaction between an ultrasonic wave and a rough BII. To do so, a spring model was considered to determine the equivalent stiffness K of the BII. The stiffness contributions related (i) to the partial contact between the bone and the implant and (ii) to the presence of soft tissues at the BII during the process of osseointegration were assessed independently. K was found to be comprised between 1013 and 1017 N/m3 depending on the roughness and osseointegration of the BII. Analytical values of the reflection and transmission coefficients at the BII were derived from values of K. A good agreement with numerical results obtained through finite element simulation was obtained. This model may be used for future finite element bone-implant models to replace the BII conditions.

Transmission of Lamb waves across a partially closed crack: Numerical analysis and experiment.

The transmission characteristics of Lamb waves across a partially closed through-thickness crack in a plate are investigated numerically and experimentally. In the numerical analysis, the spectral element method is used to simulate the transmission of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across a crack in a low-frequency range. The analysis is carried out for an open crack with traction-free surfaces as well as for a partially closed crack modeled as a spring-type interface characterized by normal and tangential stiffnesses. The transmission ratios of both modes are obtained from the spectral amplitude of the simulated transmission waveforms for different crack lengths and interfacial stiffnesses. The numerical results show that the transmission ratio of the S0 mode increases monotonically with the interfacial stiffness, but that of the A0 mode depends on the interfacial stiffness in a non-monotonic manner depending on the frequency. The Lamb wave transmission measurements are carried out for aluminum alloy plates with artificial slits or a fatigue crack. The experimental results for the plates with slits show reasonable agreement with the numerical results for open cracks. The measured transmission ratio of the S0 mode is shown to decrease with the tensile load applied to the plate, but that of the A0 mode shows different load dependence for different frequencies. The qualitative features of the experimental results for the fatigue crack are discussed based on the numerical simulation for closed cracks.

Damage localization method for plates based on the time reversal of the mode-converted Lamb waves.

A damage localization method based on the time reversal focusing of the mode-converted scattered Lamb wave is proposed for plate structures with a non-symmetric defect in the thickness direction. Dual transducers are attached symmetrically on the upper and lower surfaces of the plate to selectively emit and receive the lowest-order symmetric (S0) and antisymmetric (A0) modes. The localization of damage is achieved by the numerical time-reversed (TR) simulation of the mode-converted Lamb wave generated at the defect. To investigate the validity of the proposed method, the signals of the Lamb waves in a plate with a partial-thickness notch are numerically simulated by the three-dimensional elastodynamic finite integration technique (EFIT). When the S0 mode is emitted in the damaged plate, not only the S0 mode is scattered but also the A0 mode is generated due to mode conversion at the notch. Similar mode conversion behavior is confirmed when the A0 mode is emitted. The time reversal of the mode-converted scattered Lamb waves creates focused spots at the damage location without using baseline data for the undamaged plate. The proposed method reduces the magnitude of the artifacts compared to the time reversal of the non-mode-converted Lamb wave, and yields the focused spot whose size is associated with the size of the notch and the half wavelength of the time-reversed wave mode. Furthermore, the proposed method is applied to a plate with a notch-type defect adjacent to an a priori known through-thickness hole, demonstrating the damage localization in a relatively complicated structure.

Transmission characteristics of the S0 and A0 Lamb waves at contacting edges of plates.

In order to gain basic insight into the interaction between ultrasonic guided waves and structural discontinuities with contacting surfaces, the transmission characteristics of Lamb waves at contacting edges of two plates are studied experimentally. The edges of two 2.5-mm thick aluminum alloy plates are mated together to constitute a contacting interface of plates and subjected to different levels of compressive loading. The transmission measurements of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across the contacting interface are performed in a frequency range below the cut-off frequencies of the higher-order modes. As a result, it is found that the transmission coefficient of the S0 mode increases monotonically with the applied contact pressure, but the transmission coefficient of the A0 mode exhibits non-monotonic dependence on the contact pressure and the frequency showing a local minimum. For the incidence of the S0 mode, the resonance at the contacting interface is observed as a long-time oscillation tail in the transmission waveform. The resonance frequency is found to increase with the contact pressure. The experimental results are discussed in the light of the theoretical results based on the spring-type interface model. The normal and tangential stiffnesses of the contacting interface are identified from the transmission coefficients as well as from the resonance frequency. The estimated interfacial stiffnesses increase monotonically with the contact pressure, and indicate their dependence on the frequency. Implications of the present results to the Lamb-wave based characterization of the plate contact condition are discussed briefly.

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.

Transmission of Lamb waves and resonance at an adhesive butt joint of plates.

The transmission behavior of Lamb waves and the possible occurrence of resonance at an adhesive butt joint of plates are studied experimentally. To this purpose, two 2.5-mm thick aluminum alloy plates are bonded at their edges using cyanoacrylate-based adhesive. Bonded plate specimens with different joint conditions are prepared by changing the bonding procedure. The measurements are performed for the transmission characteristics of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes for the frequency range of 0.4-0.6MHz below the cut-off frequency of the higher-order modes. The experimental results show that the transmission coefficients of the S0 and A0 modes exhibit different frequency-dependent characteristics depending on the joint condition. Furthermore, for the incidence of the S0 mode at the center frequency of 1MHz, the transmitted S0 mode in weakly bonded specimens shows a long oscillation tail due to the resonance effect. The experimental results are discussed in the light of the theoretical results based on the spring-type interface model. The interfacial stiffnesses identified from the transmission coefficients are shown to be correlated with the bonding condition of the joint and give reasonable estimates of the resonance frequencies of weakly bonded specimens.

Transmission of ultrasonic waves at oblique incidence to composite laminates with spring-type interlayer interfaces.

The transmission characteristics of ultrasonic waves at oblique incidence to composite laminates are analyzed theoretically by the stiffness matrix method. The analysis takes into account the presence of thin resin-rich regions between adjacent plies as spring-type interfaces with normal and shear stiffnesses. The amplitude transmission coefficient of longitudinal wave through a unidirectional laminate immersed in water is shown to be significantly influenced by the frequency, the interlayer interfacial stiffnesses, and the incident angle. Using Floquet's theorem, the dispersion relation of the infinitely extended laminate structure is calculated and compared to the transmission coefficient of laminates of finite thickness. This reveals that the ranges of frequency and interfacial stiffnesses where the Floquet waves lie in the band-gaps agree well with those where the transmission coefficient of the finite layered structure is relatively small, indicating that the band-gaps appear even in the laminate with a finite number of plies. The amplitude transmission coefficient for an 11-ply carbon-epoxy unidirectional composite laminate is experimentally obtained for various frequencies and incident angles. The low-transmission zones observed in the experimental results, which are due to the critical angle of the quasi-longitudinal wave and the Bragg reflection, are shown to be favorably compared with the theory.

Resonance of an imperfect joint of plates by the lowest-order symmetric Lamb mode.

Resonance behavior of an imperfect joint of elastic plates subjected to the incidence of the lowest-order symmetric (S0) Lamb mode is numerically analyzed in the frequency domain by the hybrid finite element method. To this purpose, the reflection and transmission characteristics of the S0 mode are calculated for the frequency range in which the S0 mode is the only symmetric mode that can propagate in the plates. The imperfect joint is modeled as a linear spring-type interface characterized by the normal and tangential stiffnesses. As a result, it is shown that the imperfect joint of plates has two resonance frequencies at which the out-of-plane displacement amplitudes at the joint are remarkably increased. One resonance frequency depends only on the normal stiffness, and the other only on the tangential stiffness. Each resonance frequency coincides with that of a free edge of a plate, and monotonically increases with the corresponding joint stiffness. Furthermore, it is also shown that the reflection and transmission behavior of the S0 mode at the imperfect joint of the plates can be well reproduced by the one-dimensional thin-plate approximation of extensional waves when the frequency is sufficiently small compared to the resonance frequencies.

Evaluation of interlayer interfacial stiffness and layer wave velocity of multilayered structures by ultrasonic spectroscopy.

An ultrasonic evaluation procedure for the interlayer interfacial normal stiffness and the intralayer longitudinal wave velocity of multilayered plate-like structures is proposed. Based on the characteristics of the amplitude reflection spectrum of ultrasonic wave at normal incidence to a layered structure with spring-type interlayer interfaces, it is shown that the interfacial normal stiffness and the longitudinal wave velocity in the layers can be simultaneously evaluated from the frequencies of local maxima and minima of the spectrum provided that all interfaces and layers have the same properties. The effectiveness of the proposed procedure is investigated from the perspective of the sensitivity of local extremal frequencies of the reflection spectrum. The feasibility of the proposed procedure is also investigated when the stiffness of each interface is subjected to small random fluctuations about a certain average value. The proposed procedure is applied to a 16-layered cross-ply carbon-fiber-reinforced composite laminate. The normal stiffness of resin-rich interfaces and the longitudinal wave velocity of plies in the thickness direction evaluated from the experimental reflection spectrum are shown to be consistent with simple theoretical estimations.

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.

Stiffness evaluation of contacting surfaces by bulk and interface waves.

This paper describes ultrasonic measurements of normal and tangential stiffnesses of the contacting interface between polished aluminum blocks subjected to nominal contact pressures up to about 3.8 MPa. These stiffnesses were evaluated by ultrasonic spectroscopy methods for the bulk (longitudinal and transverse) wave reflection coefficients and the anti-symmetric mode interface wave velocity. The measurements revealed the interfacial stiffnesses as functions of the frequency as well as the applied contact pressure. The ratio of the tangential and normal stiffnesses is discussed in the light of foregoing theoretical and experimental findings. Furthermore, possible explanations for the frequency dependence of the measured stiffnesses are reviewed, invoking the spatial inhomogeneity of the interfacial stiffness as well as its lossy nature.