Yosuke Ishii

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 stiffnes...

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 Floquets 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.

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.

Acoustic harmonic generation in a multilayered structure with nonlinear interfaces

Acoustic harmonic generation phenomena in a multilayered structure with nonlinear interlayer interfaces are analyzed, numerically based on the finite element analysis as well as theoretically based on a perturbation analysis combined with the transfer matrix method. Results are demonstrated for a three-layered structure with two nonlinear interlayer interfaces. It is found that the amplitude of the second harmonic components depends on the incident fundamental frequency, due to the interaction of the generated harmonic components with the layered structure. As the number of layers increases, the frequency-dependence of the harmonic generation behavior becomes more complicated, and it is shown that the second harmonic amplitude becomes high at certain special frequencies.

Finite-element analysis of non-collinear mixing of two lowest-order antisymmetric Rayleigh–Lamb waves

Recently, a perturbation approach was adopted for the non-collinear mixing of plate waves in an isotropic elastic plate with quadratic nonlinearity by Ishii, Biwa, and Adachi [J. Sound Vib. 419, 390-404 (2018)] and a resonance condition was derived theoretically, namely, that a significant scattered plate wave is generated when its frequency and wavevector coincide with the sum/difference of those of its primary waves. However, that analysis assumed monochromatic plane waves that interacted everywhere in the plate. To apply the non-collinear mixing of plate waves to nondestructive evaluation of plate-like structures, the influence of the spatial and temporal finiteness of the primary waves on the generation of the scattered wave must be elucidated. To that end, the present study conducts three-dimensional dynamic finite-element analyses on the mixing of lowest-order antisymmetric Rayleigh-Lamb waves that have finite beam widths and time durations. The generation of scattered lowest-order symmetric Rayleigh-Lamb and shear horizontal waves with sum frequencies is discussed for various beam widths, intersection angles, and primary frequencies. The resonance condition derived originally for monochromatic plane waves in the aforementioned study is found to be valid even when the wave interaction is allowed only within limited space and time.

Ultrasonic bandgaps and interlaminar interface echoes of composite laminates: Analysis and experiments

Increasing applications of carbon fiber reinforced plastics (CFRP) in aerospace industry highlight the importance of nondestructive methods to characterize their mechanical properties as well as defect concentrations. In CFRP laminate structures, thin resin layers, typically of a few micron thickness, are present between plies. Their spatially periodic nature causes bandgaps for ultrasonic waves having wavelengths comparable to the ply thickness. Features of the reflection and transmission spectra of ultrasonic waves including such bandgaps can be utilized for nondestructive characterization of CFRP laminates. In particular, the oscillatory frequency dependence of the reflection or transmission spectra of ultrasonic waves near the band gaps can be used to identify the equivalent stiffnesses of interlaminar interfaces. These interfacial stiffnesses contain rich information of the mechanical soundness of the interlaminar interfaces which are otherwise difficult to evaluate with traditional ultrasonic method...

Analysis of acoustic harmonic generation in a solid with multiple nonlinear interfaces

Weak bonds and delaminations are typical examples of imperfect interfaces in multilayered structures. Nonlinear acoustic/ultrasonic methods are expected to offer a promising means to monitor these imperfect interfaces, as such interfaces behave nonlinearly when subjected to high-amplitude waves and result in the occurrence of nonlinear frequency components such as higher harmonics. Harmonic generation at a single nonlinear interface has been studied by many investigators from both theoretical and experimental points of view. In this presentation, a theoretical analysis of harmonic generation at multiple nonlinear interfaces is presented within a framework of one-dimensional elastic wave propagation in the frequency domain. The analysis is based on the perturbation expansion of the wave field by assuming the weak nonlinearity. Specifically, the second-harmonic generation is analyzed by first solving the linear transmission of the incident fundamental component, and then the propagation of the second-harmon...