Evolution of the ultrasonic resonance modes in a three-layer structure with change of material and interface adhesion properties
Authors: Liu Jing  , Xu Wei-Jiang  , Hu Wen-Xiang  ,   Institute of Acoustic, Tongji University, Shanghai 200092, China;,   Institut d'Electronique de Microélectronique et de Nanotechnologie UMR CNRS 8520, Département Opto-Acousto-Electronique, Université de Valenciennes, Valenciennes 59313, France
Published: December 2020

The quantitative non-destructive evaluation (NDE) of interface adhesion has long been a challenge for the safe use of bonding structures. It is difficult to predict the adhesion resistance force between adhesive and adhered material without performing destructive testing. Ultrasonic approach seems to be the only potential way for its NDE based on the reason of mechanical nature of the problem. Different ultrasonic techniques, such as bulk wave echography, reflection resonance, and Lamb guided waves, have been used to evaluate the interface adhesion strength. But no direct relation between the interfacial bonding strength and the ultrasonic measurement has been established. The most used compression wave echography and resonance at normal incidence are less sensitive to the interface condition, except for a disbond. It is essential that the interface should be excited with a shear stress component to increase the measurement sensibility. But it is not easy to excite the interface by using shear waves in experiment, while the use of guided waves will encounter the problems of high attenuation and mode selection as all modes are not sensitive to a certain interface in a bonded structure. A previous study has shown that the V (z) inversion technique can be used to perform a multimode measurement on a layered structure, where both compression and shear stress resonance occur. This method has the advantage in using a simple experimental setup working at the normal incidence with a focus transducer of large angular aperture. The inversed angular-frequency reflectance function R(; f) gives the resonance modes which are equivalent to the Lamb type guided modes, while it is a local determination of the wave mode, thus the difficulty in guided wave measurement above mentioned can be avoided. The first part of the paper contains the development of the theoretical model for wave propagation in a multilayered structure where three-layer sandwich bonded structures can be considered as a particular case. A weak interfacial adhesion is described by two interface compression and shear stiffness parameters, namely km and kt. By integrating the transfer matrix formalism under the non-ideal boundary conditions, the plane wave angular (incident angle) and frequency reflection coefficient function R(; f) for a liquid immersed asymmetric metal-adhesive-metal three-layer and its dispersion curves of guided mode waves with or without charge are calculated. It is confirmed that the evolutions of the reflection zeros (mode resonances) correspond to the dispersion curves of the guided waves of the same structure without charge. Furthermore, the resonance modes observed in R(; f) can be considered as a combination of the respective Lamb modes of the top and bottom single metal layers coupled through the modes conditioned by the middle adhesive layer and the its interface conditions. The second part of the paper shows the behaviors of the resonance modes by changing the parameters related to the bonding strength. The acoustical impedance, the mass density and the thickness of the adhesive layer, which are related to the cohesive property, and the shear interfacial stiffness coefficient kt which conditions the adhesive property, are changed respectively to observe the resonance mode evolutions. The mode evolutions due to each parameter are analyzed and differentiated. It can be concluded that the change in the adhesion strength of the bonding structure does not affect significantly the modes belonging to those inherent to the two adhered aluminum layers, while the coupling modes will be shifted in frequency and exchange with or replace the said inherent modes. It is expected that the obtained results in this study will be of significance for quantitatively characterizing the interfacial properties of an adhesively bonded layered structure by using the V (z) inversion technique.