# Adhesive Single-Lap Joint Evaluation Using Ultrasound Guided Waves
###### Abstract  
This work deals with the evaluation of adhesive single-lap joints using ultrasound guided waves; in particular, it is intended to characterize the signal propagation when defects are present in the adhesive joint by simulation and experimental approaches. The propagation of guided waves in the joint is developed from matrix formulations. The behavior of the guided wave modes that exist in the bonded region is characterized. It is found that its amplitudes can be estimated from the properties of the incoming wave that propagates in the non-bonded region. It is verified that the excitation of these modes is related to the degree to which the shapes of both modes match each other. A 3D simulation of two aluminum-bonded plates using 500 kHz ultrasonic transducers in a pitch-and-catch configuration was implemented using the Matlab k-Wave toolbox. Scattering effects, due to some defects located in the bond line of the joints, were simulated. The experimental setup with some artificial defects produced in the aluminum joints was used in order to compare it with the simulation. Qualitative agreement was observed between the two approaches. The observed deviation can be due to the different characteristics of the experimental and simulated defects. guided waves; ultrasounds; adhesive lap joints; simulation +
Footnote †: journal: Applied Sciences  
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Footnote 1: email: {[PERSON], [PERSON], [PERSON], [PERSON], [PERSON]  
evaluation [28]. Several studies using ultrasound guided waves to assess the bonding quality of metal/epoxy/metal joints can be found in the literature, such as comparison between air coupling and immersion techniques [29], analysis of the spectra of the lowest-order antisymmetric (A\({}_{0}\)) Lamb wave mode for tangential bond stiffness evaluation [30], defect detection in the adhesive films and evaluation of their geometry by means of a weighted root mean square damage imaging algorithm [31; 32], evaluation of interference effects of elastic waves generated by piezo sensors, excited with tone bursts of different extensions, with the length of the disbond [33], study of the non-linear Lamb wave behavior [34; 35], and development of a finite difference model for simulation and validation experiments using PZTs in bonded aluminum plates [36]. Simulation allows predicting the ultrasound wave propagation in a particular medium and can be used to prove analytical and experimental approaches. Nowadays, the implementation of numerical or grid-based methods is easy due to the advances in computational resources. Several recent works use finite element methods (FEM) to accurately simulate wave propagation through bonded lap joints [29; 33; 36; 37; 38; 39]. One of the major drawbacks of elastic wave models based on low-order finite differences or finite elements is the large number of grid points per wavelength necessary to avoid numerical dispersion. The k-Wave, which is a third-party MATLAB toolbox, uses a Fourier domain pseudo spectral method for faster simulation and reconstruction of photoacoustic wave fields and can be used alternatively. It uses less memory and is user-friendly [40; 41]. Several authors have used the k-Wave toolbox in diverse NDT applications, such as nonlinear ultrasound propagation in absorbing media [42], attenuation in ultrasonic computed tomography [43], time domain power law attenuation in tissues [44], one-sided ultrasonic nondestructive evaluation [45], high intensity focused ultrasound [46], ultrasonic transducer field modeling [47], 3-D ultrasound imaging [48], simulation of A-scan signals in ophthalmology [49], microflaw detection in carbon fiber reinforced polymers [50], and guided waves in layered structures [51; 52]. In the present paper, the authors intend to implement a 3D simulation model of two aluminum plates bonded by an epoxy adhesive, using the k-Wave tool, which, to the best of their knowledge, is a novel approach to characterizing the propagation in lap joints with defects. Simulated defects of different sizes are introduced in the adhesive.