# Numerical Voids Detection in Bonded Metal/Composite Assemblies Using Acousto-Ultrasonic Method
## 1 Introduction
The recorded wave is then analyzed using acoustic emission descriptors. This technique works in a frequency domain similar to that used in acoustic emission. Furthermore, damage detection requires knowledge of the structure in its undamaged state. The baseline data or reference signals are obtained from the undamaged state. The damage detection is then performed by comparing the received signal descriptors from the tested specimen with those of the baseline signals. [PERSON] and [PERSON] [23] investigated the correlation between the number of delamination-type defects and the acousto-ultrasonic parameters in an aluminum-composite bonded assembly, mainly using frequency parameters based on a spectral study of the detected signals. [PERSON] et al. [25; 26] used AU measurements to characterize the interlaminar strength of CFRP laminates in both longitudinal and transverse directions and to study the integrity of CFRP specimens before and after artificially induced, barely visible impact damage. This method, as the standard guided ultrasonic inspection method, is based on the interaction of the waves with the defects present in the adhesive joint. The main difference is that the wave modes and propagation paths are not well established. The signal is therefore difficult to analyze; nevertheless, it is a rich source of information that reflects the material properties, microstructure and possible presence of defects. A single experimental approach is thus not sufficient to fully understand this interaction. Compared with experimental techniques, numerical analyses can offer a more comprehensive study of wave propagation and interactions with defects in the joint. Analytical solutions for wave propagation are generally limited to infinite media or simple geometries and are therefore not accessible for most practical structures. The wave propagation solution can be approximated using numerical approaches such as finite element (FE) analysis. Three-dimensional FE approaches are beneficial, since they enable a realistic structure geometry to be considered, as well as material anisotropy or wave reflections at boundaries. Several authors [16; 27; 28; 29; 30; 31; 32; 33] focused on the modeling of wave propagation in bonded assemblies to predict the ultrasonic response. All these studies showed the defect sensitivity of various guided wave modes propagating in adhesively bonded joints and demonstrated the potential of modeling studies. [PERSON] and [PERSON] [16] developed a one-dimensional semi-analytical FE model for predicting dispersion curves and mode shapes of SH-guided waves in multilayered plates made of composite and adhesive layers. Numerical simulations were used for selecting the most appropriate SH wave modes with higher sensitivity to the bond than to the other components (the metallic plate or composite patch). Some authors [31] used the global matrix method to model wave propagation in the multilayer overlap and showed that phase and group velocity dispersion curves are highly sensitive to the bond state and bonded lap-shear joints. The study in [28] investigated two different lay-ups for the wing skin and two different types of bond defects (poorly cured adhesive and debonded interfaces). The models and the experiments confirmed that the ultrasonic energy transmission through the joint is highly dependent on the bond conditions. Using FE simulations for each of the modes A\({}_{0}\), S\({}_{0}\) and A\({}_{1}\), [PERSON] et al. [29] predicted the transmission coefficient of each mode across a lap joint consisting of parallel aluminum sheets bonded with an epoxy adhesive. [PERSON] et al. [32] used computational methods to examine the properties of double-layered, adhesive-bonded plates. They quantified the influence of adhesive bond parameters (Young's modulus, Poisson's ratio and bond thickness) on the dispersion curves. [PERSON] et al. [33] proposed a model to investigate the influence of a void in the overlap area and showed that modal damping decreased with increasing void size. [PERSON] et al.