# Numerical Voids Detection in Bonded Metal/Composite Assemblies Using Acousto-Ultrasonic Method
## 1 Introduction  
Composite materials are increasingly used as bonded reinforcements on civil engineering structures, owing to their lightness and durability [1; 2; 3]. Adhesive bonding enables physically dissimilar materials such as composites and metals to be joined. Used in the repair, reinforcement and rehabilitation of structures with composites, this extends the service life of structures. Despite their advantages, the effectiveness of bonded joints can be compromised due to the presence of adhesion defects or damage such as voids, porosity, poor adhesion or low cohesion strength. Accordingly, non-destructive testing (NDT) techniques [4; 5; 6; 7] become essential for damage or defect diagnosis using actuators/sensors installed on the same side of the structure. Defects need to be identified either during initial control or by inspection during service life. The mechanical joint behavior may be significantly impacted by the defects [8; 9]. Substantial efforts have been made to develop nondestructive testing methods to evaluate the adhesive bond integrity. Several investigations focused on adhesive joint quality inspections using ultrasonic testing methods including acoustic emission, bulk and guided (longitudinal, shear and Lamb) waves, sheragraphy, pulsed thermography, X-rays or passive thermography [10; 11; 12; 13; 14; 15; 16; 17]. For example, [PERSON] et al. [11] compared the performance of different ultrasonic non-destructive testing (contact testing, immersion testing and air-coupled) techniques for bonding quality evaluation on aluminum-epoxy-single lap joints containing debonding in the form of release film inclusions. [PERSON] et al. [12] used damping and frequency measurements to monitor a kissing-bond defect in an adhesively bonded joint between two composite strips. The results showed a nonlinear relation between the defect area and modal damping as well as frequency variations. [PERSON] et al. [15] evaluated the damage in an aluminum plate with a carbon fiber reinforced polymer (CFRP) using the amplitude change of the second-orderharmonic waves with nonlinear acousto-ultrasonic detection. [PERSON] et al. [16] demonstrated the strong potential of the low-order SH\({}_{0}\)- and SH\({}_{1}\)-like guided modes to quantify the shear properties of adhesive bond layers between an aluminum plate and a carbon epoxy composite patch. The precise monitoring of structures with composite repairs is also challenging. It is important to detect and locate a defect, to determine its size, to classify its type and to evaluate its severity. In this context, several authors proposed the use of an acousto-ultrasonic (AU) method [18; 19; 20; 21; 22; 23; 24; 25; 26; 27] to detect and assess defects. This technique was initially introduced and developed by [PERSON] [18] and was rapidly used to characterize bonding [19; 20; 21; 22]. Indeed, [PERSON] [21; 22] used the acousto-ultrasonic technique to nondestructively evaluate the mechanical performance of composite bonded joints. A good correlation between the acousto-ultrasonic wave propagation characteristics and the bonded joint shear strength was established. The monitoring principle, based on an actuator-sensor configuration, is quite similar that used in standard guided ultrasonic inspection. In the AU approach, it is not necessary to have well-defined wave propagation paths. On the contrary, the approach requires that the transmitter signal presents multiple interactions with the microstructure of the material. Moreover, this technique allows an active (emission of AU) and a passive phase to be combined with acoustic emission (AE) monitoring. This technique can combine advantageous aspects of both acoustic emission and ultrasonic techniques. Additionally, it requires the sensors to be located on only one side of the specimen. The acousto-ultrasonic technique (AU) consists of emitting an ultrasonic wave with a piezo ceramic transducer and receiving the wave after its propagation in the material using a similar transducer with an AE acquisition system.