## 2 Materials and Methods
### Acoustic Emission and Digital Image Correlation Systems Data Acquisition  
In this section, the DIC procedure is elucidated (Figure 2). The system comprises a digital camera ([PERSON] acA1300-75 gm model, Basler, Ahrensburg, Germany), a 30 mm focal length lens to cover the gauge length, external white light illumination, and an image acquisition system that captures and records images on a PC. To ensure the simultaneous data acquisition of load values with strain values retrieved from the images, the camera was synchronized with the testing machine. A random pattern must be created on the sample so that consecutive images are correlated. In this particular case, two different sprays were used. First, the entire gauge length was painted with a white spray, and then black droplets were sprayed to achieve a stochastic pattern, as illustrated in Figure 3 for a flat surface (shown as an example). Once the pattern was applied, the sample was secured in the testing machine to conduct the fatigue test and capture a sequence of images at 20 frames per second. \begin{table}
\begin{tabular}{c c c c} \hline
**Test N\({}^{\circ}\)** & **Test Description** & **Load Conditions** & **Purpose** \\ \hline \(1\) & Accelerated fatigue test & Max Load = 3000 N, f = 10 Hz, R = 0.1. & Understand sensor behavior in a fast test (few hours) \\ \hline \(2\) & Non-accelerated fatigue test & Max Load = 600 N, f = 10 Hz, R = 0.1 & Study the behavior of DIC and optical microphone under less severe and more realistic loads \\ \hline \(3\) & Damage Tolerance & Max Load = 100–1000 N, f = 10 Hz, R = 0.1. & Study the damage propagation \\  & Final increased load = 120–1200 N & phenomenon \\ \hline \end{tabular}
\end{table} 
Table 1: Testing campaign. Figure 2: This figure shows the set-up (**a**) with the sandwich structure clamped in the testing machine and the non-destructive systems installed. In subfigure (**b**), two microphones are positioned at the sides of the heat exchanger. The evaluation of the images is carried out using subsets, which are square groups of pixels. Each specific subset has its unique pattern distribution serving as the distinctive feature used for image correlation. More precisely, this pattern is sought in subsequent images to determine the displacement and the strain. For that purpose, a correlation software was utilized. The subset size was set at 20 pixels, proving to be sufficiently small to provide spatial resolution and low noise level. Regarding the point distance between subsets, the value was set to 10 pixels, allowing the capture of the displacement field with adequate resolution. The choice of values and the measurement procedure were supported by a recognized guide; more information can be found in [18]. To mimic the behavior of the extensometer, displacement values were exported from the program and strain evolution was computed afterwards. This is explained in more detailed in Section 2.3. For AE, two microphones were positioned on either side of the heat exchanger as shown in Figure 2. The microphone on the right side (identified by a yellow cable) is an Eta250 Ultra while the one on the left (identified by a white cable) is an Eta450 Ultra by XARION Laser Acoustics GmbH (Wien, Austria). These novel ultrasound microphones can measure airborne acoustic signals in a very broadband frequency range up to 1 MHz with the Eta250 Ultra and 2 MHz with the Eta450 Ultra. The measurement principle of these membrane-free optical microphones is based on a Fabry-Perot laser interferometer. In general, acoustic waves represent local pressure changes of the traversed medium, which, in this case, is air. These pressure changes induce variations of the refractive index in the air. The Fabry-Perot interferometer, located in the sensor head of the optical microphone, can measure these alterations of the refractive index and convert them into to corresponding sound pressure changes. This method enables the acquisition of acoustic signals with a bandwidth of up to several MHz in air.