## 2 Numerical Model Development and Experimental Validation
### Experimental Setup
#### 2.1.2 Experimental Testing  
As previously described, there were two stages in the experimental setup, with the first being used to determine the effect of weak adhesion on LW parameters, and the second  
Figure 2: Representation and dimensions of a SLJ along with the Cartesian axis description that is used during simulations. one to determine the real level of weak adhesion affecting the manufactured SLJs, so that a direct relationship between values is possible. Regarding the first stage, each individual part was instrumented with two piezoelectric elements PIC 255 piezoceramic (PRYY + 1119 model), with one serving as sensor and the other working as an actuator, as illustrated in Figure 2. These piezoelectric elements were chosen due to their light weight, low cost, and versatility to serve as either actuators or sensor. This versatility will also allow for further tests to be conducted and will allow for having an array of sensors to analyze large areas. A five-cycle Hanning-windowed sinusoidal burst centered at a frequency of 100 kHz [16; 17; 18; 19] was applied to the actuator by a signal generator AIM & Thurbly Thander Instruments, model TGF4042. This type of excitation signal keeps LW dispersion and attenuation at a minimum, while still maximizing sensitivity. The sensor was connected to a digital oscilloscope Tektronix, model TBS1000C, which samples and memorizes the signals. To facilitate input and output synchronization, the Hanning window signal applied to the actuator was also collected by the oscilloscope. In Figure 3 the data acquisition setup can be seen. After all LW data were acquired from the SLJs, in a second stage, the sensors and actuators were removed and the samples were subjected to tensile tests. Each part was carefully placed on an Instron 3367 machine and stressed until rupture. It is important to analyze the stress-strain curves obtained, as adhesives are inherently complex, and even when fully cured in the correct manner, variations in Young modulus over 275 Mpa can be verified [15]. This uncertainty may be higher when dealing with artificially created SLJs with weak adhesion and might cause difficulties when trying to simulate vibration data. In Figure 4, the load-displacement curves of all SLJs are depicted. As expected, four groups with distinct levels of maximum load can be identified. The group produced with two layers of release agent reveals the smallest ultimate stress, while the cases without release agent correspond to the largest loads. Therefore, the method adopted for the fabrication of SLJs based on the application of a release agent to create distinct levels of weak adhesion is quite reliable. It is also interesting to observe that the two cases without the release agent presented a larger plastic deformation, which may be caused by the adhesive material deforming under loads, instead of a clean break of the adhesive on the contact surface of the substrate, as seen for the other cases. When analyzing the samples, there is a stark contrast between the adhesive of the samples that reinforces this theory. In Figure 5, it is possible to observe the difference between the sample that had plastic deformation and the sample where the limit layer of the adhesive failed. With the maximum loads determined, all samples can now be referenced to these values, and a linear percentile analysis of Young's modulus is used to compare simulated and experimental data. It is important to note that Young's modulus is being used as it is a variable that can be calculated by the tensile test and is the main variable that is altered to determine the desired level of weak adhesion present in the simulation. Figure 3: Data acquisition setup of one SLJ, with actuator and sensor connected to a signal generator and an oscilloscope, respectively. When LW data from all 11 SLJs are analyzed and compared, it is possible to verify that no clear patterns emerge.