# Numerical Voids Detection in Bonded Metal/Composite Assemblies Using Acousto-Ultrasonic Method
## 4 Results and Discussion
### Influence of the Voids on AE Parameters  
Figure 7 shows the variation of two descriptors (amplitude and duration) evaluated in the time domain as a function of the distance between the transmitter (T) and the receiver. The data collected by the perfect sensor or obtained by the R15 sensor are shown for the reference assembly and for the \(\beta\) samples. For the perfect sensor, we can observe a significant decrease in the amplitude at the epicenter of the defect, which is more evident for the void of larger size in \(\beta\)2. The signal duration increases significantly at the epicenter of the void. For all descriptors in time domain, the characteristics of the signals received after the void are significantly equivalent to those of the reference. The simulation with the perfect sensor highlights the difficulty of detecting the defect for a sensor not located at the epicenter of the void with the conventional parameters extracted in AE in the time domain. In contrast, it highlights the effect of the void size on the descriptors calculated at the defect epicenter. Considering the actual R15 rather than the perfect sensor results in a similar variation in the amplitude as a function of the distance to the transmitter and considerably reduces the influence of the void on the signal duration. This is especially true for the smaller void, which no longer presents a significant difference from the reference material at the defect epicenter. Beyond the defect, the differences between the reference material and the material with defects are not marked or are even non-existent. This leads to the conclusion that using the R15 sensor significantly reduces the probability of detecting voids using time-domain descriptors. The variation of the descriptors in the frequency domain as a function of the distance to the transmitter is shown in Figure 8. We can observe a significant decrease in the frequency content of the signal recorded with the perfect sensor just above the defect. The frequencies around 150 kHz are attenuated compared to lower frequencies. The reduction of the frequency content evolves with the size of the defect. Indeed, the centroid frequency  
Figure 6: Simulated signal without AE sensor effect in (**a**) time domain and (**b**) frequency domain. (**c**) Fast Fourier transform (FFT) of the simulated signals recorded by the R15 sensor. is smaller than 100 kHz for the \(\beta\)2 defect and above 100 kHz for the smaller defect in \(\beta\)1. The peak frequency is also modified, but not affected by the size of the defect. It was found that the defect size has an influence on the signature of the AU signal recorded by sensor 2 and could be discriminated with the perfect sensor or in applications with wideband sensors that are not expected to modify the measured frequency range. Using the R15 sensor, a modification of the centroid frequency can be observed although the differences are much less marked. On the other hand, for the peak frequency, there is no difference compared to the reference configuration. Considering the actual R15 sensor also reduces the probability of detecting voids in the frequency domain in comparison with the perfect sensor. Figure 9a represents the fast Fourier transform (FFT) for the sensor 2 and sensor 1 signals, calculated for the reference sample and the \(\beta\) samples. Figure 8: Variation of (**a**) frequency centroid and (**b**) peak frequency versus the distance between the emitter and the perfect sensor (PS, o) or R15 sensor (\(\square\)) for the various assemblies. Figure 7: Variation of (**a**) amplitude and (**b**) duration as a function of the distance between the transmitter and the perfect sensor (PS, o) or the R15 sensor (\(\square\)) for the various assemblies. It appears that the magnitude of the frequency band at about 80-250 kHz decreased significantly with the void size, whereas the magnitude at about 50 kHz increased considerably at the epicenter of the defect.