## 3 Results and Discussion  
### Response of the Sensor with AU Method  
With the AU method, signals are generated in the middle of the gauge length for the undamaged CMC composite. The generated burst signals with a specific frequency are of the same energy but of different frequency content between 100 kHz to 1000 kHz. The evolution of the descriptors calculated on the AE signals are analysed in order to establish a link with the characteristics of the input signal mainly the frequency. Figure 3a shows the evolution of the amplitude and the several frequencies for several input frequencies. The results of Figure 3a illustrate the effect of the sensor on the detected signal. If the frequency correctly follows the change in the frequency of the input signal, the amplitude is strongly affected by the sensor response. This result is in good agreement with the calibration curve (Figure 2). The average frequency, which corresponds to the ratio between the number of counts and the duration, seems well adapted for the input frequency lower than 350 KHz. At higher frequencies, the average frequency underestimates the input frequency. The peak frequency seems more suitable than the central frequency. The latter overestimates the frequency in low frequencies. Figure 3b represents the evolution of the partial power PPi. We can observe a good agreement between the values of the several PPi (defined in Table 1) and the input frequency.  
Figure 3: (**a**) Amplitude and frequency recorded by a \(\upmu\)80 sensor for signals of different frequencies and same energy generated by an acousto-ultrasonic card. (\(\times\) Weighted Frequency, * Peak Frequency, + Central Frequency and \(\lozenge\) Average Frequency) (**b**) PPi versus input frequency. (The input signal is generated with a specific frequency equal to 150 kHz up to 950 kHz, amplitude 5 volts and rise time 20 \(\upmu\)s. (Propagation distance of 100 mm, composite material propagation medium with undamaged SiC\({}_{f}\)/SiC, actuator \(\upmu\)80 sensor).  
Figure 4 shows the evolution of the recorded energy, the damage index (\(1-D\)) and the frequency centroid as a function of strain during a tensile test of CMC. To describe stiffness loss, the variable \(D\) is used, defined through the well-known relation:  
\[D=1-\frac{E(t)}{E_{0}} \tag{1}\]  
where \(E(t)\) is the secant elastic modulus at the time \(t\) and for the strain \(\varepsilon\) and \(E_{0}\) is the initial elastic modulus. Around 0.1% a significant decrease in elastic modulus is observed due to matrix multi cracking. Damage in matrix results from cracks located in the interplay matrix, in the transverse tows and in the longitudinal tows. Above 0.6%, the elastic modulus stabilizes due to saturation of matrix cracking. The waveform is a signal with a sweeping in frequency. The signal for the actuator is the same along the test and contains various frequency components from 100 KHz to 950 KHz. The Figure 4 indicates an evolution of the recorded energy with damage, a significant decrease is observed just after matrix cracking. It is shown that waveforms are distorted with damage evolution. The recorded energy is strongly affected. The frequency centroid seems not to be affected by the evolution of damage. The same result is obtained with the average frequency and the peak frequency. This result is very important for the lifetime estimation based on the recorded energy and it shows that it would be necessary to correct the energy or the amplitude accordingly with the damage evolution.