## 4 Results and Discussion
### Identification of Critical Time  
The evolution of \(R_{AE}\) is plotted _versus_ time in Figure 8 for three experiments. This coefficient is observed to decrease first, then to reach a minimum value for \(t=t_{m}\), and then to increase up to the failure of the composite at time \(t_{R}\). This ultimate increase in AE activity was not always visible on the curves of AE energy _versus_ time, but it was revealed by this representation. The ratio \(t_{m}/t_{R}\) appears to be quite reproducible: \(t_{m}/t_{R}\) =0.57 \(\pm\) 0.06 (Figure 9). Therefore, the \(R_{AE}\) ratio may be used as a criterion for predicting the remaining lifetime of a specimen under static loading. During static fatigue test, attenuation coefficient \(B\) growths significantly during the first part of tests up to a plateau value near 50% of the rupture time (Figure 10). For each test, the slight increase of \(B\) observed during initial loading is very low compared to the one occurring during static fatigue. Therefore, the increase of attenuation coefficient \(B\) may be related to matrix crack opening and to the recession of interfaces. The detection of the plateau during the typical evolution of attenuation coefficient B may be considered as an indicator for lifetime prediction. As the minimum of coefficient \(R_{AE}\), the value plateau of \(B\) indicates the beginning of the critical damage phase and provides an estimation of the remaining lifetime. Figure 8: Evolution of the \(R_{AE}\) coefficient during the static load hold on SiC\({}_{f}\)/[Si-B-C] composites. Figure 7: Number of AE events recorded during initial loading up to the nominal load and during the static loading at a constant load. The critical damage phase prior to final rupture may be attributed to the avalanche fibers breaks, controlled by fibers oxidation and by recession of interfaces. In order to confirm this hypothesis, the coefficient \(R_{AE}\) is calculated for several damage mechanisms identified with clustering analysis of AE data. The Figure 11 show the activities of several damage mechanisms identified with the supervised analysis. During static fatigue, clusters B and D are more active. The evolution of the coefficients \(B\) obtained for the two classes A and B go through a minimum, contrary to those of classes C and D (Figure 12). For the B class (mainly fiber failure at the end of the tests), the minimum value of the coefficient \(B\) is observed around 65% of the lifetime. For the A class (mainly yarn fractures or collective fiber breaks at the end of the tests), the minimum is also observed at 65%. One may noticed that the minimum is observed only for clusters A and B corresponding to fibers breaks during the second part of the test. If the growth of the attenuation coefficient \(B\) is linked to matrix crack opening, coefficient B also allows considering the plateau observed on the evolution of attenuation coefficient \(B\) shows that matrix crack opening leads to an equilibrium state near 40%-50% of the rupture time. The significant increase of matrix crack opening pointed out before 50% of the rupture time is linked to carbon oxidation in the interphases provoking an increase in length of the debonded region of fibers in the vicinity of matrix cracks. Beyond 50% of the rupture time, the oxygen flux, determined by the degree of matrix crack opening, controls the rate of fibers break by slow crack growth. This critical time corresponds to the beginning of a second damage phase where slow crack growth in fibers is prevailing, leading to the ultimate fracture of the composite. Figure 10: Evolution of the attenuation coefficient B during the static load hold (\(\sigma/\sigma_{\rm R}=0.95\), \(\sigma/\sigma_{\rm R}=0.71\) and \(T=500\)\({}^{\circ}\)C). Figure 9: Critical times obtained with the minimum value of \(R_{\rm AE}\) and the optimum \(t_{\rm surf}\) for the Benioff law obtained with the OCM method.