## 4 Results and Discussion  
### Mechanical Analysis  
The lifetime diagram, obtained at several temperatures and under various stresses, of the composite for static fatigue at intermediate temperature is plotted in Figure 3a. All the points are aligned in the logarithmic representation and follow the power-type law:  
\[t\cdot\sigma^{n}=A \tag{8}\]  
where \(t\) is the lifetime, \(\sigma\) is the applied stress, \(A\) and \(n\) are constants depending on the material, the temperature and the environment. The stress exponent \(n\) is estimated at 3.2 \(\pm\) 0.3. A comparison between our results on composite and on the fibers in literature [34] under static fatigue at 500 \({}^{\circ}\)C (Figure 3b) shows that at intermediate and high stresses the lifetime of the composite is longer than the lifetime of the fibers. This is characterized by two different values of \(n\), \(n\) is equal to 3.2 for the composite and to 8.45 for the fibers [34]. Figure 3: (**a**) Lifetimes obtained during static fatigue at 450 \({}^{\circ}\)C, 500 \({}^{\circ}\)C and 560 \({}^{\circ}\)C under air on SiC\({}_{f}\)/[Si-B-C] composites for several applied stresses; (**b**) Lifetimes on the fibers bundles [34] and on SiC\({}_{f}\)/[Si-B-C] composites in static fatigue at 500 \({}^{\circ}\)C under air. For this range of applied stress, slow crack growth of the fibers needs the diffusion of oxygen but is controlled by the chemical reaction at the crack tip. As shown by [PERSON] and [PERSON] [34], the activation energy 129 kJ/mol corresponds to the reactivity of carbon (present in the fibers) to oxygen. In the composite the diffusion of oxygen toward the fiber surfaces is slackened by the oxygen consumption due to reaction with self-healing matrices and with interphases. Under lower stresses, the lifetimes of the composite and of the fiber bundles are similar. For this low level of stresses reaction kinetics with fiber surfaces are slower than diffusion kinetics of oxygen into the matrix crack. Hence the subcritical crack growth kinetics in dry bundles and in the fibers of the composites are similar. Stress as a function of strain is shown in Figure 4. The grey curve represents the monotonic tensile curve whereas the other curves correspond to the static fatigue curves for various ratios of stress and with some loading and unloading sequences. One may notice that strain increases significantly during the test, and that hysteresis secant loops evolve as well: the mean elastic modulus decreases whereas the loops width increases. The increase in the loops area is linked to a change in the interfacial shear stress, suggesting that some debonding occur during static fatigue. The evolution of the Young's modulus was evaluated during the tests by measuring the hysteresis loops modulus \(E_{i}\). Then the damage parameter \(D=1-E_{i}/E_{0}\) was calculated, \(E_{0}\) being the initial Young's modulus of the composite. The evolution of \(D\) is plotted _versus_ time in Figure 5, for several \(\sigma/\sigma_{\mathrm{R}}\) ratios. The biggest increase of \(D\) occurs during the loading step and the first 24 h of static fatigue. Then \(D\) is observed to rise monotonically up to the failure of the specimen. The general trend is that the highest the \(\sigma/\sigma_{\mathrm{R}}\) ratio, the highest the \(D\) parameter for similar durations of test. The final \(D\) values obtained at failure are not exactly the same: they vary in the range 0.6-0.8, and it seems that this value decreases when the \(\sigma/\sigma_{\mathrm{R}}\) ratio decreases. However it seems difficult to define a failure criterion based on the damage parameter. Figure 4: Stress _versus_ strain during static fatigue experiments for different \(\sigma/\sigma_{\mathrm{R}}\) ratios: 0.44, 0.71 and 0.95 at 500 \({}^{\circ}\)C on SiC\({}_{f}\)/[Si-B-C] composites. The grey curve represents the monotonic tensile curve.