defined by several quantities: the minimal and maximal stresses $\sigma _{\min }$ et $\sigma _{\max }$, the stress amplitude $\sigma _{a}=\frac{\sigma _{\max }-\sigma _{\min }}{2}$, and other indicators such as the stress ratio $\frac{\sigma _{\min }}{\sigma
_{\max }}$.

![image](fatigue2.png) \[cyclefatigue\]

The fatigue strength of a given material is studied through experimental campaigns designed at fixed environmental covariates to reproduce flight conditions. The trials consist in loading at a given stress level a dimensioned sample of material up to its failure or the date of end of trial. The lifetime of a specimen is measured in terms of number of cycles to failure, usually subject to right censoring.

![S-N curve[]{data-label="wohler"}](wohler.png)

The campaign results are then used to study fatigue resistance and are represented graphically in an S-N scale (see figure \[wohler\]). S-N curves highlight the existence of three fatigue regimes. Firstly, low cycle fatigue corresponds to short lives associated with high levels of stress. Secondly, during high cycle fatigue, the number of cycles to failure decreases log-linearily with respect to the loading. The last regime is the endurance limit, in which failure occurs at a very high number of cycles or doesn’t occur at all. We will focus in the following 