A statistical fatigue model covering the tension and compression Wöhler fields

A statistical fatigue model to predict the Wöhler field for any combination of _σmin${\sigma }_{min}$, _σmax${\sigma }_{max}$ or R=_σmin/_σmax$R={\sigma }_{min}/{\sigma }_{max}$ is presented. The model extends an existing model to the case of _σmax${\sigma }_{max}$ being tension and _σmin${\sigma }_{min}$ being tension or compression, and is derived based on physical, statistical and compatibility conditions, thus, eliminating the selection of arbitrary functions. The main tool to derive the model is a functional equation, which allows obtaining the most general model satisfying all the stated conditions. In particular, the regression formula for the _σmax${\sigma }_{max}$–logN$logN$ field for fixed R$R$ values is analyzed. A particular and powerful model is selected and its main properties are derived. This model is applied to some real data to illustrate its applicability to practical problems. The results seem to be very promising, especially because the model, due to its physical and statistical constraints, appears to be very robust and with a high capacity to detect outliers.