α-S-N curve: A novel S-N curve modeling method under small-sample test data using uncertainty theory

Considering the unconvincing results produced by probability theory when dealing with small sample data, this paper introduces uncertainty theory (a branch of axiomatic mathematics parallel to probability theory) to model and estimate the uncertainty of fatigue life with the small sample of fatigue test data. A new method called alpha-S-N curves is firstly proposed to describe the relationship between fatigue life and stress levels. Subsequently, general procedures are established for the determination of alpha-S-N curves based on the four basic assumptions to improve the information utilized in the estimation process and overcome the large-scatter of the small sample fatigue failure data. Finally, the developed procedures are verified by the data of aluminum alloy data and laminate panel data. The precision and stability of the developed procedures are validated by the index relative slope in comparison with the method stated in ISO 12107.