It should be noted that the fatigue test was generally only carried out at the specific load ratio of \(R_{0}\ \ \)to confirm the fatigue performance of similar structural details. In other words, theS-N curve was only applicable to describe the fatigue performance when a specific value was \(R_{0}\). On the contrary, in the actual load history, there were a lot of different conditions of stress cycle stress ratio. Therefore, it was necessary to modify the S-N curve by using the empirical constant life diagram to make it applicable to the stress cycles with different stress ratios in the history of actual loads. Some empirical constant life charts, for example Goodman, modified Goodman (i.e., Smith or Soderberg), Bagci and Gerber charts, for instance, were widely used. Nevertheless, by reanalyzing the charts above, it was known that [40] modified Goodman(i.e., Smith or Soderberg) for most materials’ fatigue limit estimates were conservative. Bagci model was optimistic for majority of materials. Gerber equation was applied to ductile materials but its application was limited by its nonlinear function. Goodman chart was suitable for brittle materials, but being conservative for ductile materials. Therefore, the empirical Goodman chart [41, 42] was adopted to modify the S-N curve as: