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: