Consider a hypothetical material. The S-N curve for this material (similar to Figure 6.1) is a straight line, if N is plotted on a log axis. At the ultimate stress, $\sigma_u$, the material can sustain 1 cycle; at 0.3 the ultimate stress, the material can withstand $10^7$ cycles. Consider that the stresses in the tests yielding these results are completely reversing.
1. Write an equation that describes the S-N curve; i.e. determine the equation that relates $\log N$ to the applied stress, $\sigma_a$.
2. Suppose a sample is exposed to $10^5$ cycles at a fully reversing load of amplitude $0.4\sigma_u$. Suppose the load amplitude is increased to $0.5\sigma_u$. How many additional cycles can the sample endure at this stress before fatigue failure is expected?