the endurance limit
Imagine a stress so gentle that no matter how many millions of times you apply it, the part just never fatigues. For some materials that magic threshold really exists, and it is called the endurance limit (or fatigue limit): a stress amplitude below which the S-N curve goes flat and the part survives essentially forever.
On the S-N curve it shows up as a horizontal shelf, usually appearing beyond about 10^6 to 10^7 cycles. For plain-carbon and low-alloy steels the endurance limit is roughly 0.35 to 0.5 of the ultimate tensile strength — a handy rule of thumb (a 600 MPa steel might have an endurance limit near 250 MPa). Physically, the idea is that below this stress a fatigue crack either never nucleates or cannot keep propagating, so the damage never accumulates to failure. Design a rotating shaft to stay below the endurance limit and, in principle, you have infinite-life design.
The crucial honesty here: not every material has a true endurance limit. Aluminum alloys, copper, and many others show no flat shelf — their S-N curve keeps sloping down forever, so there is always some stress that will eventually cause fatigue, and for them engineers quote a fatigue strength at a chosen life (say the stress giving 10^8 cycles) instead. Even for steel the endurance limit is not sacred: a corrosive environment, a bad surface finish, or periodic overloads can erase it, letting cracks grow below the nominal limit. Treat the endurance limit as a useful design target, not an unbreakable promise.
A car valve spring is designed so its peak cyclic stress stays just under the steel's endurance limit; it then survives hundreds of millions of open-close cycles over the engine's life. Raise the stress slightly above the limit and the infinite life suddenly becomes a countable, and short, one.
Below the endurance limit the S-N curve is flat — steel lasts, in principle, forever.
Aluminum and many non-ferrous alloys have no true endurance limit; their fatigue curve never flattens. Assuming a flat limit for them — or ignoring that corrosion and rough surfaces can destroy even a steel's limit — is a classic and dangerous error.