the S-N curve
/ Wohler: VER-ler /
If a part fails from repeated loading, the obvious question is: how many times can I load it before it breaks? The S-N curve is the map that answers this. You test many identical specimens, each at a different stress amplitude, and record how many cycles each survives; plotting stress (S) against cycles to failure (N) gives the fatigue lifeline of the material.
The curve slopes down and to the right: the higher the stress amplitude, the fewer cycles the part survives — a high stress kills it in thousands of cycles, a gentle stress in millions. Because the lifetimes span huge ranges, N is plotted on a logarithmic axis (10^3, 10^4, up to 10^7 or more cycles). For some materials, notably plain-carbon and low-alloy steels, the curve flattens into a horizontal shelf below a certain stress — the endurance limit — meaning that below that stress the part seems to last essentially forever. Many other materials, such as aluminum alloys, never truly flatten; their curve keeps drooping, so they have a finite life at every stress.
S-N testing is the backbone of fatigue design, but it comes with honest caveats. Fatigue data scatter a lot — nominally identical specimens can differ by factors of several in life — so the curve is really a band, and designers use safety factors or design to a low survival probability. The curve also depends on the mean stress, the surface finish, the size, and the environment, so a laboratory S-N curve from polished specimens must be corrected downward for a real, rougher, corroding part.
For a steel with an ultimate strength of 600 MPa, the S-N curve might show failure at 10^4 cycles under a 400 MPa amplitude but a flat endurance limit near 250 MPa: kept below that, the shaft runs indefinitely; nudged above it, life becomes finite and shrinks fast.
Stress versus cycles-to-failure: higher stress, shorter life; some steels flatten to an endurance limit.
Real fatigue lives scatter widely, so a single S-N line is a statistical average, not a guarantee. And the flat endurance limit is mainly a steel phenomenon — designing an aluminum part as if it had one is a dangerous mistake.