Fatigue Failure — S-N Curve

Why do parts that easily survive a single heavy pull still crack after months of ordinary use? Fatigue failure is the answer: repeated loading creates damage over many cycles, even when each cycle stays below the material's static tensile strength. The tool engineers reach for is the S-N curve, which records, for one material under one test condition, how cyclic stress level relates to the number of cycles before failure.

When To Reach For An S-N Curve

Use this method when a component faces many repeated loads rather than one peak load. Rotating shafts, springs, aircraft structures, bridges, and machine parts all live in this regime, especially in high-cycle fatigue, where elastic cycling dominates and life is measured across many repetitions.

It is the wrong tool when plastic strain is large on every cycle. In that regime, strain-life methods are usually more appropriate than an S-N reading.

One condition sits behind everything else: an S-N curve only applies to the material, surface condition, environment, and loading setup used to measure it.

Reading The Curve Step By Step

An S-N curve comes from fatigue tests. Each specimen is loaded repeatedly at a chosen stress level until it fails, and the cycle count is recorded. Plotting many results gives a stress-versus-life curve, often with $N$ on a logarithmic axis because fatigue life can span from thousands to millions of cycles. The stress axis is frequently stress amplitude, but the exact stress measure depends on the test method.

Work through it in order:

1. Check the test conditions. Read the curve only for the material, surface condition, specimen geometry, environment, and loading ratio it was measured under.
2. Find the stress level. Start from the cyclic stress measure used on the chart, often stress amplitude.
3. Read the life. Move across the curve to estimate the number of cycles to failure at that stress level.
4. Interpret with care. If the material has no clear endurance limit, lower stress may only mean longer life, not infinite life.

For one fixed material system and one fixed loading condition, the trend is simply

The curve does not hand you one formula that works for every material in every range. Engineers read it two ways: fatigue life is the number of cycles to failure at a chosen stress level, and fatigue strength is the stress level tied to a chosen number of cycles. Both come from the same curve.

A Full Reading, Start To Finish

Suppose a lab has already measured an S-N curve for one polished steel specimen under one fixed loading ratio. On that specific curve:

• a stress amplitude of $300\ \mathrm{MPa}$ corresponds to about $10^5$ cycles to failure
• a stress amplitude of $220\ \mathrm{MPa}$ corresponds to about $10^6$ cycles to failure

Now imagine your part sees a stress amplitude near $220\ \mathrm{MPa}$ under the same conditions as the test. Reading the curve gives a fatigue life of about $10^6$ cycles.

Notice what the modest stress drop did: going from $300\ \mathrm{MPa}$ to $220\ \mathrm{MPa}$ in this example changed the life estimate by roughly a factor of $10$. That does not guarantee every real part made from that steel will reach $10^6$ cycles. Notches, rough surfaces, corrosion, mean stress, and temperature can all shift real fatigue life away from the lab curve.

Where Each Step Trips People Up

Treating one S-N curve as universal. The curve depends on material, heat treatment, specimen geometry, surface condition, environment, and loading ratio. Change those and the curve changes.

Confusing static strength with fatigue resistance. A material can have high tensile strength and still fail in fatigue given enough cycles and local stress concentration.

Assuming an endurance limit always exists. Some materials are modeled with an endurance limit, where the curve flattens below a certain stress and the material may survive very large cycle counts under the test conditions. But many aluminum alloys show no clear endurance limit on a standard S-N plot. Self-check: if your material is designed by finite-life criteria, this shortcut can be seriously misleading.

Ignoring stress concentrations. Real cracks often start at holes, threads, sharp corners, or other notches, so a smooth laboratory specimen can behave very differently from a real component.

The better question is never "Does fatigue stop below this stress?" It is "For this material and this condition, what life does the data support?"

The Mental Shift That Makes It Click

If a part fails under fatigue, the useful question is rarely "Was the one-time load too big?" It is "Was the repeated load too high for the number of cycles the part had to survive?" That shift connects repeated stress to expected life in a way static strength alone never can. To feel it directly, take one point from an S-N curve and ask how the allowable stress moves if the required life grows by a factor of $10$.