Fatigue Failure — S-N Curve

Fatigue failure happens when repeated loading creates damage over many cycles, even if each cycle is below the material's static tensile strength. An S-N curve shows the basic trend: for one material under one test condition, higher cyclic stress usually means fewer cycles to failure, and lower cyclic stress usually means more cycles to failure.

If you remember one idea, remember the condition behind it: an S-N curve only applies to the material, surface condition, environment, and loading setup used to measure it.

What The S-N Curve Tells You

An S-N curve comes from fatigue tests. Each specimen is loaded repeatedly at a chosen stress level until it fails, and the number of cycles is recorded. Plotting many test results gives a stress-versus-life curve.

In many charts, $N$ is shown on a logarithmic axis because fatigue life can span from thousands to millions of cycles. The stress axis is often stress amplitude, but the exact stress measure depends on the test method.

So an S-N curve is not a universal law. It is measured data for a defined setup.

The Core Stress-Life Relationship

For one fixed material system and one fixed loading condition, the curve expresses a trend like this:

$$\text{larger } S \quad \Rightarrow \quad \text{smaller } N$$

That is the main idea. The curve does not give one simple formula that works for every material in every range.

Engineers often talk about fatigue life and fatigue strength:

• fatigue life means the number of cycles to failure at a chosen stress level
• fatigue strength means the stress level associated with a chosen number of cycles

Those are two ways of reading the same curve.

How To Read An S-N Curve Example

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. You would read the curve as a fatigue life of about $10^6$ cycles.

Why does this matter? A modest drop in stress, from $300\ \mathrm{MPa}$ to $220\ \mathrm{MPa}$ in this example, changes the life estimate by roughly a factor of $10$.

That does not mean every real part made from that steel will reach $10^6$ cycles. Notches, rough surfaces, corrosion, mean stress, and temperature can all shift the real fatigue life away from the lab curve.

When Endurance Limit Applies

Some materials are often modeled as having an endurance limit, meaning the curve becomes nearly flat below a certain stress level and the material may survive very large numbers of cycles under the test conditions.

That idea is useful only when it matches the material behavior. Many aluminum alloys do not show a clear endurance limit on a standard S-N plot. In that case, lower stress usually means longer life, but not a guaranteed infinite life.

So the better question is not "Does fatigue stop below this stress?" It is "For this material and this condition, what life does the data support?"

Common Mistakes With Fatigue Failure

Treating one S-N curve as universal

An S-N curve depends on material, heat treatment, specimen geometry, surface condition, environment, and loading ratio. Changing those can change the curve.

Confusing static strength with fatigue resistance

A material can have high tensile strength and still fail in fatigue if it sees enough cycles and local stress concentration.

Assuming endurance limit exists for every material

That shortcut can be seriously misleading for materials that are designed by finite-life criteria instead.

Ignoring stress concentrations

Real cracks often start near holes, threads, sharp corners, or other notches. A smooth laboratory specimen can behave very differently from a real component.

Where S-N Curves Are Used

S-N curves are used when components face many repeated loads, such as rotating shafts, springs, aircraft structures, bridges, and machine parts. They are especially useful in high-cycle fatigue, where elastic cycling dominates and life is measured across many repetitions.

They are less suitable as a full description when plastic strain is large on each cycle. In that regime, strain-life methods are often more appropriate.

The Practical Takeaway

If a part fails under fatigue, the question is usually not "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 in thinking is what makes the S-N curve useful. It connects repeated stress to expected life in a way static strength alone cannot.

Try A Similar Case

Take one point from an S-N curve and ask how the allowable stress changes if the required life increases by a factor of $10$. If you want to try your own version, explore a similar case and compare how the design changes when fatigue, not just static strength, controls the part.