Fatigue and S-N Curves
Why parts can fail after many repeated loads below static strength
Difficulty
Intermediate
Read time
10 min
Review status
Needs review
Concept sketch
Stress amplitude versus cycles to failure
S-N curve shape is material dependent
Overview
Fatigue describes progressive damage from repeated loading. An S-N curve relates stress amplitude to the number of cycles to failure, helping students understand endurance, scatter, safety factors, and why cyclic loading can be more dangerous than one static load.
How to read it
- Read stress amplitude or alternating stress on the vertical axis.
- Read cycles to failure on the horizontal axis, usually with a log scale.
- Compare operating stress against the curve for the target life.
- Look for whether the material is assumed to have an endurance limit.
When to use it
- Rotating shafts, springs, gears, aircraft structures, and machine parts under repeated loads.
- Estimating whether a stress level is acceptable for a target number of cycles.
- Understanding why notches, surface finish, or corrosion can sharply reduce life.
- Distinguishing static strength from cyclic durability.
What fatigue means
Fatigue is damage that accumulates under repeated or fluctuating stress. A part can survive one load application but still fail after many cycles if cracks initiate and grow over time.
What an S-N curve shows
An S-N curve plots stress level against number of cycles to failure. The vertical axis is usually stress amplitude or alternating stress, while the horizontal axis is number of cycles, often shown on a logarithmic scale.
Scatter and testing
Fatigue data has significant scatter because surface finish, defects, environment, mean stress, size, and manufacturing history can all affect life. Engineers treat S-N data statistically rather than as one perfectly sharp curve.
Design interpretation
A lower stress amplitude generally means longer fatigue life. Some steels show an endurance-limit-like region, while many nonferrous metals do not have a true horizontal limit. Course assumptions matter a lot in fatigue problems.