Fatigue is the gradual damage that occurs when a material is loaded and unloaded many times. A part can fail by fatigue even when the maximum stress is below the yield strength, which makes fatigue especially important in bridges, aircraft, shafts, springs, and machine parts. The S-N curve is a key engineering tool because it relates stress amplitude to the number of cycles a material can survive before failure.
It helps engineers choose safe stress levels for parts that experience repeated loading.
On an S-N curve, the vertical axis is usually stress amplitude and the horizontal axis is the number of cycles to failure on a logarithmic scale. Higher stress amplitudes usually cause failure in fewer cycles, while lower stress amplitudes allow much longer life. Fatigue failure often begins with tiny cracks at stress concentrations such as holes, scratches, notches, or welds, then cracks grow a little during each cycle until sudden fracture occurs.
Some steels show an endurance limit, a stress amplitude below which fatigue failure is unlikely for a very large number of cycles.
Understanding Engineering: Fatigue and the S-N Curve
A fatigue test uses many identical specimens. A machine bends, pulls, twists, or presses each one repeatedly at a chosen load level. Engineers record the cycle count when each specimen breaks.
The results naturally vary because real materials contain different tiny defects. For this reason, an S-N curve is based on many tests rather than one result. It is often treated as a statistical guide.
A design may use a curve that represents a low probability of failure, not the average test result. This gives a margin for normal variation in material quality and service conditions.
The load cycle has more detail than its size alone. The maximum and minimum stress set both the stress amplitude and the mean stress. A part pulled in tension throughout its cycle usually has a shorter life than one that experiences the same amplitude while alternating evenly between tension and compression.
Tensile mean stress tends to hold a crack open, making growth easier. Compressive mean stress can partly close the crack during part of the cycle.
Engineers account for this effect with correction methods and test data matched to the expected loading pattern. The stress ratio is useful because it states how the minimum load compares with the maximum load.
Surface condition matters greatly because fatigue damage usually starts at the surface. A polished specimen can last far longer than a rough machined part under the same nominal stress. Threads, keyways, sharp corners, weld toes, corrosion pits, and tool marks all raise local stress.
This local peak may be much larger than the stress calculated from force divided by area. Designers reduce the problem by using smooth changes in shape, generous corner radii, careful weld details, and good surface finishing.
Processes such as shot peening place the surface in compression, which can slow the opening of small cracks. Corrosion protection matters for the same reason, since pits make strong crack starting sites.
Once a crack is found, engineers may stop using an S-N approach alone. They measure or estimate crack size, then use fracture mechanics to predict how quickly it will grow. The key loading quantity is the stress intensity range, found by subtracting minimum stress intensity from maximum stress intensity.
It depends on load, crack length, component shape, and crack location. Inspections are then scheduled before a crack reaches a critical size. Students should distinguish safe life design from damage tolerant design.
Safe life replaces a part after a planned number of cycles. Damage tolerant design accepts that small flaws may exist, then relies on inspection and controlled crack growth. Both approaches appear in vehicles, rotating equipment, rail systems, and aircraft structures.
Key Facts
- Stress amplitude is σa = (σmax - σmin) / 2.
- Mean stress is σm = (σmax + σmin) / 2.
- Stress ratio is R = σmin / σmax.
- An S-N curve plots stress amplitude, S, versus cycles to failure, N, often with N on a logarithmic scale.
- Fatigue failure can occur when σmax is below the yield strength, σy, because microscopic damage accumulates over many cycles.
- For crack growth, the stress intensity range is ΔK = Kmax - Kmin, and larger ΔK generally increases crack growth rate.
Vocabulary
- Fatigue
- Fatigue is progressive damage and eventual failure caused by repeated or fluctuating stresses.
- S-N Curve
- An S-N curve is a graph showing the relationship between stress amplitude and the number of cycles to failure.
- Endurance Limit
- The endurance limit is the stress amplitude below which some materials can survive a very large number of cycles without fatigue failure.
- Stress Amplitude
- Stress amplitude is half the difference between the maximum and minimum stress in one loading cycle.
- Crack Initiation
- Crack initiation is the early stage of fatigue when microscopic cracks begin at defects, notches, surfaces, or other stress concentrators.
Common Mistakes to Avoid
- Assuming below yield means safe is wrong because fatigue can cause failure at stresses lower than the yield strength after many cycles.
- Reading the S-N curve with a linear cycle axis is wrong because the number of cycles is usually plotted on a logarithmic scale.
- Using maximum stress instead of stress amplitude is wrong when the S-N data are based on alternating stress, because σa = (σmax - σmin) / 2 controls the curve value.
- Ignoring surface defects and notches is wrong because fatigue cracks often start at stress concentrations where local stress is much higher than the nominal stress.
Practice Questions
- 1 A steel shaft cycles between σmax = 180 MPa and σmin = 20 MPa. Calculate the stress amplitude, mean stress, and stress ratio R.
- 2 An S-N curve shows failure at 10^5 cycles for σa = 260 MPa and failure at 10^6 cycles for σa = 200 MPa. If a part is loaded at σa = 260 MPa for 300,000 cycles, should you expect it to survive based only on this curve? Explain briefly.
- 3 A plate with a small drilled hole and a polished plate are made from the same material and experience the same cyclic nominal stress. Which plate is more likely to develop a fatigue crack first, and why?