Why Fatigue Failures Keep Happening
Fatigue is the leading cause of in-service structural failure in mechanical components. It is also the failure mode that most often surprises engineers who have not worked with it directly — parts fail at stresses well below the static yield strength, after many cycles, with no obvious warning. A shaft that has been running for months suddenly fractures. A weld that looked fine on inspection cracks under cyclic loading. The fracture surfaces show the characteristic beach marks and ratchet marks of fatigue, and the post-mortem investigation reveals that the design never properly accounted for the cyclic load environment.
This guide covers the analytical foundation for fatigue design: the S-N curve, the endurance limit concept, stress concentration effects, the Goodman diagram for combined mean and alternating stress, and the practical corrections that bring textbook theory closer to real-world performance.
The S-N Curve (Wöhler Curve)
The foundational tool for fatigue analysis is the S-N curve (stress vs. cycles to failure), developed by August Wöhler in the 19th century. It is obtained by testing specimens at different alternating stress amplitudes and recording the number of cycles to failure. Key characteristics:
- At high stress amplitudes, failure occurs in a small number of cycles (low-cycle fatigue, LCF, typically below 104 cycles)
- At lower stress amplitudes, failure occurs after many cycles (high-cycle fatigue, HCF, 105 to 107+)
- For steels, the S-N curve flattens at approximately 106–107 cycles, defining the endurance limit (Se) — a stress amplitude below which the material theoretically has infinite life
- Aluminum alloys and many non-ferrous metals do not exhibit a true endurance limit — the curve continues to slope downward at high cycle counts. Fatigue life must be quoted at a specified cycle count.
As a rough estimate for wrought steel: Se ≈ 0.5 × Su, where Su is the ultimate tensile strength. This approximation holds for Su up to approximately 1400 MPa; above that, the endurance limit does not continue to scale proportionally.
Stress Concentration Factors (Kt)
Real parts have stress concentrations — notches, holes, fillets, keyways, threads, and section changes that amplify the local stress above the nominal value. The theoretical stress concentration factor Kt is the ratio of peak local stress to nominal stress for an ideal elastic material.
The fatigue notch factor Kf relates Kt to actual fatigue behavior through the notch sensitivity factor q:
Kf = 1 + q × (Kt − 1)
where q ranges from 0 (completely insensitive to notch) to 1 (fully sensitive). For fine-grained, high-strength steels, q approaches 1. For cast iron and coarse-grained or low-strength materials, q is significantly lower. Values of q are tabulated in fatigue design references as a function of material tensile strength and notch root radius.
The fatigue-modified endurance limit accounting for stress concentration is:
Se’ = Se / Kf
This means a sharp notch (Kf = 3) reduces the effective endurance limit to one-third of the material’s baseline value — a severe penalty that designers must account for in geometry decisions.
Endurance Limit Modifying Factors
The laboratory S-N endurance limit applies to a small, polished, tested specimen under fully reversed bending. Real parts differ in surface finish, size, load type, temperature, and reliability requirement. The modified endurance limit for design is:
Se = ka × kb × kc × kd × ke × Se’
where the modifying factors account for:
- ka (surface finish): Ground surfaces ≈ 0.9; machined ≈ 0.8–0.9; as-forged ≈ 0.5–0.7 — a very large effect
- kb (size): Reduces with increasing diameter; approximately 1.0 for small parts, 0.7–0.8 for large shafts
- kc (load type): 1.0 for bending, ~0.85 for axial, ~0.59 for torsion (converting to equivalent bending)
- kd (temperature): Near unity at ambient; reduces above ~250°C for steel
- ke (reliability): 1.0 for 50% survival, 0.87 for 90%, 0.81 for 99%
The Goodman Diagram: Handling Mean Stress
Laboratory S-N data is typically obtained at fully reversed loading (mean stress = 0). Real applications often involve a mean (static) stress component superimposed on the alternating stress. Tensile mean stress reduces fatigue life; compressive mean stress improves it.
The modified Goodman criterion provides a conservative and widely used relationship for the failure boundary in mean stress–alternating stress space:
σa/Se + σm/Su = 1 (Goodman line)
where σa is alternating stress amplitude, σm is mean stress, Se is the modified endurance limit, and Su is ultimate tensile strength. Points below this line are considered safe for infinite life. Points above are predicted to fail. For yield safety, also check that σa + σm ≤ Sy.
Fatigue Failure Case Examples and Lessons
| Component | Failure Mode | Root Cause | Design Lesson |
|---|---|---|---|
| Rotating shaft | Transverse fracture at keyway | High Kt at keyway corner, high mean torsion | Use larger fillet radius or round-ended keyway |
| Welded bracket | Cracking at weld toe | High stress concentration at weld toe; no PWHT | Full penetration weld + post-weld grinding or peening |
| Threaded rod | Failure at first thread engagement | High Kt at thread root, axial cyclic load | Reduce shank diameter to equalize stiffness; use fatigue-rated fasteners |
| Cast housing | Cracking at section change | Sharp internal corner (Kt ~3) in casting | Generous blend radii in casting design; shot-peen surfaces |
FAQ
Q: How do I apply fatigue analysis when my part experiences variable amplitude loading rather than constant amplitude?
A: Use Miner’s rule (linear damage accumulation). For each load level i, calculate the cycle ratio ni/Ni, where ni is the number of cycles applied at stress level σi and Ni is the number of cycles to failure at that stress level (from the S-N curve). Sum the damage fractions: when Σ(ni/Ni) = 1, fatigue failure is predicted. In practice, Miner’s rule is conservative for some loading sequences and non-conservative for others, so apply an additional safety factor (typically 0.7–0.5 on the damage sum) for critical applications. For precise life prediction, consider using rainflow counting to identify the actual load cycles from a recorded load history.
Q: Does surface treatment affect fatigue life significantly?
A: Very significantly. Shot peening introduces compressive residual stresses in the surface layer, which oppose the tensile stress that drives fatigue crack growth. Improvement in fatigue life of 20–50% is common; in some cases it is higher. Carburizing and nitriding similarly improve fatigue life at the surface through both hardening and compressive residual stresses. Conversely, electroplating (especially chrome and cadmium) can reduce fatigue life by introducing tensile residual stresses and hydrogen embrittlement. For fatigue-critical parts, always evaluate the impact of surface treatments on life.
Q: What safety factor should I use for fatigue design?
A: Typical factors of safety on the fatigue limit (Se) range from 1.5 to 2.5 for well-characterized applications with good load knowledge. Higher factors (3–4) are used when loads are uncertain, the consequence of failure is severe, or material properties are variable (castings, welded joints). The Goodman criterion itself is somewhat conservative for ductile materials, so a factor of 1.5–2.0 on Se combined with Goodman is reasonable for most engineering applications. For safety-critical components (aircraft, pressure vessels, medical devices), the combination of detailed analysis, testing, and defined safety margins is specified by the applicable standard.
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