Calculator
Use direct notch sensitivity, or estimate it from notch radius and material parameters.
Example data table
| Scenario | Kt | q method | Inputs | Kf |
|---|---|---|---|---|
| Direct q | 2.50 | Direct | q=0.80 | 2.20 |
| Peterson | 3.00 | Peterson | r=1.0 mm, a=0.107 mm → q≈0.903 | 2.81 |
| Neuber | 2.00 | Neuber | r=0.5 mm, A=0.20 mm → q≈0.613 | 1.61 |
Formula used
- Notch sensitivity definition: q = (Kf − 1) / (Kt − 1)
- Fatigue stress concentration factor: Kf = 1 + q (Kt − 1)
- Peterson estimate: q = 1 / (1 + a/r) (a and r are lengths)
- Neuber estimate: q = 1 / (1 + √(A/r)) (A and r are lengths)
In fatigue design, Kt is a geometric peak-stress multiplier, while Kf reflects how much of that peak actually reduces fatigue strength. The notch sensitivity q bridges the two.
How to use this calculator
- Get Kt (and Kts if needed) from geometry charts or FEA.
- Select a method to obtain q: direct input, Peterson, Neuber, or steel quick estimate.
- If estimating, enter the notch radius r and the required material parameter.
- Optionally enter nominal σa and σm to see notch stresses.
- Click Calculate. Use the export buttons to save your result.
Article: Fatigue stress concentration factor in practical design
1) What Kf represents in fatigue
Theoretical concentration Kt describes the local peak stress from geometry, often obtained from charts or finite‑element results. Fatigue factor Kf is usually lower because materials are not perfectly notch‑sensitive. The link is notch sensitivity q, bounded from 0 to 1.
2) Typical magnitude ranges
Many common shoulder fillets and keyways produce Kt values around 1.5 to 3.5, while sharp grooves can exceed 4.0. If q is near 0.6 to 0.9, Kf may remain close to Kt. If q is near 0.2, Kf can be much lower than Kt.
3) Why notch radius matters
Increasing notch radius reduces the stress gradient severity at the root. In Peterson‑style estimates, q increases as r increases because the material can “feel” the notch more completely. At the same time, a larger r usually lowers Kt, so Kf often decreases overall.
4) Peterson length scale “a”
Parameter a is a material length scale tied to microstructure and strength. A smaller a implies higher notch sensitivity for a given radius. For many steels, a is on the order of hundredths to a few tenths of a millimeter, depending on strength level.
5) Neuber constant “A”
Neuber’s form uses A with the same units as radius and enters as √(A/r). Larger r reduces √(A/r), pushing q upward. Use A from a trusted reference for your alloy and heat treatment, or treat it as a calibration constant.
6) Strength effects and sensitivity
High‑strength materials can be more notch‑sensitive because the plastic zone is smaller. That often means higher q for the same geometry. When you only have ultimate strength data, the “steel quick estimate” option approximates a and then computes q from radius.
7) Using Kf with cyclic stresses
If you provide nominal alternating stress σa and mean stress σm, the calculator also shows notch‑scaled values. A common workflow is to compute nominal σa from a load range, then apply Kf to get the local alternating stress for fatigue checks.
8) Practical tips and sanity checks
Always confirm Kt and Kts from the correct geometry and loading mode. Keep units consistent for r, a, and A. Ensure Kf stays between 1 and Kt when 0 ≤ q ≤ 1. For critical components, validate with test data or detailed local‑strain approaches.
FAQs
1) What is the difference between Kt and Kf?
Kt is the elastic peak-stress multiplier from geometry. Kf is the effective fatigue multiplier, reduced by notch sensitivity q. Kf is computed from Kt and q.
2) What range should q fall into?
q is typically between 0 and 1. Values near 0 indicate low notch sensitivity, while values near 1 indicate high sensitivity where Kf approaches Kt.
3) Can Kf ever be greater than Kt?
Not when q is between 0 and 1. With the standard relation Kf = 1 + q(Kt − 1), Kf remains between 1 and Kt.
4) Which method should I pick for q?
Use direct q if you have test-based values. Use Peterson or Neuber when you have notch radius and a material parameter. The steel quick estimate is a fallback when only strength data are available.
5) Why does increasing radius sometimes change q upward?
In gradient-based estimates, a larger radius reduces the severity of the stress gradient, which increases the estimated notch sensitivity q. However, Kt usually drops with larger radius, often lowering Kf overall.
6) How should I enter stress data?
Enter σa as the alternating amplitude (half the stress range). Enter σm as the mean stress. If you only know a fully reversed cycle, use σm = 0.
7) Does this replace a full fatigue standard check?
No. It estimates local fatigue multipliers. For certification or safety-critical design, combine Kf with appropriate S-N data, mean-stress correction, surface and size factors, and a validated design standard.