Fatigue Stress Concentration Factor Calculator

Evaluate notch effects using fatigue concentration factors accurately. Compare direct sensitivity and Peterson radius methods. Visualize stress amplification trends with exports, examples, and guidance.

Calculator Input

Use direct q input or Peterson radius method.

Responsive 3 / 2 / 1 input layout
Used for all stress values on the page.
Choose the way q should be defined.
Theoretical elastic stress concentration factor.
Enter q directly between 0 and 1.
Use the same length basis as a.
Material sensitivity constant for the notch.
Stress amplitude before notch amplification.
Average stress over the fatigue cycle.
Used for the Goodman safety estimate.
Also used in the Goodman relation.
Reset

Plotly Graph

The chart tracks how Kf and local alternating stress change as q varies from 0 to 1.

Example Data Table

Component Kt q Kf Nominal Alt. Stress Local Alt. Stress
Grooved shaft 1.90 0.55 1.495 48.00 MPa 71.76 MPa
Shoulder fillet 2.20 0.68 1.816 72.00 MPa 130.75 MPa
Keyway section 2.75 0.74 2.295 90.00 MPa 206.55 MPa
Thread root 3.10 0.82 2.722 110.00 MPa 299.42 MPa

These rows show how sharper notches and higher q values raise local fatigue stress.

Formula Used

The fatigue stress concentration factor connects the theoretical notch effect to the real fatigue response of a material.

Kf = 1 + q × (Kt − 1)

Where:

For Peterson approximation:

q = 1 / (1 + a / r)

Where:

Local alternating stress is estimated with:

σa,local = Kf × σa,nominal

Goodman safety estimate used here:

n = 1 / ((σa,local / Se) + (σm,local / Sut))
Interpretation note: Kf always falls between 1 and Kt when q stays between 0 and 1. A larger q means the material follows the notch more strongly under fatigue loading.

How to Use This Calculator

  1. Select the stress unit that matches your design data.
  2. Enter the theoretical stress concentration factor, Kt.
  3. Choose either direct q input or Peterson approximation.
  4. If using Peterson mode, provide notch radius and constant a.
  5. Enter nominal alternating stress and nominal mean stress.
  6. Provide endurance limit and ultimate strength for the Goodman estimate.
  7. Press Calculate to show the result above the form.
  8. Use the CSV or PDF buttons to export the result summary.

8 FAQs

1) What is the fatigue stress concentration factor?

It is the factor that amplifies nominal cyclic stress at a notch during fatigue loading. Unlike Kt, it includes material sensitivity through q, so it better reflects actual fatigue behavior.

2) Why is Kf usually smaller than Kt?

Real materials are not perfectly notch sensitive. Because q is often below 1, the fatigue response does not fully reach the theoretical elastic concentration, so Kf remains lower than Kt.

3) What does notch sensitivity q represent?

q measures how strongly a material reacts to a notch under cyclic loading. A value near 0 means weak sensitivity. A value near 1 means fatigue behavior nearly follows the theoretical notch effect.

4) When should Peterson approximation be used?

Use Peterson approximation when you know the notch radius and an appropriate material constant a. It offers a practical way to estimate q when direct notch sensitivity data is unavailable.

5) Does mean stress matter in fatigue calculations?

Yes. Mean stress changes fatigue margin significantly. Tensile mean stress usually reduces life, which is why this calculator includes a Goodman-based safety estimate alongside Kf and local alternating stress.

6) Can Kf ever be less than 1?

No, not in the standard relation used here. Since Kt is at least 1 and q stays between 0 and 1, Kf remains 1 or greater.

7) What inputs improve result quality most?

Accurate Kt, realistic q or Peterson data, and properly corrected endurance properties matter most. Poor notch geometry estimates can easily shift Kf and local stress predictions.

8) Is this calculator enough for final design approval?

It is a strong screening tool, not a replacement for full fatigue verification. Final approval should consider surface finish, size effects, residual stress, multiaxial loading, and validated material data.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.