BIZOMAT MAKEOS · Strength
Fatigue Notch Factor from Stress Concentration
How much does this notch, fillet or groove reduce fatigue strength?
Notch sensitivity (Peterson) and the fatigue stress concentration factor Kf from the theoretical factor Kt, the notch radius and the material’s tensile strength or characteristic length.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Theoretical stress concentration factor Kt | Elastic stress concentration factor for the geometry from charts or FEA. | |
| Notch root radius | mm | Radius at the root of the notch, fillet or groove. |
| Material constant | choice | Estimate the material constant for steels, or enter it. |
| Tensile strength (steel estimate) | MPa | Ultimate tensile strength (used for the steel estimate). |
| Peterson constant a | mm | Peterson’s characteristic length for the material from fatigue data (entered mode). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Theoretical stress concentration factor Kt
- What it is
- The theoretical (elastic) stress concentration factor for the notch, fillet or groove: the peak stress divided by the nominal stress, from stress concentration charts or finite element analysis.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The fatigue factor rises in line with Kt, scaled by the notch sensitivity.
- Get it right
- Use the chart for the right load type (bending, tension or torsion); the same shape has different Kt for each.
What this means: Notch root radius
- What it is
- The radius at the bottom of the notch, fillet or groove where the stress peaks, from the drawing or by measuring the part.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger root radius raises the notch sensitivity, bringing the fatigue factor closer to Kt.
- Get it right
- This is the root radius, not the depth or width of the groove.
What this means: Material constant
- What it is
- Whether the tool estimates Peterson’s material constant from tensile strength using its steel relation, or uses a constant you supply from fatigue data.
- Units and format
- Choose one of 2 options from the list: Estimate for steel from tensile strength; Enter Peterson constant a.
- Example
- The form opens with “Estimate for steel from tensile strength” selected as a worked example. Choose the option that matches your case.
- Get it right
- The tensile-strength estimate is for steels only; for other metals, choose to enter the constant.
What this means: Tensile strength (steel estimate)
- What it is
- The ultimate tensile strength of the steel, from the material certificate or specification, used to estimate Peterson’s constant. Ignored when you enter the constant yourself.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stronger steel gives a smaller constant, so it is more notch sensitive.
- Get it right
- Use ultimate tensile strength, not yield strength.
What this means: Peterson constant a
- What it is
- Peterson’s characteristic length for the material, which sets how sensitive it is to notches. It comes from published fatigue data for the material and is only used when you choose to enter it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger constant lowers the notch sensitivity and the fatigue factor.
- Get it right
- It is a length in millimetres; some sources give it in inches, so convert first.
Method and formulas
- Steel estimate: a ≈ 0.0254 × (2070 ÷ Su)^1.8 mm (Su in MPa).
- Peterson: q = 1 ÷ (1 + a/r).
- Kf = 1 + q (Kt − 1); multiply nominal alternating stress by Kf.
- Example: Kt 2.2 with a 1 mm radius in 700 MPa steel gives q = 0.84831 and Kf = 2.018.
Limitations
- Empirical notch sensitivity; for very small radii or high-strength steels use measured data.
- Kt must match the load type (bending, axial or torsion).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Turn a chart Kt into the effective fatigue factor
- Compare fillet radii on a shaft shoulder
- Feed the Goodman fatigue tool
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Notch sensitivity q
- Fatigue factor Kf
- Reduction compared with Kt
Interpreting the result
- A larger radius lowers Kt and gives the material less notch sensitivity benefit; both effects are captured here.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 200–211. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Notches: where cracks start
In Metal Fatigue by the Numbers
What it covers: How fillets, holes, keyways and grooves raise local stress, why the fatigue notch factor is smaller than the theoretical one, and how a fillet radius decides a shaft's life.
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Open the Fatigue Notch Factor from Stress Concentration calculator