Fatigue Notch Factor Kf (Notch Sensitivity)
A shoulder, groove, or hole raises stress by the chart factor Kt, but a steel part in fatigue feels only part of it.
Example
You enter
- Theoretical stress-concentration factor Kt (from a chart) 1.65
- Notch (fillet) radius r (in) 0.1181
- Ultimate strength Sut (psi) 100000
- Load type bending
You get
- Fatigue stress-concentration factor 1.55
- Neuber constant 0.0622 sqrt(in)
Checked against published worked examples from: McGraw-Hill (Shigley, Mischke, Budynas).
Details, formula, and sources
ScopeKf = 1 + q (Kt - 1). Neuber's notch sensitivity q comes from the fillet radius and the ultimate strength, so a generous radius in soft steel forgives the notch and a sharp one in hard steel does not. A 100 kpsi shaft with a 0.118 in shoulder fillet and Kt 1.65 has q = 0.85 and Kf = 1.55 in bending. Multiply the alternating stress by Kf before the fatigue checks. Steel, 50 to 250 kpsi (to 220 in torsion); Kt comes from a chart. A design aid; test data govern.
Formula or tablesqrt(a) [sqrt(in)] = 0.246 - 3.08e-3 Sut + 1.51e-5 Sut^2 - 2.67e-8 Sut^3 (bending/axial) or 0.190 - 2.51e-3 Sut + 1.35e-5 Sut^2 - 2.67e-8 Sut^3 (torsion), Sut in kpsi; q = 1/(1 + sqrt(a)/sqrt(r)); Kf = 1 + q (Kt - 1).
Source and editionNeuber's notch-sensitivity equation with the steel Neuber constants (Shigley, Mischke and Budynas, Mechanical Engineering Design, Ch. 6, Eqs. 6-32 to 6-35), by name; it reproduces Shigley Example 6-6 (Sut 690 MPa = 100 kpsi, r = 3 mm, Kt = 1.65: sqrt(a) = 0.0622 sqrt(in), Kf = 1.55).
Free accessStandard published fatigue relations; Kt (from a chart), the notch radius, and the strength are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field nameskt, notch_radius_in, ultimate_strength_psi, load_type, kf, neuber_constant
- Notch sensitivity Neuber q = 1/(1 + sqrt(a)/sqrt(r))Shigley Eq. 6-34
- Neuber constant cubic fits in Sut (kpsi) for bending/axial and torsion, steelShigley Eqs. 6-35a, 6-35b
- Kt entered from a chart (Peterson; Shigley Table A-15)scope of this tile