Calculate stress concentration factor Kt for holes, fillets, notches, and grooves. Compare nominal vs. peak stress with fatigue notch factor.
Geometric discontinuities — holes, notches, fillets, and grooves — create local stress concentrations that can be several times higher than the nominal applied stress. The stress concentration factor Kt quantifies this amplification: σ_max = Kt × σ_nom.
This calculator covers four common geometric configurations: circular holes in flat plates, shoulder fillets in stepped shafts, U-notches, and circumferential grooves. For each geometry, it computes Kt from established empirical relationships (Peterson's stress concentration factors), then calculates the peak stress at the feature and the fatigue notch factor Kf for cyclic loading assessment.
Understanding stress concentrations is critical for preventing fatigue failure — most fatigue cracks initiate at geometric stress risers. The visual stress distribution and parameter variation table help engineers optimize fillet radii, hole sizes, and notch geometries to minimize Kt while meeting functional requirements. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Fatigue failures account for the majority of mechanical component failures, and nearly all start at stress concentrations. This calculator helps engineers identify critical locations, quantify stress amplification, and optimize geometry to reduce peak stresses.
The parameter variation table is especially valuable during design iteration — it shows exactly how much benefit you gain from increasing a fillet radius or decreasing a hole size, enabling data-driven design decisions without finite element analysis.
Hole in Plate: Kt ≈ 3.0 − 3.13(d/W) + 3.66(d/W)² − 1.53(d/W)³ U-Notch: Kt ≈ 1 + 2√(t/r) Fatigue Notch Factor: Kf = 1 + q(Kt − 1) Where: • Kt = theoretical stress concentration factor • Kf = fatigue notch factor • q = notch sensitivity (0 to 1, material dependent) • d = hole diameter, W = plate width • t = notch depth, r = notch root radius
Result: Kt = 2.73, peak stress = 136.5 MPa
For d/W = 10/100 = 0.1: Kt = 3.0 − 3.13(0.1) + 3.66(0.01) − 1.53(0.001) = 2.73. Peak stress = 2.73 × 50 = 136.5 MPa at the hole edge.
The definitive reference for Kt values is "Peterson's Stress Concentration Factors" by Walter Pilkey and Deborah Pilkey. This handbook contains fitted equations and charts for hundreds of geometric configurations derived from elastic solutions and finite element analyses. The formulas in this calculator are simplified versions suitable for preliminary design.
A stress concentration factor of Kt = 3 doesn't simply reduce fatigue life by a factor of 3. The relationship between Kt and fatigue life is nonlinear and depends on the S-N curve slope, mean stress, and material behavior. A part with Kt = 3 operating at half the nominal endurance limit may still fail in fatigue — always apply proper fatigue analysis methods.
When stress concentrations cannot be eliminated, they can be managed. Relief grooves, generous radii, surface treatments (peening, nitriding), and load redistribution through design changes all help. The goal is to either reduce Kt geometrically or improve the local material resistance to fatigue crack initiation.
For an infinite plate with a circular hole under uniaxial tension, the exact elastic solution gives Kt = 3.0 at the hole edge. The stress must flow around the hole, concentrating at the narrowest cross-section.
Kt is the theoretical (elastic) stress concentration factor from geometry alone. Kf is the fatigue notch factor that accounts for material sensitivity — some materials are less affected by sharp notches.
Increase fillet radii, use gradual transitions, add relief notches, or reduce the size of holes relative to the part width. Even small increases in fillet radius dramatically reduce Kt.
For fatigue, use Kf instead of Kt. Materials with low notch sensitivity (like cast iron) have Kf < Kt, while high-strength steels may have Kf ≈ Kt.
Notch sensitivity q ranges from 0 (not sensitive, Kf = 1) to 1 (fully sensitive, Kf = Kt). It depends on material, notch radius, and loading type. Harder materials tend to have higher q.
No — Kt ≥ 1 by definition. A value of 1 means no stress concentration (uniform stress field). Sharp corners can produce Kt → ∞ in theory, which is why sharp internal corners should always be avoided.