KEVOS® MAKEOS · Strength
Fatigue Design Check (Corrected Endurance, Notch, Mean Stress, Life)
Will this notched part survive its fluctuating load indefinitely, and if not, how many cycles will it last?
Fatigue check of a notched part under a fluctuating stress: the endurance limit corrected by your surface, size, load, temperature and reliability factors, the fatigue notch factor from the stress concentration factor and notch radius (as the fatigue notch factor tool), alternating and mean stresses from the nominal maximum and minimum, safety factors by Goodman, Soderberg and Gerber with a first-cycle yield check (as the Goodman fatigue tool), and the finite life from the S-N line for the equivalent fully reversed stress (as the S-N fatigue life tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Material | ||
| Ultimate tensile strength | MPa | Ultimate tensile strength. |
| Yield strength | MPa | Yield strength. |
| Test-specimen endurance limit (0 = estimate as 0.5 Su, at most 700 MPa) | MPa | Rotating-beam endurance limit of polished specimens; 0 estimates it as half the tensile strength, capped at 700 MPa (steels). |
| Endurance correction factors | ||
| Surface factor | Surface factor for the finish (machined, ground, as-forged; your value). | |
| Size factor | Size factor for the section size. | |
| Load factor | Load factor (1 bending, about 0.85 axial, 0.59 torsion). | |
| Temperature factor | Temperature factor. | |
| Reliability factor | Reliability factor (1 for 50%, about 0.868 for 99%). | |
| Notch and load | ||
| Stress concentration factor | Theoretical stress concentration factor for the notch geometry and load type. | |
| Notch radius | mm | Notch root radius (for the notch sensitivity). |
| Nominal maximum stress | MPa | Largest nominal stress in the cycle (without the notch). |
| Nominal minimum stress | MPa | Smallest nominal stress in the cycle. |
| Safety factor required | Safety factor you require. | |
| Cycles required (if below infinite life) | cycles | Cycles the part must last if it cannot reach infinite life. |
Method and formulas
- S_e = k_a k_b k_c k_d k_e S_e′.
- Neuber constant a = 0.0254 (2070 ÷ S_u)^1.8 mm; q = 1 ÷ (1 + a ÷ r); K_f = 1 + q(K_t − 1) (as the fatigue notch factor tool).
- σ_a = K_f (σ_max − σ_min) ÷ 2; σ_m = K_f (σ_max + σ_min) ÷ 2.
- Goodman n = 1 ÷ (σ_a ÷ S_e + σ_m ÷ S_u); Soderberg uses S_y; Gerber the parabola; yield n = S_y ÷ (σ_a + |σ_m|) (as the Goodman fatigue tool).
- Finite life: σ_ar = σ_a ÷ (1 − σ_m ÷ S_u); N from the S-N line through 0.9 S_u at 10³ and S_e at 10⁶ (as the S-N fatigue life tool).
- Example: S_e = 177.07 MPa and K_f = 1.9709 give σ_a 78.835 MPa, σ_m 118.25 MPa and a Goodman factor of 1.5569.
Limitations
- Correction factors and the S-N line are estimates; tested data for the material and finish govern.
- Uniaxial stress; combined stresses need an equivalent (von Mises) alternating and mean stress.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a shaft shoulder, hole or groove under cyclic load
- Find the life of a part that does not reach infinite life
- See how surface finish and notch radius affect fatigue
Who it is for
- Design engineers
- Reliability engineers
- Mechanical engineers
What you get
- Corrected endurance limit and fatigue notch factor
- Alternating and mean stresses
- Safety factors and finite life
Interpreting the result
- A larger notch radius and a better surface finish are usually the cheapest fatigue improvements.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 200–211, 280, 358. Topic reference; no source tables or recommended settings are reproduced.
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Open the Fatigue Design Check (Corrected Endurance, Notch, Mean Stress, Life) calculator
