Estimate fatigue cycles using stress and strain approaches. Include mean stress effects for better decisions. Export results quickly for documentation and routine checks today.
| Case | Model | σa (MPa) | σm (MPa) | σ′f (MPa) | b | Correction | Estimated Nf (cycles) |
|---|---|---|---|---|---|---|---|
| A | Basquin | 220 | 40 | 1000 | -0.09 | Goodman | ≈ 1.5×106 |
| B | Basquin | 180 | 0 | 950 | -0.10 | None | ≈ 4.3×106 |
| C | Coffin-Manson | — | 20 | 1000 | -0.09 | Morrow | ≈ 2.0×105 |
Repeated loading can initiate small cracks even when peak stress stays below yield. Engineers use fatigue-life models to screen designs, prioritize tests, and plan inspections. Treat the result as guidance that complements measured material data. Use conservative assumptions when inputs are uncertain or service is safety-critical.
High-cycle fatigue is mostly elastic and often exceeds about 105 cycles, where S–N fits work well. Low-cycle fatigue includes plasticity and often falls below about 105 cycles, favoring strain-life models. Components can transition between regimes as loading shifts.
Basquin relates alternating stress to life: σa = σ′f (2N)b. The exponent b is usually negative; many steels fall roughly between −0.05 and −0.12 in high-cycle fits. Use σ′f and b from your material’s test data whenever possible.
Mean tensile stress reduces life by accelerating crack growth, so designers transform the actual σa, σm into an equivalent fully reversed amplitude. Goodman uses a linear relation to Sut, Gerber uses a parabolic curve, and Soderberg references Sy for added conservatism. If σm approaches the chosen strength limit, the correction becomes invalid.
The Coffin–Manson–Basquin equation adds an elastic term and a plastic term: εa = (σ′f/E)(2N)b + ε′f(2N)c. The exponent c is also typically negative and controls the low-cycle slope. Because total strain is used, this approach can capture plasticity effects that the S–N fit cannot.
Elastic modulus converts stress into elastic strain in the strain-life equation. Typical room-temperature values are about 210000 MPa for steels and about 70000 MPa for many aluminum alloys. Use the modulus matching your temperature and alloy, because even modest changes can shift the elastic term and move the solved life.
Cycles convert to time using time = N/f. At 10 Hz you accumulate 36000 cycles per hour. If loading includes pauses, overloads, or variable amplitudes, calendar time differs from this simple estimate, and spectrum methods are required.
Fatigue data shows scatter from finish, size, residual stress, and environment. Treat computed life as an estimate, not a guarantee. Verify constants (σ′f, b, ε′f, c) from credible tests, and validate critical parts with component testing.
Use stress-life for predominantly elastic, high-cycle situations. Use strain-life when plastic strain is expected, for low-cycle loading, or when you have ε–N constants. If uncertain, run both and compare conservatively.
σa is the alternating stress amplitude, equal to half the stress range. σm is the mean stress, the average of maximum and minimum stress in a cycle. Fully reversed loading has σm ≈ 0.
Goodman is often conservative for ductile metals under tensile mean stress compared with Gerber. If you have supportive test data or design standards allowing it, Gerber can be a better fit, but verify for your material and surface condition.
Mean-stress corrections have denominators that approach zero as σm nears Sut or Sy. That indicates the chosen correction is outside its valid range. Reduce σm, change correction, or reassess the loading definition.
Variable amplitude loading requires cycle counting and damage accumulation, such as Miner’s rule, using a full spectrum. This calculator is best for a single representative cycle. For spectra, compute damage per block and sum.
The example values are illustrative to show workflow and typical parameter magnitudes. They are not a substitute for tested constants from your specific alloy, heat treatment, and surface finish. Always replace them with verified data.
The model predicts cycles to failure based on stress or strain, not frequency. Frequency only converts cycles into elapsed time. However, at very high frequencies or elevated temperatures, material behavior can change, so validate assumptions.
Estimate fatigue life fast, compare models, and export results.
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.