Fatigue Life Calculator Formula
Understand the math behind the fatigue life calculator. Each variable explained with a worked example.
Formulas Used
Fatigue Life (N)
cycles = pow(stress_amp / fatigue_coeff, 1 / fatigue_exp)log10(N)
log_cycles = log10(pow(stress_amp / fatigue_coeff, 1 / fatigue_exp))Variables
| Variable | Description | Default |
|---|---|---|
stress_amp | Stress Amplitude (Sa)(MPa) | 300 |
fatigue_coeff | Fatigue Strength Coefficient (Sf')(MPa) | 900 |
fatigue_exp | Fatigue Strength Exponent (b) | -0.1 |
How It Works
Basquin's Law for Fatigue Life
Fatigue failure occurs when a material is subjected to repeated cyclic loading below its static strength. Basquin's equation relates stress amplitude to the number of cycles to failure.
Formula
Sa = Sf' × (2N)^b or equivalently N = (Sa / Sf')^(1/b) / 2
Sf' is the fatigue strength coefficient (approximately the true fracture strength), b is the fatigue exponent (typically -0.05 to -0.15 for metals), and N is the number of reversals to failure (2N = cycles).
Worked Example
A steel component with Sf' = 900 MPa, b = -0.1, subjected to 300 MPa stress amplitude.
- 01Sa/Sf' = 300/900 = 0.3333
- 02N = (0.3333)^(1/(-0.1)) = (0.3333)^(-10)
- 03N = (1/0.3333)^10 = 3.0^10 = 59,049 cycles
Frequently Asked Questions
What is the endurance limit?
Some materials (notably steels) exhibit an endurance limit: a stress below which fatigue failure theoretically never occurs. For steels, it is roughly 40-50% of UTS. Aluminum and most non-ferrous metals do not have a true endurance limit.
How does mean stress affect fatigue?
A tensile mean stress reduces fatigue life compared to fully reversed loading. Corrections like the Goodman, Gerber, or Soderberg diagrams adjust the allowable stress amplitude based on mean stress.
What factors reduce fatigue life?
Surface roughness, stress concentrations (notches, holes), corrosive environment, elevated temperature, and residual tensile stresses all reduce fatigue life. Shot peening and polishing can improve it.
Ready to run the numbers?
Open Fatigue Life Calculator