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.
stress_amp = 300fatigue_coeff = 900fatigue_exp = -0.1
- 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
Ready to run the numbers?
Open Fatigue Life Calculator