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

VariableDescriptionDefault
stress_ampStress Amplitude (Sa)(MPa)300
fatigue_coeffFatigue Strength Coefficient (Sf')(MPa)900
fatigue_expFatigue 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
  1. 01Sa/Sf' = 300/900 = 0.3333
  2. 02N = (0.3333)^(1/(-0.1)) = (0.3333)^(-10)
  3. 03N = (1/0.3333)^10 = 3.0^10 = 59,049 cycles

Ready to run the numbers?

Open Fatigue Life Calculator