Fatigue Life Calculator Formula

Understand the math behind the fatigue life calculator. Each variable explained with a worked example.

Use the Fatigue Life Calculator

Formulas Used

Cycles to Failure (Nf)

cycles = pow(stress_amp / fatigue_coeff, 1 / basquin_exp)

Variables

VariableDescriptionDefault
stress_ampStress Amplitude (Sa)(MPa)200
fatigue_coeffFatigue Strength Coefficient (Sf')(MPa)900
basquin_expBasquin Exponent (b)-0.1

How It Works

Fatigue Life Estimation (Basquin Relation)

Repetitive loading below the static strength can cause failure through fatigue crack growth.

Formula

Sa = Sf' (2Nf)^b or equivalently Nf = 0.5 (Sa / Sf')^(1/b)

This simplified form (Basquin equation) relates stress amplitude Sa to cycles to failure Nf. The fatigue strength coefficient Sf' and exponent b are material properties obtained from testing. Typical b values range from -0.05 to -0.15.

Worked Example

A steel component with Sf'=900 MPa, b=-0.1, subjected to 200 MPa stress amplitude.

stress_amp = 200fatigue_coeff = 900basquin_exp = -0.1
  1. 01Sa/Sf' = 200/900 = 0.2222
  2. 021/b = 1/(-0.1) = -10
  3. 03Nf = (0.2222)^(-10) = approximately 6,046,618 cycles
  4. 04This is above 10^6, suggesting effectively infinite life for many applications.

Ready to run the numbers?

Open Fatigue Life Calculator