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## 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.

Esempio Risolto

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

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