Advanced Fatigue Life Analysis

Advanced fatigue analysis with Palmgren-Miner cumulative damage, rainflow cycle counting, and variable amplitude duty cycles.

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▸Formula · assumptions · example(ASTM E466 (Axial fatigue) · DIN 50100 (Wöhler S-N testing) · FKM Guideline (Analytical strength))

Formula

\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_{ut}} = \frac{1}{n_f} \quad (\text{Goodman}), \quad \frac{\sigma_a}{S_e} + \left(\frac{\sigma_m}{S_{ut}}\right)^2 = \frac{1}{n_f} \quad (\text{Gerber})

High-cycle fatigue life assessment under fluctuating stress cycles with mean stress corrections (Goodman, Gerber, Soderberg).

Assumptions

  • · Marin endurance limit correction factors applied: surface finish ka, size kb, reliability kc, temperature kd
  • · Fatigue notch factor Kf = 1 + q(Kt - 1) computed using Neuber notch sensitivity q
  • · Infinite life target validated when alternating stress σa remains strictly below endurance limit Se

Worked example

Worked example — Stepped Shaft under Fluctuating Load (σmax = 280 MPa, σmin = 40 MPa, Sut = 600 MPa, Se = 220 MPa)

Alternating stress σa = 120 MPa, mean stress σm = 160 MPa. Modified Goodman safety factor nf = 1.23 against infinite fatigue life limit.