Fatigue Life Estimator (S-N Curve)

What Is Metal Fatigue? Metal fatigue is the progressive cracking of a material under repeated cyclic loading — even when peak stresses are well below the material’s tensile strength. Fatigue failure is responsible for 50–90% of all mechanical failures in structural components. Famous fatigue failures include the de Havilland Comet crashes of 1954 (caused by stress concentrations at square windows) and the collapse of the Silver Bridge in West Virginia in 1967.

The S-N Curve (Wöhler Curve) The S-N curve plots cyclic stress amplitude (S) vs. number of cycles to failure (N). It was developed by August Wöhler, a German engineer who conducted systematic fatigue tests on railway axles between 1858 and 1870 in Germany. Higher stress amplitude → fewer cycles to failure. Lower stress → more cycles.

Basquin’s Power Law The mathematical description of the S-N curve: N = (σ_f’ / σ_a)^(1/b) Or equivalently: σ_a = σ_f’ × (2N)^b Where: σ_a = stress amplitude (MPa), σ_f’ = fatigue strength coefficient (≈ UTS for steels), b = fatigue strength exponent (typically −0.05 to −0.12), N = cycles to failure.

Endurance Limit (Se) Many steels exhibit an endurance limit — a stress level below which fatigue failure will never occur, regardless of cycles. For steels: Se ≈ 0.5 × UTS (for UTS < 1400 MPa). Above this stress, the part will eventually fail. Aluminum alloys do NOT have a true endurance limit — they will eventually fail at any stress amplitude, just after more cycles. The endurance limit applies to fully reversed bending (R = −1). Surface finish, size, reliability, and mean stress all reduce the endurance limit.

Stress Concentration Factor (Kt) Notches, holes, fillets, and threads concentrate stress — effectively multiplying the local stress. Effective stress amplitude = Kt × nominal stress amplitude. A stress concentration factor of 2 halves the fatigue life dramatically (often by orders of magnitude). Smooth surfaces, compressive residual stresses (shot peening), and generous radii all improve fatigue life.

Mean Stress Effects (Goodman Diagram) The S-N curve assumes fully reversed stress (mean stress = 0). Mean tensile stress reduces fatigue life. Modified Goodman criterion: σ_a / Se + σ_m / UTS = 1. Gerber parabola: σ_a / Se + (σ_m / UTS)² = 1 (less conservative, often more accurate). Compressive mean stress actually improves fatigue life — used in shot peening and pre-stressing.

Common Material Fatigue Parameters Structural steel (A36): Se ≈ 200 MPa, UTS ≈ 400 MPa. High-strength steel (4340, HT): Se ≈ 500–700 MPa, UTS ≈ 1000–1400 MPa. Aluminum 6061-T6: no endurance limit. At 10⁷ cycles: ~95 MPa fatigue strength. Titanium Ti-6Al-4V: Se ≈ 500–620 MPa, UTS ≈ 900 MPa. Gray cast iron: Se ≈ 100–170 MPa.

Safety Factor in Fatigue Design A safety factor of 1.5–2.0 on stress amplitude is typical for well-characterized loading. Variable amplitude loading (random vibration) requires damage accumulation analysis (Miner’s rule). Miner’s rule: Σ(ni/Ni) = 1 at failure. Conservative and widely used despite known limitations.