Fatigue Crack Growth

Paris law: da/dN = C(ΔK)^m — S-N curve and fracture mechanics

N: 0 cycles | a: 1.0 mm | ΔK: 0 MPa√m | da/dN: 0 m/cycle

Δσ (MPa) 150

Paris exponent m 3.0

Paris coeff C (×10⁻¹²) 10

K_IC (MPa√m) 50

Paris law: da/dN = C(ΔK)^m, where ΔK = Δσ √(πa) · F(a/W) is the stress intensity factor range. Three regimes: threshold (ΔK < ΔK_th, no growth), Paris (stable power-law), fracture (K_max → K_IC). S-N (Wöhler) curve: log N_f vs log Δσ — endurance limit near 10⁷ cycles. The fracture mechanics approach links crack size, stress, and material toughness K_IC.