Fracture Mechanics — Crack Tip Stress Intensity Factor

Linear elastic fracture mechanics (LEFM): K_I, K_II, plastic zone, Griffith criterion

Stress field σ(r,θ) near crack tip

Crack geometry & loading mode

K_I vs crack length

Plastic zone shape

G = K²/E (energy release rate)

Applied stress σ∞ (MPa) 100 Half-crack length a (mm) 10.0 Fracture toughness K_Ic (MPa√m) 30 Mode mixity ψ (0°=Mode I) 0° Young's modulus E (GPa) 200