Fracture Toughness and Stress Intensity Calculator
Calculate stress intensity factor K, critical crack size, and fracture toughness.
Apply linear elastic fracture mechanics (LEFM) for metals, ceramics, and polymers.
Linear Elastic Fracture Mechanics (LEFM) LEFM describes the stress field near a crack tip in a linear elastic material. Developed by George Irwin (USA, 1957), building on Griffith’s energy theory (1921). The stress intensity factor K quantifies the crack tip stress intensity: K = Y × σ × √(π × a) Where: Y = geometry factor (dimensionless, ~1.0 for simple cases) σ = applied stress (MPa) a = crack half-length for internal crack, or crack length for surface crack (m) K is in MPa·√m (or ksi·√in)
Fracture Criterion Fracture occurs when K ≥ K_IC (plane strain fracture toughness). K_IC is a material property measured by standard tests (ASTM E399). Mode I (opening): normal stress perpendicular to crack — most common and critical.
Typical K_IC Values (MPa·√m) Metals: Steel (high strength, 4340): 50–100 | Aluminum 7075-T6: 24–31 Titanium Ti-6Al-4V: 44–66 | Copper: 30–40 | Cast iron: 6–20 Ceramics: Alumina (Al₂O₃): 3–5 | Silicon nitride: 5–9 | Glass: 0.6–1.0 Polymers: Polycarbonate: 1.0–2.6 | Epoxy: 0.3–0.6 | PMMA: 0.7–1.6 Composites: CFRP: 20–50 | GFRP: 7–12
Critical Crack Size a_c = (K_IC / (Y × σ))² / π Any crack larger than a_c will propagate catastrophically. Fracture toughness determines the maximum allowable defect size for a given stress.
Geometry Factors Y Center crack in infinite plate: Y = 1.0 Single edge crack in semi-infinite plate: Y = 1.12 Through crack at edge of finite plate: Y = 1.0–1.5 (depends on a/W ratio)