Fracture Toughness Rechner — Formel
## Fracture Toughness and Stress Intensity
Fracture mechanics predicts whether a crack will grow catastrophically. The stress intensity factor KI characterizes the stress field near a crack tip, and fracture occurs when KI reaches the material's fracture toughness KIc.
### Formula
**KI = Y × sigma × sqrt(pi × a)**
where Y is a dimensionless geometry factor (1.12 for an edge crack), sigma is the remote applied stress, and a is the crack length. If KI >= KIc, the crack propagates unstably.
Fracture mechanics predicts whether a crack will grow catastrophically. The stress intensity factor KI characterizes the stress field near a crack tip, and fracture occurs when KI reaches the material's fracture toughness KIc.
### Formula
**KI = Y × sigma × sqrt(pi × a)**
where Y is a dimensionless geometry factor (1.12 for an edge crack), sigma is the remote applied stress, and a is the crack length. If KI >= KIc, the crack propagates unstably.
Lösungsbeispiel
A plate with a 5 mm edge crack under 150 MPa stress (Y=1.12, KIc=50 MPa√m).
- a = 5 mm = 0.005 m
- KI = 1.12 × 150 × sqrt(pi × 0.005)
- KI = 168 × sqrt(0.01571) = 168 × 0.1253 = 21.06 MPa√m
- Safety factor = 50 / 21.06 = 2.37 (crack is stable)
- Critical crack = (50 / (1.12 × 150))² / pi × 1000 = 28.2 mm