Fracture Toughness Calculator Formula
Understand the math behind the fracture toughness calculator. Each variable explained with a worked example.
Formulas Used
Stress Intensity Factor (KI)
ki = geometry_factor * stress * sqrt(pi * a_m)Fracture Safety Factor
safety_factor = kic / (geometry_factor * stress * sqrt(pi * a_m))Critical Crack Length
critical_crack = pow(kic / (geometry_factor * stress), 2) / pi * 1000Variables
| Variable | Description | Default |
|---|---|---|
stress | Applied Stress (sigma)(MPa) | 150 |
crack_length | Crack Half-Length (a)(mm) | 5 |
geometry_factor | Geometry Factor (Y) | 1.12 |
kic | Fracture Toughness (KIc)(MPa√m) | 50 |
a_m | Derived value= crack_length / 1000 | calculated |
How It Works
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.
Worked Example
A plate with a 5 mm edge crack under 150 MPa stress (Y=1.12, KIc=50 MPa√m).
stress = 150crack_length = 5geometry_factor = 1.12kic = 50
- 01a = 5 mm = 0.005 m
- 02KI = 1.12 × 150 × sqrt(pi × 0.005)
- 03KI = 168 × sqrt(0.01571) = 168 × 0.1253 = 21.06 MPa√m
- 04Safety factor = 50 / 21.06 = 2.37 (crack is stable)
- 05Critical crack = (50 / (1.12 × 150))² / pi × 1000 = 28.2 mm
Ready to run the numbers?
Open Fracture Toughness Calculator