Fracture Toughness⚠ unverified
Physics / Materials · Compute the mode I stress intensity at a crack
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| stress | stress | Pa | 1.0 | Far-field applied stress |
| crack_length | cracklength | m | 1.0 | Characteristic crack length |
| geometry_factor | geometryfactor | — | 1.0 | Dimensionless geometry factor Y. Default is 1.0 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | KI | Pa*m^0.5 | Mode I stress intensity factor, in pascals times square root of metres (Pa*m^0.5) |
The science & history
Understanding the Parameters
- $\sigma$, $a$ — larger stress or longer crack → higher $K_I$ ($a$ under the square root).
- $Y$ — from handbooks for edge cracks, finite width, etc.
- $K_I$ — compare to material $K_{Ic}$ for brittle fracture assessment.
Derivation (Approaching a Proof)
Linear elastic fracture mechanics: near a crack tip, singular stresses scale as $K/\sqrt{2\pi r}$. For a central crack $2a$ in an infinite plate, $K_I = \sigma\sqrt{\pi a}$. Geometry factor $Y$ generalises that solution.
History
Griffith, Irwin, and LEFM established $K$ and $K_{Ic}$ as the language of brittle fracture control.
Related Concepts: Stress Intensity Factor, Factor of Safety, Von Mises Stress
Notes: Registry calculator fracture-toughness (unverified). Computes $K_I$, not a material
database $K_{Ic}$. Near-duplicate of stress-intensity-factor.