Fracture Mechanics
Will this existing crack grow — and how long until it matters?
1. What is it?
Cracks concentrate stress infinitely in theory; ordinary stress contours are meaningless at a crack tip. Fracture mechanics instead tracks:
- Stress intensity factor K — how strongly the crack tip is driven (units MPa·√m). Compare to the material's fracture toughness K_IC: K ≥ K_IC means sudden unstable fracture.
- J-integral — an energy measure of crack-tip driving force, valid beyond linear elasticity.
- Paris law growth: under repeated loading, da/dN = C·(ΔK)^m. Given a crack, how many cycles until critical?
"This pressure vessel has a 2 mm surface crack. Will it survive 10,000 pressure cycles?"
2. When do I use it?
| Use when | Don't use for |
|---|---|
| Existing cracks or flaws from manufacturing | No crack present → use [Static Structural](static-structural.md) or [Fatigue](vibration-fatigue.md) |
| Damage tolerance assessment (aerospace, pressure vessels) | Large-scale yielding → elastic-plastic fracture (research tier) |
| Remaining life prediction for cracked structures | 3D mixed-mode propagation → research kernels only |
| Material selection based on fracture toughness |
Use cases
| Problem Type | Industry | Example |
|---|---|---|
| Critical crack size | Aerospace | Aircraft fuselage crack tolerance |
| Fatigue life prediction | Automotive | Suspension component crack growth |
| Weld integrity | Offshore/Pipeline | Girth weld flaw assessment |
| Delamination | Composites | Panel edge debonding |
| Pressure vessel flaw assessment | Energy/Chemical | Boiler tube crack evaluation |
| Bone fracture orthopaedics | Biomedical | Femoral implant crack risk |
3. The flow
Linear Elastic Fracture (LEFM)
- Design — geometry with crack defined
- Boundary — material (E, ν, K_IC) + loads
- Mesh — generate (refine at crack tip)
- Simulate → Fracture (XFEM) → set crack parameters
- Results — K_I, K_II, K_III, J-integral, safety factor
Fatigue Crack Growth
- Design — geometry with initial crack
- Boundary — material (C, m Paris constants) + cyclic load
- Mesh — generate
- Simulate → Fatigue Crack Growth → set cycle count
- Results — crack length vs cycles, remaining life
4. Reading your results
Stress Intensity Factor
| Value | Meaning |
|---|---|
| K < K_IC | Crack is stable |
| K = K_IC | Onset of rapid fracture |
| K > K_IC | Unstable fracture |
Safety factor: K_IC / K_applied > required (typically 2-4).
J-Integral
Energy release rate. Compare to critical J_IC for elastic-plastic fracture.
Crack Growth
| Result | Meaning |
|---|---|
| da/dN | Crack growth rate per cycle |
| Cycles to failure | Number of cycles until critical crack length |
| Critical crack size | Size at which K = K_IC |
5. Boundaries of truth
What's validated
| Case | Reference | Error |
|---|---|---|
| Westergaard center crack | Analytical | < 1% |
| Compact tension (CT) | ASTM E399 | < 3% |
| DCB cohesive | Published | < 5% |
What's NOT covered
- Elastic-plastic fracture — LEFM only (small-scale yielding)
- 3D mixed-mode propagation — research kernels only
- Dynamic crack propagation — static/quasi-static only
- Environmental effects — no stress corrosion or creep crack growth
Common mistakes
| Mistake | Fix |
|---|---|
| Coarse mesh at crack tip | Use focused mesh with ≥ 6 elements near tip |
| Missing fracture toughness | Add K_IC to material |
| Large-scale yielding | LEFM invalid — use elastic-plastic (research) |
| Wrong Paris constants | Use material-specific C and m |
See also
- [Static Structural](static-structural.md) — for uncracked structures
- [Fatigue](vibration-fatigue.md) — for initiation without crack
- [Dynamics](dynamics.md) — for dynamic fracture
Keep exploring
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