EngiRef / Materials Engineering Formula
Fracture Toughness (Irwin, LEFM)
Fracture Toughness (Irwin, LEFM): Mode I stress intensity factor (Irwin's linear-elastic fracture mechanics relation). A Failure Theories formula in materials…
Failure Theories
Specification
- Name
- Fracture Toughness (Irwin, LEFM)
- Discipline
- materials
- Category
- Failure Theories
- LaTeX
- K_I = Y \sigma \sqrt{\pi a}
- Description
- Mode I stress intensity factor (Irwin's linear-elastic fracture mechanics relation)
- Conditions
- Y is geometry factor; a is crack length. Irwin's LEFM stress-intensity relation - Griffith's own criterion is the energy balance G = 2γs; the two agree for linear-elastic, plane-strain conditions with a small plastic zone.
- Can solve for
- Kᵢ, σ, a
- Tags
- fracture, toughness, crack, griffith, stress, intensity
Variables
| Symbol | Name | Unit | Si Unit | Imperial Unit |
|---|---|---|---|---|
| Kᵢ | Stress Intensity Factor | MPa·√m | MPa·√m | - |
| Y | Geometry Factor | - | - | - |
| σ | Applied Stress | Pa | Pa | psi |
| a | Crack Length | m | m | in |
Common questions
- What is the Fracture Toughness (Irwin, LEFM) formula?
- Mode I stress intensity factor (Irwin's linear-elastic fracture mechanics relation). It sits under Failure Theories, Materials engineering in the EngiRef reference.
- What do the symbols in the Fracture Toughness (Irwin, LEFM) formula mean?
- In Fracture Toughness (Irwin, LEFM), Kᵢ is stress intensity factor in MPa·√m; Y is geometry factor; σ is applied stress in Pa; a is crack length in m.
- When does the Fracture Toughness (Irwin, LEFM) formula apply?
- Fracture Toughness (Irwin, LEFM) holds under this condition: Y is geometry factor; a is crack length. Irwin's LEFM stress-intensity relation - Griffith's own criterion is the energy balance G = 2γs; the two agree for linear-elastic, plane-strain conditions with a small plastic zone.