Fracture Toughness Calculator
Calculate the stress intensity factor and compare to fracture toughness to assess crack stability.
Stress Intensity Factor (KI)
21.06 MPa√m
Stress Intensity Factor (KI) vs Applied Stress (sigma)
सूत्र
## 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.
हल किया गया उदाहरण
A plate with a 5 mm edge crack under 150 MPa stress (Y=1.12, KIc=50 MPa√m).
- 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
अक्सर पूछे जाने वाले प्रश्न
What is the geometry factor Y?
Y accounts for the specimen shape and crack location. For a center crack in an infinite plate, Y = 1.0. For an edge crack, Y = 1.12. For specific geometries, Y can be found in fracture mechanics handbooks or by finite element analysis.
What are typical fracture toughness values?
Mild steel: 50-100 MPa√m, aluminum 2024-T3: 26 MPa√m, titanium: 55-115 MPa√m, glass: 0.7 MPa√m, concrete: 0.2-1.4 MPa√m. Higher values mean more resistance to crack growth.
How does thickness affect fracture toughness?
Thicker specimens tend toward plane strain conditions, giving the minimum (conservative) KIc value. Thin specimens experience plane stress and show higher apparent toughness. Standard tests specify minimum thickness requirements.
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