Tools › Structures › Damage Tolerance › Center Crack › Example
Centre crack under a general in-plane state: K_I, K_II from the crack-frame far field and G = (K_I² + K_II²)/E
| Tool | Center Crack |
| Source | Irwin, G. R. (1957). "Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate." Journal of Applied Mechanics, Vol. 24, pp. 361–364; Sih, G. C. (1966). "On the Westergaard Method of Crack Analysis." International Journal of Fracture Mechanics, Vol. 2, pp. 628–631. |
| Level | Graduate |
Problem
A 0.1 in plate carries N_xx = 5,000, N_yy = 15,000 and N_xy = 3,000 lb/in and contains a through crack of half-length 0.25 in along x. Find K_I, K_II, the effective K, the T-stress and the energy release rate in plane stress (E = 10 Msi).
Inputs to Enter
- N_xx = 5000, N_yy = 15000, N_xy = 3000 lb/in, t = 0.1 in
- a = 0.25 in, β = 0; plane stress, E = 10 Msi, ν = 0.33
- r = 0.3 in, θ = 90°
Answers
- σ_yy∞ = 150 ksi, τ_xy∞ = 30 ksi, σ_xx∞ = 50 ksi
- K_I = 150√(π·0.25) = 132.9 ksi√in, K_II = 26.59 ksi√in, K_eff = 135.6 ksi√in
- T-stress = σ_xx∞ − σ_yy∞ = −100 ksi (Sih's correction to Westergaard)
- G = (K_I² + K_II²)/E = 1,837.8 lb/in; probe at r = 0.3 in: σ_yy = 271.4 ksi, σ_xx = 171.4 ksi
Notes
The tool's default inputs are this case (values from a harness run of the default form).