Tools › Structures › Damage Tolerance › Center Crack › Example
Westergaard / Irwin: centre crack under uniaxial tension, K_I = σ√(πa) = 88.62 ksi√in
| Tool | Center Crack |
| Source | Westergaard, H. M. (1939). "Bearing Pressures and Cracks." Journal of Applied Mechanics, Vol. 6, pp. A49–A53; 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. |
| Level | Graduate |
Problem
A 0.1 in plate carries 10,000 lb/in in y and contains a through crack of half-length 0.25 in normal to the load. Find the Mode I and Mode II stress intensity factors.
Inputs to Enter
- N_xx = 0, N_yy = 10000 lb/in, N_xy = 0, t = 0.1 in (σ = 100 ksi)
- a = 0.25 in, β = 0; plane stress, E = 10 Msi, ν = 0.33
- r = 0.3 in, θ = 90° (probe just beyond the tip)
Answers
- K_I = σ√(πa) = 88.62 ksi√in; K_II = 0
- SI (689.5 MPa, 6.35 mm): K_I = 17.72 MPa√m
- Build checks: crack faces traction-free; σ_yy ahead of the tip → K_I/√(2πr) (ratio 1.0001 at r = 1e-4 a); σ_xx = −σ on the faces (Sih's T-stress)
Notes
Change the default loads to N_yy = 10000 alone. K is converted to ksi√in / MPa√m in PHP because the unit dictionary has no Pa·m^0.5.