Tools › Structures › Stress Concentrations › Circular Inclusion › Example
Goodier (1933): rigid circular inclusion under uniaxial tension, plane stress ν = 0.3, radial stress 1.51 S at the pole
| Tool | Circular Inclusion |
| Source | Goodier, J. N. (1933). "Concentration of Stress Around Spherical and Cylindrical Inclusions and Flaws." Transactions of the ASME, Journal of Applied Mechanics, Vol. 55, APM-55-7, pp. 39–44. |
| Level | Graduate |
Problem
A 0.1 in plate of 10 Msi modulus and Poisson's ratio 0.3 (plane stress) carries 10,000 lb/in in y and contains a perfectly bonded rigid circular inclusion of 0.25 in diameter. Find the interface radial stress at the pole on the load axis, the debonding factor K_rad and the maximum interface shear stress.
Inputs to Enter
- N_xx = 0, N_yy = 10000 lb/in, N_xy = 0, t = 0.1 in (S = 100 ksi)
- D = 0.25 in; plane stress; E_1 = 10 Msi, ν_1 = 0.3; inclusion type: rigid
- r = 0.125 in (interface), θ = 0 (load-axis pole)
Answers
- σ_rr at the pole = 1.510 S = 151.0 ksi; K_rad = 1.510 (Goodier's classical value for ν = 0.3)
- Maximum interface shear stress 0.741 S = 74.1 ksi at θ = 45°
- Matrix displacement on the interface is zero (rigid), checked to 1e-13 at the build
Notes
Change the loads to N_yy alone, ν_1 to 0.3 and the inclusion type to rigid. K_rad is referred to S_1.