The stress field near the tip of a crack in a plate subjected to membrane and bending loads and undergoing large deflections, is investigated by performing an asymptotic analysis in the context of von Karman plate theory. It is demonstrated that the crack tip fields in the von Karman theory are identical to those derived by Williams in the context of Kirchhoff plate theory. However, the determination of the crack tip stress intensity factors requires the solution of a large deflection, and hence nonlinear problem that couples the membrane and bending loads. This effect is illustrated through the solution to three simple problems involving cracked plates: An infinite strip with a semi-infinite crack under pressure and then shearing is used for the first two problems. A pressure loaded circular plate with a center crack is used for the third problem. In the infinite strip problems the energy release can be obtained exactly. A simple, approximate, but quite accurate solution is given for the circular plate problem. Nonlinear finite element computations are performed to obtain the individual stress intensity factors and energy release rates. These results are compared to the analytical results. The solutions demonstrate that coupling of the in-plane, or membrane, stress intensity factors to the out-of-plane, or bending, stress intensity factors. They also provide benchmarks against which nonlinear FEM procedures for computing stress intensity factors can be checked. Such problems are relevant to fracture analyses of shell structures such as aircraft fuselages, ships, and liquid storage tanks.

References:

1. C.Y. Hui, A. T. Zehnder, and Y.K. Potdar, "Williams meets von Karman: Mode coupling and nonlinearity in the fracture of thin plates," to appear in International Journal of Fracture, 1999.

2. A.T. Zehnder, and C.Y. Hui, "Stress intensity factors for plate bending and shearing problems," Journal of Applied Mechanics, 61, 1994, 719-722.

3. M.J. Viz, D. Potyondy, A.T. Zehnder, C.C. Rankin, E. Riks, "Computation of membrane and bending stress intensity factors for thin cracked plates," International Journal of Fracture, 72, 1995, 21-38.

4. C.Y. Hui and A.T. Zehnder, "A theory for the fracture of thin plates subjected to bending and twisting moments, International Journal of Fracture, 61, 1993, 211-229.

5. M.J. Viz, A.T. Zehnder, and J.D. Bamford, "Fatigue fracture of thin plates under tensile and transverse shear stresses", in Fracture Mechanics, 26 ASTM STP 1256, Reuter et al. eds., 1995, 631-651.