Williams meets von Karman: Mode coupling and nonlinearity in the fracture of thin plates

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 character of the near tip fields is identical to those of the linear plate theory. However, the determination of the crack tip stress intensity factors requires the solution of a large deflection, and hence nonlinear, problem due to the coupling of the membrane and bending modes. This effect is illustrated through the solution of three fracture problems involving plates of simple geometries loaded by pressure, tension and shearing. In two of these problems, the energy release rate is obtained exactly. Nonlinear finite element computations are performed to obtain the stress intensity factors and energy release rate associated with tension, bending and shearing. These results are compared to the theoretical results for energy release rate and stress intensity factors.