Shape prediction and stability analysis of Mode-I planar cracks

This paper presents a numerical technique for simulating stable growth of Mode-I cracks in two and three dimensions, using energy release rate and its derivatives. The crack growth model used in the numerical simulation is based on the concept of maximizing potential energy of the system released as cracks evolve. Therefore, a series of quadratic programming (QP) problems with linear constraints and bounds are solved to simulate stable growth of Mode-I planar cracks. The derivative of energy release rate provides a stability condition for crack growth in structures and can be regarded as a discretized influence function that represents the strength of the interaction among crack extensions at different crack tips in 2-D and different locations along a crack front in 3-D. The energy release rate and its derivative are accurately calculated by the analytical virtual crack extension method [Engng. Fract. Mech. 59 (1998) 521; 68 (2001) 925] in a single analysis. Numerical examples are presented to demonstrate the capabilities of the proposed approach. Examples include a central crack subjected to wedge forces in a 2-D finite plate, a system of interacting thermally induced parallel cracks in a two-dimensional semi-infinite plane and a 3-D penny-shaped crack embedded in a large cylinder, pressurized in a central circular region.