Quasi-static Modeling of Non-planar Crack Growth With/without Open Kinks

Quasi-static non-planar growth of a crack is simulated by using the maximum energy release rate criterion. When a crack is under compression, the evaluation of energy release rate involves the solution to (1) frictional contact problems, where the fractured surfaces are constrained by a friction law, and/or (2) crack opening problems, where the fractured surfaces are constrained by traction free condition. We adopt the boundary integral equation method to solve such mixed mode (mode I and II) non-planar crack problems: the tensile traction on the crack is iteratively eliminated by allowing the opening dislocation, and the friction law is satisfied by using the re-calculated normal traction at each iteration. We assume a slip-weakening Coulomb friction law to eliminate infinite tensile stresses in the vicinity of crack tips and it enables us to investigate applied load conditions for non-planar surface to close over the crack. Our preliminary result shows that when the peak stress of the slip weakening law is high (like classical singular crack models), an artificial cut under uniaxial compression extends with open kinks, which is consistent with laboratory observations.