Transient analysis of stationary interface cracks in orthotropic bi-materials using oscillatory crack tip enrichments

The problem of an interface crack between two orthotropic layers under dynamic loading is analyzed. Special crack tip enrichment functions are incorporated into the standard finite element shape functions to exactly reproduce oscillatory stress and displacement fields near the tip of the interface crack. Moreover, kinematics of displacement and its gradients across the crack face and material interface are also modeled by partition of unity enrichments. Special attention is given to extraction of stress intensity factors by utilizing a proper form of the interaction integral for orthotropic bi-materials. Advantages of this method of extracting stress intensity factors over the conventional displacement extrapolation technique are discussed. Several bi-material configurations with both vanishing and non-vanishing oscillatory indexes are solved using the interaction integral and the results are compared with the available data in the literature. Effects of employing oscillatory crack tip enrichments and validation of the path-independent J-integral are also discussed.