Application of the coupled criterion to interface crack growth in the end-notched flexure test considering friction between the crack faces

A novel computational analysis is developed to model mode II fracture of a bimaterial specimen in an End Notched Flexure test considering frictional sliding contact between the crack faces. In the Comninou contact model of interface cracks, the frictional contact zone at the tip of an interface crack between dissimilar linear elastic materials entails a stress singularity, which is weaker than the square root singularity. This weak singularity results in a zero Energy Release Rate (ERR) \(G_{II}=0\) in such cracks. Therefore, the classical Griffith criterion cannot be used to predict crack growth in this case. To address this challenging issue, a new approach based on the Coupled Criterion (CC) introduced by Leguillon (Eur. J. Mech. A/Solids 21, 61-72, 2002), which adopts the Finite Fracture Mechanics (FFM) hypothesis proposed by Hashin (J. Mech. Phys. Solids, 44, 1129-1145, 1996), is developed. The CC is satisfied when both the stress and incremental energy criteria are satisfied simultaneously. A novel CC implementation is required to address the nonlinearity caused by the frictional contact between the interface crack faces, particularly the frictional dissipation of energy during the growth of such interface cracks. The methodology developed involves Finite Element Analysis (FEA) to compute shear stress and relative displacements along the crack path, the change of the potential energy and the energy dissipated by friction. Finally, the implemented CC provides the critical load and finite crack advance at the initiation of crack propagation. The numerical study presented considers various combinations of isotropic materials and friction coefficients.