Interface Crack Approaching a Three-Material Joint

Abstract

The problem of an interface crack that approaches a three-material joint with two interfaces is analyzed in this paper. Two possible cases are considered: the crack that lies at the interface between materials A and B, approaching the joint of materials A, B, and C, deflects into the interface between materials A and C or into the interface between materials B and C. Analysis is performed within restrictions imposed by the linear elastic fracture mechanics (LEFM), linear elastic behavior of materials, and the small plastic zone around the crack tip, based on the crack deflection criterion proposed by He and Hutchinson. That criterion is applied in this paper to a joint of the three homogeneous isotropic materials. The energy release rates for the crack deflection into one interface or the other are compared to each other, and, based on this comparison, a conclusion is drawn as to which of the two interfaces the crack would deflect. If the value of the ratio of the energy release rates GBC/GAC is greater than the ratio of the corresponding fracture toughnesses of the two interfaces, the crack will deflect into the BC interface. If this ratio is smaller than the ratio of the corresponding fracture toughnesses, the crack will deflect into the AC interface. Knowing the ratio of energy release rates for deflection into one interface or the other can be used for designing the interface, namely for prediction of the direction of further crack propagation.