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.
Highlights
IntroductionSince the pioneering works of Williams [1], Erdogan [2], England [3], Malyshev and Salganik [4], and Rice and Sih [5], interface fracture mechanics has developed significantly
Fracture mechanics applications to problems of cracks at bi-material interfaces is a topic that has been attractive to numerous researchers in recent years, since this is a discipline which is still developing
One of the first analytical models of fractures at bi-material interfaces was presented in a paper by Williams [1]
Summary
Since the pioneering works of Williams [1], Erdogan [2], England [3], Malyshev and Salganik [4], and Rice and Sih [5], interface fracture mechanics has developed significantly. This development has stemmed from the necessity of studying the behavior of such cracks in various engineering problems, including depositing a metal layer to a composite substrate in the airplane industry, analysis of interior damages and flaws in composite materials, or delamination of multi-layer materials like thermo-insulating coatings, as in Foraboschi [6,7,8]. The biggest contribution of this paper was an analytical expression for the stress and displacement fields in the zone of a strong singularity, which lies close to the tip of the
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