# Interface Crack Approaching a Three-Material Joint
## 4 Conclusions  
The problem of a crack at the interface between two materials approaching a three-material joint was considered in this paper. In the case considered, the crack that lies along the interface between the two materials A and B deflects into the interface between materials A and C or into the interface  
Figure 6: Variation of the real and imaginary parts of the stress intensity factors for the crack that deflects into the AC interface, in terms of angle \(\omega\). between materials B and C. The criterion as to which of the two interfaces the crack deflects into is defined based on a criterion proposed by [PERSON] and [PERSON] [23]. Based on the calculations performed, the following conclusions were drawn:  
A curve representing the variation (in terms of angle \(\omega\)) of the ratio of the two energy release rates for the crack that deflects into the BC interface and into the AC interface (\(G_{BC}\)/\(G_{AC}\)) was obtained. For values of the (\(G_{BC}\)/\(G_{AC}\)) ratio above this curve, the crack deflects into the AC interface, and for values of the (\(G_{BC}\)/\(G_{AC}\)) ratio below this curve, the crack deflects into the BC interface. Analysis of the curve that represents the variation of the mode mixity with angle of material C shows that the mode mixity for the case of crack deflection into the AC interface has lower values than the mode mixity for the case of crack deflection into the BC interface. For crack propagation along the BC interface the mode mixity increase (of up to about 30\({}^{\circ}\)) means that the imaginary part of the stress intensity factor is predominant, which corresponds to the shearing mode of the crack propagation. After reaching the maximum value, the mode mixity decreases and reaches a zero value, meaning that the share of the imaginary part of the stress intensity factor decreases, and at its zero value there is only a real part of the stress intensity factor, i.e., the crack propagation is completely in the tearing mode. For crack propagation along the AC interface the mode mixity remains almost constant, i.e., the share of the imaginary part of the stress intensity factor, (the crack propagation mode) remains almost the same. Analysis of the curves that represent variation of the real and imaginary parts of the stress intensity factors for the crack that deflects into one interface or the other, in terms of angle \(\omega\), showed that the real part of the stress intensity factor for the case of crack deflection into the BC interface obtains negative values for larger values of angle \(\omega\), which be explained by possible overlap of the crack surfaces. This overlap can be explained by taking into account the LEFM restrictions on the crack surfaces. If one did not take into account these restrictions, the problem would have to be considered within the framework of elastic-plastic fracture mechanics. For the case of crack propagation along the AC interface, there is no overlapping (jamming) of the crack surfaces and the crack is able to \"freely\" propagate along the interface with increasing load and angle \(\omega\) (this is the extension of material C). The presented theoretical considerations of the interface crack approaching a three-material joint could be used in trying to understand some micro-cracking phenomena during the fatigue loading of engineering materials, like steel or nodular cast iron, [41; 42]; this might be a direction for future research. The criterion proposed by [PERSON] and [PERSON] could be used to predict the behavior of an interface crack approaching the three-material joint and to \"design\" interfaces between the materials to \"force\" the crack to deflect into one of them. This could be applied in the design of composite, cellular, or other complex materials, both at the micro and the nano levels. Conceptualization, J.M.D. and R.R.N. ; methodology, B.H. ; software, J.M.D. ; validation, R.R.N. and R.U. ; formal analysis, J.M.D. ; investigation, J.M.D. ; data curation, B.H; writing--original draft preparation, J.M.D. and R.R.N.