A Study of a Crack Close to a Bi-material Interface

For a composite material in a 2-D problem, the crack close to the bi-material interface— impinging the interface by a certain angle or within the interface— may occur. This study reviews the fracture mechanics, simulation techniques and the propagation criteria for both the two categories of the near-interface crack. Given the different degrees to which the two categories have been studied, this study extends the research of each.

For a crack that lies within the bi-material interface, it has been extensively studied about its fracture mechanics, kinking criterion and numerical simulation. For this kind of crack, this study focuses on the simulation of the kinking progress. XFEM (extended finite element method) is used as a basic simulation tool. The complex stress intensity factors and are first calculated for the interfacial crack. Then a kinking criterion is considered to judge the propagation direction (according to the different combination of materials, interfacial toughness and the loading phase angles, the crack could either propagate along the interface or deviate into a certain phase). When the kinked crack starts deviating from the interface by a small distance, a novel method developed by Wu is introduced to correctly extract the stress intensity factors and . Thus, the kinking progress of an interfacial crack is simulated by combining XFEM with a kinking criterion and a novel domain form of interaction integral method. A MATLAB code is developed to fulfill the kinking simulation. From the examples that include different propagation lengths, mesh sizes and boundary conditions, the propagation paths of the kinked interfacial cracks can be directly seen. The results show good stability and convergency.

For the crack inclined to a bi-material interface by a certain angle, the fracture mechanics is more complicated than an interfacial crack. The singularity coefficients have three cases: a). one real singularity coefficient ( ), b). two different real singularity coefficients ( ) and c). two conjugate complex singularity coefficients ( ). Until now, most of the studies focus on calculating its singularity coefficients. There are also some studies concerning a crack perpendicular to the interface which is an extreme case. This study first derived the stress and displacement fields of a crack inclined to an interface by a certain angle which may not equal 0 or . The derived stress fields are given in the Appendix B in an explicit form. The stress fields of the three different cases are compared with previous works. Based on the derived stress and displacement fields, three series of extrapolation equations are developed to extract the stress intensity coefficients for all the three singularity cases.

Five examples are studied as implications of the three series of the extrapolation equations. The stress values directly ahead of the inclined crack are gained from a series of ABAQUS models. After the stresses are substituted into the corresponding extrapolation equations, the stress intensity coefficients could be obtained.

The extrapolation curves show a good linearity and the extrapolated stress intensity factors coincide well with previous known results.