Near-interfacial and interfacial fracture simulation by the extended finite element method

Abstract

Design of composite structures in many important industrial applications requires good understanding of the fracture behavior in the vicinity of material interfaces. In this study, near-interfacial and interfacial fractures are modeled by the extended finite element method (XFEM), a numerical technique developed recently to model crack propagation. In the XFEM, a crack, or a discontinuity in displacements, is represented by enriching the nodes around the crack with additional degrees of freedom associated with enrichment interpolation functions. Among the advantages of the XFEM are that no remeshing is needed; the crack path is independent of the finite element mesh; it is applicable to preexisting cracks as well as evolving cracks; and it is numerically robust although extra implementation efforts are needed. In order to deal efficiently with changes in the geometry and mesh topology, the level set method (LSM), an algorithm used to track evolving interfaces, is introduced and combined with the XFEM. The XFEM is first applied to the simulation of near-interfacial crack propagation in a metal-ceramic layered structure. Experimental evidence indicates that, in a ceramic-metal-ceramic sandwich structure, a near-interfacial crack in the ceramic layer can be drawn to or deflect away from the metal layer depending on the difference in elastic properties across the interface. To model near-interfacial fracture, only the Heaviside functions are used for the XFEM, and the vector IBM method, an improvement to the original LSM, where the IBM is adapted to the nature of crack propagation problems, is employed for efficient evaluation of the enrichment functions. The crack propagation paths predicted by the XFEM simulation are found to be consistent with the experimental observation. In the simulation of the interfacial fracture, a bi-material plate with a crack on the interface is modeled. In the proposed scheme, the nodes on the crack are enriched with only the Heaviside functions. The stress intensity factor analysis demonstrates that such an enrichment strategy can produce satisfactory results for interfacial fracture problems.