Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

Abstract

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported. KEY WORDS: EFG, SIF, T-stress, interface crack, MTPS, crack propagation. INTRODUCTIONComposite materials are often subjected to extreme mechanical and thermal loading conditions that make them susceptible to damage through crack formation. Studies on the modelling of fracture in composites, range from nanoscale to macroscale analysis. Useful insight into the study of fracture may be gained through analysis at the microscale. At this level, the constituent materials are represented separately, i.e. the material is non-homogenous usually consisting of dissimilar materials or bi-materials separated by an interface [1].A propagating crack at the microscale may often impinge on the bi-material interface at an angle. The associated singular stress field consists of two different orders of singularity which may be either complex conjugates or real [2][3]. In addition, a crack tip that meets an interface of two materials may grow along it or penetrate into the neighbouring material. The criterion for such a crack to kink into the neighbouring material is different from the criterion governing the crack propagation in a homogenous material. The development of a proper numerical 2 method and an efficient approach to predict the angle of crack propagation, including kinking of an interface crack, can be very useful in the study of fracture of composites.Mesh-based methods like the finite element method (FEM) and the boundary element method (BEM) pose difficulties for crack propagation problems due to extensive meshing and remeshing. Although the extended finite element method (XFEM), based on the partition-of-unity approach, eliminated some of the difficulties, the enrichment functions depend on the crack tip loc...

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