13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 2. Conoidal boundary fractures emanating from the edge of the indented region. 3. Computational Results-Indentation Fracture The region at the outer boundary of the test plate is subjected to singular stress fields due to the mixed boundary conditions imposed by the indentation. It can be shown that even when indentation is made by flexible flat test plates, the edges of the indented geomaterial will experience stress concentrations that are singular. The boundary of the indenter is therefore a location where indentation fracture can initiate. The objective of this paper is to demonstrate the influences of fracture development on the load displacement relationship for a rigid test plate. We consider the axisymmetric indentation of the surface of an isotropic elastic half-space region by a smooth flat rigid indenter of radius a (Figure 2). The process of crack initiation and crack extension is most conveniently handled using a computational approach that can model the quasi-static crack extension process. The analysis of crack extension during indentation can be performed via a variety of computational schemes. These can include either finite element methods or boundary integral equation methods or combinations of these. The application of finite element techniques to fracture extension is well established; it requires the specification of criteria both for the initiation of crack extension and for the location of the orientation of the crack path. These relationships applicable to brittle elastic fracture initiation and extension are available in the literature on fracture mechanics [38]. In modelling crack extension via the finite element method, re-meshing is an important feature that ensures accuracy of both the local and global stress fields. Adaptive re-meshing techniques have been used quite effectively to examine crack extension in brittle geomaterials such as concrete and rock [39]. An alternative to re-meshing involves extensive graded mesh refinement in the vicinity of the singular crack tip element and allows crack extension to take place at element boundaries. Alternative schemes, such as the boundary element method, provide greater flexibility when examining the crack extension process. The primary advantage of integral equation-based concepts such as the boundary element method or the displacement discontinuity method is that the domain rearrangement resulting from the crack extension process requires only an incremental change in the boundary element mesh or along the displacement discontinuity line of the crack extension. We shall illustrate here the application of the boundary element scheme to examine the process of quasi-static conoidal crack extension in the geomaterial originating at the boundary indenter. The application of boundary element schemes to problems in fracture mechanics originated with the work of Cruse and Wilson [40] and has been extended by a number investigators [41-43] to include a variety of problems including cracks with frictional interfaces. The review [44] gives a comprehensive survey of research related to boundary element formulations in fracture mechanics. Further details of the application of boundary element techniques to crack indentation problems are given in [13] and summarized here for completeness.
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