13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- vicinity of the boundary of the indenter (Figure 1) can be obtained through a computer based search technique. The location of the point of maximum tensile stress will be characterized by the local coordinates 0η and 0ψ and will depend only on Poisson’s ratio. This technique allows the location of the orientation and length of a starter crack and the boundary element meshing is structured to accommodate this starter crack and a semi-infinite domain (Figure 4). Figure 4.The location and orientation of starter crack. 3.2. Onset and Orientation of Crack Extension The onset of crack extension can be based on a number of criteria applicable to brittle geomaterials. An elementary criterion for onset of crack extension is the attainment of a critical value of the Mode I stress intensity factor; i.e. I IC K K= (17) The orientation of crack extension has to take into account the influence of both stress intensity factors. The criterion used is that proposed by Erdogan and Sih [47]. The maximum stress criterion assumes that the crack will extend in the plane that is normal to the maximum stress ψψ σ shown in Figure 4b and according to I II sin (3cos 1) 0 K K ψ ψ + − = (18) Other criteria, such as crack extension along paths where II 0 K = , are possible [48] but in this study the criterion (18) is used. 4. Numerical Results The objective of the study is to examine the extent to which the load displacement of the rigid indenter is influenced by the development of boundary fracture. The results can be presented in relation to a load-displacement relationship for the rigid indenter, taking into account the parameters that control the crack initiation and extension process described previously and documented in detail in [13]. Figure 5a illustrates the results for the load-displacement relationship for the case where the orientation of the starter crack is determined from procedures outlined in Section 3.2. Figure 5b illustrates similar results derived by assuming a priori that the starter crack is oriented normal to the boundary of the indented surface. Results for the load-displacement relationships for
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