13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Fig. 8 shows furthermore, that the numerical J values in the center of the specimen (symmetry plane) are larger and at the surface smaller than the analytical values. A comparison of the analytical solution with Jan = 0.71 mJ/mm2 and the average numerical solution with Jnum = 0.80 mJ/mm2 shows a good and plausible approximation. Thanks to crystal plasticity the activities on various slip systems can be revealed. To get an idea of the size of the zone with slip activities the accumulated shear strain is shown in Fig. 9 in front of the crack tip and at the surface for an indenter displacement of 0.5 µm. As known from the fracture mechanics, the plastic zone is in the symmetry plane due to plane strain smaller than at the surface. The influence of the asymmetric specimen geometry can be also seen. The fixing is located on the left side and the loading takes place on the right side. Here, the load results to RF3 = 25 N and to RF1 = 10 N. Figure 9. Accumulated shear strain ahead of the crack tip at a indenter displacement of 0.5 µm for an orientation {011}<01̅1> of the crack system, exemplary details were chosen in the symmetry plane and at the surface. 5. Conclusion In this paper we presented a three dimensional finite element model of a notched single crystalline tungsten micro cantilever which is deflected in the bending test by a nanoindentation device. The model was applied to study the influence of friction and indenter geometry on the stress field around the crack (notch) characterized by the stress intensity factor K or the J-integral. The results show that with increasing friction coefficient μ the lateral force increases linearly and with it the J-integral decreases linearly. Furthermore, the indenter tip geometry plays an important role. Based on these numerical results following recommendations can be made regarding the experimental setup. To exclude the influence of the indenter tip geometry, the displacement should not be measured at the indenter tip but at a point slightly ahead of the indenter (outside the penetration area). The simulations show that otherwise the error of the J-integral can reach up to 12% (e.g. in case of an axisymmetric Berkovich tip like indenter with a tip radius of 2 µm). If only the displacement of the indenter tip is experimentally accessible, an indenter with a large contact area (e.g. a wedge indenter) is recommended as localized penetration is prevented and the error in J is minimized.
RkJQdWJsaXNoZXIy MjM0NDE=