13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Indenter R2 and indenter R10 are simplified axisymmetric simplifications of the common Berkovich tip; contrary to the common tip radius of a Berkovich tip of less than 20 nm, the elected tip radiuses are 2 and 10 µm. The values in parentheses correspond to the mesh size at the contact. To demonstrate the effect of an increased contact surface a wedge tip was chosen resulting in line loading instead of point loading. Beside these displacement controlled simulations load controlled bending simulations are also performed where concentrated point loads (in z- and y-direction) are applied on a surface in place of contact conditions (referred as concentrated force). The advantage of this load condition is that normal (RF3) and lateral force (RF1) can be chosen independently. The concentrated point load has also been replaced with a surface pressure normal to beam surface (referred as pressure). As expected the indenter penetration strongly depends on the indenter tip geometry. Fig. 3 shows the computed displacement of the material beneath and near the indenter in the z-direction for the three different indenter tip geometries (Indenter R2, Indenter R10 and Wedge R10) and the force controlled loading (Concentrated Force / Pressure) at the same indenter tip depth of 11.1 µm with a friction coefficient of µ = 0.2. It becomes apparent that tips with a small radius lead to a more localized deformation beneath the indenter tip. On the one hand, the difference between the displacement of the indenter tip (experimentally easy measurable) and the displacement at the beam surface is relative large. This causes an indenter dependent error in the displacement measurement. On the other hand the indentation with a small tip radius (R = 2 µm) results in a larger lateral force RF1 in relation to the normal force RF3. With a wedge indentation the deformation is more homogeneous. Thus, in the experimental setup with the wedge tip the measured displacement is more accurate. Several simulations were performed to evaluate the influence of the lateral forces on the stress field at the crack tip. In linear elastic fracture mechanics (LEFM) the stress intensity factor K characterizes this stress field. The critical stress intensity factor KIc, which leads to crack growth is also called fracture toughness. a) Indenter R2 (0.2 µm) b) Indenter R10 (0.5 µm) c) Wedge R10 (0.5 µm) d) Concentrated Force / Pressure Figure 3. Displacement in z-direction of the material in the symmetry plane in the vicinity of the indenter for different indenter tip geometries at the same indenter tip displacement. The indenter with R = 2 µm shows in a) a substantially greater penetration compared to R = 10 µm in b), to the wedge tip in c) and the concentrated force and pressure in d). X Z RP
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