## 3 Results
### Analysis of Simulation Results  
The simulation was computed for different normal pressures and topographies. This section focuses on the influence of the topography on the contact area and the geometry of the gap. To compare the simulation results to the metallographically prepared sinter joints (compare Figure 13), a cross section of the simulation domain is shown in Figure 16. The simulation results are shown for a normal pressure of \(100\times 10^{3}\,\mathrm{Pa}\) which corresponds to the 50 N initial contact force (compare Figure 15). The left image depicts the results for the upwards-facing surface and the right image shows the results for the sidewards-facing surface. The data plot aspect is identical for both images and the axes are evenly spaced. Please note the different exponents of the labels of the y-axes, which differ in one order of magnitude.  
The gap of the upwards-facing surface is much smoother than the sidewards-facing surface. This is a direct consequence of the original surface roughness, but this visualization emphasises the significance of the roughness. Furthermore, the contact points between the two topographies are visible. It is apparent that the gap geometry of the upwards-facing surfaces facilitates the formation of sinter bridges between molecules of the green parts, increasing the overall contact ratio.  
To analyse the entire simulation domain with respect to its influence on the contact ratio, the distribution of the gap height was plotted in a histogram. The occurrence of specific gap height bins can then be compared between the two topographies. To depict contact cells, a bin of a separate color is used. Figure 17 shows the gap height histogram for the upwards-facing topography and Figure 18 for the sidewards-facing topography.  
Figure 16: Cross-section of simulation results: (**left**) upwards- and (**right**) sidewards-facing surface.  
Figure 15: Contact ratio of the sintered joint as a function of the initial contact force.  
The results show that the overall number of load-carrying cells, the contact ratio of the simulation, is similar for both topographies. This is expected, as the normal stress is limited due to the plasticity model, and thus if each contact cell transmits the stress limit the overall number will be roughly the same. The focus of the simulation, however, lies on the three-dimensional contact geometry. The histograms show the complex distribution of the local gap heights.  
The histograms can be compared to the medium gap height that is measured in the experiment. In the experiments conducted for this study, the mean gap height for the upwards-facing topography is 29.7 \(\times\) 10\({}^{-6}\) m. The mean gap height of the deformed simulation from Figure 17 is 30.2 \(\times\) 10\({}^{-6}\) m, which is remarkably close. This height can be measured only after the sintering process, while the simulation represents the situation before sintering. Apparently, the sintering process does not significantly change the overall gap geometry but modifies cells that have a small gap height.  
In the experiments conducted for this study, the mean gap height for the sidewards-facing topography is 70 \(\times\) 10\({}^{-6}\) m. The mean gap height of the deformed simulation from Figure 18 is 61.7 \(\times\) 10\({}^{-6}\) m. The comparison of the mean gap heights shows that the simulation is very close to the real gap geometry in the contact area.