## 4 Results and Discussion
At higher pressures (forces), frictional effects are reduced due to decreasing tangential displacements; this is evident from the results in Figure 4.  
In Figure 5, then, the distributions of the standard von Mises effective stress \(\sigma_{\rm e}\), based on deviatoric stresses, are shown at maximum pressing load for both of the two frictional models in Equations (1) and (2). The reason for showing the distribution of this quantity is, of course, that it is directly related to the plastic constitutive behaviour of the material, regardless of whether pressure sensitivity effects are accounted for or not. The results show clear differences between the predictions from the two models, as in the case of a constant coefficient of friction, where stresses are significantly higher. This indicates that the simulation results differ considerably when it comes to the plastic deformation at the maximum pressing load. Again, this certainly emphasizes the need to accurately describe the frictional behaviour. In Figures 6 and 7, then, the very important first principal stress \(\sigma_{1}\) is shown at two different values of the average relative material density during the pressing sequence for both of the two frictional models. This is performed in order to see the history dependence of the first principal stress and to properly evaluate the plastic (isotropic) deformation. This stress is directly related to cracking in the powder compact at an appropriate failure criterion and, accordingly, is of most interest in the present context. Evidently, there are no tensile stresses present in the predictions for either of the models, which suggests that cracking is very limited (or nonexistent) during the loading part of the process. The two friction models give quite similar results, even though, in the case of a constant frictional coefficient,  
Figure 8: Results from the FEM simulations. Results for the maximum first principal stress (MPa) are plotted during unloading as a function of time \(t\) (seconds). Note that \(t=0\) represents the start of unloading and that at \(t=0.016\), the upper punch loses contact with the material. as shown in Equation (1), stresses are, in general, more compressive (this corresponds to the maximum tensile failure criterion). This effect is rather small, though. As for the history dependence, it is clear that the difference between the predictions from the two models is more pronounced earlier in the compaction process. This is due to the results shown in Figure 2, indicating that the friction coefficient attains a maximum at medium-sized contact pressures and then decreases slowly to a value close to 0.2 (relevant for standard Coulomb friction). It should also be mentioned that in the case of a friction coefficient described in Equation (2), the predictions show some deviation from axisymmetry. This is, of course, a numerical artefact due to the advanced contact model described above. The deviations from axisymmetry are, however, small, and we concluded that they will not in any way alter the general conclusions from this study, as outlined below. The corresponding first principal stress results during and after unloading are, in the context of possible crack initiation and growth, more interesting because, in this case, tensile stresses are present and compressive stresses are reduced. Accordingly, explicit stress values become important, and showing stress trajectories is not the most informative way to present the results. Instead, in Figure 8, explicit values for the maximum value of the first principal stress, using both frictional models, are shown during the unloading part of the compaction process. The results in Figure 8 show that initially, during the unloading process, the predictions based on the two frictional models at issue differ, but rather rapidly, they become close.