## 4 Results and Discussion
At around \(t=0.016\) s (\(t=0\) represents the start of unloading), the upper punch loses contact with the material, and after that, the (residual) stress in the powder is almost constant, as could be expected because no external loading is then present. Then, the predictions from the two frictional models are essentially equal. It should be noted, however, that the stress determined using the frictional model in Equation (2) becomes tensile well before the loss of contact (not so for the corresponding analysis based on Equation (1)). The residual tensile stresses after unloading are low; based on the results, they are approximately 1-3 MPa. This is, however, in the same range as the measured fracture stresses for hard metal green bodies. Accordingly, it is of great importance to accurately predict the stress state during unloading in order to avoid crack formation and growth (for simplicity, based on a maximum principal stress criterion) during the compaction process. Fortunately, though, it seems that when possible tensile stresses are concerned, the values are not very much dependent on the frictional description used, as clearly shown in the explicit results in Figure 8. It should be mentioned, though, that a mixed principal stress criterion could complicate matters. In this context, it should be mentioned that measuring residual stresses in a powder material, as in the context of this study, can be a difficult task to achieve due to its porous character. However, different techniques for this purpose exist. Pertinent techniques include sharp (Vickers and Berkovic) indentation, Refs. [23; 24; 25; 26; 27] which is probably the most attractive alternative to neutron and X-ray tilt techniques [28] (techniques such as hole drilling [29], layer removal [30], or blunt indentation are not relevant in the present case). Accordingly, measuring (tensile) residual stresses in a powder compact is a possible task to attempt; this is certainly an essential and necessary complement to the simulation predictions at issue here and is applicable in a more practical situation. The latter statement is particularly valid when indentation is performed, remembering that the length scales involved allow for the use of microindentation testing. Nanoindentation would, in this case, introduce the necessity of using some kind of strain gradient plasticity model and more accurate contact area determination. It goes almost without saying that this would substantially complicate the interpretation of the experimental results and also introduce (unnecessary) material characterization matters. In summary, then, it can be concluded that the results in Figures 4-7 indicate clearly that in order to predict field variables at compaction, it is necessary to use an accurate and pressure-dependent frictional model. This particularly concerns the relative density and the von Mises effective stress. This is a very important conclusion pertinent to an industrial situation where the pressing/sintering of geometrically complicated cutting tools is at issue. Assuming a constant coefficient of friction, as is performed in the Coulomb friction model, would render the results substantially less useful for industrial applications (due to the inaccurate predictions of the density distribution and the plastic deformations before sintering), even though the constitutive model used here is a complicated one based on pressure sensitivity. The simulation results, however, also show that when possible (residual) tensile stresses, during and after unloading of the compact, are concerned, explicit values are not very much dependent on the frictional description. This is shown in Figure 8. Even though the procedure is detailed for cemented carbide powders, it could also be directly applied to other types of materials such as soils, bio-based aggregate storage and pharmaceutical applications, as well as to the constitutive characterization of rock materials (see, for example, [31; 32; 33; 34]).