## 1 Introduction  
Powder compaction is a widely used manufacturing method since it has high productivity and often is close to the net shape. For instance, cutting inserts are manufactured by compacting spray-dried refractory carbide and metal powder mixtures containing tungsten carbide into a predefined shape, followed by sintering to full density and posttreatment.  
After compaction, the density is uneven, which is a substantial disadvantage. Density gradients and residual stresses in powder compacts (green bodies) can result in shape distortion and cracking after pressing and subsequent sintering. For the purpose of predicting the shape after sintering, the finite element (FE) method is very useful [1] for mechanical field determination and other matters, particularly when frictional effects as described in [2] are present [3]. Compaction and sintering simulations, where friction is important to consider, are specifically useful when designing and manufacturing press tools; since they shape distortion, those can be compensated for.  
It was shown by [PERSON] et al. [4] that frictional effects at low stresses are important to consider. In [4], an instrumented die was used to determine the frictional behaviour between the die and powder, but at low stresses, unexpected results were discovered. In the above-mentioned study [2], friction is assumed to be a function of normal pressure but not of density. According to the discussion above, in [2], a tungsten carbide powder was studied.  
In a previous study [3], the effect of friction on the density distribution after pressing was investigated using FE simulations. It was found that the results were very much dependent on the frictional model. Consequently, substantial efforts have to be devoted to such modelling in order to achieve accurate results.  
Presently, drawing upon the numerical achievements in [3], the aim is to investigate the stress state in a powder compact during loading and after unloading. In particular, tensile stresses are of interest, as such stresses can lead to cracking during both compaction and sintering, relying on a criterion based on maximum principal stresses. It is expected that frictional effects are also substantial in this case, and therefore, such behaviour is investigated in detail.  
In this study, two different frictional models are implemented into a commercial FE software (see details below), and relevant results are compared and discussed. An extended Drucker-Prager CAP model by [PERSON] and [PERSON] [5] is relied upon. Alternatives exist, for example [6; 7; 8; 9; 10], but this model is directly relevant for hard metal materials. The material parameters in the constitutive model have been determined by [PERSON] et al. in [11] and are representative of a common WC-Co powder used for cutting inserts. In [11], optimization and inverse modelling was employed, see for example [12; 13; 14; 15].  
As already stated, the purpose of this study is to determine the effect of different frictional models on the tensile stresses developing during compaction loading and unloading. The approach is, as mentioned above, detailed for tungsten carbide powders but is relevant for the pressing of other powder materials as well, such as stainless steel powders and rock materials.