The effect of wall friction in the compaction of pharmaceutical tablets with curved faces: a validation study of the Drucker–Prager Cap model

The compaction of porous materials can be modelled using micromechanical or phenomenological approaches. The micromechanical models are developed for either dense random packings or near fully dense ductile materials. Phenomenological models have been developed to describe the response of the material over a range of relative densities encountered in powder metallurgy, ceramics or composites industries. Pharmaceutical powders are particular in that their initial relative density (RD) is between 0.2 and 0.4, which is significantly lower than for other powder materials. In this paper, we analyse the die compaction of pharmaceutical powders using a variable parameter Drucker–Prager type cap model. The model was calibrated for microcrystalline cellulose using a die instrumented with radial pressure sensors, which is also used to measure the coefficient of friction between powder and die wall. The relative density distribution in tablets is examined with special reference to the friction interaction between powder-die and powder-punches. The predictions of the model are compared with experimental density maps obtained from surface hardness tests carried out on cross-sections of the tablets. Two situations are considered where the die and punches are unlubricated and lubricated, which result in opposite density distribution trends. The result suggests that if the material is subjected to high triaxiality stress, then the phenomenological models can be applied for low initial apparent density powders.