Modelling the compaction behaviour of powders: application to pharmaceutical powders

Stress and density changes in axi-symmetric compaction of pharmaceutical powders are analysed numerically. Data measured in a compression cycle are used with a calibration procedure to assess the mechanical behaviour of powders in compaction based on a Drucker–Prager Cap model. This model is based on the elastic–plastic theory and takes into account the macroscopic characteristics of powders such as cohesion and global friction between particles. Moreover, a yield function is used to limit the admissible stresses in a tablet during a compaction cycle. This yield function depends on the first and second invariants of the stress tensor: pressure and stress deviation. To represent the plastic compaction mechanisms, a strain hardening function is used to expand the yield function with increasing volumetric strain. A finite element method coupled to the finite strain plasticity theory is used to calculate stress and strain changes in a tablet during compression and decompression. The die wall friction is estimated from the transmission effort to the lower punch with the modified equation of Shaxby and Evans. This model and the calibration procedure are applied to lactose powder. Mechanical properties calculated are compared to the experimental data measurements with a Jenike shear cell. The relative density distribution at the end of compaction and after the unloading is analysed. The normal pressure on the die is numerically estimated and analysed in terms of load transferred from powder to die during compaction and load restitution to tablet during decompression.