Considerations about the theoretically expected crushing strength of tablets from binary powder mixtures: Double layer tablets versus arithmetic additivity rule

The theoretically expected breaking strength of tablets from powder mixtures is often calculated by the weighted arithmetic mean from the breaking strength of the single components, which corresponds to a linear interpolation. The validity of this additivity of fracture strength shall be evaluated by the underlying model of parallel couplings. It assumes the components linked in parallel with respect to the direction of loading during diametrical strength testing. Parallel couplings were experimentally realised by the preparation of double layer tablets from crystalline and spray-dried lactose on the one hand and from maltitol and metamizol-sodium on the other. Constant total true volumes of the single substances and of layered powders in varying ratios of true volume were compressed on an eccentric tabletting machine to constant geometric mean punch force. Simulated crushing profiles of parallel couplings were derived from force–displacement profiles measured during diametrical compression of the one-component tablets. At given finely graded deformation levels, the forces exerted by the components during loading were added in the proportion of the true volume fractions of the components in the coupling. The results from the experiments and from the simulations are in good accordance. They demonstrate that a linear change of the crushing strength in dependence on the true volume fraction of the components can only be assumed if the single components deform to the same extent up to the point of fracture. This behaviour was approximately found with the parallel lactose system. In all other cases it must be expected that the crushing strength of parallel systems will be lowered beneath the weighted arithmetic mean values or even below the crushing strength of the single components. The latter was observed with the maltitol–metamizol combinations. Thus, if tablets from binary powder mixtures exhibit a crushing strength depression, this is not necessarily an indication of weak bonding between the components or of structural defects.