Use of first derivative of displacement vs. force profiles to determine deformation behavior of compressed powders

Displacement (D) vs. force (F) profiles obtained during compaction of powders have been reported by several researchers. These profiles are usually used to obtain mechanical energies associated with the compaction of powders. In this work, we obtained displacement-force data associated with the compression of six powders; Avicel PH101, Avicel PH301, pregelatinized corn starch, anhydrous lactose, dicalcium phosphate, and mannitol. The first three powders are known to deform predominantly by plastic behavior while the later ones are known to deform predominantly by brittle fracture. Displacement-force data was utilized to perform in-die Heckel analysis and to calculate the first derivative (dD/dF) of displacement-force plots. First derivative results were then plotted against mean force (F') at each point and against 1/F' at compression forces between 1 and 20 kN. Results of the in-die Heckle analysis are in very good agreement with the known deformation behavior of the compressed materials. First derivative plots show that materials that deform predominantly by plastic behavior have first derivative values (0.0006-0.0016 mm/ N) larger than those of brittle materials (0.0004 mm/N). Moreover, when dD/dF is plotted against 1/F' for each powder, a linear correlation can be obtained (R2=>0.98). The slopes of the dD/dF vs. 1/F' plots for plastically deforming materials are relatively larger than those for materials that deform by brittle behavior. It is concluded that first derivative plots of displacement-force profiles can be used to determine deformation behavior of powders.