THE COMPACTION BEHAVIOR OF PARTICULATE MATERIALS - AN ELUCIDATION BASED ON PERCOLATION THEORY

An approach based on percolation theory and principles of mechanics has been used to elucidate the relationship between the normalized solid fraction P of compacts and compressive pressure sigma during compaction. The series of linear region comprising the P = f(ln-sigma) relationship has been shown to be a manifestation of the different stages, namely, powder --> flexible compact --> rigid compact --> continuum solid body, which the particulate system goes through during compaction. The transitions from one state to another are signified by percolation thresholds which occur in crossover regions. Near the percolation thresholds, there is a deviation in the P = f(ln-sigma) relationship. Thus, different relationships exist between P and ln sigma near the percolation thresholds and away from the percolation thresholds. All the powders exhibited a particulate bond percolation threshold P(cs) where a continuous interparticle network of bonds spanning the system is formed. Other percolation thresholds were identified as the rigidity threshold P(R) and the percolation threshold of the pores P(ca). The rigidity threshold P(R) is the point where the flexible incipient percolating cluster of the particles becomes rigid and was exhibited by soft materials. The pore percolation threshold P(ca) is the point where the pores cross over from a percolating continuous interconnected structure to disconnected isolated structures. In other words, it signifies the transition from a particulate system to a continuum. Under the conditions of cold compression used in this study, only highly ductile materials exhibited P(ca). A brittle-ductile transition P(T), where the deformation behaviour gradually changes from a predominantly brittle to a predominantly plastic one, was also identified. The exhibition of P(R), P(T) and P(ca) in the P = f(ln-sigma) profile is therefore dependent on the mechanical properties of the materials. Thus, the approach offers a way of classifying materials into soft or hard and ductile or brittle.