A Theoretical Derivation of the Similarity of Dynamic Compaction Processes of Powder Media in Dies

Abstract

Multiple shock compactions of powder media within a die with a rigid punch are theoretically investigated. First, similarity of dynamic compaction processes for a powder medium of a simple type is exhibited through nondimensionalized one-dimensional equations. The similarity is established after determination of three parameters, i.e., the ratio S* of the lateral surface to the cross-sectional area of the medium, the ratio M* of the mass of the punch to that of the powder medium filled in the die, and the compaction energy per unit powder volume e. The similarity indicates that the particle velocity, specific volume and pressure have the same variation with respect to nondimensional time at all points in the medium with various cross-sections and initial lengths so long as S* is kept fixed at a certain value, i.e., at the same proportional nondimensional point in the medium. The density distributions of the green compacts are necessarily identical, and so is the mean density in all compactions. Second, it is shown in one of the nondimensionalized equations that wall frictional influence in a compaction where S* → 0 is not present, while the wall frictional influence is extremely large when S* is very large, which implies that the mean densities of the compacts are larger in compactions with smaller S*. Two types of compactions can be obtained for any powder medium because the equation used is applicable to any medium.