Nonunique Dynamic Equilibrium Constitutive Relation of Metal Powder Depending on its Microstructure

It was observed in an earlier work by Morimoto et al. [Inst. Phys. Conf. Ser. No. 70, Oxford 1984, p. 427] that the dynamic compact of an aluminium powder medium had greater flakiness and contiguity ratio than the static compact of the same density. This observed difference in micro structure is used to explain their result that the dynamic pressure of the medium is higher than the static pressure for a given density: the degree of rotation of particles during compaction is assumed to decrease for higher strain rates, because of the shorter time available, causing an increase in plastic particle deformation in the compaction direction, and increased resistance to the compaction. The normal Hugoniot equation derived, in which the mean strain rate averaged over a single steady wavefront is introduced, indicates that a rise of the normal Hugoniot with an increase in the strain rate results macroscopically from the increase in the propagation velocity of the wavefront. The multiwave Hugoniot equation is found to depend on the strain rate history of a given material. In compactions of a metal powder medium by punch impact, the wavefronts passing through the medium are approximately steady if the punch mass is sufficiently larger than the medium mass. But both the number of wavefronts arising during the compaction and the amplitudes of the strain waves, and hence the strain rate histories, vary with compaction conditions such as punch mass and initial punch velocity. This implies that a dynamic equilibrium constitutive relation for the medium will depend on the compaction conditions, and therefore cannot be determined uniquely for any two compactions.