Analysis of the dynamic radial compaction of granular media

Abstract

The previously developed continual approximation is used to analyze the radial axisymmetric compaction of a granular medium in the presence of a rigid undeformable rod on the symmetry axis. It is shown that, during pulsed loading, high densities close to those corresponding to the nonporous state can be attained due to inertia effects. The influence of the initial radial dimensions of the rod-powder-medium system on the compaction process is analyzed. The problem is found to be scale invariant under various constraints imposed on the ratio of the characteristic dimensions.Introduction. This paper is a continuation of studies [1, 2], devoted to a semi-empirical description of the compaction of a granular medium, in particular, nanopowders based on aluminum oxide [3][4][5]. The compaction of a granular medium is considered in the continual approximation of a plastically hardened porous solid [6-9]. The characteristics of the AM and α-AM nanopowders studied, experimental compression adiabats, and empirically constructed hardening functions are given in [1,5]. The latter were used to formulate a closed system of rheological equations and to perform a quasistatic analysis of the radial axisymmetric compaction of nanopowders [1] performed in magnetic-pulsed compaction experiments [3][4][5]. In [2], a model was constructed that takes into account the effect exerted on the compaction dynamics by the inertial properties of the powder-shell system, which play a decisive role in fast magnetic-pulsed compaction. For the radial compaction of a granular medium in the presence of a rigid rod of radius r m on the symmetry axis, the following differential equation was obtained to describe the dynamics of the powder-medium interface [R = R(t)] subjected to external magnetic pressure p c (t):