Quasi-static compaction of porous propellant beds. I. Modeling ball powder experiments with deformed spheres in a regular lattice

Abstract

A simple but physically-based model describing compaction of granular energetic materials is presented for the case where the grains deform plastically. The model assumes an ideal porous bed consisting of initially uniform spherical particles arranged in a cubic lattice. As the bed is loaded, the spheres are flattened at each contact; particle volume is conserved by allowing the radius of the uncontacted portion of the particle to expand. The contact forces are approximated as a constant stress (termed Meyer yield stress) multiplied by the contact area. The equations describe compaction from the initial lattice density (point contacts) until either contact surfaces on a grain begin touching each other or second nearest neighbor interactions occur. In actual porous beds, the particles are unlikely to be arranged in any long-range regular lattice because of random packing and variations in particle shape and size. Since initial bed densities are often between those of simple and face-centered cubic lattices, a mix of these two lattices is used to approximate an actual bed. In another approach to modelling actual porous beds, average lattice parameters (for initial packing density and number of contacts per particle) are used within the generalized equations for the regular lattices. Each approach successfully models quasi-static compaction data reported previously for ball propellants.