Compaction processes in granular beds composed of different particle sizes

Abstract

A piston impacting a granular bed will cause the material to compact; the strength of a granular bed is significant during weak impact relating to piston speeds of 100m∕s. The strength associated with the granular structure is described as the intergranular stress; this is the resistance of a granular bed to compaction which can be measured by carefully constructing experiments. The compaction process may then be modeled by solving a hyperbolic system of equations that utilizes these data to close the system. The compaction behavior of a porous material is particle-size dependent; to accurately describe the response of two granular beds that may be of different particle sizes and distributions, it is essential that the intergranular stress is derived for each particle bed. This work uses recent compaction experiments to derive intergranular stress curves for prepressed conventional HMX material that is of nonuniform distribution with a mean diameter of 40μm and a microfine HMX of more uniform distribution of mean diameter <5μm. Steady-state compaction waves in the solid material are analyzed: initially the solid is assumed to behave as an incompressible medium. The speed and extent of compaction can be simply determined through the solution of a quadratic equation. Following this, the assumption is relaxed allowing changes in solid-phase density; a complicated equation of state makes the use of numerical methods mandatory. The speed of steady-state waves in HMX due to low impact compaction can be determined within 2% accuracy using the simple closed solution based on solid incompressibility, which is a function of the initial material porosity and density, piston speed, and the intergranular stress of the granular bed. This analysis reveals the difference between the weak impact response of a coarse nonuniform bed and a fine almost uniform granular bed that are initially loaded to 75% of the theoretical maximum density. The fine particle beds have increased resistance to compaction meaning that the extent of compaction is reduced and the speed of compaction waves are faster. The long-term objective of this research is the study of combustion and detonation in granular beds; a two-phase flow capability is required to simulate this type of problem. A multiphase flow model is utilized to simulate the complete low impact response of HMX that includes gas-phase effects. The time-dependent flow rapidly attains steady-state conditions; these solutions agree with the steady-state solutions of the reduced problem described above. Dissipation due to compaction is analyzed and compared with other dissipative processes within the system.