Quantifying 3D time-resolved kinematics and kinetics during rapid granular compaction, Part I: Quasistatic and dynamic deformation regimes

Abstract

Impacts in granular materials occur over a velocity range of a few hundred m/s in manufacturing processes to several km/s during asteroid impacts. Different energy dissipation mechanisms are activated during impacts based on the kinetic energy of the impactor and the properties of the granular material. Material response during impact can be classified into two broad regimes – quasi-static and dynamic – characterized by the nature of grain and pore deformation and the deformation morphology of grain interfaces. In the quasi-static regime, all energy from the impactor is utilized in pore (or void) collapse, while in the dynamic regime, excess energy after pore closure leads to material melting or jetting and often to non-planar grain interfaces. To understand the transition between the quasi-static and dynamic regimes, in-situ measurements of temperature, local stresses, and porosity at the grain scale are critical but often not possible due to short timescales and inherent heterogeneity of granular materials. In this work, we use X-ray phase contrast imaging (XPCI) to visualize grain-scale deformation during rapid granular compaction and observe phenomena such as plastic flow-induced pore collapse, compaction wave propagation, and the morphology of the grain-grain interfaces. Alongside these experiments, we develop and validate a mesoscale numerical model that incorporates each sample’s microstructure and captures realistic plasticity and thermal effects. Using this validated model, we quantify the temperatures, pressures, and porosity as granular materials are compacted in both quasi-static and dynamic deformation regimes. By comparing our results with existing theoretical models, we find that the continuum definitions of quasi-static and dynamic regimes needs to be updated for a realistic heterogeneous granular media. Specifically, the two regimes can coexist in the same assembly of grains at different time instants due to spatial heterogeneity and rapid dissipation of impact energy away from the point of impact. Finally, we quantify the energies associated with different dissipation mechanisms for individual grains using coupled numerical and analytical techniques. Our methodology allows us to obtain full 3D kinematics and kinetics of rapidly compacted granular materials at both the mesoscale and the grain scale.