Ramifications of projectile velocity on the ballistic dart penetration of sand

With the advent of novel in-situ experimental measurement techniques, highly resolved quantitative observations of dynamic events within granular media can now be made. In particular, high speed imagery and digital analysis now allow for the ballistic behaviors of sand to be examined not only across a range of event velocities but across multiple length scales. In an attempt to further understand the dynamic behavior of granular media, these new experimental developments were implemented utilizing high speed photography coupled with piezo-electric stress gauges to observe visually accessible ballistic events of a dart penetrating Ottawa sand. Projectile velocities ranged from 100 to over 300 meters per second with two distinct chosen fields of view to capture bulk and grain-scale behaviors. Each event was analyzed using the digital image correlation technique, particle image velocimetry from which two dimensional, temporally resolved, velocity fields were extracted, from which bulk granular flow and compaction wave propagation were observed and quantified. By comparing bulk, in situ, velocity field behavior resultant from dart penetration, momentum transfer could be quantified measuring radius of influence or dilatant fluid approximations from which a positive correlation was found across the explored velocity regime, including self similar tendencies. This was, however, not absolute as persistent scatter was observed attributed to granular heterogeneous effects. These were tentatively measured in terms of an irreversible energy amount calculated via energy balance. Grain scale analysis reveals analogous behavior to the bulk response with more chaotic structure, though conclusions were limited by the image processing method to qualitative observations. Even so, critical granular behaviors could be seen, such as densification, pore collapse, and grain fracture from which basic heterogeneous phenomena could be examined. These particularly dominated near nose interactions at high projectile velocities. Resulting empirical models and observations from all approaches provide a baseline from which other studies across may be compared, a metric against which penetrator effectiveness may be evaluated, and an alternative way to validate computationally based analyses. Velocity analysis was further contrasted with piezo-resistive stress gauge data in an effort to pair heterogeneous mechanisms in the bulk stress response. Phenomena such as grain fracture and densification were successfully observed in conjunction with a unique stress signature. Comparing stress responses across the tested velocity spectrum confirm conditional similitude with deviations a low projectile velocities attributed to domination by heterogeneous mechanisms.

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