Velocity Regimes for Sphere Penetration of Granular Materials

SHOCK COMPRESSION OF CONDENSED MATTER - 2019: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, 2020

Penetration depth is the most important parameter in terminal ballistics. Here only the case of projectiles penetrating granular medium is considered. Laboratory and field tests have shown that projectile characteristics such as mass, size, and nose shape, and target characteristics such as strength and density determine the depth of penetration. Analyses of full flight data recorded by onboard data acquisition system (G-Rec) are presented. These tests have revealed very high decelerations at impact with extensive particle fracture along the path of the projectile. Particle size distribution analysis of the sample collected from the projectile tip shows two to three orders of magnitude reduction in size. For similar impact velocities and target densities, Poncelet's coefficient does not vary with tip shape.

Europhysics Letters, 2009

The penetration by a gravity-driven impact of a solid sphere into a granular medium is studied by two-dimensional simulations. The scaling laws observed experimentally for both the final penetration depth and the stopping time with the relevant physical parameters are here recovered numerically without the consideration of any microscopic solid friction but with dissipative collisions only. Dissipative collisional processes are thus found as essential in catching the penetration dynamics in granular matter whereas microscopic frictional processes can only be considered as secondary effects.

Canadian Journal of Physics, 2004

We study the penetration of steel spheres dropped vertically into a container of loosely packed, small glass beads. We find that the penetration depth of the spheres increases linearly with the incident momentum of the projectile, but with a zero-momentum intercept that can be either positive or negative. This behavior can be understood by modelling the granular medium as a non-Newtonian fluid with a yield stress and an effective viscosity. We derive the scaling behavior of the viscosity and find agreement with our experimental results. 83.80.Fg, 47.50.+d Résumé : Nous étudions la pénétration de billes d'acier tombant verticalement dans un récipient contenant de la fine grenaille de verre. Nous observons que la pénétration augmente linéairement avec la quantité de mouvement du projectile, mais avec une valeur à l'origine non nulle qui peut être positive ou négative. Ce comportement peut se comprendre en modélisant le milieu comme un fluide non-Newtonien avec un effort d'écoulement et une viscosité efficace. Nous obtenons ici le bon comportement d'échelle de la viscosité et un bon accord avec les données expérimentales.

EPJ Web of Conferences

Due to the opacity of most granular materials, it is often desirable to have three dimensional (3D) particle tracking techniques beyond optical imaging to explore granular dynamics. Using inertial measurement units (IMU) embedded in a projectile, we obtain the trajectory of projectile impacting on a granular medium under microgravity using tri-axial acceleration and angular velocity data. In addition to the standard algorithm for reconstruction, we emphasize solutions to various sources of error to determine projectile trajectory accurately.

International Journal of Impact Engineering, 2015

This paper presents an experimental and numerical study on the penetration of granular materials by small-arms bullets. In the experimental tests, five different types of granular material (0-2 mm wet sand, 0-2 mm dry sand, 2-8 mm gravel, 8-16 mm crushed stone and 16-22 mm crushed rock) were impacted by four different types of smallarms bullets (7.62 mm Ball with a soft lead core, 7.62 mm AP with a hard steel core, 12.7 mm Ball with a soft steel core and 12.7 mm AP with a tungsten carbide core). The tests were carried out using different rifles to fire the projectiles, while the granular materials were randomly packed in a 320 mm diameter specially-designed steel tube. In all tests, the initial projectile velocity and the depth of penetration in the granular material were measured for each bullet type. In the numerical simulations, a discrete particle-based approach was used to model the behaviour of sand during bullet impact. The method works with discrete particles that transfer forces between each other through contact and elastic collisions, allowing for a simple and robust treatment of the interaction between the sand particles and the bullet which is represented by finite elements. An important observation from the study is that the penetration depth in dry sand is strongly influenced by deviation of the bullet from its original trajectory. Good agreement between the available experimental results and the numerical predictions is also in general obtained.

Mechanics Research Communications, 2015

In this study, a transparent sand surrogate was employed along with high-speed imagery to un-intrusively visualize the penetration of a spherical projectile into the center of a saturated granular target, representing angular sand, at speeds ranging between 60 and 150 m/sec. The transparent sand was made by saturating an angular granular fused quartz waste product with a matched refractive index pore fluid made of sucrose. A distinct zone of opacity was observed travelling ahead of the projectile. The opacity zone appears circular during initial penetration and transitions into the shape of an elongated cone in shots with higher initial velocities. Some healing was also observed with time and some increase in transparency was observed. Some of the opacity is attributed to dilatancy of the granular fused quartz during penetration, and healing is attributed to flow of pore fluid into the dilated zone.

Geotechnical Testing Journal, 2019

In this study, two experimental techniques are compared, for the purpose of visualizing projectile penetration at speeds ranging between 60 and 150 m/s into granular media. The two techniques are half space penetration into a transparent synthetic soil surrogate and quarter space penetration of an opaque natural sand and transparent soil surrogate, against an observation window. In both techniques a pneumatic projectile accelerator was employed to launch the projectiles and high-speed imagery was employed to visualize the penetration events, un-intrusively. Transparency in transparent targets was achieved by saturating angular fused quartz with a refractive index matched pore fluid made of sucrose. Comparison of both techniques suggests that their results are complimentary. In particular, the terminal depth of penetration is not significantly inhibited by shooting in quarter space. Additionally, both techniques permitted visualizing distinct dilations zones ahead and around penetration. Each technique offers a number of distinct advantages. In particular, half space penetration reduces the possibility of projectile diversion and is much safer, while quarter space penetration allows for visualizing penetration into opaque targets at a finer scale than that achieved in half space penetration.

Physical Review E, 2022

We consider the penetration dynamics of a vertical cylinder into a dry granular medium subjected to successive impacts. The depth of the impactor below the free surface z_N first evolves linearly with the impact number N and then follows a power-law evolution z_N ∝ N^1/3. The depth reached by the cylinder after a given number of impacts is observed to increase with the impact energy, but to decrease with its diameter and the density of the granular medium. We develop a model that accounts for the quasistatic and inertial granular forces applying on the cylinder to rationalize our observations. This approach reveals the existence of two intrusion regimes for large and small impact numbers, allowing all data to be rescaled on a master curve. Then, we extend the study to the effect of sidewalls on the dynamics of the impactor. We show that lateral confinement changes the dependence of the impactor depth on the impact number z_N(N). This effect is accounted for by considering the increase of the granular drag with the lateral confinement.

Materials

The aim of this work is to simulate the fragmentation of bullets impacted through granular media, in this case, sand. In order to validate the simulation, a group of experiments were conducted with the sand contained in two different box prototypes. The walls of the first box were constructed with fiberglass and the second with plywood. The prototypes were subjected to the impact force of bullets fired 15 m away from the box. After the shots, X-ray photographs were taken to observe the penetration depth. Transient numerical analyses were conducted to simulate these physical phenomena by using the smooth particle hydrodynamics (SPH) module of ANSYS® 2019 AUTODYN software. Advantageously, this module considers the granular media as a group of uniform particles capable of transferring kinetic energy during the elastic collision component of an impact. The experimental results demonstrated a reduction in the maximum bullet kinetic energy of 2750 J to 100 J in 0.8 ms. The numerical resul...

An object falling in a fluid reaches a terminal velocity when the drag force and its weight are balanced. Contrastingly, an object impacting into a granular medium rapidly dissipates all its energy and comes to rest always at a shallow depth. Here we study, experimentally and theoretically, the penetration dynamics of a projectile in a very long silo filled with expanded polystyrene particles. We discovered that, above a critical mass, the projectile reaches a terminal velocity and, therefore, an endless penetration.