M.J. Forrestal

An empirical equation for penetration depth of ogive-nose projectiles into concrete targets

Summary We conducted depth of penetration experiments with ogive-nose projectiles concrete targets with unconfined compressive strengths of nominally 14 MPa (2 ksi), 35 MPa (5 ksi), and 97 MPa (14 ksi). From our data and the data presented by Canfield and Clator [ J. A. Canfield and I. G. Clator , Development of a scaling law and techniques to investigate penetration in concrete. NWL Report No. 2057, U.S. Naval Weapons Laboratory, Dahlgren, VA (1966) ] [1], we developed an empirical equation for penetration depth of ogive-nose projectiles penetrating concrete targets at normal impact. Our penetration equation contains a single, dimensionless empirical constant that depends only on the unconfined compressive strength of the target. We determine the empirical constant from penetration depth versus striking velocity data with six sets of penetration data for striking velocities between 250 and 800 m/s. Predictions are in good agreement with all six data sets.

A split Hopkinson bar technique for low-impedance materials

An experimental technique that modifies the conventional split Hopkinson pressure bar has been developed for measuring the compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths such as elastomers at high strain rates. A high-strength aluminum alloy was used for the bar materials instead of steel, and the transmission bar was hollow. The lower Youngs modulus of the aluminum alloy and the smaller cross-sectional area of the hollow bar increased the amplitude of the transmitted strain signal by an order of magnitude as compared to a conventional steel bar. In addition, a pulse shaper lengthened the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance specimen. Experimental results show that the high strain rate, compressive stress-strain behavior of an elastomeric material can be determined accurately and reliably using this technique.

A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials

This paper presents a split Hopkinson pressure bar technique to obtain compressive stress-strain data for rock materials. This technique modifies the conventional split Hopkinson bar apparatus by placing a thin copper disk on the impact surface of the incident bar. When the striker bar impacts the copper disk, a nondispersive ramp pulse propagates in the incident bar and produces a nearly constant strain rate in a rock sample. Data from experiments with limestone show that the samples are in dynamic stress equilibrium and have constant strain rates over most of the test durations. In addition, the ramp pulse durations can be controlled such that samples are unloaded just prior to failure. Thus, intact samples that experience strains beyond the elastic region and postpeak stresses can be retrieved for microstructural evaluations. The paper also presents analytical models that predict the time durations for sample equilibrium and constant strain rate. Model predictions are in good agreement with measurements.

Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths

Summary We conducted perforation experiments with 25.4-mm diameter, 0.50-kg, 3.0-caliber-radius-head, ogival-nose rods and 178-mm-thick concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths. For impact velocities between 300 and 1100 m/s, our data showed that residual velocities for the 140 MPa concrete were less than 20% lower than that for the 48 MPa concrete. Thus, for a factor of three increase in unconfined compressive strength, we measured relatively minor changes in ballistic perforation performance. We explained these results qualitatively with post-test observations and triaxial material experiments with the 48 and 140 MPa concrete materials.

Penetration into soil targets

Summary We developed penetration equations for ogival-nose projectiles that penetrated soil targets after normal impact. The spherical cavity-expansion approximation simplified the target analysis, so we obtained closed-form penetration equations. To verify our model, we conducted field tests into soil targets with 23.1 kg, 95.25 mm diameter projectiles and obtained rigid-body decelerations and final penetration depths. Model predictions show good agreement with measurements for five tests conducted at an impact velocity of 280 ms −1 .

Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar.

We present pulse shaping techniques to obtain compressive stress-strain data for elastic-plastic materials with a split Hopkinson pressure bar. The conventional split Hopkinson pressure bar apparatus is modified by placing a combination of copper and steel pulse shapers on the impact surface of the incident bar. After impact by the striker bar, the copper-steel pulse shaper deforms plastically and spreads the pulse in the incident bar so that the sample is nearly in dynamic stress equilibrium and has a nearly constant strain rate in the plastic response region. We present analytical models and data that show a broad range of incident strain pulses can be obtained by varying the pulse shaper geometry and striking velocity. For an application, we present compressive stress-strain data for 4340 Rc 43 steel.

Penetration into ductile metal targets with rigid spherical-nose rods

We developed penetration equations for rigid spherical-nose rods that penetrate ductile metal targets. The spherical cavity-expansion approximation and incompressible and compressible elastic-perfectly plastic constitutive idealizations simplified the target analyses, so we obtained closed-form penetration equations. We compared predictions from our models with previously published penetration data and results from Lagrangian and Eulerian wavecodes.

Perforation of aluminum plates with ogive-nose steel rods at normal and oblique impacts

Abstract Perforation experiments were conducted with 26.3 mm thick, 6061-T651 aluminum plates and 12.9 mm diameter, 88.9 mm long, 4340 R c = 44 ogive-nose steel rods. For normal and oblique impacts with striking velocities between 280 and 860 m/s, we measured residual velocities and displayed the perforation process with X-ray photographs. These photographs clearly showed the time-resolved projectile kinematics and permanent deformations. In addition, we developed perforation equations that accurately predict the ballistic limit and residual velocities.

Penetration of confined aluminum nitride targets by tungsten long rods at 1.5–4.5 km/s

Abstract A series of 26 terminal ballistics experiments was performed to measure the penetration of simple confined aluminum nitride targets by a long tungsten rod. Impact velocities ranged from 1.5 to about 4.5 km/s. The experiments were performed in the reverse ballistic mode using a two-stage light-gas gun. Penetrator diameter, D, was 0.762 mm (0.030 in). The length-to-diameter ratio for the penetrator was L D = 20 for nearly all the tests and never less than L D = 15 . Primary instrumentation for these experiments was four independently timed, 450 kV flash X-rays. These X-rays provided four views of the penetrator-target interaction during the penetration event from which the following data were determined: p = penetration depth as a function of time, Lr = remaining length of penetrator as a function of time, as well as final penetration depth, target hole geometry, spatial distribution of the eroded rod material, etc. From these data, u = d p d t = speed of penetration into the target and ν c = d (L−L r ) d t = speed of “consumption” of the long rod were obtained.

Performance evaluation of accelerometers used for penetration experiments

We present a Hopkinson bar technique to evaluate the performance of accelerometers that measure large amplitude pulses, such as those experienced during projectile penetration tests. An aluminum striker bar impacts a thin Plexiglas or copper disk placed on the impact surface of an aluminum incident bar. The Plexiglas or copper disk pulse shaper produces a nondispersive stress wave that propagates in the aluminum incident bar and eventually interacts with a tungsten disk at the end of the bar. A quartz stress gage is placed between the aluminum bar and tungsten disk, and an accelerometer is mounted to the free end of the tungsten disk. An analytical model shows that the rise time of the incident stress pulse in the aluminum bar is long enough and the tungsten disk length is short enough that the response of the tungsten disk can be accurately approximated as rigid-body motion. We measure stress at the aluminum bar-tungsten disk interface with the quartz gage and we calculate rigid-body acceleration of the tungsten disk from Newtons Second Law and the stress gage data. In addition, we measure strain-time at two locations on the aluminum incident bar to show that the incident strain pulse is nondispersive and we calculate rigid-body acceleration of the tungsten disk from a model that uses this strain-time data. Thus, we can compare accelerations measured with the accelerometer and accelerations calculated with models that use stress gage and strain gage measurements. We show that all three acceleration-time pulses are in very close agreement for acceleration amplitudes to about 20,000 G.