Danny J. Frew

Pulse Shaping Techniques for Testing Brittle Materials with a Split Hopkinson Pressure Bar

We present pulse shaping techniques to obtain compressive stress-strain data for brittle materials with the split Hopkinson pressure bar apparatus. The conventional split Hopkinson pressure bar apparatus is modified by shaping the incident pulse such that the samples are in dynamic stress equilibrium and have nearly constant strain rate over most of the test duration. A thin disk of annealed or hard C11000 copper is placed on the impact surface of the incident bar in order to shape the incident pulse. After impact by the striker bar, the copper disk deforms plastically and spreads the pulse in the incident bar. We present an analytical model and data that show a wide variety of incident strain pulses can be produced by varying the geometry of the copper disks and the length and striking velocity of the striker bar. Model predictions are in good agreement with measurements. In addition, we present data for a machineable glass ceramic material, Macor, that shows pulse shaping is required to obtain dynamic stress equilibrium and a nearly constant strain rate over most of the test duration.

PENETRATION OF GROUT AND CONCRETE TARGETS WITH OGIVE-NOSE STEEL PROJECTILES

Abstract We conducted depth of penetration experiments into grout and concrete targets with ogive-nose steel projectiles. Powder guns launched 0.064 kg, 12.9 mm diameter projectiles into grout targets with unconfined compressive strengths of 13.5 M Pa (2.0 ksi) and 21.6 MPa (3.1 ksi). For the concrete targets, powder guns launched projectiles with length-to-diameter ratios of 10; a 0.48 kg, 20.3 mm diameter rod, and a 1.60 kg, 30.5 mm diameter rod. Concrete targets had unconfined compressive strength of 62.8 M Pa (9.1 ksi) for the 0.48 kg rods and unconfined compressive strength of 51.0 MPa (7.4 ksi) for the 1.60 kg rods. For these experiments, penetration depth increased as striking velocity increased until nose erosion became excessive. Thus, we determined experimentally the striking velocities corresponding to maximum penetration depths. Predictions from a previously published model are in good agreement with data until nose erosion becomes excessive.

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.

Dynamic Compressive Response and Failure Behavior of an Epoxy Syntactic Foam

The high-strain-rate compressive behavior of an epoxy syntactic foam is examined in this study. A pulse-shaped split Hopkinson pressure bar (SHPB), modified for low-impedance material testing, was used to ensure that the samples deformed under dynamic equilibrium and at a nearly constant strain-rate. Dynamic stress equilibrium in the specimen was monitored for each experiment using piezoelectric force transducers mounted close to the specimen end-faces. Quasi-static experiments were also conducted to demonstrate rate effects of the foam, as well as to study its failure behavior. It was determined that the compressive strength of the foam increased with strain rate up to a transition strain rate of between 550 and 1030 s 1. For experiments conducted at strain rates above this transition range, strain-rate-induced damage caused the compressive strength of the foam to decrease. Based on the experimental results, a constitutive model with strain-rate and damage effects was developed, which described the test data well.

Penetration into low-strength (23 MPa) concrete: target characterization and simulations

A combined experimental, analytical, and computational research and development program investigates the penetration of steel projectiles into low-strength concrete. Laboratory-scale material property tests conducted at the US Army Waterways Experiment Station on the concrete provide the data used in parameter estimation for a geomaterial constitutive model. The experiments and the model are described as well as the procedure used to fit the material model to the experimental data. The model accurately reproduces the data and predicts experimental results not used in the evaluation of model constants. The model, used in conjunction with an explicit transient dynamic finite element code, accurately predicts deceleration and depth of penetration of 3 CRH ogive-nosed 4340 steel penetrators.

Dynamic small strain measurements of a metal specimen with a split Hopkinson pressure bar

When a conventional split Hopkinson pressure bar (SHPB) is used to investigate the dynamic flow behavior of ductile metals, the results at small strains (ɛ≲2%) are not considered valid owing to fluctuations associated with the early portion of the reflected signal and the nonequilibrated stress state in the specimen. When small-strain behavior is important, such as in the case of determining the elastic behavior of materials, the accuracy of a conventional SHPB is not acceptable. Using a pulse-shaping technique, the dynamic elastic properties can be determined with a SHPB, as well as the dynamic plastic flow. We present a description of the experimental technique and the experimental results for a mild steel. The dynamic compressive stress-strain curve is composed of a lower strain-rate elastic portion and a high strain-rate plastic flow portion.

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.