International Journal of Impact Engineering

Published by Elsevier
Print ISSN: 0734-743X
Publications
The ability to capture projectiles intact at hypervelocities opens new applications in science and technology that would either not be possible or would be very costly by other means. This capability has been demonstrated in the laboratory for aluminum projectiles of 1.6 mm diameter, captured at 6 km/s, in one unmelted piece, and retaining up to 95% of the original mass. Furthermore, capture was accomplished passively using microcellular underdense polymer foam. Another advantage of capturing projectiles in an underdense medium is the ability of such a medium to preserve a record of the projectile's original velocity components of speed and direction. A survey of these experimental results is described in terms of a dozen parameters which characterize the amount of capture and the effect on the projectile due to different capture media.
 
The ability to capture hypervelocity projectiles intact opens a new technique available for hypervelocity research. A determination of the reactions taking place between the projectile and the capture medium during the process of intact capture is extremely important to an understanding of the intact capture phenomenon, to improving the capture technique, and to developing a theory describing the phenomenon. The intact capture of hypervelocity projectiles by underdense media generates spectra, characteristic of the material species of projectile and capture medium involved. Initial exploratory results into real-time characterization of hypervelocity intact capture techniques by spectroscopy include ultra-violet and visible spectra obtained by use of reflecting gratings, transmitting gratings, and prisms, and recorded by photographic and electronic means. Spectrometry proved to be a valuable real-time diagnostic tool for hypervelocity intact capture events, offering understanding of the interactions of the projectile and the capture medium during the initial period and providing information not obtainable by other characterizations. Preliminary results and analyses of spectra produced by the intact capture of hypervelocity aluminum spheres in polyethylene (PE), polystyrene (PS), and polyurethane (PU) foams are presented. Included are tentative emission species identifications, as well as gray body temperatures produced in the intact capture process.
 
This paper is concerned with constructing a high-G drop impact test condition for investigating the impact induced failure phenomenon of the solder ball array located in the chip packaged printed circuit board. An impact environment satisfying the JEDEC B service conditions was constructed using an instrumented drop tower tester. Fifteen wafer-level CSP chips were installed on a standard printed circuit board (PCB) with a dimension of 132 × 77 × 1 mm<sup>3</sup>. A number of these chip packaged PCB bonded with four different compositions of solder joints with or without lead using the surface mounted technology were studied. During the drop impact tests, the chip packaged PCB circuit was monitored using the multi-event detector system (ETAC) to examine whether circuit fails or not. In addition, the drop impact dynamic response of the PCB and the acceleration at the prescribed location of the drop table were recorded. Transient stress responses in the solder joints were provided using the LS-DYNA explicit code. Numerically predicted failure locations of the solder joints are close to those observed from actual drop impact experiments.
 
There is a need for more faithful simulation of space debris impacts on various space vehicles. Space debris impact velocities can range up to 14 km/sec and conventional two-stage light gas guns with moderately heavy saboted projectiles are limited to launch velocities of 7–8 km/sec. Any increases obtained in the launch velocities will result in more faithful simulations of debris impacts. It would also be valuable to reduce the maximum gun and projectile base pressures and the gun barrel erosion rate. In this paper, the results of a CFD study designed to optimize the performance of the NASA Ames 0.5″ gun by systematically varying seven gun operating parameters are reported. The optimum set of changes in gun operating conditions were predicted to produce an increase in muzzle velocity of 0.7 – 1.0 km/sec, simultaneously with a substantial decrease in gun erosion. Preliminary experimental data have validated the code predictions.
 
This paper describes the design, analysis and field test of a 0.7 m (28 in) conical shaped charge (CSC). The shaped charge was designed and analyzed using an analytical code for preliminary analyses and parametric studies to determine an approximate design that could satisfy the program requirements as well as the geometrical and weight constraints. The goal was to design a shaped charge that could produce approximately a 25 cm (9.8 in) diameter, 6 m (19.7 ft) deep hole in rock and concrete. Preliminary results, obtained with the analytical code, were verified independently with a hydrocode. After the shaped charge was designed and analyzed, it was fabricated and field tested by firing it into Tuff rock. The shaped charge fulfilled the program requirements and the test results closely agreed with the analyses.
 
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 for nearly all the tests and never less than . 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, = speed of penetration into the target and of “consumption” of the long rod were obtained.
 
Forty terminal ballistics experiments were performed to measure the penetration of simple confined boron carbide targets by long tungsten rods. Impact velocities ranged from 1.5 to about 5.0 km/s. The experiments were performed in the reverse ballistic mode using a two-stage light-gas gun. For tests with velocities 1.493 ≤ v ≤ 2.767 km/s, the penetrator diameter was 1.02 mm (0.040 inch). For tests with impact velocities v ≥ 2.778 km/s the penetrator diameter was 0.762 mm (0.030 inch). For tests in the velocity range 2.335 < v < 2.761 km/s both penetrator sizes were used. The length-to-diameter ratio for the penetrator was for all but the three highest velocity tests; in these three tests . 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 target hole geometry, spatial distribution of the eroded rod material etc. From these data, , of the long rod and final penetration depth were obtained.
 
The performance of confined AD995 Alumina against 20 tungsten long rod penetrators was characterized through reverse ballistic testing. The semi-infinite ceramic target was cylindrical with a diameter approximately 30 times the rod diameter. The target configuration included a titanium confinement tube and a thick, aluminum coverplate. The impact conditions ranged from 1.5 to 3.5 km/s with three or four tests performed at each of six nominal impact velocities. Multiple radiographs obtained during the penetration process allowed measurement of the penetration velocity into the ceramic and the consumption velocity, or erosion rate, of the penetrator. The final depth of penetration was also measured.Primary penetration approaches 75% of the hydrodynamic limit. Secondary penetration is very small, even at 3.5 km/s. The effective Rt value decreased from 90 kbar to 70 kbar with increasing impact velocity over the range of velocities tested.In tests in which the ratio of target diameter to penetrator diameter was reduced to 15, Rt, dropped by 30% to 50%. When a steel coverplate was used, total interface defeat occurred at 1.5 km/s.
 
The area of hypervelocity impact and associated high energy is one of extreme interest in the research community. A specific example of this emphasis is the US Air Force test facility at Holloman Air Force Base which specializes in the field of hypervelocity impact testing. This Holloman AFB High Speed Test Track (HHSTT) is currently working to increase the speed of their test vehicle to above Mach 10. As the test sled's speed has increased into the Mach 8.5 range, a material interaction has developed which causes “gouging” in the rails or the sled's “shoes” and this starts a process that can result in catastrophic failure. In the tests that do not structurally fail, the rails and shoes are damaged. Previous efforts in investigating this event have resulted in a choice of the most suitable computer code (CTH), and a model of the shoe/rail interaction. However, the specific materials present in this impact problem were not available in CTH. In this work, the specific materials present at the HHSTT (VascoMax 300 and 1080 Steel) will be characterized using the Split Hopkinson Bar Test and a Johnson–Cook constitutive model will be developed. The model will then be validated by comparison to a series of Taylor impact tests. The coating materials utilized on the rails at the HHSTT will also be evaluated using a Taylor impact test.
 
Results of an experimental series performed utilizing a three-stage gun to obtain precise material property equation of state (EOS) data for a titanium alloy (Ti6-Al-4V) at extreme pressure states that are not currently attainable using conventional two-stage light-gas gun technology is reported herein. What is new is the technique being implemented for use at engagement velocities exceeding 11 km/s. Shock-velocity in the target is being determined using 100 μm diameter fiber-optic pins and measuring shock transit times over a known distance between two parallel planes. These fiber-optic pins also indicate that the flyer-plate bow and tilt is comparable to two-stage light-gas gun technology. The thermodynamic state of the flyer plate prior to impact has also been determined both experimentally and calculationally. In particular, the temperature, and hence the density of the flyer-plate is also well known prior to impact. Results of these studies indicate that accurate Hugoniot information can be obtained using the three-stage light gas gun. This new test-methodology has extended the EOS of Ti6-Al-4V titanium alloy to stresses up to approximately 250 GPa.
 
The computational technique of Smoothed Particle Hydrodynamics (as implemented in the hydrocodes AUTODYN-2D and AUTODYN-3D) has been used to simulate the impact of hollow shaped charge jet projectiles onto stuffed Whipple bumper shielding. Due to limited availability of material models, the interim Nextel/Kevlar-Epoxy bumper was modelled as an equivalent thickness of aluminium. Stuffed Whipple bumper shields are used for meteoroid and debris impact protection of the European module of the International Space Station (the Columbus APM). A total of 56 simulations were carried out to investigate the impact processes occurring for shaped charge jet impact. Sensitivity studies were carried out on the influence of projectile shape, pitch, yaw and strength at 11 km/s to determine the range of debris cloud morphologies. The debris cloud structure was shown to be highly dispersed, and no projectile remnant was observed at the centre of the cloud. The mass of an aluminium sphere producing equivalent damage to a shaped charge jet projectile was in the range 1.5 to 1.75 times greater than the mass of the shaped charge jet projectile. Upon loading by the dispersed debris cloud, the interim bumper failed by spallation, producing fragments moving at 2 km/s or less. The fragments distorted the rear wall (pressure wall) of the shield but did not perforate it. The experimental data show rear wall deformation but to a lesser degree. Perforation of the rear wall, observed for one test, was not reproduced by the simulation. Nextel/Kevlar-epoxy material models are required to reproduce correctly the interim bumper failure under debris cloud loading.
 
To assist in the interpretation of crater populations on space-exposed surfaces from the Solar Maximum Satellite and the Long Duration Exposure Facility (LDEF), we conducted laboratory simulations of cosmic-dust impacts into aluminum 1100 targets with ∼3.2 mm diameter soda-lime projectiles at velocities (V) between 0.7 to 7 km/s. The resulting crater diameters (Dc) conform to current cratering equations, while crater depths (Pc) are somewhat deeper, yielding typical Pc/DC ratios of 0.58 at V > 6km/s. Similar values (Pc/Dc > 0.55) are found forcraters in aluminum surfaces retrieved from the Long Duration Exposure Facility, which were produced at impact velocities as high as 20 km/s. The value of Pc/Dc = 0.5 that is being used: by many should be abandoned; a Pc/Dc = 0.58 is recommended. Similarly, we demonstrate that mass loss of the target, as determined by pre- and post-shot weight measurements, can be almost an order of magnitude less than mass losses that would be inferred from crater-volume measurements. This difference is due to substantial internal deformation of the target which permits large volumes of material to be deformed, and displaced without physical ejection and dislodgment.
 
Projectiles with three different nose shapes (blunt, hemispherical and conical) have been used in gas gun experiments to penetrate 12 mm thick Weldox 460 E steel plates. Based on the experimental results, the residual velocity curves of the target material were constructed and compared. It was found that the nose shape of the projectile significantly affected both the energy absorption mechanism and the failure mode of the target during penetration. The ballistic limit velocities were about equal and close to 300 m/s for hemispherical and conical projectiles, while it was considerably lower for blunt projectiles. Blunt projectiles caused failure by plugging, which is dominated by shear banding, while hemispherical and conical projectiles penetrated the target mainly by pushing the material in front of the projectile aside. Also, the residual velocity curves were influenced by nose shape, partly due to the differences in projectile deformation at impact. The experimental study, given in this part of the paper forms the basis for explicit finite element analysis using the commercial code LS-DYNA presented in Part II of the paper.
 
In Part I of this paper, projectiles with three different nose shapes (blunt, hemispherical and conical) were used in gas gun experiments to penetrate 12 mm thick Weldox 460 E steel plates. It was found that the nose shape of the projectile severely affected both the energy absorption and the failure mode of the target structure during penetration. This part of the paper describes numerical simulations of the problem investigated experimentally. A constitutive model of viscoplasticity and ductile damage for projectile impact has earlier been developed and implemented in the explicit finite element code LS-DYNA. Numerical simulations involving this model have been carried out, and the results are compared with the experimental data. However, numerical problems associated with the element mesh were detected, and adaptive meshing was found necessary in order to obtain reliable results for conical projectiles. From the numerical simulations it is found that the LS-DYNA code is able to describe the different failure modes without any predefined defects in the element mesh if special care is taken, and good agreement is in general obtained between the numerical simulations and experimental results.
 
The charpy impact energy of Al–12Si and Al–12Si–3Cu cast alloys was measured in terms of the total absorbed energy. The standard charpy specimens 10×10×55 mm with a 2 mm V-notch were prepared from the castings. Effect of process variables and microstructural changes on the impact toughness of Al–12Si and Al–12Si–3Cu cast alloys was investigated. The results indicate that combined grain refined and modified Al–12Si–3Cu cast alloys have microstructures consisting of uniformly distributed α-Al dendrites, eutectic Al–Si and fine CuAl2 particles in the interdendritic region. These alloys exhibited better impact toughness in the cast condition compared with the same alloy subjected to only grain refinement or modification.
 
The crater morphology of impacts in the velocity range between 8 and 17 km/s has been investigated Glass projectiles with diameters between 20 ωm and 200 ωm were impacted on targets of gold, tungsten, iron and aluminum. Data have been compiled for the dependence of the crater diameter Dc and the crater depth Tc on the projectile velocity.
 
Increasing demands on orbital debris shielding systems have spurred efforts to develop shields that are more efficient than the standard single-bumper system. For example, for a given total bumper mass, experiments at velocities near 7 km/s have shown that a multiple-bumper system is more efficient than a single bumper in preventing wall perforation. However, the performance of multiple bumper systems at velocities above 7 km/s is unknown. To address this problem, the cadmium surrogate-material technique described by Schmidt et al. [1] has been extended to two dual bumper systems. A complete dimensional analysis is developed to include similarity requirements for the intermediate layers. Results of experiments, for impact angles of 0° and 45°, are presented and compared to those for single bumpers, along with limited results for an equal-mass four-bumper shield. Surprisingly, for scaled velocities near 16 km/s at normal incidence, a single bumper defeats impactors approximately 30% larger in diameter than multiple bumpers of the same total areal density.
 
An account of the life and work of the virtually unknown artillerist James Glenie is given and after a general biography of his difficult life, we briefly examine his engineering-mathematical contributions under some major separate headings. Glenie's lasting claim may well be the delivery of his own Antecedental Calculus, though this is no more than introduced here; some description of its inception and use is given but the justification for his immense claims for it remains to be fully assessed. Other papers of Glenie are simply listed here.
 
A piece of written printed evidence informs us that Richard Jack [W. johnson, Int. J. Impact Engng, 12(1), 123–140 (1992)] was on a British expedition sent out to attack French Guadaloupe and Martinique in 1758/9 (see Fig. 1). Jack, however, died in this latter year and his will was proved, by his wife, on 8 May 1759. As the French Island of Guadaloupe capitulated on 1 May 1759, reflection leads one to realize that Jack could not have been present during the final days of fighting for this island. This latter deduction is examined and various facets of its implications are considered. Among other things it is considered that there is a certain lack of credibility about Jack's presence in the Caribbean in the years mentioned.This Note is a companion to a paper [W. johnson, Int. J. Impact Engng, 13(4), 567–574 (1991)] about Robins' misjudgment of the destination of the British Caribbean expedition of 1739 and the unsuccessful British assault on Cartagena, in 1741, in which the famous novelist-surgeon, Tobias Smollett participated.
 
Static identation and low and high velocity impact tests are conducted on specimens with a circular clamped test area. Monolithic A1 2024-T3 and 7075-T6, various grades of Fibre Metal Laminates (FML), and composites are tested. The energy to create the first crack for FML with aramid and carbon fibres is comparable to fibre reinforced composite materials and is relatively low compared to A1 2034-T3 and FML with R-glass fibres (GLARE). GLARE laminates can show a fibre critical or aluminium critical failure mode. The dent depth after impact of FML is approximately equal to that of the monolothic aluminium alloy. The damage size of FML after impact is considerably smaller than of glass and carbon fibre composite materials. The maximum central deflection during low velocity impact loading is approximately equal to the static deflection at the same energy (i.e., area under load-deflection curve). This deflection can be modelled using the simplified Von Kármán equations neglecting the contribution of the in-plane displacements. For these calculations the shape of the specimen under load was measured. This shape was approximately independent of the central deflection and the type of material.
 
Richard Jack (flourished 1742–1756) a teacher of mathematics, gave uncorroborated evidence in the Court Martial of Sir John Cope and contributed to the strength of the allegation of the latter's cowardice at the battle of Preston-pans in the second Jacobite Rebellion of 1745. This last matter was a significant part of the Bibliography of British Mathematics and its Applications: Part II, 1701–1760, by Wallis and Wallis, of which the principal subject was the 18th century military engineer-scientist-political pamphleteer Benjamin Robins. As published knowledge about Jack and his work in standard biographies is either miniscule or non-existent, this paper attempts to increase his visibility.
 
Some remarks in favour of the start-up of a European Solids Mechanics Conference are first made.A very brief outline of Robins' life is then given, followed by a review of his collected papers. He was born in Bath, England, in 1707 and died at Fort St David, India, in 1751. This should place in time the man with whom the lecture is concerned. Several scientific topics to which he made contributions.—the ballistic pendulum, the whirling machine, air resistance sustained by solid shot and the Magnus effect—are described about the changes in his professional inclinations and personal ambitions with time.There was, and has been since the 1730s, controversy about Robins' work between Continental and English scientists. The author briefly details some of the exchanges on this score and uses it to suggest that 1992 is a year after which greater efforts might be made to attain more objective opinions on the history of European mechanics than hitherto. Some of the difficulties which stand in the way are noted and a few suggestions are made for improving the situation.That workers in mechanics come better to appreciate their subject's history is a theme here explicitly and implicitly advocated.
 
Particle launch experiments were performed to study application of the enhanced hypervelocity launcher (EHVL), i.e. the third-stage addition to the two-stage gun, for launching micron to millimeter sized particulates at velocities unobtainable with a standard two-stage light gas gun launch. Three types of particles or fliers were tested along with several barrel designs. For micron scale particles fine-grain polycrystalline ceramics were impacted and fractured, launching particulate clouds at velocities of 15 km/s. Multiple titanium particles ∼400 μm diameter embedded in plastic were “shotgun” launched to velocities of 10 km/s. Flier plates of 3 mm diameter by 1 mm thick Ti6Al4V were launched to 19 km/s. All experiments used a second-stage projectile with graded density facing impacting a flier in an impact generated acceleration reservoir. This paper describes the modification and adaptation of the Sandia EHVL to provide micrometeoroid simulation capabilities.
 
We review “A brief description of the Modern System of Small Arms as adopted in the various European armies” by J. Schön and its introduction by A. Mordecai to indicate that they summarise the technology of both firearms and their manufacturing technology in the mid 19th century, a critical point in their development.
 
This paper is concerned with the material behavior of Ti-6-22-22S titanium alloy as a function of strain rate and temperature. Results of measurements of the material behavior at compressive loading under uniaxial stress conditions over a strain rate range of 10−4 s−1 to 103 s−1 and under uniaxial strain conditions at shock-wave loading with a strain rate of ∼105 s−1 are presented. The test temperature was varied from 20°C to 620°C. The uniaxial stress compression tests revealed a rather strong strain rate sensitivity and temperature dependence of failure and flow stresses. In plate impact tests, the dynamic yield stresses at plastic deformations of 0% and 0.2% and dynamic strength (spall strength) were measured as a function of temperature. The strain-rate and the temperature dependencies of the yield stress obtained from the uniaxial stress tests and from the shock-wave experiments are in good agreement and indicate that the thermal activation mechanism of plastic deformation of the alloy is maintained at strain rates up to 105 s−1 at least. The relative decrease in the yield strength in the plate impact tests much exceeds the spall strength decrease. That is considered as an evidence, that the spall strength magnitude is influenced more by the contribution of the nucleation of voids rather than by the growth of voids.
 
An Eulerian wavecode was used to simulate the impact, penetration, and detonation of a 23-mm high-explosive projectile into a water-filled tank. The pressure–time response is compared with results from an experiment conducted by Lundstrom and Andersen (Symp. on Shock and Wave Propagation, Fluid–Structure Interaction, and Structural Responses, 1989). Computed peak pressures and impulses compare well with the experimental values.
 
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.
 
In order to obtain dynamic mechanical properties of carbon materials, i.e., two kinds of polycrystalline graphites and a C/C composite, plate impact experiments with simultaneous three poly vinylidene difluoride (PVDF) stress gauges were conducted using a one-stage powder gun system. By this measurement system, Hugoniot curves, rarefaction wave velocities and stress–strain (S–S) curves could be obtained. The Hugoniot curves were valid, rarefaction wave velocities increased with the plateau stress in the specimen, and the slope of the S–S curve was consistent with that of the Hugoniot curve. These dynamic mechanical properties of the carbon materials are useful not only for the understanding of the dynamic behavior but also for impact fracture behavior.
 
The dynamic crushing behavior of 2D cellular structures is studied by finite element method using ABAQUS/Explicit code. The influences of cell irregularity and impact velocity on the deformation mode and the plateau crush pressure are investigated. Two irregularity-generating methods are used. One is the disorder of nodal locations of a regular hexagonal honeycomb and the other is based on the 2D random Voronoi technique. The results show that the deformation in an irregular honeycomb is more complicated than that in a regular honeycomb due to its cell irregularity. At a low impact velocity, a Quasi-static mode with multiple random shear bands appears, while at a higher impact velocity, a Transitional mode is found, i.e., a mode with localized random shear bands and layerwise collapse bands. Finally, at a much higher impact velocity, a Dynamic mode appears with a narrow localized layerwise collapse band near the crushed end. The velocities for transition between modes are evaluated and expressed by empirical equations. Deformation anisotropy is found in the response of disordered honeycombs but it vanishes with the increase in the irregularity. Statistical results show that the relative energy absorption capacity of cellular materials can be improved by increasing their cell irregularity. This effect is obvious especially at an impact velocity near the mode transition velocity.
 
A statistical model of a tensile strength is implemented into the SALE-2D hydrocode. The well-tested 2D code has been modified to handle multi-material problems and strength effects. The key element of the model is the Grady-Kipp-Melosh kinetic model of tensile strength, adopted to hydrocode calculations. The resulting numerical algorithm allows to estimate general features of the atmospheric breakup of meteoroids and fracturing around impact craters.
 
This paper presents recent developments in the three-dimensional EPIC-3 code and the two-dimensional EPIC-2 code. The EPIC-3 work provides a new symmetric arrangement of tetrahedral elements which is more accurate than the traditional non-symmetric arrangement. The EPIC-2 work provides an algorithm and examples of fragment distributions which occur after impact. Included are numbers of fragments for various sizes, masses, momenta, and kinetic energies.
 
Spherical soda-lime glass projectiles 50, 150, 1000 and 3175 μm in diameter (Dp) in aluminum targets (series 1100; “annealed”) of variable thickness T, were used to determine how the penetration-hole diameter (Dh) varied as a function of Dp/T at a constant impact velocity of 6 km/s. The target thickness ranged from infinite half-space geometries to 0.8 μm thick foils. Virtually identical morphologies characterize the penetration holes, no matter what projectile size, at equivalent Dp/T conditions. The relative hole diameter (Dh/Dp) decreases systematically with increasing Dp/T from Dh ≅ 4Dp for massive targets, to Dh = Dp for very thin foils. A modest dependence on the absolute projectile size is observed; comparatively small cracters, yet relatively large penetration holes are produced by the smallest (50 μm) impactors. Nevertheless, linear dimensional scaling seems suitable for first-order estimates of Dp from the measurement of Dh and T on space-exposed surfaces. The projectile fragments and the debris dislodged from the target were intercepted by witness plates that were located behind the target. The dispersion angle of this debris cloud depends on the thickness of the target. In addition, millimeter-sized impactors are collisionally fragmented with greater ease than small impactors. Furthermore, we observe that systematic changes in the specific energy of dislodged projectile and target material occur as a function of Dp/T. While linear scaling of target and projectile dimensions is a useful framework to explain many observations and associated shock processes, we suggest that consideration of the absolute and relative shock-pulse duration in the projectile (tp) and target (tt) may ultimately be the more useful approach. It implicitly accounts for all dimensions and, additionally, for specific impact velocities and pertinent material properties, via equations-of-state, for the impacting pair.
 
The high strain rate (600 s−1) compression deformation of a 316 L metallic hollow sphere (MHS) structure (density: 500 kg m−3; average outer hollow sphere diameter: 2 mm and wall thickness: 45 μm) was determined both numerically and experimentally. The experimental compressive stress–strain behavior at high strain rates until about large strains was obtained with multiple reloading tests using a large-diameter compression type aluminum Split Hopkinson Pressure Bar (SHPB) test apparatus. The multiple reloading of MHS samples in SHPB was analyzed with a 3D finite element model using the commercial explicit finite element code LS-DYNA. The tested MHS samples showed increased crushing stress values, when the strain rate increased from quasi-static (0.8 × 10−4 s−1) to high strain rate (600 s−1). Experimentally and numerically deformed sections of MHS samples tested showed very similar crushing characteristics; plastic hinge formation, the indentation of the spheres at the contact regions and sphere wall buckling at intermediate strains. The extent of micro-inertial effects was further predicted with the strain rate insensitive cell wall material model and with the strain rate sensitive behavior of MHS structure similar to that of the cell wall material. Based on the predictions, the strain rate sensitivity of the studied 316 L MHS sample was attributed to the strain rate sensitivity of the cell wall material and the micro-inertia.
 
The aim is to investigate the influence of 3D effects on the efficiency of three processes for percussive rock drilling, viz., hammer drilling, down-the-hole drilling and churn drilling, each based on the use of tube-shaped members. A 3D axisymmetric finite element study is carried out for systems with idealised geometries. The efficiencies obtained are compared with formulae obtained from 1D analyses. It is found that the efficiencies based on 3D analyses are generally slightly lower than those based on 1D analyses. The difference is typically about 4% for hammer drilling, of the order of a percent or less for down-the-hole drilling, and practically non-existent for churn drilling. In the case of hammer drilling, the reduction of efficiency due to 3D effects is found to be slightly larger for tubes with relatively thin walls than for tubes with massive cross-sections. The lower efficiency in 3D is partially due to contributions to the kinetic and potential energies from components of velocity and stress which do not promote the performance of work on the rock. It is concluded that from a practical point of view, there is no need of 3D corrections of the 1D results for efficiency except possibly in the case of hammer drilling.
 
A totally conservative Eulerian 3D numerical code which conserves mass, momentum and energy both in the source and remap steps is developed. Mass, momentum and kinetic energy are conserved simultaneously during the remapping. The use of special form of linear viscosity makes the code more tolerant to the time step, leaving the second order of accuracy. Multimaterial flows including those contaminated by dust particles may be investigated using this program. The performance of the code is illustrated by modeling the Shoemaker-Levy 9 impact against Jupiter. Penetration of nonuniform fragments with complex structure into the Jovian atmosphere is investigated.
 
A high-speed stereo-vision system is employed to quantify dynamic material response during buried blast loading. Deformation measurements obtained using 3D image correlation of synchronized, patterned stereo-vision images obtained with an inter-frame time in the range 16 μs ≤ t ≤ 40 μs indicate that (a) buried blast loading initially induces highly localized material response directly under the buried blast location, with severity of the blast event a strong function of depth of explosive burial, (b) for relatively shallow (deep) depth of explosive burial, plate surface velocities and accelerations exceed 220 m s−1 (100 m s−1) and 6 × 106 m s−2 (1.5 × 106 m s−1) during the first 30 μs (80 μs) after detonation, respectively.In addition, full-field plate deformation measurements demonstrate that the specimen experienced (c) measured effective strains exceeding 8% (5%) and effective strain rates exceeding 4000 s−1 (1500 s−1) during the first 50 μs (80 μs), respectively and (d) a blast-induced, circularly symmetric, transient bending wave was induced in the plate that travels with radial velocity of Mach 2 (1.25) during blast loading.By combining the Cowper–Symonds constitutive relation with full-field strain and strain rate measurements, well-defined yield boundaries are evident on the plate surface during blast loading; the presence of spatial gradients in yield stress has the potential to affect plate failure processes during transient blast loading events.
 
Degree of asymmetry versus time difference between opposing strain gauges. Degree of asymmetry is defined as the difference in lines RR 1 and RR 4 .
Comparison of calculational simulations (indicated as faint line) of the velocity history in experiment L1 with the measured velocity history (dark line).
Computational simulation of the velocity history in experiment L1 indicating the effect of yield strength on the simulations.
In this study we provided an experimental test bed for validating features of the Arbitrary Lagrangian Eulerian Grid for Research Applications (ALEGRA) code over a broad range of strain rates with overlapping diagnostics that encompass the multiple responses. A unique feature of the ALEGRA code is that it allows simultaneous computational treatment, within one code, of a wide range of strain-rates varying from hydrodynamic to structural conditions. This range encompasses strain rates characteristic of shock-wave propagation (107/s) and those characteristics of structural response (102/s). Most previous code validation experimental studies, however, have been restricted to simulating or investigating a single strain-rate regime. What is new and different in this investigation is that we have performed well-controlled and well-instrumented experiments, which capture features relevant to both hydrodynamic and structural response in a single experiment. Aluminum was chosen for use in this study because it is a well-characterized material. The current experiments span strain rate regimes of over 107/s to less than 102/s in a single experiment. The input conditions were extremely well defined. Velocity interferometers were used to record the high strain-rate response, while low strain rate data were collected using strain gauges. Although the current tests were conducted at a nominal velocity of ∼ 1.5 km/s, it is the test methodology that is being emphasized herein. Results of a three-dimensional experiment are also presented.
 
In spite of its importance to the aerospace and automobile industries, little or no attention has been devoted to the accurate modelling of the shot-peening process. It is therefore the purpose of this study to conduct dynamic elasto-plastic finite element analysis of the process using a realistic multiple impingement model using a rate sensitive material. In this analysis, we implement a novel “symmetry cell” approach to examine the impact effect of a large number of rigid and deformable shots on a high-strength steel target made from AISI 4340. A number of convergence tests, which account for element size and stiffness of contact elements, were carried out. In addition, efforts were devoted to determine the appropriate material damping parameters needed to dampen unwanted numerical oscillations associated with the explicit solver of LS-DYNA for this class of problems. The model was used to predict the effect of peening intensity and coverage upon the mechanically induced residual stress field and the plastic zone development for different classes of materials.
 
In this paper we present the results from a combined experimental, analytical, and computational penetration program. First, we conducted a series of depth-of-penetration experiments using 0.021 kg, 7.11 mm diameter, 71.12 mm long, vacuum-arc-remelted 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.5 and 1.3 km/s using a 20 mm powder gun into 254 mm diameter, 6061-T6511 aluminum targets with angles of obliquity of 15°, 30°, and 45°. Next, we employed the initial conditions obtained from the experiments with a new technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function derived from the dynamic expansion of a spherical cavity (which accounts for compressibility, strain hardening, strain-rate sensitivity, and a finite boundary) to represent the target. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test radiographs.
 
In this paper, we document the results of a combined experimental, analytical, and computational research program that investigates the penetration of steel projectiles into limestone targets at oblique angles. We first conducted a series of depth-of-penetration experiments using 20.0 g, 7.11-mm-diameter, 71.12-mm-long, vacuum-arc-remelted (VAR) 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.4 and 1.3 km/s using a 20-mm powder gun into 0.5 m square limestone target faces with angles of obliquity of 15° and 30°. Next, we employed the initial conditions obtained from the experiments with a technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function based on the dynamic expansion of a spherical cavity to represent the target. Due to angle of obliquity we developed a new free surface effect model based on the solution of a dynamically expanding spherical cavity in a finite sphere of incompressible Mohr–Coulomb target material to account for the difference in target resistance acting on the top and bottom sides of the projectile. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test castings of the projectile trajectories.
 
This paper describes an experimental, analytical and numerical investigation of the penetration and perforation of circular Weldox 460 E steel plates with different thicknesses struck by a blunt projectile at various impact velocities. In the experimental tests, a compressed gas gun was used to launch the sabot mounted projectile at impact velocities well above and just below the ballistic limit of the target plates. Nominal hardness, diameter, length and mass of the projectile were kept constant in all tests. The target plate was clamped in a rigid circular frame, and the thickness was varied between 6 and . Measurements were made of the initial and residual velocities, and the ballistic limit velocity and the residual versus impact velocity curve were obtained for each target thickness tested. In addition, a digital high-speed camera system was used to photograph the penetration event. The experimental findings from the tests are presented and discussed, and the results are used to assess some empirical, analytical and numerical models. It is shown that especially the results obtained by the finite element approach are encouraging in terms of predicting the response of the plates examined.
 
To study the high strain rate shear behaviour of Ti–6Al–4V, hat-shaped specimens have been used in a compression split Hopkinson bar set-up. With this technique, highly concentrated shear strains are obtained which eventually cause strain localization and adiabatic shear bands (ASB). Because of the complex stress distribution in the specimen, interpretation of the experimental results is not straightforward. In this paper, results of a comprehensive experimental and numerical study are presented, aiming at a more judicious use of hat-shaped specimens and a fundamental understanding of the obtained results. Specimens with different dimensions are considered. It is found that the width of the shear region and the radius of the corners are the most important parameters. The first mainly affects the homogeneity of stresses and deformations in the shear zone and the presence of a hydrostatic stress next to the shear stress, while the latter primarily governs the initiation of the ASB. The relation between the global measured response and the local material behaviour is studied. It is shown that, within certain limits, the shear stress in the shear region can be extracted from the measured force. Several experiments which have been interrupted at a certain level of deformation have been carried out. The microstructure could thus be observed at different stages: onset of strain localization, formation of ASBs, initiation and propagation of micro-cracks.
 
In this study, Ti–6Al–4V and Al plates were joined by explosive welding at various explosive loads. Tensile-shear, bending, hardness, microstructure and corrosion behaviours of the explosively joined samples were investigated. At the end of the tensile-shear tests carried out according to ASTM D 3165-95 standard, no seperation was observed in the interfaces of the joined samples. The results of the bending tests also showed no sign of any distinctive seperation, crack and tear in the interfaces. The highest hardness values were measured in regions next to interfaces. The optical microscope and SEM examinations revealed that an increment in wavelength and amplitude was observed with increasing explosive load. It is seen from the corrosion test results that materials loss was high at the beginning of the corossion tests but the rate of material loss decreased later on. Furthermore, increasing deformation with increasing explosive load increased the materials loss in corrosion tests.
 
The core of the 7.62-mm, armor-piercing APM2 projectile is very strong, but also brittle. A combined analytical, numerical and experimental investigation examined the conditions to fracture the core. The analytical model is based on a Timoshenko beam analysis, where the projectile is idealized as a semi-infinite cylinder. A 3-D numerical model of the core, impacting against the edge of a metallic plate, was then used to investigate transient effects, the influence of constitutive model assumptions, and the influence of target properties on the magnitude of projectile bending strains. Results are then compared to experimental data. Numerical simulations of the full (jacketed) projectile were also investigated, and it is demonstrated that the erosion strain of the jacket is a critical parameter for successful simulations.
 
The effects of heat treating Inconel 718 on the ballistic impact response and failure mechanisms were studied. Two different annealing conditions and an aged condition were considered. Large differences in the static properties were found between the annealed and the aged material, with the annealed condition having lower strength and hardness and greater elongation than the aged. High strain rate tests show similar results. Correspondingly large differences were found in the velocity required to penetrate material in the two conditions in impact tests involving 12.5 mm diameter, 25.4 mm long cylindrical Ti-6-4 projectiles impacting flat plates at velocities in the range of 150–300 m/s. The annealed material was able to absorb over 25 percent more energy than the aged. This is contrary to results observed for ballistic impact response for higher velocity impacts typically encountered in military applications where it has been shown that there exists a correlation between target hardness and ballistic impact strength. Metallographic examination of impacted plates showed strong indication of failure due to adiabatic shear. In both materials localized bands of large shear deformation were apparent, and microhardness measurements indicated an increase in hardness in these bands compared to the surrounding material. These bands were more localized in the aged material than in the annealed material. In addition, the annealed material underwent significantly greater overall deformation before failure. The results indicate that lower elongation and reduced strain hardening behavior lead to a transition from shear to adiabatic shear failure, while high elongation and better strain hardening capabilities reduce the tendency for shear to localize and result in an unstable adiabatic shear failure. This supports empirical containment design methods that relate containment thickness to the static toughness.
 
The plastic deformation behavior of nickel–iron alloy Inconel 718 in shear was measured at strain rates of 0.01 s−1 and up to 3000 s−1 with a quasistatic torsion machine and a split torsional Hopkinson bar, respectively. The measurements were analyzed to determine Johnson–Cook parameters and obtain material constitutive information needed for finite element simulations.
 
An experimental investigation has been performed to investigate the ballistic performance of ceramic tiles as a function of the extent of confinement. A secondary objective of the study was to generate experimental data for ceramic modelling validation studies. Two impact velocities were used for the testing, nominally 1.52 and 1.79 km/s. The depth-of-penetration (DOP) into the backup steel cylinder was the measure of penetration performance. 99.5%-pure aluminium oxide tiles, 2.54-cm thick, were used for the study. Confinement was changed by varying the type and thickness of a cover plate. Differential ceramic tile performance, calculated from the DOP measurements and baseline penetration into semi-infinite steel, varied in the range ≈ 1.5-2.8, depending upon the type of confinement and the impact velocity. The data are compared with other data in the literature, and conclusions are made concerning ceramic tile performance as a function of confinement and impact velocity.
 
This paper presents an experimental and numerical investigation on low velocity perforation (in the velocity range 3.5–15.8 m/s) of AA5083-H116 aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical blunt-nosed projectile. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA in order to investigate the effects of anisotropy, dynamic strain aging (causing negative strain rate sensitivity) and thermal softening in low velocity impacts on the present aluminium alloy. Dynamic strain aging has been shown to influence both the predicted force level and fracture, while thermal softening only influences fracture prediction. No significant effect of plastic anisotropy has been observed.
 
The interest regarding use of aluminium alloys in lightweight protective structures is today increasing. Even so, the number of experimental and computational investigations giving detailed information on such problems is still rather limited. In this paper, perforation experiments have been performed on AA5083-H116 aluminium plates with thicknesses varying between 15 and 30 mm impacted by 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and a digital high-speed camera system was used to photograph the penetration and perforation process. Based on these measurements, impact versus residual velocity curves of the target plates were constructed and the ballistic limit velocity of each target was obtained. An analytical perforation model from the open literature is then used to predict the ballistic limit velocity, and excellent agreement with the experimental data is found. The experimental results are finally compared to similar experiments on steel and concrete targets, and the capacity of the different materials is evaluated in relation to total weight.
 
The stress–strain behaviour of the aluminium alloy 7075 in T651 temper is characterized by tension and compression tests. The material was delivered as rolled plates of thickness 20 mm. Quasi-static tension tests are carried out in three in-plane directions to characterize the plastic anisotropy of the material, while the quasi-static compression tests are done in the through-thickness direction. Dynamic tensile tests are performed in a split Hopkinson tension bar to evaluate the strain-rate sensitivity of the material. Notched tensile tests are conducted to study the influence of stress triaxiality on the ductility of the material. Based on the material tests, a thermoelastic–thermoviscoplastic constitutive model and a ductile fracture criterion are determined for AA7075-T651. Plate impact tests using 20 mm diameter, 197 g mass hardened steel projectiles with blunt and ogival nose shapes are carried out in a compressed gas-gun to reveal the alloy's resistance to ballistic impact, and both the ballistic limit velocities and the initial versus residual velocity curves are obtained. It is found that the alloy is rather brittle during impact, and severe fragmentation and delamination of the target in the impact zone are detected. All impact tests are analysed using the explicit solver of the non-linear finite element code LS-DYNA. Simulations are run with both axisymmetric and solid elements. The failure modes are seen to be reasonably well captured in the simulations, while some deviations occur between the numerical and experimental ballistic limit velocities. The latter is ascribed to the observed fragmentation and delamination of the target which are difficult to model accurately in the finite element simulations.
 
Top-cited authors
Odd Sture Hopperstad
  • Norwegian University of Science and Technology
Gerald Nurick
  • University of Cape Town
Norman Jones
  • University of Liverpool
Tore Børvik
  • Norwegian University of Science and Technology
Hong Hao
  • Curtin University