Impact fragmentation of high-velocity compact projectiles on thin plates: a physical and statistical characterization of fragment debris

The high-velocity impact of a projectile onto a structure results in the creation and energetic expulsion of fragments of the interacting materials. The nature of this fragment debris is of concern in certain applications. Although more broadly applicable, the present study is motivated by a need to characterize the size and velocity distribution of fragments generated by orbital debris impacting external components of spacecraft structure, such as shielding and radiators. In this effort, statistical relations are developed to predict size, momentum and trajectory distributions of the debris. The underlying physics applied are those used in the fields of impact mechanics, thermodynamics of shocks, and statistical fragmentation. Equations from impact mechanics lead to predictions for mass, global momentum, and excess energy of the fragment debris. Relations from shock thermodynamics are developed to partition the initial kinetic energy into thermal and mechanical energies, and therefore to predict mass fractions of solid, liquid and vapor components and the subsequent dispersing motion of this fragment debris. Statistical methods of the energy-based Maxwell-Boltzmann type are pursued to characterize the inherently stochastic fragmentation event, emphasizing the extremes of fragment size and velocity. Computational simulations of impact events and data from impact fragmentation experiments are exploited in validating the underlying theoretical assumptions and the resulting impact fragmentation model.     

The effect of geometric scale on impact induced fragmentation, and its application to the design of dual plate armor

An analysis is presented which predicts that, for a fixed impact velocity, impact induced fragmentation becomes more severe as geometric scale increases. Test data is presented which supports this prediction, and which allows calculation of material dependent coefficients. The analysis was based on a minimization with respect to radius, for an expanding body, of a total energy density term (expansion kinetic energy per unit volume plus surface energy per unit volume). The test configuration was a steel sphere impacting an aluminum plate, with fragmentation recorded by a stack of spaced witness panels. The tests were run at full and half scale. Correlation between testing and analysis was achieved for the number of fragments perforating the front witness panel when a term analogous to a threshold energy was introduced. While the fragment count showed a dependence on geometric scale, the relative depth of penetration (number of witness panels perforated) did not. This suggested that the targets were fragmented, but that the projectile remained in one piece. A reduction in penetration depth with increasing impact velocity was seen, and was attributed to increased projectile deformation. For cases where the projectile would fragment (for example, if a harder target material were used), the effect of geometric scale on the performance of dual plate armor is predicted by analysis. The prediction is that, for impact velocities where projectile breakup at the outer plate of dual plate armor is a factor, the armor required to stop a large scale projectile can be lighter, on a relative basis, than the armor required to stop a small scale projectile.     

Behind-armor debris from the impact of hypervelocity tungsten penetrators

Behind-armor debris is the main mechanism by which targets are destroyed by projectile impact. The behind-armor debris generated from the impact of tungsten heavy alloy (THA) penetrators with a length-to-diameter ratio (L/D) of 20 against 6061-T6 aluminum targets was characterized. Behind-armor debris characteristics described were the number of debris particles, their positions, and their size distribution. Experiments were performed against two nominal target thicknesses, 100 and 150 mm, and covered a velocity range from 1.7 to 2.6 km/s. Two methods of obtaining data were used—radiographs were taken of the behind-armor debris, and perforation patterns were generated on steel witness packs placed behind the aluminum target. Debris particles recovered from the witness packs were also studied. Results are discussed for the effect of changes in target thickness and impact velocity on behind-armor debris particle characteristics.     

EFP垂直侵彻靶后破片云描述模型

针对靶后破片是影响装甲保护能力和聚能装药毁伤的主要问题,基于EFP垂直侵彻的靶后破片,建立其初始靶后破片云的数学描述模型,并在此基础上采用有限元仿真软件AUTODYN-3D对EFP垂直侵彻钢靶形成靶后破片的过程进行数值模拟。数值模拟结果与靶场实验结果进行对比,结果表明:仿真的EFP成型参数、靶后破片空间分布状态和靶板开孔特征均与实验较为吻合。因此,证明该仿真模型和所得靶后破片云初始描述模型具有较高的可信度,可以为EFP对装甲目标的毁伤评估方面提供一定的参考。     

EFP垂直侵彻靶后破片云描述模型

针对靶后破片是影响装甲保护能力和聚能装药毁伤的主要问题,基于EFP垂直侵彻的靶后破片,建立其初始靶后破片云的数学描述模型,并在此基础上采用有限元仿真软件AUTODYN-3D对EFP垂直侵彻钢靶形成靶后破片的过程进行数值模拟。数值模拟结果与靶场实验结果进行对比,结果表明:仿真的EFP成型参数、靶后破片空间分布状态和靶板开孔特征均与实验较为吻合。因此,证明该仿真模型和所得靶后破片云初始描述模型具有较高的可信度,可以为EFP对装甲目标的毁伤评估方面提供一定的参考。     

Ballistic Penetration of Dyneema Fiber Laminate

UHMWPE fiber (Dyneema) reinforced composites are an important class of materials for armors.These materials provide superior ballistic performance to the armor, such as the military armor systems requiring a reduction in back-armor effects or a substrate for hardened facings of steet or ceramic. The reported work characterized the ballistic impact and mechanical performance of Dyneema fiber in composite laminates. The capability of the laminate to absorb ballistic impact energy was influenced by the impact velocity and the laminate areal density. Two kinds of penetration were compared and a two-step model for the penetration was proposed.     

A model for deformation and fragmentation in crushable brittle solids

A unified framework of continuum elasticity, inelasticity, damage mechanics, and fragmentation in crushable solid materials is presented. A free energy function accounts for thermodynamics of elastic deformation and damage, and thermodynamically admissible kinetic relations are given for inelastic rates (i.e., irreversible strain and damage evolution). The model is further specialized to study concrete subjected to ballistic loading. Numerical implementation proceeds within a finite element context in which standard continuum elements represent the intact solid and particle methods capture eroded material. The impact of a metallic, spherical projectile upon a planar concrete target and the subsequent motion of the resulting cloud of concrete debris are simulated. Favorable quantitative comparisons are made between the results of simulations and experiments regarding residual velocity of the penetrator, mass of destroyed material, and crater and hole sizes in the target. The model qualitatively predicts aspects of the fragment cloud observed in high-speed photographs of the impact experiment, including features of the size and velocity distributions of the fragments. Additionally, two distinct methods are evaluated for quantitatively characterizing the mass and velocity distributions of the debris field, with one method based upon a local energy balance and the second based upon global entropy maximization. Finally, the model is used to predict distributions of fragment masses produced during impact crushing of a concrete sphere, with modest quantitative agreement observed between results of simulation and experiment.     

Ballistic impact response of laminated hybrid materials made of 5086-H32 aluminum alloy,epoxy and Kevlar® fabrics impregnated with shear thickening fluid

The ballistic impact behavior of hybrid composite laminates synthesized for armor protection was investigated. The hybrid materials, which consist of layers of aluminum 5086-H32 alloy, Kevlar® 49 fibers impregnated with shear thickening fluid (STF) and epoxy resin were produced in different configurations using hand lay-up technique. The hybrid materials were impacted by projectiles (ammunitions of 150 g power-point) fired from a rifle Remington 7600 caliber 270 Winchester to strike the target at an average impact velocity and impact energy of 871 m/s and 3687 J, respectively. The roles of the various components of the hybrid materials in resisting projectile penetration were evaluated in order to determine their effects on the overall ballistic performance of the hybrid laminates. The effects of hybrid material configuration on energy dissipation during ballistic impacts were investigated in order to determine a configuration with high performance for application as protective armor. The energy dissipation capability of the hybrid composite targets was compared with the initial impact energy of low caliber weapons (according to NATO standards) in order to determinate the protection level achieved by the developed hybrid laminates. Deformation analysis and penetration behavior of the targets were studied in different stages; the initial (on target front faces), intermediate (cross-section), and final stages (target rear layers). The influence of target thickness on the ballistic impact response of the laminates were analyzed. Differences in ballistic behavior were observed for samples containing Kevlar® impregnated with STF and those containing no STF. Finally, mechanisms of failure were investigated using scanning electron microscopic examination of the perforations.     

Establishing a predictive method for blast induced masonry debris distribution using experimental and numerical methods

When subjected to blast loading, fragments ejected by concrete or masonry structures present a number of potential hazards. Airborne fragments pose a high risk of injury and secondary damage, with the resulting debris field causing major obstructions. The capability to predict the spatial distribution of debris of any structure as a function of parameterised blast loads will offer vital assistance to both emergency response and search and rescue operations and aid improvement of preventative measures. This paper proposes a new method to predict the debris distribution produced by masonry structures which are impacted by blast. It is proposed that describing structural geometry as an array of simple modular panels, the overall debris distribution can be predicted based on the distribution of each individual panel. Two experimental trials using 41 kg TNT equivalent charges, which subjected a total of nine small masonry structures to blast loading, were used to benchmark a computational modelling routine using the Applied Element Method (AEM). The computational spatial distribution presented good agreement with the experimental trials, closely matching breakage patterns, initial fragmentation and ground impact fragmentation. The collapse mechanisms were unpredictable due to the relatively low transmitted impulse; however, the debris distributions produced by AEM models with matching collapse mechanisms showed good agreement with the experimental trials.     

Quantitative analysis of debris clouds from SiC-fiber-reinforced silicon nitride bumpers

In order to investigate the dynamic response of lightweight ceramic matrix bumpers against hypervelocity projectile impact, silicon carbide continuous-fiber-reinforced silicon nitride matrix composite plates were prepared and subjected to the impact experiments using duralumin projectiles in the velocity range of 2.2 to 3.6 km/s. The debris clouds of the composites were taken by flash, soft X-ray radiography, and the fragmentation of the bumpers and the spatial distribution of the main parts of the debris clouds were quantified in mass, velocity and kinetic energy and compared with those of monolithic duralumin bumpers and monolithic silicon nitride ceramic bumpers. Almost all the average mass and kinetic energy of the in-flight fragments of the composite were smaller than those of the duralumin and monolithic ceramics. The composite provided thinner distributions of the mass and kinetic energy densities of its debris in an area extending farther from the ballistic line for higher impact velocity, while the monolithic ceramics gave massive and energetic debris distributions in a narrow area around the ballistic line. Total mass and kinetic energy of the composite debris were smaller than those of the duralumin, and for impacts over 3 km/s the volumetric energy density of the composite debris was comparable to that of the duralumin. Embedding the fibers to a ceramic matrix was thought to give the composite the heterogeneous microstructure to result in a non-uniform dynamic response of the composite, followed by the bumper fragmentation and the debris dispersion.     

Ballistic limit equations in ballistic and shatter regions

Ballistic limit equations are used to predict the damage of spacecraft subjected to impacts by space debris and meteoroids. This paper presents two new ballistic limit equations for impact velocities in the ballistic and shatter regions, respectively. The methodology used to develop the two ballistic limit equations involves the energy balance law and Cohen's debris cratering model. A very often form for ballistic limit equations based on the crater depth in a semi-infinite target was used for the both equations. The limit velocity between the ballistic and shatter regions was expressed as a non-dimensional equation in this paper. Agreement observed between existing and proposed results confirmed the validity of the presented equations.     

Ballistic resistance of high hardness armor steels against 7.62 mm armor piercing ammunition

Although advanced lightweight composite based armors are available, high hardness steels in military vehicles are often used to provide ballistic protection at a relatively low cost and is an interesting material due to its widespread usage in vehicle structure. In this study, ballistic limit of 500 HB armor steel was determined against 7.62 mm 54R B32 API hardened steel core ammunition. Lagrange and smoothed particle hydrodynamics (SPH) simulations were carried out using 3D model of bullet and high hardness armor target. Perforation tests on 9 and 20 mm thickness armor were performed to validate simulation methodology. Also material tests were performed for armor steel and ammunition hardened steel core to develop Johnson–Cook constitutive relations for both strength and failure models. Finally, results from 3D numerical simulations with detailed models of bullet and target were compared with experiments. The study indicates that the ballistic limit can be quantitatively well predicted independent of chosen simulation methodology, but qualitatively some differences are seen during perforation and fragmentation. As shown in results, good agreement between Ls-Dyna simulations and experimental data was achieved by Lagrange formulation with the full bullet model.     

Quantitative analysis of debris from SiC-fiber-reinforced aluminum-alloy targets impacted by spherical projectiles

Silicon-carbide-continuous-fiber-reinforced aluminum matrix composite targets were impacted with duralumin projectiles at velocities from 2.9 km/s to 4.3 km/s. The debris from the composite targets was monitored by flash, soft x-ray radiography. The spatial distribution of the leading half of the debris were quantified in terms of mass, velocity, and kinetic energy and compared with that of debris from monolithic aluminum-alloy targets. A material effect on the debris production was found through the experiment so that fragments from the composite targets were smaller in mass and size, but more in number than those from the monolithic bumper. An increase of the impact velocity brought the enhancement of fragmentation in the leading edge part of the debris produced from both the composite and the monolithic targets in comparison with lower velocity impacts. The 4.3 km/s impact for the composite gave the spatial densities of debris mass and kinetic energy biased toward the periphery of the debris cloud, while other lower velocity impacts gave the different densities biased toward a gun axis. Such peripheral distribution of debris was found at an impact velocity of 3.5 km/s for the monolithic target. In the present velocity range, the composite debris always exhibited its larger peripheral distribution than the monolithic one did.     

Predicting orbital debris shape and orientation effects on spacecraft shield ballistic limits based on characteristic length

We propose the use of “characteristic length,” based on radar cross section, as a metric for comparing the performance of orbital debris impactors of differing shapes, and the use of NASA's standard breakup model (SBM) “flake” shape as the representative particle for predicting orbital debris penetration effects. We also propose the use of a 26-view methodology for examining non-spherical particles such as cylinders, rectangular prisms, octahedrons, etc., with the intent to describe their potential impact orientations while minimizing the number of hydrocode runs needed to develop orientation-dependent ballistic limit curves. Using this methodology and the smooth particle hydrodynamic code (SPHC), we predict the ballistic limit for SBM-based particles against a typical spacecraft dual-wall shield at normal obliquity and velocities of 7, 8, and 12 km/s. Finally, we compare these results with ballistic limits produced by spherical impactors of the same characteristic length as the SBM-based particles.     

A quantitative analysis of computed hypervelocity debris clouds

This paper presents quantitative analyses of computed hypervelocity debris clouds due to aluminum spheres, rods and disks impacting aluminum bumper plates. The computations were performed using an algorithm to convert distorted Lagrangian finite elements to meshfree particles. The analyses were performed using a new postprocessing algorithm. The combination of this computational approach and this postprocessing algorithm is also used to characterize behind-armor debris due to tungsten rods impacting steel plates at ballistic velocities, and the results are compared to test data. The quantitative analyses are an extension of previous qualitative comparisons to radiographs of hypervelocity debris clouds.     

Bio-inspired armor protective material systems for ballistic shock mitigation

Severe transient ballistic shocks from projectile impacts, mine blasts, or overhead artillery attacks can incapacitate an occupant at low frequencies, or sensitive equipment at high frequencies, if they are not properly attenuated by armor protective systems. Unique challenges exist in developing armor protective systems for mitigating both low and high frequency ballistic shocks due to the lack of robust design methodology, the severe dynamic loading conditions, and the uncertainties in predicting ballistic shock responses.Nature offers engineers a blueprint of highly effective, efficient, and adaptive material designs to protect certain regions from external threats. This paper presents the modeling, analysis, design, optimization, fabrication, and experimental validation of bone-inspired armor protective material systems for reducing projectile penetrations and alleviating ballistic shocks at both low and high frequencies. The optimized bone-inspired armor protective material system has a soft–stiff–soft–stiff material distribution pattern based on bone-foramen and osteonal-bone material systems. Analysis and experimental results demonstrated that the bone-inspired armor protective material systems have excellent capabilities for drastic ballistic shock mitigation, weight savings, and significant reductions in penetration and load transmission under ballistic loading conditions.     

Response of simulated propellant and explosives to projectile impact—II. Fragmentation

This paper is the second of a series concerned with the penetration and perforation phenomena in two types of propellant and explosive simulant, named Propergol, due to the impact at normal incidence of both blunt and conically-tipped steel strikers. The collision results in fragmentation, plug formation and generation of a cloud of debris that includes particles of measurable dimensions traveling with significant velocities. Both the fragment size and area as well as the ejecta mass are determined experimentally as a function of Propergol specimen thickness and impact velocity or energy. The cumulative number of fragments as a function of size for the Propergol is uniformly found to be a bi-linear semi-logarithmic relationship with the bifurcation occurring at the mean crystal radius. Individual crystals and the crater generated are examined by means of a scanning electron microscope.

A phenomenological model of the fragmentation process is constructed, based on an assumed spherical shape of the fragments and the bi-linear fragment distribution, using energy methods. This is combined with a perforation analysis that considers the process to be sequentially composed of initial indentation, fragmentation, and sliding and deflection of the Propergol disks. An evaluation of this model providing fragment volumes as a function of impact velocity is compared with experimental results and found to be in good agreement.     

An engineering model to predict perforation damage to plates impacted by high velocity debris clouds

This paper describes experiments and the development of a model to predict damage to metallic plates impacted by high velocity, multi-particle debris clouds. The experiments involved single steel spheres fired at a steel shatter plate at speeds near 1.5 and 2.0 km/sec to generate the debris clouds. In each series of tests, the impact velocity was controlled, and a witness plate was placed at increasing distances behind the shatter plate to observe the effects of debris particle dispersion on plate damage. This paper focuses on the variations, with plate spacing, in the size of the central region removed from the witness plates. The central hole size model compares the post impact kinetic energy distribution in a witness plate impacted by a debris cloud to the free impact residual kinetic energy in an equivalent plate impacted by an L/D=1 steel cylinder, at the ballistic limit velocity. This approach permits extension of the model to other plate materials through utilization of existing ballistic limit velocity data.     

Modeling and validation of full fabric targets under ballistic impact

The impact of three different projectiles (0.357 Magnum, 9-mm FMJ and 0.30 cal FSP) onto Kevlar® was modeled using a commercial finite-element program. The focus of the research was on simulating full-scale body armor targets, which were modeled at the yarn level, by reducing to a minimum the number of solid elements per yarn. A thorough validation of the impact physics was performed at the yarn level, single-layer level, and a full body armor system. A verification was performed by checking the numerical model against analytical predictions for yarn impact. For one-layer and multiple-layer targets validation consisted on matching experimental data of pyramid formation recorded by an ultra-high-speed camera. The full-scale targets were also instrumented with nickel–chromium wires that stretch with the yarn during the penetration event. The wires provided a second validation data set since the numerical model can reproduce the signal recorded by the wires. The third and final validation of the model is provided by a comparison of the ballistic limit predicted by the model and data obtained in tests. This is a check of the failure model used in the numerical simulations. This paper shows that the main features of the impact physics are well reproduced by the finite-element model. Prediction of ballistic limits for the 9-mm FMJ and FSP projectiles were within the scatter of the tests, while for the 0.357 projectile the difference was only 15%.     

聚能装药侵彻靶后破片的空间分布特征

准确掌握靶后破片的空间分布规律是有效开展聚能装药对装甲目标内部环境毁伤效应评估的先决条件。通过试验和有限元仿真对典型聚能装药侵彻不同倾角靶板产生靶后破片过程进行了研究,结果表明:射流穿透靶板瞬间,大量碎片在靶后形成"椭圆体"破片云,随着靶板倾角增大,靶后破片云朝着靶后法线一侧偏转,其水平截面(与射流轴线垂直的截面)由圆形逐渐变为椭圆,但靶后破片间最大飞行夹角始终保持在90°左右。