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.     

Whipple shield performance in the shatter regime

A series of hypervelocity impact tests have been performed on aluminum alloy Whipple shields to investigate failure mechanisms and performance limits in the shatter regime. Test results demonstrated a more rapid increase in performance than predicted by the latest iteration of the JSC Whipple shield ballistic limit equation (BLE) following the onset of projectile fragmentation. This increase in performance was found to level out between 4.0 and 5.0 km/s, with a subsequent decrease in performance for velocities up to 5.6 km/s. For a detached spall failure criterion, the failure limit was found to continually decrease up to a velocity of 7.0 km/s, substantially varying from the BLE, while for perforation-based failure an increase in performance was observed. An existing phenomenological ballistic limit curve was found to provide a more accurate reproduction of shield behavior that the BLE, prompting an investigation of appropriate models to replace linear interpolation in shatter regime. A largest fragment relationship was shown to provide accurate predictions up to 4.3 km/s, which was extended to the incipient melt limit (5.6 km/s) based on an assumption of no additional fragmentation. Alternate models, including a shock enhancement approach and debris cloud cratering model are discussed as feasible alternatives to the proposed curve in the shatter regime, due to conflicting assumptions and difficulties in extrapolating the current approach to oblique impact. These alternate models require further investigation.     

5A06铝合金单层板超高速撞击弹道极限分析

日益增长的空间碎片对在轨航天器的安全运行构成了严重威胁,毫米级空间碎片的防护已成为航天器结构设计必须考虑的问题之一.航天器的蒙皮是抵御空间碎片超高速撞击的最基本防护结构.采用数值仿真并结合试验验证的方法,对5 mm厚5A06铝合金单层板承受2A12铝合金球形弹丸正撞击下的弹道极限进行了研究.研究表明,在验证实验速度范围内,数值仿真结果与实验结果吻合良好;使用数值仿真对实验速度以上的区间进行拓展研究,获得了其弹道极限曲线和弹道极限方程;数值仿真和实验结果与已有经验方程对比表明,经验方程与具体材料的弹道极限有较大偏差,因此,应具体问题具体分析.     

Metallic witness packs for behind-armour debris characterisation

For the experimental characterisation of behind-armour debris so-called metallic witness packs can be used. A metallic witness pack consists of an array of metallic plates interspaced by polystyrene foam sheets. To quantify the fragment mass and velocity from the corresponding hole area and position in the individual witness plates, perforation threshold curves must be available to provide the ballistic limit velocity for each plate as a function of the fragment mass. Furthermore, the relation between the fragment impact velocity and hole size should be known. This paper presents the results of a collaborative study between Defence Research Establishment, Valcartier (DREV) and TNO Prins Maurits Laboratory, The Netherlands. The first phase of this project is an experimental study to develop perforation threshold and hole-growth curves for two metallic witness pack configurations. In addition, it is shown that a hydrocode can be succesfully used to predict perforation threshold velocities.     

近地轨道航天器微流星及空间碎片风险度分析研究

以单防护屏防护结构为例,根据描述其防护性能的撞击极限方程,微流量及空间碎片环境数学模型,建立了航天器结构的有限元分析模型,进行了航天器在微流星及空间碎片环境下风险度的初步分析,其结论可供工程实践参考。     

Integral model for the description of the debris cloud structure and impact

The purpose of the present paper is to introduce a new integral model capable to describe the evolution of the debris clouds originated after normal-impacts of orbital debris over a Whipple shield. This work had been developed at Alenia Spazio in the context of a degree thesis. Several numerical SPH simulations of debris impacts on a Whipple shield configuration were performed to determine the ballistic limit and to compare it with semi-empirical damage equations. In the present paper, the numerical simulations were used to investigate the typical behaviour of experimental debris clouds ([6] and [9]) and to support the development of the integral model.

With respect to previous papers ([1], [2], [3], [10]) in which a spherical shell-wise debris cloud was considered, here we try to introduce more realistic assumptions. We approximate the cloud's shape also introducing ejecta veil effects, which produce a multiplication of the deposited momentum upon the underneath wall. In the present model, the most peculiar hypothesis is a cinematic self-similar behaviour that is, whatever the shape is, the debris cloud evolves keeping unchanged its shape. Then, the material is opportunely distributed inside a volume and the choice of that distribution is described taking into account the results of the numerical simulations. Knowing the spatial material distribution and treating the cloud as a fluid, we can estimate the load time history and the drag-unitary force induced by the cloud impacting upon the rear wall. Of course, such a method uncouples the dynamic response of the rear wall from the evolution of the debris cloud. The balances of mass, momentum and energy allow three global and unknown parameters to be determined. The one-dimensional theory of impact ([10]) is used to take into account the conversion of part of the initial kinetic energy into internal thermal energy. No integration of differential equations is performed since complex propagation phenomena are taken into account through the effects they globally produce. The model still presents some free parameters related to the integral formulation. These parameters cannot be calculated through any balance condition, but they must be imposed to get a good, global reproduction of the debris cloud. The choice of these parameters is still the weak aspect of the method, and it depends on the consideration of the results obtained with more sophisticated tools, as, for instance, SPH simulations. The spatially defined load time history obtained with the debris cloud integral model can be used for further analysis on the back up plate.     

Fragmentation of targets during ballistic penetration events

An analytical target fragmentation model is developed to predict the number of armor debris fragments produced in a ballistic penetration event. The model employs an energy balance to estimate the energy available to propagate cracks in the target material and thus produce an estimate of the mean number of behind-armor debris fragments. The expected number of behind-armor debris fragments agrees well with the results of conventional ordnance velocity target penetration behind-armor debris tests. This analytical fragmentation model and test results were used as the basis for the development of a means of calibrating the parameters of a Weibull statistical distribution function to predict the probability distribution of the number of debris fragments produced in a ballistic impact. It was concluded that the armor fragmentation model was a good predictor of the number of fragments produced in a ballistic penetration event deserving further investigation.     

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.     

The ballistic performance of metal plates subjected to impact by projectiles of different strength

In this paper, the ballistic performance of monolithic, double- and three-layered steel plates impacted by projectiles of different strength is experimentally investigated by a gas gun. The ballistic limit velocity for each configuration target is obtained and compared based on the investigation of the effect of the number of layers and the strength of projectiles on the ballistic resistance. The results showed that monolithic plates had higher ballistic limit velocities than multi-layered plates for projectiles of low strength regardless their nose shape, and also the ballistic limit velocities of plates decreased with the increase of the number of layers. Moreover, monolithic plates showed greater ballistic limit velocities than multi-layered plates for ogival-nosed projectiles of high strength, and also the ballistic limit velocities of plates decreased with the increase of the number of layers. However, monolithic plates had lower ballistic limit velocities than multi-layered plates for blunt-nosed projectiles of high strength, and also the ballistic limit velocities of plates increased with the increase of the number of layers. The differences in the ballistic limit velocities between various impact conditions can be related to the transitions of perforation mechanisms and failure models of plates and projectiles.     

A comparison of NASA,DoD, and hydrocode ballistic limit predictions for spherical and non-spherical shapes versus dual- and single-wall targets,and their effects on orbital debris penetration risk

All earth-orbiting spacecraft are susceptible to impacts by these particles, which can occur at extremely high speeds and can damage flight- and mission-critical systems. The traditional damage mitigating shield design for this threat consists of a “bumper” that is placed several cm away from the main “inner wall” of the spacecraft. Typical orbital debris risk analyses that include ballistic limit equations (BLEs) and curves (BLCs) assume that orbital debris particles are spherical in shape. However, spheres are not a common shape for orbital debris; rather, debris fragments might be better represented by other regular or irregular solids. This paper presents the results of a study comparing BLCs developed by NASA and the DoD for velocities up to 4 km/s considering spheres, cubes, and a “flake” shape that was proposed within NASA's Standard Breakup Model to represent orbital debris. It also compares performance of these shapes using hydrocodes at higher velocities (7–12 km/s), and generates a combined BLC for these shapes for the entire orbital debris velocity regime. In addition to shape, a multi-view method is used to examine the effects of a variety of cube and flake impact orientations on BLC, as well as a “characteristic length” parameter developed by NASA to compare the particle shapes on the basis of their radar cross section. The developed non-spherical BLCs are then evaluated for overall penetration risk considering the orbital debris environment. Their predictions of risk are compared to that predicted using sphere-based BLCs. This methodology is then extended to a single-wall shield design for velocities up to 15 km/sec, and the results of DoD predictions for a sphere and cube are compared with NASA predictions for a sphere having the same characteristic length. The results indicate that we may be over-predicting orbital debris risk for dual-wall shields by a factor of two—and for single walls by a factor of four—by limiting our analyses to spheres instead of using more representative debris shapes, such as cubes and flakes, and its characteristic length as the primary particle parameter.     

A comparison of ballistic limit with adaptive-mesh Eulerian hydrocode predictions of one- and two-plate aluminum shielding protection against millimeter-sized Fe–Ni space debris

Hypervelocity collisions with space debris (SD, natural meteoroids and man-made artifacts) can significantly affect the performance of spacecraft. Here, I compare (1) the predictions of the Cour-Palais/Christiansen (C-P/C) ballistic limit equations (BLEs) spacecraft shield models with (2) the predictions of the response of those shields generated by an adaptive-mesh Eulerian hydrodynamic code, incorporating Mie-Grüneisen solid mechanics and a simple material-failure model, running on a modern PC, for hypervelocity collisions with millimeter-sized iron–nickel (Fe–Ni) spheres. The results show that the shield thicknesses predicted by the C-P/C BLEs are consistent with the adequacy of the shield response predicted by the hydrodynamic modeling. Although several hydrocodes have been used to validate the C-P/C BLEs, validating them with an (inherently computing resource-efficient) adaptive-mesh Eulerian hydrodynamic code for this impact regime appears to be novel.     

Experimental investigation on the ballistic resistance of monolithic and multi-layered plates against ogival-nosed rigid projectiles impact

In this paper, the ballistic performance of single, two-, three- and four-layered steel plates impacted by ogival-nosed projectiles were experimentally investigated. Thin multi-layered plates arranged in various combinations of the same total thicknesses were normally impacted with the help of a gas gun. Ballistic limit velocity for each configuration target was obtained and compared based on the investigation of the effect of the air gap between layers, the number, order and thickness of layers on the ballistic resistance of targets. The results show that the thin monolithic targets have greater ballistic limit velocities than multi-layered targets if the total thickness less than a special value, and also the ballistic limit velocities of multi-layered targets decrease with the increase of the number of layers. Otherwise, the moderate thickness monolithic targets give lower ballistic limit velocities than multi-layered targets. Furthermore, the ballistic limit velocities of in-contact multi-layered targets are greater than those of spaced multi-layered targets. The order of layers affects the ballistic limit velocities of multi-layered targets, the ballistic resistance of the multi-layered targets is better when the first layer is thinner than the second layer.     

泡沫铝防护屏的Whipple防护结构弹道极限数值模拟研究

为研究泡沫铝板作为防护屏的Whipple防护结构抵御空间碎片超高速撞击的特性,模仿泡沫金属的生产原理建立了泡沫金属细观结构几何模型,结合自编的光滑质点流体动力学程序进行了超高速撞击数值仿真,通过与实验对比验证了模型的有效性.分别对相对密度为23.2%的理想均匀和非均匀开孔泡沫铝板作为防护屏的Whipple防护结构进行了数值仿真,得到了它们的弹道极限曲线,并与实心铝板作为防护屏的Whipple防护结构进行了对比分析.结果表明,相同面密度的泡沫铝板相对于实心铝板能够在更低的速度上将弹丸粉碎、液化及气化.泡沫铝板作为防护屏,在总体上拥有更好的防护性能;相同面密度的理想均匀泡沫铝板的防护性能总体上优于非均匀泡沫铝板.     

Ballistic Limit of Single and Layered Aluminium Plates

Abstract: This paper presents an experimental and finite‐element investigation of ballistic limit of thin single and layered aluminium target plates. Blunt‐, ogive‐ and hemispherical‐nosed steel projectiles of 19 mm diameter were impacted on single and layered aluminium target plates of thicknesses 0.5, 0.71, 1.0, 1.5, 2.0, 2.5 and 3 mm with the help of a pressure gun to obtain the ballistic limit in each case. The ballistic limit of target plate was found to be considerably affected by the projectile nose shape. Thin monolithic target plates as well as layered in‐contact plates offered lowest ballistic resistance against the impact of ogive‐nosed projectiles. Thicker monolithic plates on the other hand, offered lowest resistance against the impact of blunt‐nosed projectiles. The ballistic resistance of the layered targets decreased with increase in the number of layers for constant overall target thickness. Axi‐symmetric numerical simulations were performed with ABAQUS/Explicit to compare the numerical predictions with experiments. 3D numerical simulations were also performed for single plate of 1.0 mm thickness and two layered plate of 0.5 mm thickness impacted by blunt‐, ogive‐ and hemispherical‐nosed projectiles. Good agreement was found between the numerical simulations and experiments. 3D numerical simulations accurately predicted the failure mode of target plates.     

Experimental study of agglomerated-cork-cored structures subjected to ballistic impacts

The present paper examines the high-velocity impact behaviour of agglomerated cork-cored structures. The ballistic performance was studied by impact-perforation tests. Three different types of specimens were tested: an agglomerated cork, two spaced thin aluminium plates, and a pair of thin aluminium plates separated by an agglomerated-cork core. The behaviour of the agglomerated cork and the effects of the cork core were analysed in terms of the ballistic limit, residual velocity, and energy absorption. The ballistic limit of cork-cored structures increased slightly, whereas the absorbed energy was strongly augmented by the presence of the cork core.     

Modified Cour-Palais/Christiansen damage equations for double-wall structures

Ballistic limit equations (BLEs) are used for the damage prediction of spacecraft in a meteoroid and space debris environment. For double-wall configurations, the Cour-Palais/Christiansen equations have been modified to yield a general approach including the influence of the shield thickness. The ratio of shield thickness to particle diameter is considered as additional parameter in the equations. These equations result in the single-wall equation when the shield thickness approaches zero. The modifications can also be applied to other BLEs. Impact tests have been performed in order to validate the modified equations. In this paper, the test results are compared to the modified BLEs. Especially in the hypervelocity region, the new equations are more suitable for configurations with very thin shields than the original ones.     

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.     

Three dimensional hypervelocity impact simulation for orbital debris shield design

This paper assesses a Whipple shield impact simulation method which is both accurate and computationally efficient. The paper documents the simulation methodology and results of Whipple shield simulations at an oblique impact angle of 30°. These results are compared with HVI experiments to demonstrate the accuracy of the simulation technique. In addition, simulations of Whipple shields in the velocity regime above 8km/s were completed and the results compared to published ballistic limit equations to demonstrate the reliability of these equations. Finally, the paper documents computational efficiency of the simulation technique.     

Selecting enhanced space debris shields for manned spacecraft

A research program was funded by the European space agency (ESA) to improve and optimize the shields used to protect the manned elements of the international space station (ISS) against impacts of micro-meteoroids and orbital debris. After a review of existing shielding systems and after a series of light gas gun (LGG) experiments to screen interesting new materials and configurations, the research focused on shields with a metallic outer bumper, an intermediate stuffing and an inner metallic wall (representing the pressure shell of a manned spacecraft). Additional LGG experiments were performed on several configurations, with bumpers containing aluminum foam or made from titanium and aluminum super-alloys and with several combinations of stuffing materials. The comparison of the test results showed that ceramic cloth (Nextel) plus aramid fabric (both 2D and 2.5D Kevlar weaving) used as intermediate bumper gave a good protection compared to the overall area density requested. Configurations with by-layered aluminum foam bumpers (sandwich panels with asymmetric Al face sheets and a core made from Al foam) and Kevlar stuffing showed excellent resistance to normal impacts at about 6.5 km/s. However, the influence of material properties varying from batch to batch and threshold phenomena made ranking among the tested options rather difficult. The test campaign showed that it was rather difficult to improve over the already good ballistic performances of the debris shields developed by Alenia Spazio for the ISS manned elements. The by-layered Al-foam bumper and Kevlar stuffing configuration was selected for additional tests, including low velocity and oblique impacts, to develop ballistic limit curves.