Research and development on hypervelocity impact protection using Whipple shield: An overview

Ken Wen , Xiao-wei Chen , Yong-gang Lu

a State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing,100081, China

b Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang, Sichuan, 621999, China

Keywords:Space debris Hypervelocity impact Debris cloud Whipple shield Ballistic limit

ABSTRACT

1. Introduction

The increasing human space activities, especially commercial aerospace like “Star-link” mission of SpaceX, make the space environment hostile sharply[1].Figs.1 and 2 shows the increasing number and mass of objects in Earth orbit in recent years, respectively[2].The number of space debris and the collision probability between spacecrafts and space debris increase correspondingly.Once the space debris impacted onto the spacecraft, the impact velocity could be greater than 10 km/s. The hypervelocity impact can have a wide range of effects on spacecraft(mechanical damage and functional failure), that has raised great concern about spacecraft safety [3].

The common spacecraft protection against space debris includes active protection and passive protection[4,5].The active protection comprises evasive maneuvers to the space debris, mitigation and removal of the space debris. The passive protection refers to implementing shields to defend meteoroids and space debris particles which cannot be tracked. The active protections are the significant ways to deal with space debris and practically improve the space environment. But, in terms of technique and economy, the passive protection is still effective and indispensable at present and in the near future.

The protection shield is placed on the spacecraft to defend the hypervelocity (greater than 3.0 km/s) impact of space debris. The traditional protection structure is on the basis of Whipple shield,a gapped dual-wall system proposed in 1947 [6], as shown in Fig. 3.The thin bumper(front plate)is placed at a relatively small distance away from the main wall (rear plate) of the spacecraft. The space debris impacts onto the thin bumper,endures acute fragmentation and phase transition and forms a debris cloud. The debris cloud comprises numbers of solid fragments, droplets and vapors. Formation of the debris cloud disperses the kinetic/momentum of space debris and spread the“point load”into an“area load”so as to effectively protect the spacecraft. Debris cloud produced by the hypervelocity impact of space debris also influence the generation and evolution of space debris.

The protection of Whipple shield against hypervelocity impact comprises three closely related steps: First is the interaction between the space debris (projectile) and bumper, where the projectile crushes and phase changes; Second is the movement and diffusion of the impact-induced debris cloud; Third is the resist of the rear plate to debris cloud. The interaction between the projectile and bumper is the foundation of debris cloud formation.The diffusion degree of debris cloud affects rear plate damage. The damage of rear plate reveals the structural characteristics of debris cloud, and further reflects the interaction between the projectile and bumper. Since last decades, the study of the protection structures against hypervelocity impact has been quite extensive, and basically, all works focus on these three steps.

Fig.1. Monthly effective number of objects in Earth orbit adopted from NASA [2].

Fig. 2. Monthly effective mass of objects in Earth orbit adopted from NASA [2].

In 1990,Anderson et al.[7]reviewed the works of hypervelocity impact and protection. In recent years, more scholars have summarized the works in this field.In 2000,Schneider and Sch¨afer[8]summarized the acceleration technology commonly applied in hypervelocity impact experiment,and discussed the launch level of various equipment. In 2008, Schonberg [9] commented the development of the ballistic limit of dual-wall spacecraft shield.In 2010,Schonberg [10] presented an overview of the application of composite structural system and material in Earth-orbiting spacecraft protection. In the same year, Liu et al. [11] summarized the advancement of hypervelocity impact tests at China Aerodynamics Research and Development Center (CARDC). In 2013, at the 12th Hypervelocity Impact Symposium,Rudolph[12]reviewed the radio frequency emission from hypervelocity impact plasmas.

Recently, Cao et al. [13] reviewed the laser-driven flyer technique and micro-space debris hypervelocity impact tests in China Academy of Space Technology. In the same year, Schonberg [14]gave a conference report at the 13th Hypervelocity Impact Symposium,summarized comprehensively the studies of hypervelocity impact phenomena and its application on spacecraft protection.In 2016, Schonberg [15] summarized the development of dual-wall structure, especially the developments in last three decades. In 2018,Di et al.[16]published a review on debris cloud produced in hypervelocity impact. These works reviewed the progress of hypervelocity impact and protection from different perspectives,and all of them provide references for related researchers.

Fig. 3. Schema and a specimen of Whipple shield.

It is worthy to mention Inter-Agency Space Debris Coordination Committee (IADC), whose purpose is to exchange information on space debris research between member space agencies,to facilitate opportunities for cooperation in space debris research, and to review the progress of ongoing cooperative activities and to identify debris mitigation options. The committee compromise a Steering Group and four Working Groups, where Working Group 3 is specialized to study the space debris protection. The continually updated protection manual from Working Group 3 is useful for the study of hypervelocity impact and protection [17,18].

This paper reviews the research and development on hypervelocity impact protection using Whipple shield (the impact velocities ranging from 2 km/s to 10 km/s), especially focus on the mechanism and process of the protection using Whipple shield.At first, we introduce the main research methods: ground-based experiment and numerical simulation. Then, three steps in Whipple shield protection including the interaction between the projectile and bumper, the movement and diffusion of the debris cloud,and the interaction between the debris cloud and rear plate are introduced in order. Potential improvements of the protection performance focusing on these three steps are presented. Representative works in the last decade are mentioned specifically.Finally, we give some prospects and suggestions for future studies in this area.

2. Research methods for hypervelocity impact and protection

One major application of researches on hypervelocity impact and protection is to protect on-orbit spacecraft against the threaten of space debris.While there are a little work analyzing the systems retrieved after exposure to space environment[19,20],it is hard to perform numerously on-orbit tests.Two basic methods in this area are ground-based experiment and numerical simulation.

For the ground-based experiment, the on-orbit hypervelocity impact is simulated in lab.A projectile simulating the space debris,is accelerated into hypervelocity by launch equipment,and impacts onto a shield simulating the spacecraft protection structure.Ground-based experiment techniques comprise three parts: projectile launch technique, process monitoring technique and result statistics technique. Numerical simulation based on some basic physical principles is usually used to simulate hypervelocity impact.Numerical simulations for hypervelocity impact include but not limit to finite elemental method and smoothed particle hydrodynamics,which belongs to grid method and meshless method,respectively. The ground-based experiment and numerical simulation for hypervelocity impact and protection are introduced in this section.

2.1. Ground-based experiment of hypervelocity impact and protection

In the ground-based experiment, a projectile is accelerated by launch equipment to impact the protection structure under the witness of monitoring equipment.Ground-based experiment is an essential method to assess the protection capability of the shield.The bulkhead (rear plate) shown in Fig. 3 is usually replaced by a specialized plate,namely witness plate,which is helpful to evaluate the impact phenomenon.

Projectile and plate made of aluminum are commonly employed for ground-based experiment, according to space debris environment and spacecraft material(the debris density is usually assumed to be 2.8 g/cm3).Besides,for the numerous micro-meteors in space,projectile of other materials,such as steel,ice and rocks,have also been studied [21-24].

Spherical projectile is mostly used in ground-based experiments. Attitude of the spherical projectile itself does not need additional attention because of the symmetry [25-31]. Moreover,for the large number of cubic and square fragments produced by satellite disintegration [28,32], projectiles with other shapes have also been studied via ground-based experiment [33-37].

For the millimeter-size space debris is the main potential threaten to shields,the projectiles of millimeters are widely tested in ground-based experiments.The impact velocity is determined by the launch equipment and projectile size (projectile mass). Basically, the higher projectile mass, the slower impact velocity. The velocities ranging from 2 km/s to 10 km/s for millimeter-size projectile could be successfully achieved in lab.

In terms of projectile launch technique, light-gas gun, electrostatic and plasma accelerators,electromagnetic rail guns,explosive coil accelerator, exploding wire (foil) acceleration and shaped charge [8,38-48] are mostly used. Their accelerating capabilities are different. Light-gas gun includes one-stage, two-stage and multi-stage light gas gun. The higher stage of gas gun, the higher launch level and design complexity.In general,two-stage light-gas gun is the most common equipment [45,49], which could accelerate a ～1g projectile to about 8.5 km/s. The magnetically driven hyper-velocity Z accelerator at Sandia [43] can accelerate aluminum flyer at ～ 45 km/s and copper flyer at ～ 22 km/s. The magnetically driven flyer equipment has been further developed in China Academy of Engineering Physics,and the pulse generator CQ-4 can accelerate aluminum flyer at 8.7 km/s with a good flatness[40,50]. These experimental techniques of extremely high velocity are useful for the research of protection during interplanetary flights, where the impact velocities generally exceed 15 km/s.

Process monitoring techniques comprise projectile velocity measurement, image acquisition, and radiation measurement, etc.The methods of projectile velocity measurement include electric probe, magnetic induction, laser shading, laser interferometry(VISAR), and X-rays flash photography. Flash X-rays radiography[51], optical high-speed camera [52-54] and laser shadowgraph technology [55,56] are used to obtain the debris cloud images,where flash X-ray photography is the most common. Piekutowski[51] used the flash X-ray photograph to obtain numerous of highquality debris cloud images. In recent years, Kurosawa et al. [57]used ultra-high-speed photography to obtain image of the hypervelocity jetting during oblique impacts of spherical projectile.Ultrahigh-speed Sequence Laser Shadowgraph Imager (USLSI) has been developed rapidly at CARDC [58-62]. As an important phenomenon in the process of hypervelocity impact, the electromagnetic radiation has also attracted widespread attention[12,63-65].

Result statistics technique in this area mainly comprises measurement, collection and in-situ detection techniques. Due to the high velocity of the impact, the interaction between the projectile and bumper, and the movement and diffusion of debris cloud are often completed in several microseconds,which make difficulty for the process monitoring. So, the importance of results statistics is equal to,or even more than the importance of process monitoring.A more detailed understand of the impact situation could be obtained by measuring the impacted plate and witness plate[66-68],and by collecting projectile and plate fragments with soft material[69-71]. Recently, an in-situ detection method of thin plate damage [72-75] has been built, which is of great significance for both theoretical study and engineering application.

In fact,the movement and diffusion of the debris cloud,and the interaction between the debris cloud and rear plate have been widely and deeply studied through ground-based experiments.However, due to the extremely short time of the interaction between the projectile and bumper, it is difficult to directly observe the interaction in lab. To some extent, the current studies of the interaction between the projectile and bumper basically depend on numerical simulations,in addition to the inversion and speculation of witness plate damages. Databases collected from ground-based experiments are extremely useful to validate numerical simulations and to establish the behavior of tested materials in the hypervelocity impact conditions.

2.2. Numerical simulation of hypervelocity impact and protection

Ground-based experiment cannot be carried out in large quantities for the high cost of time and money, and the high requirement of experiment ability. Numerical simulation is relatively simple, economical and robust, which could not only make up for the absence of experiment under extreme impact conditions,but also provide a guidance for experiment design. Numerical simulation assists to acquire a fully understand and verification of the entire process and the underlying physics of impact phenomenon.Numerical algorithm and material model are two basic issues for hypervelocity impact simulation.

In terms of numerical algorithm in this area, a lot of attempts have been made based on traditional grid methods, such as Lagrangian algorithm [76-78], Eulerian algorithm [79,80], ALE algorithm [81]. However, it is hard to accurately simulate hypervelocity impact and protection with traditional grid methods due to the large deformation and fragmentation of material. Among grid algorithms, CTH [82], a Eulerian software package under development at Sandia National Laboratories Albuquerque, is useful[83,84]. A two-step Eulerian solution scheme is used in CTH. The first step is a Lagrangian step in which the cells distort to follow the material motion. The second step is a re-mesh step where the distorted cells are mapped back to the Eulerian mesh[82].

Meshless algorithm is widely applied in this area. The origination of meshless algorithm is later than the grid algorithms, but it has a good application prospect in the fields of hypervelocity impact, explosion, crack growth and metal processing [85]. Chen et al.[86]reviewed the development of meshless algorithms in the past 20 years in detail. Smoothed Particle Hydrodynamics (SPH)[87-91], Material Point Method (MPM) [92-96], Optimal Transportation Meshfree (OTM) [97], Combined Particle-Element Method (CPEM) [98,99] and etc. Especially SPH have been applied well.Besides,Andres et al.[100]also extended molecular dynamics to the simulation of hypervelocity impact and protection.

SPH is a Lagrangian meshless method[101],which uses a set of interpolation points to discretize the fluid volume. Each point carries discrete values of the calculated field and intrinsic data,and is controlled by governing Eq.s. Based on the convolution of variables through a kernel (or its gradient), the velocity and pressure gradients could be estimated. At present, SPH has been incorporated to some commercial software like AUTODYN, LS-DYNA and Pronto[102,103].

The traditional meshless method still has some insufficiencies including tensile instability and higher computational cost [98].Although a lot of improvements have been proposed for the pure meshless method [87,88,104,105], it appears that the mixed or hybrid particle-mesh method will be more suitable for the simulation of hypervelocity impact and protection [106-108]. Johnson et al. [99,109-113] presented many pioneering works of coupling methods, and got a lot of valuable results. In 2020, He et al. [114]applied the adaptive FEM-SPH to the simulation of impact-induce debris cloud, and got a great progress on the fragment identification which is difficult for the traditional meshless method.

Material model is another important issue in numerical simulation. Eq. of state (EOS) and strength model are two significant models in the numerical simulation of hypervelocity impact and debris cloud [79,115-117]. In order to calculate shock phenomena,the EOS of a material must be defined and implemented.Examples are the Mie-Grüneisen type Eq.s and tabular data like the SESAME library published by the Los Alamos National Laboratories.Strength models describe the material constitutive response. There are phenomenological strength models and physically-based strength models. Whilst the strength effects are not important regarding debris formation,they are important in determining the final crater hole sizes in the target plates. Strength models also offer the possibility to implement yield or failure criteria of any kind.They also have an important role in the fracture process.Besides,the artificial viscosity parameter and failure criteria would also affect simulation results.

Numerical simulation had been widely adopted to study the effect of impact parameters on the characteristics and the damage ability of debris cloud. Currently, more studies focus on the innovation in pre- and post-processing of numerical simulation,including new material models,new modeling method[118-120],and improvement of post-processing algorithm[121].The fragment distribution in debris cloud was obtained through SPH particle assignment algorithm and fragment identification algorithm in CARDC. Combined with Monte Carlo method, they proposed an engineering debris cloud model [122,123].

In general, although the numerical simulation in this area still need further development, it has become indispensable. With the applications of many novel numerical algorithms for the simulation of hypervelocity impact and protection,these numerical algorithms would be promoted and validated through known impact results.Besides, different numerical methods and material models would also be compared through predicting the same impact problem,which could identify their effectiveness.

3. Interaction of projectile and bumper

The process and phenomena of the impact protection using Whipple shield are studied through ground-based experiments and numerical simulations. The impact failure mechanism, phase transition mechanism and characteristics of debris cloud are studied well, and some optimal design of the protection material and structure are proposed.Basically,the process of the impact and protection has three steps: the interaction between the projectile and bumper, the movement and diffusion of the debris cloud, and the interaction between the debris cloud and rear plate. Hereinafter, we would review these works in order.

The interaction between the projectile and bumper under hypervelocity impact is transient,usually in a few microseconds.The projectile endures acute fragmentation and phase transformation,accompanied by plasma generation. The interaction between the projectile and bumper determines the characteristics of the bumper perforation and the characteristics of the debris cloud,and ultimately determines the rear plate damage. In terms of the interaction between the projectile and bumper, the wave propagation,the dynamic fragmentation of material,the electromagnetic radiation, the bumper perforation and the shield improvement inspired by the analysis of this step are introduced.

3.1. Wave propagation and evolution

The wave propagation and evolution in spherical and cylindrical projectiles are widely studied. For cylindrical projectile, the collision surface is flat and that is easy to analyze theoretically. For spherical projectile, only one geometry dimension is needed, and the impact attitude does not require special consideration. However,the impact surface of spherical projectile is not flat,that makes the wave propagation and evolution nonlinearly. The wave propagation and evolution in the projectiles with different shapes are usually different.

In the 1960s, Maiden et al. [124,125] studied the wave propagation and evolution for cylindrical projectile impact. Fig. 4 illustrates the interaction process of shock wave and rarefaction wave within one-dimensional wave theory. Through one-dimensional characteristic method, Maiden et al. analyzed the overtake and unload of rarefaction wave to the shocked material, and got the representation of the overtake location. As shown in Fig. 5, shock waves S1and S2generate and propagate into the projectile and the plate respectively, while rarefaction waves R1and R2would generate and transmit towards the axis of symmetry because of the finite diameter of the projectile. R1and R2would result in the ejection of both projectile and plate material in a rearward direction. Later, shock wave S2reaches and reflects at the back of plate and generates rarefaction wave R3,which leads to tensile failure of the plate material. In 1967, Madden [126] further analyzed the problem by two-dimensional stress wave theory, and considered the influence of lateral rarefaction wave R1on the formation of debris cloud.

Fig. 4. The shock wave propagation analysis through characteristic method [124,125].

Fig. 5. Wave patterns in the projectile and the impacted target [124,125].

Yew et al. [127] also proposed three different modes of twodimensional stress wave evolution that may appear in the cylindrical projectile, as shown in Fig. 6. Consistent with Maiden’s conclusion of one-dimensional stress wave,the axial fracture of the plate is caused by the rarefaction wave R3.The axial fracture of the projectile depends on the lateral rarefaction wave R1, the axial rarefaction wave R4and the axial shock wave S1. The twodimensional wave propagation and evolution analysis could explain the competition mechanism between lateral rarefaction wave R1and axial rarefaction wave R4. And further, it successfully explained the fragmentation mechanism of projectiles with different axis-diameter ratio, and the lateral and axial diffusion of debris cloud.

The curved surface of spherical projectile would result in highly non-linear wave interaction in the projectile and plate, which makes the difficulty for the theoretical analysis of wave propagation. However, the spherical projectile is convenient in experimental launching without considering the attitude of the projectile itself. The spherical projectile impacting onto thick plate of transparent material have been studied experimentally to observe the destruction of projectile and the propagation of shock wave [67].Numerical simulation is the main way to study the wave propagation and evolution for spherical projectile impact.

Fig. 6. 3 cases of the interactions between shock wave and rarefaction wave [127].

Alme and Rhoades [128] calculated the cases that 9.5 mm diameter aluminum projectiles impact onto thin plates at speeds of 6-14 km/s through Arbitrary Lagrangian Euler (ALE) algorithm.They found that the wave front was close to an ellipsoid and the pressure distribution was non-linear.Kipp et al.[83]calculated the histories of the minimum principal stress at five points on the projectile axis through CTH. These studies revealed that the rarefaction waves from sphere boundaries partially unload the shock waves and the unloading process is nonlinear, and the interaction of wave systems are self-similar for the spheres with different diameters.

Ang [129] considered the kinematic characteristics of the interaction process between spherical projectile and bumper.With the penetration of spherical projectile into thin plate, the collision points on the projectile and plate are changing, that is different from that of cylindrical projectile impact.To study the onset of the reversed jet,Ang analyzed the moving velocity of the collision point between spherical projectile and plate, as shown in Fig. 7. D is the sphere diameter; Wpis the shock wave speed in sphere; Wtis the shock wave speed in plate; α is the tangent angle at the collision point.Ang[129]assumed that jet initiates when the shock velocity is greater than the collision point velocity.Before the generation of jet, the wave system evolution in the projectile and plate could be described with one-dimensional theory.

Fig. 7. Sketch impact point velocity after a spherical projectile impacting on target[129].

Grady and Kipp [130] modeled the pressure history on the impact axis of the sphere,as shown in Fig.8.They divided the entire pressure history into two phases according to the effect of the rarefaction wave.In the first phase, the pressure on the axis is not affected by rarefaction wave.As analyzed by Ang[129],the pressure remains the initial impact pressure ph, which can be calculated through shock wave theory.In the second phase,the pressure drops to Bernoulli pressure pb. The duration of the first phase τ1is determined by the arrival time of lateral rarefaction wave. The duration of the second phase τ2is determined by the arrival time of axial rarefaction wave from the rear of the projectile or axial rarefaction wave from the free surface of plate. When the platethickness-to-sphere-diameter ratio t/D is large, the pressure time history is illustrated in Fig.8(b).When t/D is small,τ2may even be shorter than τ1.

Recently, Wen et al. [26] proposed a geometrical propagation model (GPM) to describe the geometrical propagation characteristics of the wave front after the generation of jet,and analyzed the intensity and speed decay of shock waves.Wen and Chen[27]also modeled the rarefaction waves reflected from thin plate surface,and analyzed the influence of the initial impact conditions on the evolution of the wave system as well as debris cloud structure[131].

Since the space debris is mostly irregular[32,132,133],the wave propagation in the projectiles of cube and some other irregular shapes have also been studied. It was found that the debris cloud characteristics and damage ability are related to the projectile shape[33-37].Example is that cylinders impacting in the direction of their axis were considerably more effective penetrators than spheres of the same mass [134]. For non-spherical projectile, the attitude and orientation have more influences on the debris cloud and its damage ability [135-137].

Fig. 8. Model of on-axis pressure history for a sphere impacting on plate [130].

The wave propagation and evolution in the plate could affect the damage of plate. Piekutowski [28] qualitatively explained the formation and development of perforation holes in bumper through the wave analysis.In recent years,Liu et al.[72-75,138]conducted a detailed analysis of the wave propagation in the plate,and further developed an in-situ damage identification technique, which has been effectively proved.

3.2. Dynamic fragmentation

The dynamic fracture and failure of material is an important foundation of explosion and impact. It’s impossible to analyze the hypervelocity impact and protection without the consideration of dynamic fracture and material failure. At the same time, the experimental results of the hypervelocity impact and protection could verify the dynamic fracture and failure theory.Grady and his colleagues are the pioneers in this field [139-141].

Grady studied the dynamic fragmentation of materials based on energy principle. By seeking the minimum energy to energy equilibrium,fracture strength,fracture time and fragment size could be obtained. The theorical results for brittle materials compare well with experimental results, while for the ductile material, the theorical results are not satisfactory.Further,Grady solved the energy equilibrium relationship based on a minimum time criterion, and obtained Eq. (1), which agrees with the experimental results of ductile material.

where Psis the ductile fracture strength;ρ is the density; c0is the bulk velocity;Y is the yield strength;εcis the critical strain;tsis the fracture time; ˙ε is the strain rate;s is the nominal fragment size.

On this basis, Grady proposed three failure mechanisms for fracture states of material at different strain rates: Brittle fracture for low strain rate,dominated by fracture strength;Ductile fracture at medium strain rate,dominated by yield stress;Liquid fracture for high strain rate, dominated by surface tension. These works accomplished the fracture criterion theory of macroscopic scale.

Referring to hypervelocity impact and protection using Whipple shield,the magnitude of impact-produced tensile stress is expected to be much higher than the theoretical fracture strength of material Ps.Since the time for reaching the maximum stress in the material is short,it seems reasonable to expect that the size of fragments is affected only by the strength of the maximum stress Pm.Yew et al.[127]replaced the fracture strength Psin Eq.(1)with the maximum stress Pmto obtain a new expression of fracture time and fragment size as,

where γ, a function of the current temperature, is the surface energy of liquid. The distribution of the fragment size could be calculated based on the distribution of maximum stress Pm. At the same time, Yew et al. [127] thought that Eq.s (1) and (2) over predict the intensity of the catastrophic fragmentation process on the basis of experiments. They altered the theory by introducing an effective breakdown stress Pe, and Pe

where Kcthe fracture toughness of the material;R is a characteristic dimension of material achieving shock state of Pm.

The aforementioned equations to estimate the fragment size and fracture strength based on the Grady spall criterion have been widely used in the research of hypervelocity impact. In addition,Grady et al.[141-143]proposed a non-homogeneous fragment size distribution function on the basis of Poisson distribution,which is a large improvement of the traditional Mott distribution [144].

Generally,it is hard for a single theory of dynamic fragmentation to suit for both ductile and brittle materials.The works of Zhou and his colleagues [145,146] are commendable in the dynamic fragmentation field. Based on the theory of Grady [147], Zhou et al.[146] proposed the rapidest unloading theory in dynamic fragmentation which is suitable for both ductile and brittle materials.

Fig. 9. Fragmentation-initiation threshold velocity as a function of t/D for spherical projectile [25,148].

Piekutowski[25,148] studied the spallation threshold of spherical projectile in hypervelocity impact experimentally, and summarized the dimensionless function of the projectile’s fragmentation-initiation threshold velocity, as shown in Fig. 9.According to a large number of experimental results, Piekutowski proposed that when the plate-thickness-to-sphere-diameter ratio is larger than 0.16 (t/D > 0.16), the threshold velocity maintains to 2.6 km/s.When t/D<0.16,the threshold velocity increase with the decrease of t/D. Fig. 10 shows the sketch and photograph of the projectile deformation at fragmentation-initiation. Hao et al.[149]simulated the spallation and fragmentation of the projectile backside through AUTODYN,studied the propagation and attenuation of the stress pulse under different impact conditions, and further discussed the influence of stress pulse on fragmentation.

3.3. Phase transition, plasma and radiation

Phase transition of the projectile and plate is one of the prominent phenomena of hypervelocity impact,which is also one of the protection mechanisms of Whipple shield. The penetration ability of solid fragment is much higher than that of melted fragment and vaporized fragment. But even for vaporized fragment, the impulsive loading could cause the bend and spall of the subsequent structures[150,151].Rumiantsev and Mikhaylin[152]analyzed the phase transition effect on efficiency of screen protection against elongated hypervelocity projectiles. Anderson et al. [7] discussed the importance of phase transition in debris cloud dynamics.

For aluminum-on-aluminum impact, the material would begin to melt for an impact about 5 km/s,and begin to vaporize at 10 km/s[25]. For the on-orbit impact between space debris and protection structure, the melt and vaporization are dominant in the debris cloud. Phase transition would influence the shield performance[153]. A simple explain for the degraded penetration ability of liquid and gaseous fragment is that the thermal softening caused by shock wave reduces the average kinetic energy of debris cloud.Besides,only the tension needs to overcome for the fragmentation of the melted or vaporized material, that results in smaller fragments.

Schonberg [154] proposed a first-order accurate scheme to determine the materials amount in three states in a debris cloud created by a hypervelocity impact of cylindrical projectile and thin plate.He calculated the residual energy in the projectile and plate materials upon release from their respective shocked states, and estimated the material state with elementary thermodynamic principles.For the materials in mixed phase,the percentage of solid and liquid was obtained through linear interpolation.However,the Schonberg method can only calculate the percentage of each state,while the real distribution and location of phase-changed materials cannot be described.

Piekutowski [155] proposed a method to estimate the state of material in all-aluminum debris cloud produced by spherical projectile.The peak impact pressure was calculated based on the shock wave theory.A linear pressure distribution on the shot-line axis of projectile was assumed. The state distribution was obtained through the state equation and the relationship between particle velocity and material pressure,as shown in Fig.11(a).As depicted in Fig. 11(b), the state distribution of the entire projectile could be estimated by assuming that the material states normal to the shotline axis are consistent. Composition of material in the mixedphase region was assumed to vary linearly between the incipientand complete-melt points. This model provides a feasible method for calculating the state distribution and location of materials.

The impact-induced melt of aluminum could be achieved easily,with the current experimental launch capability. The melt can be confirmed by metallographic analysis of the fragments on witness plate, and by the shape change of melted fragments during the diffusion of debris cloud [155]. However, it is difficult to generate vaporization of a reasonable-sized aluminum projectile. Comparatively, impact-induced vaporization of other projectile and target materials,notably cadmium,lead,and zinc,could be achieved with a less impact velocity [156]. Fig. 12 shows the structural characteristics of the cadmium debris cloud with vaporization [25].Obviously,the expansion of the liquid and vapor fragments would influence the structure and velocity distribution of debris cloud.Schmidt et al. [157] used cadmium as the surrogate material of aluminum to simulate the vaporization of debris cloud. Combined with scale analysis, they further discussed the aluminum orbitaldebris shield performance for the impact at 18 km/s.

Fig.10. Illustration of deformation and spall failure of spherical projectiles [25,148,149].

Fig.11. Schematic of Piekutowski’s phase distribution calculating method [155].

Fig.12. New features of debris cloud gasification in impact test using Cd [25].

Ionization would possibly appear, along with the phase transition when materials undergo hypervelocity impact. Ionization produces multiple bands of electromagnetic radiation, such as visible spectroscopy emission [158], infrared-emitting phenomenon[159]and radio frequency emission[12].It was found that the electromagnetic interference of ionization generated during hypervelocity impact can cause mechanical damage to spacecraft equipment [65]. Recently, Song et al. [160,161], Ju et al. [162], Liu et al. [163], Li et al. [164], Fletcher et al. [165] studied the characteristics of plasma through experimental,theoretical and numerical methods.Tang et al.[166]measured the damage of electromagnetic radiation caused by hypervelocity impact on the logical chip module.

At the same time, the temperature characteristics of debris cloud can be measured using the plasma and electromagnetic radiation phenomena. For the measured electromagnetic radiation data,there are two main analysis methodologies:One is to take the experimental object as a black body and calculate its temperature using Planck black body radiation function;The other is to analyze the experimental characteristic spectral lines according to the principle of atomic spectrum, and obtain the temperature information. Ward et al. [158] obtained the debris cloud temperature according to the first way, and found that the experimental value was higher than that calculated by CTH. Ma et al. [167,168]measured the electromagnetic radiation in the ejecta region, according to the second methodology. The measured waveband was selected from 250 nm to 340 nm. Using Boltzmann diagram method, the relationship between ejecta cloud temperature and impact condition was fitted as:

where T is the ejecta cloud temperature; D is the projectile diameter; V0is the impact velocity. The bumper thickness in their experiments was 2.0 mm.Besides,temperatures were analyzed using the configuration fitting method, and the results were basically same to the Boltzmann diagram method [169]. In addition to measuring the temperature at a certain time, time-resolved spectroscopy was also used to obtain the temperature change over time after impact [64,170]. However, most of the radiation measurements were“average”temperature over both time and space,and it was difficult to obtain the temperature distribution at a certain time.

Numerous numerical simulations have also focused on the phase transition of material after hypervelocity impact. Quintana et al. [171] calculated the impact-induced phase transition of material using CTH software.The results showed that:The influence of material strength on the phase transition is negligible at impact velocities above 10 km/s, and the phase state of material could be judged based on the initial pressure or the final temperature; The strength influence is obvious at impact velocities below 10 km/s,and it is recommended to use the final temperature to judge the phase state of material. Holian and Burkett [79] adopted Eulerian algorithm to calculate the phase distribution, and the results showed that the calculated temperature of material depends on the equation of state.

In the numerical simulation related to phase transition, the Eq.of state plays an important role.Compared to common Eq.s of state,GRAY three-phase incomplete EOS, Tillotson EOS, ANEOS Eq.s of state [172,173], and SESAME complete equations of state database[174] are more suitable for impact-induced vaporization. These equations have been used for calculating the debris cloud phase distribution produced by sphere impact [175]. Fig. 13 shows the time-resolved phase distribution of debris cloud obtained by embedding the SESAME database in AUTODYN [175]. The impact velocity was 15 km/s and the materials were aluminums. In the legend of Fig. 13, “2.0” represents completely vaporization state,“1.0” represents completely liquid state, and “0” represents completely solid state. It can be seen that three phase states may coexist in a debris cloud. The model in Fig. 11(b) is basically consistent with this calculation result, except for the separation between different states. Taking the sphere (or ellipsoid) characteristics of shock waves and rarefaction waves into consideration,a more reliable phase distribution model could be obtained theoretically.

Fig.13. Computed phase distribution using SESAME state data base [175].

3.4. Hole on the bumper

There are perforation holes on the thin plate impacted by the hypervelocity projectile. For the impact of orbital debris, the thin plate is actually the shield or component of a spacecraft, and its damage needs to be detected and evaluated. Currently, there are detection methods based on acoustic emission [72,73], PVDF sensors [176] and resistive grid [177-179], which can realize damage detection, location and damage degree measurement of orbiting spacecraft.

Fig. 14 shows the perforation holes on thin plates of different thicknesses impacted by spheres.The arrow in each hole identifies the location of cross section whose micrographic is shown to the left of the hole photographs. As the plate thickness increased, the size of perforation holes increased, the holes tended to be less circular, and the lip morphology became more complex [28].Generally, the formation of perforation hole could be divided into two stages:punching in the early stage and continuous stripping in the later stage. The material at the edges of the holes is the remaining material after stripping. Piekutowski [28] qualitatively developed a description of the hole-formation sequence according to the wave system acting in the thin plate.

In terms of the size of perforation hole,a theoretical calculation method based on energy has been proposed[180],but it is mainly suitable to the critical penetration of medium-thick targets and lower impact velocity.Most of the Eq.s used for hole size prediction are empirical.In the 1960s,Maiden[181]proposed an empirical Eq.for the hole size of a thin plate impacted by a sphere as,

where Dhis the hole diameter; D is the sphere diameter; ctis the plate sound speed;V0is the impact velocity;t is the plate thickness.It can be seen that the hole size depends on the sphere diameter,the plate thickness,and particularly linearly depends on the impact velocity. Based on Eq. (5), the empirical prediction Eq. has been extended and modified.Sorenson[182]considered the influence of plate shear strength, Swale [183] considered the influence of the density of sphere and plate, Schonberg [184] considered the influence of incidence angle,and Hill [185] considered the influence of the projectile strength.

The regression models for the prediction of hole-diameter are of the form:

where ρpand ρtare densities of the sphere and plate respectively;cpand ctare the sound speeds of the sphere and plate respectively;θ is the angle of sphere impact;C1and C2are constants[186].Abbas et al. [186] gave a set of values of parameter piin Eq. (6) using genetic algorithm as p1=0.08, p2= 0.62, p3= 0.03, p4= 0.88, and p5=-0.08.It can be seen that V0/ctand t/D were the major factors.For specified sphere diameter, as the impact velocity and plate thickness increase, and/or the plate strength decreases, the holediameter increases. In addition to the models as Eq. (6), some other models do not follow the above form [187-189], while the main factors determining the hole-diameter are consistent.

Loft et al. [190] analyzed the effect of sphere rotation on the hole-diameter. Through experimental studies, Piekutowski et al.[29,31] found that the hole-diameter strongly depends on the strength of thin plate, and the impact velocity has a significant effect on the hole-diameter when t/D is great.Myers et al.[191]found that the hole-diameter in the heated plate is significantly larger than that of room temperature. Basically, the studies about perforation performances under extreme conditions are relatively limited.

The theoretical analysis of hole formation mechanism and hole size prediction is of significance, which could provide some references for the formation mechanism of debris cloud. Besides, the perforation of bumper directly determines the mass contribution of bumper to debris cloud, and the study of perforation is also beneficial to the study of characteristic distribution of debris cloud.

3.5. Improvement of the bumper

Fig.14. Photographs and cross sections of holes in plates [28].

The research on the interaction between the projectile and bumper guides the improvement of the bumper material and structure. At the same time, these improved structures with advanced bumpers need more aiming research and analysis.

Initially,the protection structures of hypervelocity impact were mostly in all-metal material. The improvement of bumper mainly focused on the plate morphology. Based on the dynamic analysis,various forms such as corrugated bumper, N-shaped bumper, and net-shaped bumper have been proposed [192]. Silnikov et al.analyzed the efficiency of needle structure at hypervelocity impact[193].These structures change the geometrical interaction between the projectile and bumper during impact, and at a certain extent,improve the protection ability of the shield.

Further,some new bumper materials have been proposed,such as Ti-6Al-4V material [194], Nextel and Kevlar-epoxy material[195], Aramid fiber and its compound with ceramic. These materials have higher protection abilities. Besides, the self-repairing ionomer [196] has a smaller perforation hole than traditional aluminum material, resulting a slighter damage of bumper fragments to subsequent structure. Wu et al. [197] and Ren et al. [39]took the energetic materials as bumper to promote the deceleration and fragmentation of projectile through the impact-induced chemical reaction.

Some bumper structures have also been proposed and applied.Hou et al. [198] analyzed the pressure-time curve of the impact process between impendence gradient plate and projectile. They found that the high impedance material placed at the front can increase the peak pressure, while the relative lower impedance material placed at the rear makes the shock unload slower and increases the duration of the shock, that leads to a more complete fragmentation of the projectile.Besides,it was found that material compressibility may increase the impact pressure at hypervelocity impact [199-201], and thus the influence of compressibility on debris cloud may need more attention [202].

In recent years, Klavzar et al. [203] added Ni metal coating to aluminum metal foam, which effectively improved the protection performance, but at the same time increased the structural area density. Higashide et al. [204] found that CFRP has a better performance than aluminum plate of the same area-density when the plate thickness is large, but the improvement is not prominent for the thinner plate.Song et al.[205]proposed a composite laminate as bumper, and evaluated its protection performance through experiment and numerical simulation. In addition, Zhang et al.[58,59] proposed Al/Mg composite structure bumper, Ti/Al/Nylon composite structure bumper, and Huang et al. [41] proposed amorphous reinforced structure bumper as shown in Fig. 15.Aleksandr and Igor [206] did a preliminary experimental and numerical study of the bumper with high-impedance ceramic coating.These new structures of bumpers have significantly improved the protection capability of the shields against hypervelocity impact.In order to further improve the performance of shields, Destefanis et al. [207] conducted a comparative study on the protective performance of various forms of bumper structure,with the support of European Space Agency.

4. Movement and diffusion of debris cloud

After the interaction between the projectile and bumper, the damage and fragmentation of projectile are basically completed,and then the fragments would diffuse inertially and form an expanding debris cloud. The movement and diffusion of debris cloud can reflect the interaction between the projectile and bumper at a certain extent.More importantly,it affects directly the impact and damage on the subsequent structure.

In this section,the characteristic information of debris cloud and some representative debris cloud models are introduced. The improved Whipple shields with filled material in the gap between the double-layer plates, namely filling-type Whipple shield, are also introduced.

4.1. Characteristics of debris cloud

A debris cloud containing solid and even phase-changed fragments would be produced by the hypervelocity impact of the projectile and bumper.Fig.16 shows a debris cloud produced by the impact of spherical projectile [25]. The characteristics of debris cloud depend on a variety of factors including the material and geometry of projectile and plate, impact angle and velocity, and ambient temperature, etc.

Piekutowski [25] performed a series of hypervelocity impact experiments since the 1990s, provided a lot of accessible data and experimental images, and systematically analyzed the structural characteristics of debris cloud. It is one of the most outstanding work in this field. Piekutowski proposed that the structure of a typical sphere-induced debris cloud consists three major features:the eject veil (Fig. 17 left), the external bubble of debris (Fig. 17 middle), and the internal structure (Fig. 17 right). The internal structure is composed of a front, a center and a rear element. The internal structure contains most of projectile material and a small amount of plate material, of which the front and center elements are denser.

Fig.15. Amorphous reinforced plate (left) and Al/Mg impedance-graded plate (right) [41,59].

Fig. 16. Debris cloud produced by hypervelocity impact of 9.53 mm sphere and 1.549 mm plate [25].

Fig.17. Features and elements of debris cloud [25].

In the ground-based experiment,the three-dimensional spatial distribution of debris cloud is projected to a two-dimensional graph through flash X-ray photography technique [54] and laser shadow photography technique [11,56]. The projection process would inevitably result in some superposition of information and it is difficult to accurately and comprehensively unfold the spatial distribution of debris cloud.Swift et al.[208]set grids on the trajectory to partition the debris, and quantitatively described the velocity,mass, and material distribution of the debris cloud produced by sphere. They found that the debris cloud is an empty shell structure, and almost all material is distributed on the thin shell. Piekutowski [25] obtained a thin layer of debris cloud (Fig.18(b)) by placing a dissector plate with a slit(Fig.18(a)),and found that there are actually two layers of material in the internal structure of the debris cloud. In Fig.18, the layer pointed by the arrow is the front layer of internal structure,while the large shaded area is the second layer of internal structure.

Fig.18. Photograph of the dissection of debris cloud produced by spherical projectile[25].

A similar experiment was performed for the debris cloud produced by copper disk projectile impacting aluminum plate. The copper has worse transmittance than aluminum under X-rays,and thus the materials of projectile and plate could be easily distinguished. The materials of the disk projectile and plate are respectively distributed on two thin shells, and the internal structure of debris cloud do not distribute in two layers like that produced by spherical projectile [209].

The relationship between the internal structure of debris cloud and initial impact conditions has also attracted considerable attention. Piekutowski [25] found experimentally that as impact velocity increases, the diameter of the large central fragment and the average diameter of fragments at the rear element of internal structure decrease with the power-law of impact velocity.Changing the t/D ratio do not alter the power-law dependence but do change the fragment diameters. The fitting relations are:

where dfis the diameter of the large central fragment (spherical equivalent diameter); dmis the average diameter of fragments at the rear element; V0is the impact velocity. The experimental fragment diameter was further compared with diameter computed through Grady relationship.

To represent velocity feature of debris cloud, the velocities of a series of measurement points were measured by Piekutowski[25].With the change of t/D and impact velocity,the velocity direction of the edge fragment would change, and the spray angle of debris cloud would be different. The spray angle represents the angle between the most-outer fragment velocity vector and the impact line. In addition, the expansion velocity of rear element and the axial velocity of center element were affected by the projectile materials[25].Akahoshi et al.[71]also gave a detailed discussion of the spray-angle as a function on initial impact conditions.

Compared with experiment,numerical simulation is convenient for observing debris cloud information in a high time resolution,and it is often used to study the characteristics of debris cloud.Zhang et al. [210] arranged measurement points in the simulation model to analyze the motion of debris cloud. They accurately obtained the debris cloud structure and the location of measurement points, and reduced the post-processing error of numerical simulation.However,this method was relatively tedious and the manual analysis was lack of quantitative standards. SPH algorithm is commonly used in numerical simulation to obtain the overall distribution of debris cloud. But SPH algorithm is not reliable for the particulars of debris cloud. To reproduce the random of fragmentation caused by the inherent flaws of material, a stochastic factor could be adopted [144].

Fig.19. Debris cloud simulated with adaptive FEM-SPH method [114].

There is also a special problem for the study of the debris cloud characteristics in numerical simulation, which is “fragment identification”. In 1995, Benz et al. [211] proposed a boundary identification method based on the cumulative damage factor for fracture, that is, particles at the fracture location constitute the fragment boundary. Zhang et al. [121] proposed a FEM-SPH-FEM method. The FEM model was built at the beginning and then the calculation was converted in SPH.In the end,the calculation results were transferred to FEM for fragment identification. Liang et al.[212] used sub-grids to construct particles into a linked list, and then used breadth-first search algorithms to determine particle affiliation in the connected graph.Liang et al.built the convex hulls of the fragments, deleted the particles inside the fragments, and obtained the boundaries and size of large fragments.

Fahrenthold and Horban [106,107] used particles and finite elements simultaneously but not redundantly to represent different physical effects, and proposed an improved hybrid particleelement method. In 2020, He et al. [114] used FEM-SPH adaptive method, transformed the large deformed material into particle from element, and got an effective and accurate identification of fragment. After the impact, the fragment still exists in the form of element, and the shape of the fragment can be obtained directly.Further, the distribution of threaten fragments in debris cloud can be given by statistical methods. The debris cloud of aluminum sphere at 2.54 km/s simulated by this method is shown in Fig.19.It is worth mentioning that if the meso-modelling was combined,the FEM-SPH adaptive method would be suitable for the impact simulation of advanced materials such as fiber material,impedance gradient material and metal foam.

Besides, the projectile shape [33-37], bumper structure[120,213-216], impact angle [217-220], ambient temperature[191,221-224]and other factors also have significant effects on the characteristics of debris cloud, but the relevant research schemas are generally similar.

4.2. Debris cloud model

Within a short time,the debris cloud would reach a stable state,and the structure of debris cloud would not greatly change. The debris cloud diffuses in the gap between the double-layer plates with a self-similar structure. Many simple and effective models have been proposed to describe theoretically the structure and motion of debris cloud.

In this field, the initial efforts focused on the conservation of momentum and energy, and tried to construct the motion models of debris cloud with some artificial parameters [225-227]. Swift model is an outstanding one [226]. Swift model assumed that the mass of debris cloud is uniformly distributed in a spherical shell,as shown in Fig. 20, and the movement of debris cloud could be decomposed into the axial movement of mass center and the radial expansion. Taking the projectile and plate perforation into the conservation of momentum, the axial velocity and expansion velocity can be directly obtained. Based on energy conservation, the kinetic energy of the projectile was transformed into axial kinetic energy, expansion kinetic energy, and the energy consumed by fragmentation and phase transition.According to the damage level,the energy consumed by fragmentation and phase transition per unit mass could be adjusted and the expansion velocity could be obtained. The velocities in different parts of debris cloud can be calculated directly by the superimposing of velocities.Swift model is relatively simple, has a significant engineering application and can explain some basic problems [228].

Fig. 20. Swift debris cloud model [226].

For the debris cloud produced by disk projectile, Piekutowski[209] proposed a simple theoretical model based on experimental results in 1990. The model described the structure of debris cloud based on five measurement points, as shown in Fig. 21. The velocities of the five measurement points include the axial velocity of the mass center V1,the radial velocity of the mass center Vrad,the front velocity Vf,the rear velocity Vr,and the front velocity Vcuof the plate material. These velocities can be obtained experimentally. In addition, the axial velocity V1of the mass center can be obtained through the conservation of momentum. The front velocity Vf, the rear velocity Vr,and the front velocity Vcuof the plate material can be calculated based on one-dimensional shock wave theory.

Fig. 21. Model of debris cloud proposed by Piekutowski [209].

Fig. 22. Corvonato debris cloud model [232].

Bless [229] improved theoretically Piekutowski’s model, and built a model based on four characteristic velocities. The axial velocity of the mass center and the front velocity of Piekutowski model were combined in Bless model. The four characteristic velocities could be obtained through a relatively simple shock analysis.Based on Piekutowski model,Yew et al.[127]combined Grady spallation theory and the lateral velocity results at the thin plate edge proposed by Elliot [230], and obtained theoretically the characteristic velocities and fragment diameters of the debris cloud produced by disk projectile.

The debris cloud model proposed by Cohen [231] is applicable when the debris cloud is all solid fragments or a composition of solid fragments with some liquid droplets.The ratio of liquid phase to solid phase in the debris cloud is obtained by interpolation calculation, and the expression of solid fragments is extended to solid-liquid mixed phase. Further, taking the debris cloud spray angle, impact velocity, bumper thickness, and gap distance into consideration, the model can predict the depth of cratering penetration loaded by debris cloud on witness-block.

Corvonato et al. [232] introduced an integral model capable to describe the evolution of debris cloud. The model included a forward cloud and a reverse jet,as shown in Fig.22.The model relied on the self-similar evolution of debris cloud, and used the Bernoulli’s lemniscate as the shape function of debris cloud.

Sch¨afer [233] split the debris cloud of spherical projectile into three parts: a large central fragment, spall’s fragments of the projectile, and fragments of the thin plate (bumper), as shown in Fig. 23. A spherical shell and an ellipsoidal shell were used to represent the distributions of spall’s fragments and bumper fragments respectively. An exponential distribution function was assumed for the mass distribution of the spall’s fragments. The bumper fragments were assumed to distribute uniformly.

It should be noted that the aforementioned debris cloud models are only applicable to the normal-impact of metal projectile onto thin metal plate.Some debris cloud models for different materials,different bumper structures,and different impact angles were also developed in recent years. Wang et al. [33] proposed a model to predict debris cloud induced by hypervelocity impact of different shape projectiles on multi-plate structure.Huang et al.[122]used a large number of experiment and simulated results to develop an engineering debris cloud model suitable for both normal and oblique impact. Francescon et al. [234] proposed an engineering model to describe the debris cloud generated by sandwich plate subjected to both normal and oblique impacts.

Fig. 23. Sch¨afer debris cloud model [233].

4.3. Restricted movement and diffusion of debris cloud

As mentioned above,a large number of new materials and new structures have been used for the bumper of shield to improve protection performance. These changes enhance the interaction between the projectile and bumper. Many other improvements of shield structures focus on the movement and diffusion of debris cloud.

The simplest and most direct way is to increase the distance between the double-layer plate and expand the diffusion range of debris cloud. Since the double-layer plate structure (Whipple shield) was proposed, the gap distance was an important design parameter [6].

Generally speaking, filling other materials or structures in the gap could be regarded as the improvement of shield. The supplementary filled material will influence the movement and diffusion of debris cloud, thereby affect the damage ability of debris cloud.These improved structures could be called as generalized fillingtype protection structures, as shown in Fig. 24. For example, on the basis of the double-layer plate, the structure with some extra thin plates at the gap, is called as the multi-wall protection structure, which is one of generalized filling-type protection structure[235].

As early as 1970,Richardson et al.[225]discussed the protection mechanism of multi-wall structure against hypervelocity impact.Many researchers [236-240] have also conducted experiments to study the protection capability of multi-wall structure.Wang et al.[33]combined the experimental and simulated results to establish a debris cloud models of multi-wall structure.Wen et al.[60,61,241]added wood and light materials between the double-layer plates,that has successfully improved the protection performance.

New structures such as foam-filled protective structures[242,243]andhoneycombsandwichmaterials[93,132,213,244,245]have a more significant effect on debris cloud movement and diffusion. At the same time, foam and honeycomb materials have lower density than metal materials, that is more conducive to engineering applications, thus it will be one of the main research directions in the future.

High-pressure vessels impacted by hypervelocity projectile is also a very important category in the field of space debris protection.High-pressure gas could be regarded as filling materials.After the impact of high-pressure vessel by hypervelocity projectile, the internal high pressure would also restrict the movement and diffusion of debris cloud as well as the perforation hole on vessel wall [246-250].

5. Interaction of debris cloud and witness/rear plate

Debris cloud produced by the hypervelocity impact with bumper will directly impact and damage the spacecraft bulkhead or subsequent component. The impact of debris cloud has some influences on these neighboring structural parts [251,252]. In the ground-based experiment,the damage of debris cloud to bulkhead is evaluated by the damage on the rear plate.Based on the damage of rear plate and specified failure criterion,ballistic limit curve and ballistic limit euqation could be established to quantitatively represent the protection capability of shield,which is an important research area of the interaction between the debris cloud and rear plate. Besides, by setting rear plates of different thicknesses and different materials,the information of the interaction between the projectile and bumper can be reversely analyzed.So,the rear plate is also called as witness plate.

Fig. 24. Multi-wall and honeycomb sandwich structure effect on the dispersion of debris cloud [235,244].

5.1. Ballistic limit of Whipple shield

The protection performance of a structure is usually characterized by ballistic limit curve or ballistic limit equation [253]. The complete penetration (perforation) and the detached spall of the rear plate are the common two failure criterions.The ballistic limits corresponding to different failure criterions would generally be different. The ballistic limit can be expressed in the forms of projectile threshold velocity, projectile threshold size, plate threshold thickness, etc. The creation of ballistic limit curve and the ballistic limit Eq.is a combination of modelling integrated with experiment and materials science, which brings great conveniences to the engineering design of protection structure.

Fig.25 shows the typical ballistic limit curves of metal Whipple shields [254]. The ballistic limit thickness represents the critical thickness of the bumper with which the shield would be failed under the impact.The two curves represent the cases of Al and Cd for both projectile and shield,respectively.The ballistic limit curve of Whipple shield is usually segmented. Taking the Al-Al curve as an example,before the first peak,the projectile keeps intact,so the higher the impact velocity, the stronger its penetration capability.Then, the projectile becomes shatter and is broken into a debris cloud, its penetration capability starts decrease. As the impact velocity continues to increase, for the completed fragmentation and increasing kinetic energy of the debris cloud, the penetration capability of debris cloud increases again. The curve reaches the second peak, when the material of debris cloud starts melt. When melted fragments appear, the penetration capability decreases again until the completed melt of debris cloud.As shown in Cd-Cd curve,the velocity continues to increase and material vaporization would occur. Fig. 25 illustrates sufficiently the influence of fragmentation and phase transition on the protection performance against hypervelocity impact.

Fig. 25. Ballistic limit thickness of dual-wall structure [254].

The ballistic limit equation is the analytical equation of ballistic limit curve. The ballistic limit Eq. of metal Whipple shield was originally proposed by Cour-Palais [255] at the Hypervelocity Impact Symposium in 1969, and Christiansen [256] modified the Eq. in 2001, and then Reimerdes et al. [257] further modified the equation in 2006.

Recently, with the development of shield design and artificial intelligence, shield performance prediction based on artificial neural networks and machine learning techniques [258,259] have also been proposed. Artificial neural networks and machine learning techniques are well suited to solve problems in classification, regression and novelty detection-particularly in high dimension problem spaces such as dynamic impact events.

Ryan et al.[259]found that machine learning techniques could offer improved accuracy over conventional semi-analytical methods. Further, the Creativity Machines process was applied to design weight optimized Whipple shields, which is depicted in Fig.26.For the uphill climb,once a new minimum weight Whipple shield design is created,it becomes the new standard against which subsequent designs are compared.

Some simplified calculations of ballistic limit based on debris cloud models and/or large central fragments were performed. In 1990, Piekutowski [209] used the debris cloud distribution model to calculate the load history on the rear plate, and compared the calculation results with experiment observations. In 1995, Cohen et al. [231] predicted the depth of cratering penetration into witness plate, taking the debris cloud spray angle, impact velocity,bumper thickness, and gap distance into consideration. In 2011,Ryan et al. [253] estimated the penetration performance of debris cloud according to that of the large central fragment, while the large central fragment data was obtained experimentally[25].The result was compared well with the experimental result,as shown in Fig. 27. Wen et al. [260] analyzed the characteristics of the large central fragment, and got a quantitative function of the large central fragment depending on the initial impact conditions, and further acquired the ballistic limit equation.

Fig. 26. Schematic depiction of the CM process for designing a new Whipple shield [259].

Fig. 27. Whipple shield ballistic limit curves and a new curve based on calculation[253].

Numerical simulation is an alternative method to obtain the penetration capability, momentum and energy distribution and load history of debris cloud.However,the most popular algorithm for hypervelocity impact simulation, SPH, has deficiencies like tensile unstable, high time complexity, and difficulty in applying physical boundaries, which limit the application of numerical simulation for assessing the shield performance.Even so,due to its economic and fast advantages, the numerical simulations can still be helpful for ballistic limit [118,261].

Currently,Whipple shields are no longer limited to simple metal material.Many new protection materials and structures have been proposed. Besides, there are a large number of thermal protection materials, glass windows and pressure vessels in spacecraft, and these structures and materials are also susceptible to hypervelocity impact[17,18].Hu et al.[35]and Schonberg et al.[34]discussed the ballistic limit of non-spherical projectiles. Ryan et al. [132,262]studied the ballistic limit of various advanced materials and structures.

5.2. Information on the witness plate

Debris cloud produced from orbital collision will become new space fragments and continue to pose threat to orbital spacecraft.Except for the evaluation of shield’s performance,the debris cloud produced by hypervelocity impact should also be fully understood for the formation and evolution of space debris. The formation of debris cloud by hypervelocity impact is extremely transient, and the in-situ detection is relatively difficult. The analysis of the witness plate could provide some important information of debris cloud. In the ground-based experiment, two witness plates could be placed to witness the reverse jet and the forward debris cloud respectively, as shown in Fig. 28.

For the thin witness plate, its perforation and/or spallation reflect the characteristics of debris cloud.As mentioned above,the damage of rear witness plate is actually the evidence to assess the shield ballistic limit.Piekutowski et al.[25]analyzed and classified the damage on the witness plate experimentally,and discussed the relationship between the rear witness plate damage and debris cloud structure. Loft et al. [264] conducted a large number of experiments to observe the damage of rear plate caused by debris cloud,and compared the results with hydrodynamic simulation.It was found that the hydrodynamic simulation could not fully display the damage of debris cloud to rear plate.Guan et al.[66]and Wen et al. [265] quantitatively studied the relationship between the damage area of rear witness plate and impact conditions.

In recent years, Zhang et al. [58,59] evaluated the protection capabilities of the shields with Al/Mg impedance-graded and Ti/Al/Nylon impedance-graded bumpers by the damage of rear witness plates. Wen et al. [55,61,266] analyzed the structure of the debris cloud generated by lightweight stuffed structures, and evaluated the protection capabilities of these structures.Nishida and his team[223,263,267,268] carried out a large number of experiments, and analyzed the effects of temperature and material on the debris cloud and reverse jet according to the damage of witness plates.

Kim et al.[269]presented a traceback method for predicting the initial impact conditions through analysis of the dispersion characteristics of debris. The dispersion area of the debris on the witness plate were investigated for the determination of the impact conditions. Jae et al. [270] effectively determined the fragments of various shapes through the analysis of trajectory similarity and quantitatively evaluated the threat of the fragment to witness plate.

Thick and soft witness plate can be used to collect the fragments of debris cloud.Akahoshi et al.[69]impacted thin aluminum plate with cylindrical polyethylene projectile,and used capture material made of konjak (jelly-like Japanese food made from the konjak flour) to collect and measure the fragment position and mass information. Shumikhin et al. [271] used light foam materials to collect reverse jet after impact, and analyzed the characteristics of reverse jet fragments, as shown in Fig. 29. Masuyama et al. [272]established an automation of the experimental data evaluation method, and evaluated the debris cloud generated by plates in different materials through the method.

Fig. 28. The set-up and photographs of experiment with witness plates [263].

5.3. Improvement of the rear plate

Limited by manufacture and assembly requirements of spacecraft, it is difficult to adopt complex structures as the bulkhead.Even so, in ground-based experiments, some tentative improvements of the rear plate of Whipple shield have also been studied.Although there is still a long way from practical application, the improvements of rear plate are helpful for the understanding of hypervelocity protection. A tentative improved structure of rear plate was proposed by Wen et al. [60], in which the rear wall combining light materials and an aluminum plate was used to replace the simple rear plate,as shown in Fig.30.It is found that the structure can improve the protection capability against debris cloud, while the principle and optimal design still need more comprehensive studies.

6. Summary and suggestion

Fig. 30. Sketch of Whipple shield and rear combined wall shields [60].

Hypervelocity impact and protection is of great significance in the fields of aerospace and planetary defense. The protection of spacecraft against space debris of millimeter size is one of the direct applications of hypervelocity impact.Structures based on Whipple shield are studied and analyzed to defend the hypervelocity impact.The protection of these structures includes three steps: the interaction between the projectile and bumper, the movement and diffusion of the debris cloud, and the interaction between the debris cloud and witness plate, which have been widely studied through ground-based experiment and numerical simulation.Some improved structures have also been proposed, focusing on these three steps.

Two orientations are suggested for future research in this area:One is the engineering orientation, i.e., to directly serve the engineering application of hypervelocity impact and protection, and provide support for the corresponding scientific research.The other is the scientific orientation, i.e., to explore the protection mechanism of basic structures, guide the experiments of hypervelocity impact, and make contribution to material science and physical science.

The engineering orientation should aim at actual requirement,make attempts for exploratory, advanced and deployable protection structures. The evaluation methods of the performance of various structures and the engineering models for the impactinduced debris cloud should be proposed to guide the shield design. The scientific orientation should focus on the interdisciplinary research and explore the underlying physics of the hypervelocity protection.The propagation and evolution of wave system,the dynamic fragmentation of materials and the related electromagnetic radiation phenomenon should be studied and discussed in detail.Simultaneously,the scientific orientation and engineering orientation promote each other.

For both the scientific and engineering orientations, the research methods are ground-based experiment and numerical simulation. The developments in this area still rely on the developments of these two methods, which should be continuously improved.

For the ground-based experiment, developments include but not limit to:

· Improving the launch ability with a more range of impact conditions,including the material,mass,size,and velocity of the projectile;

· Adopting high-resolution and high-accuracy diagnostic technique to acquire information, including impact velocity,debris cloud image, impact-induced plasma and radiation;

· Using novel and abundant methods for result analysis,including scanning electron microscope (SEM), Energy Dispersive X-ray (EDX) spectrometer, artificial neural networks and machine learning methods;

· Testing advanced materials and configurations for hypervelocity impact in complex environments, such as fiber materials, foam materials, multi-wall structures, and sandwich structures under different ambient temperatures.

For numerical simulation, developments include but not limit to:

· New modeling methods, advanced algorithms and accurate material models, which could be calibrated with each other on the basis of accessible test results;

· Simulating advanced materials and configurations for hypervelocity impact under extreme environment which is hard for the ground-based experiment;

· Establishing a complete simulation and evaluation method of hypervelocity impact protection capability;

· …The research on hypervelocity impact protection based on Whipple shield has a practice application. The high-temperature and high-pressure phenomenon induced by the hypervelocity impact also provide a basis for the research of frontier sciences.Currently, four specific issues are suggested for the research of Whipple shield and its improved structure: the development of Whipple shield structure, the characteristics of the debris cloud produced by new structure,the phase transition in the debris cloud and the advanced numerical simulation methods.

1. The combination of multi-layer plates instead of single-layer metal plate is the main development trend of Whipple shield.The applications of advanced fiber woven materials, multifunctional density-graded materials, honeycomb and metal foam materials, will change the characteristics of the debris cloud.The study of the relationship between different materials/structures and the debris cloud characteristics will improve the design of protection materials/structures.

2. The studies of the debris clouds produced by the high attackangle impact and/or fiber woven materials, multi-functional density-graded materials, honeycomb and metal foam materials are very limited. There is a lack of corresponding debris cloud models and penetration performance research. For improved Whipple shields, personalized determination of ballistic limit equations is closely related to their application development and optimization design. The understanding of the debris cloud characteristics needs to be transformed from the mass/phase distribution of the debris cloud to the quantitative characteristics of the single fragment in the debris cloud.

3. Limited by the experimental techniques, the impact tests at higher speeds (>8 km/s) that consider phase transition especially vaporization,are rare.The analysis of the characteristics of the multi-phase debris cloud is still phenomenological, and there is no suitable theoretical model of the multi-phase debris cloud. Research on phase transition of the oblique incidence and/or advanced shields has not been systematically carried out.Existed equations of state, material parameters and numerical calculation methods are difficult to simulate the three-phase debris cloud.4. Numerical simulation has become an important method for studying debris clouds produced by hypervelocity impact.Equations of state and material parameters for fiber woven materials, multi-functional density-graded materials, honeycomb and metal foam materials under hypervelocity impact conditions are necessary.Fragment identification is a key step to transform the debris cloud research from macroscopic state analysis to quantitatively statistics analysis. The FEM-SPH adaptive method combines the advantages of the grid method and meshless method. Combined with anisotropic material models and meso-modeling methods, the FEM-SPH adaptive method could simulate the complex protection materials/structures.At the same time,the FEM-SPH adaptive method has a better expansibility to simulate the phase transition in the debris cloud.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (11627901, 11872118). The authors wish to acknowledge the constructive comments by the editor and reviewers that have greatly improved this paper.