Jianwen Xie, Yuanfeng Zheng, Zhenyang Liu, Chengzhe Liu, Aoxin Liu, Pengwan Chen,Haifu Wang

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

Keywords: Reactive material projectile Hydrodynamic ram Enhanced structural damage Liquid-filled tank Impact

ABSTRACT A series of ballistic experiments were performed to investigate the damage behavior of high velocity reactive material projectiles (RMPs) impacting liquid-filled tanks, and the corresponding hydrodynamic ram (HRAM) was studied in detail.PTFE/Al/W RMPs with steel-like and aluminum-like densities were prepared by a pressing/sintering process.The projectiles impacted a liquid-filled steel tank with front aluminum panel at approximately 1250 m/s.The corresponding cavity evolution characteristics and HRAM pressure were recorded by high-speed camera and pressure acquisition system, and further compared to those of steel and aluminum projectiles.Significantly different from the conical cavity formed by the inert metal projectile, the cavity formed by the RMP appeared as an ellipsoid with a conical front.The RMPs were demonstrated to enhance the radial growth velocity of cavity, the global HRAM pressure amplitude and the front panel damage, indicating the enhanced HRAM and structural damage behavior.Furthermore, combining the impact-induced fragmentation and deflagration characteristics, the cavity evolution of RMPs under the combined effect of kinetic energy impact and chemical energy release was analyzed.The mechanism of enhanced HRAM pressure induced by the RMPs was further revealed based on the theoretical model of the initial impact wave and the impulse analysis.Finally,the linear correlation between the deformation-thickness ratio and the non-dimensional impulse for the front panel was obtained and analyzed.It was determined that the enhanced near-field impulse induced by the RMPs was the dominant reason for the enhanced structural damage behavior.

1.Introduction

Hydrodynamic ram (HRAM) is known as the phenomenon that occurs when a high velocity projectile penetrates a liquid-filled container or tank and transfers kinetic energy to the liquid.HRAM can produce significant pressure inside the liquid and may cause significant structural failure to the tank wall.For fuel tanks filled with flammable fuel, HRAM may further cause fuel leakage, ignition and even detonation.The HRAM effect in fuel tanks is identified as one of the most important factors in aircraft vulnerability, especially for military aircraft,since the fuel tanks impacted by high velocity projectiles may cause catastrophic failure such as aircraft loss [1].For this consideration, anti-air weapons, such as missiles and close-in weapons, usually achieve lethal strikes on military aircraft fuel tanks by projecting high velocity fragments or projectiles.Thus,research on the damage mechanism of HRAM is not only an important basis for the structural design of fuel tanks, but also a major requirement in the development of efficient damage weapons.

The HRAM mechanism may be briefly summarized as an energy transfer process from a high velocity projectile to the surrounding liquid, and can be described in following four phases:

(1) The shock phase.The initial impact of the projectile with the front tank wall produces the initial impact wave, which propagates through the liquid.Subsequently, the projectile perforates the tank wall and enters the liquid.

(2) The drag-cavity phase.As the projectile passes through the liquid,it gradually decelerates and transfers kinetic energy to the liquid due to viscous drag.Disturbed liquid begins to flow from the projectile path,forming a conical cavity behind the projectile, while generating a radial pressure field.

(3) The cavity oscillation phase.As the cavity expands to its maximum size, it begins to shrink and collapse.The cavity then undergoes repeated cavity collapse cycles, which produce multiple oscillation pressures.

(4) The exit phase.Once the residual kinetic energy is sufficient,the projectile further perforates the rear tank wall and exit the liquid.

For a better understanding of HRAM and the corresponding fluid-structure interaction, considerable research has been carried out to investigate the HRAM pressure, cavity evolution and structural damage.In general,the HRAM pressure consists of three main parts: initial impact pressure, drag pressure and collapseoscillation pressure.The initial impact wave generated during the initial impact had a high pressure amplitude but a short duration[2].McMillen et al.found that the initial impact wave propagating through water gradually decayed as the propagation distance increased or the θ decreased, where θ is the angle away from the free surface[3].The drag pressure following the initial impact wave was mainly concentrated in the region in front of the projectile.McMillen and Disimile found that its amplitude decreased with decreasing the projectile kinetic energy, and also decayed rapidly with distance [4,5].The collapse pressure was generated and radiated outward as the cavity shrank to its minimum size.This pressure also decayed rapidly with distance,and its attenuation law was approximately correlated to a cubic polynomial[5].Due to the air acting like a spring within the cavity, the first collapse was followed by repeated cavity collapse cycles, where multiple oscillation pressures were produced, although the pressure gradually decreased with each cycle [6,7].

With the cavity evolution and HRAM pressure loading, the structural damage to the liquid-filled tank occurred correspondingly.The above four phases contributed to the structural damage in different mechanism and to different extent,which were also closely related to the tank size and the projectile kinetic energy.During the shock phase, the pressure loading with high amplitude and short duration mainly led to damage in the vicinity of the impact point.This phase was also found to be one of the main causes of failure for the tank with large size or in the case of low-strength projectiles[5].However, for a tank with similar size as the cavity, the structural damage was closely related to the cavity phase [8].In addition, the severe structural damage of the entry panel was concentrated in the vicinity of both the panel joints and the fragment perforation sites,whereas the severe structural damage of the exit wall was in the vicinity of the fragment perforation sites [9].Varas et al.found that both the velocity of the steel projectile and the filling level had a significant influence on the deformation of the liquid-filled aluminum tube.The effect of velocity was to generate localized bulge near the impact point,while the filling level mainly produced the global deformation on the tube [10].Ren et al.investigated the deformation and failure modes of water-filled vessel impacted by steel projectiles with different nose shapes.They found that the projectile with larger nose shape coefficient could produce more severe damage to the rear panel,which could lead to tearing cracks with obvious plastic deformation[11].

In addition to experimental research, based on the numerical algorithms such as Arbitrary Lagrangian-Eulerian (ALE) and Smoothed Particle Hydrodynamics (SPH), the cavity evolution,HRAM pressure and tank wall deformation were well reproduced in the simulation[12-14].Furthermore,by developing the theoretical models involving projectile motion, cavity growth and HRAM pressure, the damage mechanism of each phase was further analyzed[15-17].The above research indicates that great progress has been made in the experimental, numerical and theoretical research of HRAM.However,the projectiles considered in the above studies were fabricated by inert metals such as aluminum, steel,and tungsten,and the energy source of HRAM was demonstrated to be the projectile kinetic energy only.For traditional anti-air weapons projecting inert metal fragments, the kinetic energyonly damage mechanism faces great challenges in attacking wellprotected fuel tanks due to the single energy source and insufficient energy level, which is also a major bottleneck limiting the development of anti-air weapons.

In recent years, the military applications of reactive materials have attracted much attention.Reactive materials are a class of new energetic materials, which are extremely insensitive under normal conditions.However, these materials will be initiated to deflagrate violently under extreme loading such as explosive driving or high velocity impact[18,19].Significantly different from explosives,reactive materials have two typical characteristics:delayed reaction and non-self-sustaining reaction.The delayed reaction characteristic refers to that, the initiated reactive material (under extreme loading)needs to undergo a specific initiation delay time before deflagration occurs.The initiation delay time is closely related to the material properties and loading conditions [20,21].Non-self-sustaining reaction characteristic refers to that the initial deflagration of reactive material is not sufficient to initiate the remaining unreacted material,while the continuous input of external energy is necessary to sustain the following reaction [22].Thus, reactive damage elements (projectiles, jets, etc.) prepared by reactive materials will be initiated to deflagrate during penetrating the target, which have both kinetic energy penetration capability and chemical energy deflagration damage capability.These combined effects of kinetic energy and chemical energy can enrich the damage energy source and significantly enhance the damage energy level.

Among the reactive materials, polymer-based metallic reactive materials are the most widely studied.Polytetrafluoroethylene/aluminum (PTFE/Al) is a typical polymer-based metallic reactive material, in which Al will react with the fluoride produced by the decomposition of PTFE under certain conditions(like high velocity impact) as follows:

PTFE/Al reactive material is generally fabricated into reactive damage elements followed a cold uniaxial pressing/sintering process, such as reactive material projectiles (RMPs) [23].However,this RMP has a relatively low density and strength compared to metal projectiles.For the purpose of improving density and strength,heavy metal like tungsten(W)is often added to the PTFE/Al reactive material.Extensive studies on PTFE/Al/W RMPs have been carried out, involving mechanical properties, energy release characteristics and damage effect.Wang et al.investigated the influence of different W contents on the compression properties and impact sensitivity of PTFE/Al/W composites [24].The results showed that the dynamic strength of PTFE/Al/W composites increased significantly with the increased W content, but the initiation delay time and absorbed critical energy before reaction also increased.Xu et al.studied the effects of impact velocity and front panel thickness on the energy release characteristics of PTFE/Al/W RMPs [25].The results demonstrated that increasing the impact velocity and the front panel thickness could increase the initiation ratio of RMPs,thus enhancing the energy released behind the target.Moreover, a series of ballistic experiments showed that when high velocity PTFE/Al/W RMPs impacted aluminum plates,a large amount of chemical energy and gaseous products were released during the impact-induced deflagration, by which the structural damage to the aluminum plates was significantly enhanced due to the combined damage mechanism of kinetic energy and chemical energy [26-28].

In addition to the enhanced structural damage, the impactinduced deflagration also generates a wide range of hightemperature fields up to thousands of K, which enhances the ignition capacity to combustible targets.For attacking fuel tank targets,these enhancements in structural damage and ignition capacity are precisely the key to enhancing the damage effect.Compared to steel projectiles,PTFE/Al/W RMPs with a steel-like density were found to significantly reduce the impact velocity required to rupture the fuel tank,and could effectively ignite the internal fuel[29,30].In addition,the impact-induced deflagration characteristics of RMP gave it a unique interior ignition mechanism when impacting the fuel tank,which was novel and efficient[31].However,current studies mainly focus on the verification of the enhanced damage effect of RMPs impacting fuel tanks, and few studies on the fluid-structure interaction and damage mechanism have been reported.Most importantly,the process of RMPs penetrating liquid inside the fuel tank has not been observed, and the corresponding cavity evolution and HRAM pressure characteristic are still unclear.These studies are important for understanding the enhanced damage characteristics of RMPs when attacking fuel tanks.

In the present work, ballistic experiments of PTFE/Al/W RMPs impacting liquid-filled tanks were carried out.The liquid-filled tank was filled with water, as water could mitigate fire that would obscure observation of the cavity evolution.In addition, considering the initial velocity of projectiles of the existing anti-air warhead and the attenuation due to air, the velocity of the projectiles before impacting the tank in the presented experiment was about 1250 m/s.Based on the comparative analysis with the inert metal projectile, the unique cavity evolution and HRAM characteristics of RMPs impacting the liquid-filled tank were discussed.In addition, the enhanced structural damage behavior of liquid-filled tank by RMPs impact was further revealed.

2.Experimental setup

2.1.Projectiles

In this study, preparation of PTFE/Al/W RMPs followed a pressing/sintering process.The preparation process is briefly presented here.Firstly,powders of PTFE(DuPont PTFE 9002-84-0,type MP 1000), Al (Hunan Goldsky Aluminum Industry High-Tech Co.,Ltd., Changsha, China, JT-4) and W (Hunan Goldsky Aluminum Industry High-Tech Co.,Ltd.,Changsha,China)were mixed uniformly in vacuum.The mixture was further dried in vacuum at 50°C for about 24 h.Then the dried mixtures were pressed in a steel mold under the pressure of 200 MPa,with a dwell time of approximately 6 min.Finally,the pressed samples underwent a sintering cycle in a vacuum sintering furnace.As depicted in Fig.1(a), during the sintering cycle, the pressed samples were first heated to 380°C at a rate of 50°C/h,and kept at this temperature for 6 h.Following this,the pressed samples were cooled to 310°C at a rate of 50°C/h and kept at this temperature for 4 h,and thereafter were further cooled to ambient temperature at a rate of 50°C/h.

Two types of PTFE/Al/W RMPs with a dimension of Φ10 mm × 10 mm were prepared, type A (steel-like density, hereafter referred to as RMP-A)and type B(aluminum-like density,hereafter referred to as RMP-B), as shown in Fig.1(b).The mass ratio of component, theoretical material densities (TMD) and other parameters of PTFE/Al/W RMPs were listed in Table 1.In particular,the PTFE to Al mass ratio was constant at 73.5%/26.5%, which was determined by zero-oxygen-balance.As shown in Fig.1(c)-1(d),steel projectiles (AISI 1045 steel) and aluminum projectiles (Al-2024) with the same size were also prepared for contrast experiments,and the mass of steel projectile and aluminum projectile are 6.17 g and 2.18 g, respectively.

2.2.Liquid-filled tank

The diagram of liquid-filled tank used in this study is shown in Fig.2.The frame of liquid -filled tank had a size of 520 mm × 400 mm × 500 mm, which was made of 15 mm thick AISI 1045 steel.The target panels were made of 2024 aluminum,and were fixed to the tank frame with fixed frames and twelve equally spaced bolts,as shown in Fig.2(b).Both the front panel and rear panel had a size of 330 mm×400 mm,and the size of loading area is 250 mm × 320 mm, as shown in Fig.2(c).Considering the penetration ability of projectiles,the thickness of the front panel(h)included 3 mm and 6 mm, while the thickness of the rear panel remained constant at 8 mm.Additionally, two 30 mm thick transparent polycarbonate (PC) panels were adopted to be the observation window, which were stiff enough to guarantee that the impact process could be clearly recorded.The liquid-filled tank was filled with water to its maximum storage of approximately 60.8 L during the experiments,and the transducers were submerged into the water through the transducer holes at the top of the liquidfilled tank.The liquid-filled tank was sealed with rubber sealing strips to avoid fluid leakage, which also had a cushioning effect.

2.3.Experimental arrangement

Fig.1.Projectiles preparation: (a) Preparation technology and sintering temperature history of RMPs; (b) RMPs; (c) Steel projectile; (d) Aluminum projectile.

Table 1Parameters of RMPs.

The experimental arrangement is shown in Fig.3.A 14.5 mm ballistic gun was used to launch the projectile,which was fixed to the cartridge through a nylon sabot.The velocity of projectile was controlled by adjusting the amount of black powder inside the cartridge.Along the shooting line, the sabot stripper, velocity probes and liquid-filled tank were arranged successively.After the projectile flew out of the muzzle,the sabot would quickly separate in flight and be blocked by the sabot stripper.The initial impact velocity(v0)of the projectile was measured by the velocity probes and the electronic timer,and the distance between the velocity probes was 300 mm.

A high-speed camera(Phantom v1840),which was just facing the observation window, was used to record the entire process.In addition, the underwater pressure was measured by a pressure acquisition system, which included two pressure transducers(Yangzhou Kedong Electronic Co., Ltd., Yangzhou, China, type KD2101L)and a data acquisition device(Sichuan Top Measuring and Control Technology Co., Ltd., Chengdu, China, type VIB-2000).The pressure transducers had a range of 50 MPa,a rise time of less than 2 μs,and a sampling frequency of 10 MHz.The two transducers were installed at 105 mm(CH1)and 210 mm(CH2)axially away from the front panel respectively.The visual images recorded by the highspeed camera were used to analyze the cavity evolution inside the tank,and the pressure recorded by the transducers was the basis for analyzing the HRAM pressure characteristic.

3.Experimental results

3.1.Cavity evolution

To investigate the difference in cavity evolution characteristics between RMPs and inert metal projectiles, the cavity evolution caused by steel projectile is presented first,as shown in Fig.4.The initial time corresponded to the moment when the projectile impacted the front panel.A spark-like impact flame was generated in front of the front panel,but it had a duration of only 0.5 ms.Upon perforating the front panel and entering the water,a narrow conical cavity was formed behind the projectile, and its axial growth velocity was significantly higher than the radial growth velocity.As the steel projectile arrived the rear panel, its residual velocity was extremely low.Following this moment, the cavity grew to its maximum size soon.The maximum diameter (Dmax) of cavities were 176.4 mm(h=3 mm)and 168.2 mm(h=6 mm)respectively.Subsequently, the cavity began to shrink, resulting in subsequent collapse and oscillation.For steel projectiles, the cavity evolution was dominated by the energy transferred from the projectile to surrounding water, and this energy was influenced by both the initial kinetic energy(E0)of projectile and the front panel thickness[10].Since the initial kinetic energy were almost the same, the residual kinetic energy of the steel projectile after perforating the front panel decreased as the front panel thickness increased,leading to the decrease in the cavity size.

The typical images of cavity evolution caused by RMP-A are shown in Fig.5.When the front panel thickness was 3 mm, the RMP-A had already perforated the front panel at about 0.060 ms,and the initial cavity was also formed, as shown in Fig.5(a).A hemispherical initial shock wave propagating along the penetration axis could be clearly observed.Different from the spark-like impact flame caused by steel projectiles, a brighter cluster-like deflagration flame was generated by the impact of RMP-A, and its duration reached about 1 ms.The initial cavity formed by RMP-A presented as an ellipsoid with a sharp front at 0.260 ms, which was shorter than the cavity formed by steel projectile.As the cavity gradually grew (0.360-1.260 ms),the sharp cavity front expanded rapidly and gradually merged with the ellipsoidal cavity rear.The cavity grew to its maximum diameter of 186.1 mm at about 2.660 ms,which appeared as an ellipsoid with a conical front.More importantly, some black flocculent products could be observed on the cavity surface.These phenomena indicated that reactive material continued to deflagrate inside the cavity, releasing chemical energy while generating a large number of gaseous products,which may enhance the growth velocity of the cavity.However, the axial velocity decay of RMP-A in water was more significant,resulting in a lower axial growth velocity of cavity than that of the steel projectile.After growing to the maximal diameter,the cavity began to shrink and collapse,during which multiple water columns spurted from the bullet hole on the front panel.

Fig.5.Typical photographs of RMP-A impacting liquid-filled tank: (a) h = 3 mm, v0 = 1213 m/s; (b) h = 6 mm, v0 =1230 m/s.

The typical images of RMP-A impacting liquid-filled tank(h= 6 mm) are shown in Fig.5(b).As the front panel thickness increased to 6 mm, the cluster-like deflagration flame became brighter, and its duration was further increased to approximately 3 ms.Within 0.048-0.148 ms,obvious deflagration flame could be observed on the cavity surface, which also indicated RMP-A continued to deflagrate inside the cavity.According to the method described in Ref.[20],this phenomenon also indicated that the initiation delay time was most likely to be within 48 μs.The cavity reached its maximum diameter of 190.7 mm at about 2.548 ms,which still appeared as an ellipsoid with a conical front.It is worth noting that although the increased front panel thickness led to the decrease of the residual kinetic energy of RMP, the maximum diameter of the cavity and the duration of the deflagration flame still increased.This phenomenon indicated that both the initiation ratio and the deflagration intensity of RMP increased significantly with the increased front panel thickness, which was exactly one of the typical impact-induced deflagration characteristics of PTFE/Al/W RMPs[25].Therefore,the cavity evolution after RMP entering water is influenced by both the kinetic energy transfer process and the deflagration chemical energy release process, which is a novel mechanism.

The images of cavities with maximum diameter are shown in Fig.6, and the corresponding data involving cavity evolution are listed in Table 2.Experimental results showed that, the ellipsoidal cavity formed by the RMP was significantly different from the conical cavity formed by inert metal projectile.Compared with inert projectiles with similar initial kinetic energy, the cavity formed by the RMP had a larger radial size but a smaller axial size.The maximum diameter of cavity formed by RMP-A increased by about 5.5%(h=3 mm)and 13.4%(h=6 mm)compared with that of steel projectiles,and the RMP-B increased by about 7.7%(h=3 mm)compared with aluminum projectile.In addition, the duration of deflagration flame caused by RMP-B further increased to about 5 ms, which indicated the initiation ratio might further improve compared with the situation of RMP-A (h= 6 mm).However, the cavity size of RMP-B decreased significantly compared to that of RMP-A due to the significantly reduced initial kinetic energy.This phenomenon also indicated that the cavity evolution of PTFE/Al/W RMP was dominated by the combined effect of both kinetic energy and chemical energy, which is much more complex.

3.2.HRAM pressure

The HRAM pressure caused by steel projectile and RMP-A(h=3 mm)is shown in Fig.7.The zero moment of the time-axis in the figure corresponds to the projectile impacting the front panel.It could be observed that the global characteristics of HRAM pressure caused by RMP-A were similar to those of steel projectile.The corresponding characteristics of each phase were recorded, including initial impact wave and collapse wave.Since the drag pressure decayed significantly with distance [5], no obvious drag pressure peak was observed in the pressure curve due to the relatively long distance between pressure transducers and penetration axis.

Fig.6.The moments when the cavities reached maximum diameter:(a)Steel projectile,h=3 mm;(b)Steel projectile,h=6 mm;(c)Aluminum projectile,h=3 mm;(d)RMP-A,h = 3 mm; (e) RMP-A, h = 6 mm; (f) RMP-B, h = 3 mm.

Table 2The cavity evolution characteristics.

According to the pressure characteristics,the recorded pressure was roughly divided into three parts: 0-0.3 ms, 0.3-6 ms and 6-14 ms.The first part corresponded to the shock phase of HRAM.The initial impact wave could be clearly observed with an extremely high pressure but a rapid decay.Based on the difference in the arrival time of the peak pressure at CH1 and CH2, the propagation velocity of initial impact wave was calculated to be approximately 1493 m/s.The second part corresponded to the drag-cavity phase.The pressure in this phase was closely related to the cavity evolution.Several pressure peaks with amplitudes range between 1.0 MPa and 3.5 MPa appeared in the early stage, which were much lower than the initial impact wave.As the cavity gradually shrank, the pressure gradually decreased steadily.The third part corresponded to the cavity oscillation phase, which began with the first collapse of the cavity.Multiple cavity collapse waves with amplitudes range between 1.0 MPa and 2.0 MPa were recorded in the early stage, but the pressure gradually decreased during the cavity oscillations.

Fig.7.HRAM pressure (h = 3 mm) recorded by transducers: (a) Steel projectile, v0 = 1240 m/s; (b) RMP-A, v0 = 1213 m/s.

Detailed comparison of HRAM pressure (h= 3 mm) between RMP-A and steel projectile is shown in Fig.8.The amplitude of initial impact wave caused by RMP-A was slightly higher than that of steel projectile, but both of them decayed rapidly and only lasted about 45 μs,as shown in Fig.8(a).It should be noted that the attenuation rate of the initial impact wave caused by RMP-A was significantly slower than that of steel projectile.This phenomenon indicated that the initial impact wave caused by RMP-A may be affected by rarefaction waves later than the steel projectile,which may be related to the local deflagration when RMP penetrating the front panel.In addition,only one reflected wave could be recorded after the initial impact wave of RMP, while multiple reflected waves could be observed for the steel projectile.Note that to remove the highfrequency oscillations that obscure the general trend, the pressure curves of the drag-cavity and cavity oscillation phases are displayed after the application of a low-pass filter.As shown in Fig.8(b),during the drag-cavity phase, the pressure fluctuation of RMP-A was more significant, and the amplitudes of several spikes were higher than that of the steel projectile.This phenomenon may be closely related to the deflagration of RMP inside the cavity.During the cavity oscillation phase,the amplitude of the first collapse wave caused by RMP-A was obviously higher than that of steel projectile,as shown in Fig.8(c).Moreover,the global pressure recorded at CH2 in this phase was significantly lower than the pressure at CH1.Since the cavity collapse position was close to CH1,this difference indicated that the oscillation pressure decayed significantly with distance.

The detailed comparison of HRAM pressure when the front panel thickness increases to 6 mm is also considered in Fig.9.When the front panel thickness increased to 6 mm,the amplitude of initial impact wave caused by RMP-A was still higher than that of steel projectile,and the attenuation rate was further slower than that of steel projectile, as shown in Fig.9(a).The pressure fluctuation of RMP-A during the drag-cavity phase was also more significant than that of steel projectile,especially at CH2,as shown in Fig.9(b).The time for the first cavity collapse of both RMP-A and steel projectile was advanced by about 0.6 ms, as shown in Fig.9(c).The effect of front panel thickness on shock phase pressure is further considered in Fig.10.For the same projectile, the amplitude of initial impact wave decreased significantly with the increase of front panel thickness, but the decrease extent of steel projectile was much larger than that of RMP-A.It should be noted that the attenuation rate of initial impact wave of RMP-A was further slowed as the front panel thickness increased,and the final amplitude after attenuation also increased.However, as the front panel thickness increased,both the attenuation rate and the final amplitude after attenuation of initial impact wave of steel projectile were almost the same.As presented in the previous section, the local deflagration of RMP-A was found to be more violently when the front panel thickness increased to 6 mm, which caused more significant deflagration pressure fluctuation and rarefaction wave weakening effect,finally resulting in this unique shock phase pressure characteristic.

Fig.8.Comparation of HRAM pressure between RMP-A and steel projectile (h = 3 mm): (a) Shock phase; (b) Drag-cavity phase; (c) Cavity oscillation phase.

Fig.9.Comparation of HRAM pressure between RMP-A and steel projectile (h = 6 mm): (a) Shock phase; (b) Drag-cavity phase; (c) Cavity oscillation phase.

Detailed comparison of HRAM pressure (h= 3 mm) between RMP-B and aluminum projectile is shown in Fig.11.Similar to the situation between the RMP-A and steel projectile,the initial impact wave caused by the RMP-B also had a higher amplitude and a slower attenuation rate compared to that of the aluminum projectile.The amplitude of the reflected wave of RMP-B was significantly higher than that of the aluminum projectile, and the phenomenon of multiple reflected waves was not observed for the aluminum projectile.This interesting difference in reflected waves is discussed in the following section.As shown in Fig.11(b), the pressure fluctuation of RMP-B during the drag-cavity phase was also more significant than that of aluminum projectile.During the cavity oscillation phase, the global pressure amplitude of RMP-B was higher than that of aluminum projectile especially at CH1, as shown in the enlarged figure of Fig.11(c).

3.3.Front panel damage

Since only the steel projectiles could reach the rear panel with extremely low residual velocity, almost no deformation was observed on the rear panel.Thus,the damage characteristic of the front panel was mainly concerned in this study.Fig.12 shows the damage assessment process of front panel.A laser 3D scanner(type Wiiboox Reeyee 2S)was used to scan the damaged front panel,by which the three-dimensional data of the deformed surface was obtained, and deformation nephogram was further drawn.Corresponding nephograms of the damaged front panels impacted by RMP-A and steel projectile are shown in Fig.13, and δ is the deformation.The origin of the nephogram is set to be the geometric center of the front panel,and the width and length directions of the front panel are defined as theXandYaxes, respectively.

The results showed that the front panels bulged outward(opposite to the penetration direction of projectile)after impacted by the projectiles, and the deformation decreased significantly as the front thickness increased to 6 mm.Along the impact point to the edge, the plastic deformation of the front panel gradually decreased, and the deformation contour line also gradually changed from circular shape to square shape.More importantly,the deformation of the front panel caused by RMP-A was significantly greater than that caused by steel projectile.As listed in Table 3,when the front panel thickness was 3 mm, the maximum deformation caused by RMP-A was about 16.8%greater than that of steel projectile, and the maximum deformation caused by RMP-B was about 22.6% greater than that of aluminum projectile.When the front panel thickness increased to 6 mm, the maximum deformation caused by RMP-A was about 51.4% greater than that of steel projectile.Since the HRAM and the fluid-structure interaction in the tank are the key influence factors on the deformation of panels[10,11], this enhanced structural damage indicates that RMP could significantly enhance the HRAM and the corresponding fluidstructure interaction, which is closely related to the combined effect of kinetic energy impact and chemical energy release.

Morphology of bullet hole on the front panel is shown in Fig.14,and diameter of bullet hole is listed in Table 3.It could be observed that plugging damage was caused by both the RMPs and inert metal projectiles.All the bullet holes appeared to be a quasi-circular shape, and obvious shear fracture traces could be observed on the rear side, indicating that shear was the main failure mechanism.When front panel thickness increased to 6 mm,obvious aluminum deformation phenomenon could be seen inside the bullet hole,and the diameter of the bullet hole also slightly increased compared to the case when front panel thickness was 3 mm.This indicated that the plastic deformation of both the projectile and the front panel during penetration increased with the increased front panel thickness, which might closely relate to the increased penetration resistance.Furthermore, due to its relatively low strength compared to the inert metal projectile,the RMP was more easily to deform during the penetration,resulting in a larger diameter of the bullet hole [27].Correspondingly, the diameter of the bullet hole caused by the RMP-B with a lower strength was also larger than that caused by the RMP-A.

4.Discussion

4.1.The unique ellipsoidal cavity formed by RMP

Significantly different from the conical cavity formed by inert metal projectile,a unique ellipsoidal cavity with a conical front was formed after the RMP entered water.The comparison of cavity characteristic between RMPs and inert metal projectiles is shown in Fig.15.In terms of cavity morphology, the cavities formed by the RMPs have a larger radial size than those of the inert metal projectiles, but their axial length are obviously smaller.As shown in Fig.15(b),the axial growth velocity of cavities formed by the RMPs is not only significantly lower than that of the inert metal projectiles at the initial time,but also decreases more rapidly.On the contrary,the radial growth velocity of cavities formed by the RMPs is significantly higher than that of the inert metal projectiles at the initial time,and also decreases more slowly,as shown in Fig.15(c).In addition,as the front panel thickness increases from 3 mm to 6 mm or the density of RMP decreases, the axial and radial growth velocities of cavity formed by the RMP decrease at the initial time, indicating that the residual kinetic energy after perforating the front panel has a significant influence on the initial cavity characteristics.

The difference in cavity characteristic between the RMP and the inert metal projectile is further analyzed through the recycled residual projectile and aluminum slug detached from the front panel,as shown in Fig.16.Residual projectile and several fragments of the aluminum slug could be recycled after the impact of the steel projectile and the aluminum projectile,and only part of the edge of the residual steel projectile fractured, as shown in Fig.16(a).The front of the residual steel projectile and the residual aluminum projectile had obviously deformed into a mushroom-like shape.These deformed residual projectiles presented an ellipsoidal front surface with a low drag coefficient, resulting in a larger axial growth velocity of cavity.Significantly different from inert metal projectiles, no residual projectile had been recycled after the impact of the RMP, except for several fragments of the aluminum slug, as shown in Fig.16(b).The main fragments of the aluminum slug detached from the 3 mm thick front panel fractured into two pieces,and obvious shear fracture traces could also be observed on the side.More importantly,obvious black induced by burning could be observed on the fragment front,which became more obvious as the initiation ratio of the RMP increased.These recovery results effectively demonstrate that the RMP deflagrated violently after impacting the front panel and entering water,and most of the RMP were consumed in the deflagration so that no residual projectile remained.It should be noted that the difference in the residual projectile between RMP and inert metal projectile may account for the difference in the reflected wave recorded during the shock phase.The multiple reflected waves were generated by the reflection of the initial impact wave and the followed compression waves[5],and these compression waves following the initial impact wave were found to be closely related to the penetration of residual projectile during liquid[32].Since the RMP could hardly maintain a residual projectile after perforating the front panel, the amplitude of the compression wave generated mainly by the irregular aluminum slug was significantly reduced.Moreover, a lower residual velocity or a weaker shock wave parameter also resulted in a reduced amplitude of the compression wave,as was the case for the residual aluminum projectile compared to the residual steel projectile.Furthermore, the amplitude of the compression wave decayed rapidly with distance.Thus, for the RMP and aluminum projectile, only one obvious reflected wave was recorded, corresponding to the reflection of the initial impact wave.

Fig.11.Comparation of HRAM pressure between RMP-B and aluminum projectile (h = 3 mm): (a) Shock phase; (b) Drag-cavity phase; (c) Cavity oscillation phase.

Fig.12.Damage assessment process of front panel.

Fig.13.Deformation nephogram of front panel: (a) Steel projectile, h = 3 mm; (b) RMP-A, h = 3 mm; (c) Steel projectile, h = 6 mm; (d) RMP-A, h = 6 mm.

Table 3Damage characteristic of front panel.

Fig.14.Morphology of bullet hole on front panel: (a) RMP-A, h = 3 mm; (b) RMP-B, h = 3 mm; (c) Aluminum projectile, h = 3 mm; (d) RMP-A, h = 6 mm; (e) Steel projectile,h = 6 mm.

As one of the unique characteristics,RMP will be initiated under the extreme loading of high velocity (exceeded critical initiation velocity) impact, and then deflagrates after a specific initiation delay time[21].Combined with the high-speed camera images and reference to relevant Refs.[20,24],the initiation delay time of RMPs in this paper were estimated to be on the order of 10-100 μs.Based on this unique impact-induced deflagration characteristics, the cavity evolution of RMP after water entry is described as follows,as shown in Fig.17.When impacting the front panel, the RMP first undergoes significant plastic deformation under shock loading.Meanwhile,the RMP also undergoes significant fragmentation due to the relatively low strength.Some small fragments with lower surface ignition energy will be initiated to deflagrate first, which may eject rearward,resulting in a local deflagration in the vicinity of the impact point[28].After perforating the front panel,the RMP enters water together with the aluminum slug.Furthermore, the RMP will continue to separate into many fragments, forming a fragment cloud [19,28].On the one hand, the fragment cloud and the aluminum slug are slowed by viscous drag in the water while their kinetic energy is gradually transformed into water motion,and the cavity is subsequently formed.On the other hand, after a specific initiation delay time, the initiated fragments among the fragment cloud undergo global deflagration inside the cavity,releasing amount of chemical energy.This chemical energy is also transferred to surrounding water mainly by the deflagration overpressure,which may significantly promote the growth of the cavity.Since the RMP fractures and deflagrates significantly, no residual projectile remains after the global deflagration, and the axial growth velocity of the cavity is dominated by the aluminum slug.However, due to the small mass and irregular shape, the velocity decay of the aluminum slug is rapidly,resulting in a relatively small axial growth velocity of the cavity.Finally, the aluminum slug penetrates the water in the front, while the reactive material fragment cloud deflagrates behind,resulting in an ellipsoidal cavity with a conical front.It should be noted the impact-induced fragmentation characteristics of RMP enhance its velocity decay in water, leading to a faster and more concentrated kinetic energy transfer process from the RMP to the water.Combined with the additional chemical energy released by the deflagration,the energy transfer level after entering water is significantly enhanced by the RMP,which is also responsible for the higher radial growth velocity of the cavity compared to that of the inert metal projectile.

Fig.15.Comparison of cavity characteristic between RMPs and metal projectiles: (a) Cavity morphology; (b) Axial growth velocity; (c) Radial growth velocity.

4.2.Enhanced HRAM pressure

4.2.1.Enhancementofinitialimpactwave

The initial impact wave is initially a shock wave created due to the initial impact of projectile [5].In the presented experiments,this shock wave propagated through the front panel and then the water, which was finally recorded by the pressure transducers.To further understand the difference in the HRAM pressure characteristics between the RMPs and the inert metal projectiles, the initial impact wave is described theoretically.As shown in Fig.18(a),as the projectile with an initial velocityv0impacts the front panel,two shock waves(marked as S)created propagate forward into the front panel and backward into the projectile, respectively.Behind these two shock waves,the particle velocity and the pressure jump tout1andPt1.Subsequently,as the forward shock wave propagates to the front panel/water interface,a shock wave is transmitted into the water while a rarefaction wave (marked as R) propagates backward into the front panel.Behind this shock wave in water,the particle velocity and the pressure of water jump from zero tout2andPt2, andPt2is the initial pressure amplitude of initial impact wave in water.

The following theoretical description is based on the Rankine-Hugoniot relations.The conservation of mass, momentum and energy are expressed as:

where ρ is the density,uis the particle velocity,Uis the shock velocity,Pis the pressure,eis the specific internal energy and υ is the specific volume.The subscripts 0 and 1 refer to the unshocked and shocked states, respectively.In addition, the linear relationship between the particle velocity/shock velocity is expressed as:

wherec0andsare the sound speed and the material coefficient to a given material.For the reactive mixtures,c0andsare governed by classical Voigt-Reuss-Hill mixing rules.Thec0andsof RMP-A are 3656 m/s and 1.30,and those of RMP-B are 2737 m/s and 1.51[33].The pressure of the material is then related to the particle velocity as follows:

Across both the projectile/front panel interface and the front panel/water interface,uandPshould be equal, which are also the boundary conditions to close the system of equations.At the projectile/front panel interface, the continuity conditions of interface pressure and particle velocity are written as:

Fig.16.Recovered residual projectile and fragments of the aluminum slug: (a) Inert metal projectile; (b) RMP.

where the subscripts p and t refer to the projectile and the front panel respectively.

Based on the above equations,the wave interaction between the interfaces can be described by the Hugoniots on aP-udiagram, as shown in Fig.18(b).In the presented figure, the materials for the projectile and the front panel are selected as AISI 1045 steel and 2024 aluminum [34], the initial velocity of the projectile is set as 1250 m/s.The impact pressure and particle velocity(Pt1,ut1)at the projectile/front panel interface are obtained at the intersection of the projectile and front panel Hugoniots (shown by the red dot I),and the pressure and particle velocity (Pt2,ut2) at the front panel/water interface are obtained at the intersection of the mirrored front panel Hugoniot and water Hugoniot(shown by the red dot II).In addition,considering the significant attenuation of the real shock wave as it propagates through the metal [35], the shock wave propagating in the front panel has the following attenuation:

In theP-udiagram,the mirrored Hugoniot(with attenuation)of the front panel passing through blue dot IIIintersects with the water Hugoniot at the blue dot,andis the initial pressure amplitude of the initial impact wave in water,as shown in Fig.18(b).Moreover,as the initial impact wave propagates through the water, its amplitude decays as the propagation distance increases or the θ decreases,where θ is the angle away from the front panel.McMillen found that the wave pressure in water was inversely proportional to propagation distance [3].In the case of relatively thick front panel, Disimile found that the angular distribution of the initial impact wave was correlated toP=P90·sin(θ+7°), whereP90is the wave pressure along the shot line (θ = 90°) [5].Thus, the amplitude of initial impact wave propagating to the pressure transducer can be written as:

Fig.17.Cavity evolution process under the impact of RMP.

Fig.18.Theoretical description of the initial impact wave:(a)Schematic of the projectile impacting the front panel;(b)Hugoniots on a P-u diagram based on the Rankine-Hugoniot relations.

wherePdis the amplitude of initial impact wave at the pressure transducer, anddis the distance between the pressure transducer and the impact point.

Experimental and theoretical results of the amplitude of initial impact wave at the pressure transducers are listed in Table 4, and corresponding comparison is shown in Fig.19.For steel and aluminum projectiles,the theoretical results are in good agreement with the experimental results, with an average deviation of less than 10%.This indicates that the above theoretical analysis can well describe the corresponding decay of the initial impact wave when it propagates in water,as marked in Fig.19(a).However,for RMPs,the theoretical results are significantly lower than the experimental results,with an overall average deviation of about-26%.Different from inert metal projectiles,the RMP undergoes a local deflagration soon after it impacts the front panel,and this deflagration has been demonstrated to produce significant deflagration pressure [18].Since the RMPs have similar initial velocities, the intensity of the local deflagration is closely related to the front panel thickness and the mechanical and chemical properties of RMP [25].As recorded by high-speed camera, the duration of deflagration flame at the front panel of the RMP-B(h=3 mm)was the longest,followed by the RMP-A (h= 6 mm) and the RMP-A (h= 3 mm), which also indicated the initiation ratio decreased in this order.More importantly, the average deviations between the experimental and theoretical results for the RMPs decreases in the same order as the initiation ratio,that is,the RMP-B(h=3 mm)has the largest value of -36.0%, followed by the RMP-A (h= 6 mm) with a value of-26.6%and the RMP-A(h=3 mm)with a value of-15.3%.This consistency indicates that local deflagration pressure of RMP is most likely to enhance its impact pressure,and this enhancement is further improved with the increase of initiation ratio.In addition,the attenuation rate of the initial impact wave caused by RMP is found to be significantly slower than that of inert metal projectiles,which may be closely relate to the local deflagration slowing down the entry of rarefaction wave.Thus,the enhancement of the initial impact wave induced by the local deflagration is a significant characteristic of the HRAM pressure induced by the RMP entering water.

4.2.2.Enhancementofnear-fieldimpulse

As mentioned above, the characteristic of the HRAM pressure induced by the RMP is significantly different from that of inert metal projectile, and thus the corresponding impulse is also significantly different.The impulse is the key factor in analyzing the damage dominated by HRAM.The impulse (per unit area) characteristics of the RMP and the inert metal projectile are shown in Figs.20-22.Due to the enhancement of initial impact wave, the impulse induced by RMP increases significantly compared to that of the inert metal projectile in the early stage of shock phase.However, this impulse increment of RMP-A gradually decreases in the later stage of shock phase due to the multiple reflected waves caused by steel projectile.At CH1 which is closer to the impact point, the impulse increment of RMP is significant during shock phase,cavity growth phase and cavity collapse phase.The impulse increment of RMP is further improved as the front panel thickness increases from 3 mm to 6 mm, which is also closely related to the increased initiation ratio as analyzed above.As for CH2 which is farfrom the impact point, the impulse increment of RMP-A is significantly reduced,especially during the cavity oscillation phase,while the impulse increment of RMP-B remains large.The difference in impulse characteristics between the RMP and the inert metal projectile can be analyzed as follows.On the one hand, due to the deflagration pressure of both the local deflagration in the vicinity of the front panel and the global deflagration inside the cavity, the impulse of the RMP is significantly enhanced.However, since the deflagration pressure also decays rapidly with distance, the enhancement of impulse is more significant in the near-field like CH1.On the other hand, the cavity formed by the steel projectile travels across the entire liquid-filled tank,and it passes right under CH2 as it gradually shrinks and collapses.However, due to the relatively short axial size of the cavity formed by the RMP, the corresponding collapse position is closer to the front panel, which is far away from CH2.Therefore, the global oscillation pressure of the RMP-A recorded at CH2 is relatively low than that of the steel projectile,resulting in a lower impulse during the cavity oscillation phase.Since the axial size of the cavity formed by the aluminum projectile is also significantly shorter than that of steel projectile,its collapse position is also closer to the front panel.As a result, the global oscillation pressure of the RMP-B recorded at CH2 is even slightly higher than that of the aluminum projectile as shown in Fig.11(c), thus the corresponding impulse increment compared to the aluminum projectile can be maintained.

Table 4Experimental and theoretical results of the amplitude of initial impact wave.

Fig.19.Comparison of the amplitude of initial impact wave between experimental value (column) and therotical value (curved surface): (a) Steel projectile, h = 3 mm; (b) Steel projectile, h = 6 mm; (c) Aluminum projectile, h = 3 mm; (d) RMP-A, h = 3 mm; (e) RMP-A, h = 6 mm; (f) RMP-B, h = 3 mm.

Based on the pressure characteristics, the global impulse is further divided into three stages.The first stage (stage I) is in the time interval of 0-0.5 ms,which is usually adopted to characterize the transverse loading in the liquid-filled tank under HRAM [37].The third stage (stage III) begins with the first cavity collapse, and the second stage (stage II) is between the other two stages.As shown in Figs.23(a) and 23(b), when the front panel thickness is 3 mm, the impulse increment of RMP at CH1 is significant in the first and third stages, which is further improved as the initiation ratio of the RMP increases.However,the impulse increment of RMP at CH2 is significant only in the first stage, and the impulse increment in the third stage occurs only for the RMP-B with the largest initiation ratio.This analysis further demonstrates that the enhancement of impulse induced by the RMP is significant in nearfield,which is improved with the initiation ratio but reduced with the distance away from the cavity.

4.3.Enhanced structural damage

The cross-section of the damaged front panel along the length direction are illustrated in Fig.24.Compared to the inert metal projectiles, the RMPs with similar initial kinetic energies can significantly enhance the global deformation of the front panel.The deformation of the front panel in the vicinity of the impact point is most significant, which is closely related to the extremely high HRAM pressure during the shock phase.Along the impact point to the edge of the front panel, the deformation gradually decreases due to the gradually decayed HRAM pressure and the significant influence of the bolt-fixed boundary, resulting in the deformation contour line changing from a circular shape to a square shape similar to the bolt-fixed boundary.

Fig.20.Impulse characteristic of RMP-A/steel projectile (h = 3 mm): (a) Global impulse; (b) Impulse increment of RMP.

Fig.21.Impulse characteristic of RMP-A/steel projectile (h = 6 mm): (a) Global impulse; (b) Impulse increment of RMP.

Fig.22.Impulse characteristic of RMP-B/aluminum projectile (h = 3 mm): (a) Global impulse; (b) Impulse increment of RMP.

HRAM is the result of the energy transfer process,in which the energy of the projectile is transferred to the liquid and finally to the tank walls, and thus the impulse is the key factor connecting the energy transfer process and the structural damage of the tank.Z.Rosenberg found that the panel deflection during high velocity water entry was linearly related to the impulse imparted by fluid and inversely proportional to the panel density, thickness and strength[38].This relation is usually described by non-dimensional analysis,and the correlation between the non-dimensional impulse and the deformation-thickness ratio can be obtained from experimental data through least squares correlation [39,40].The nondimensional impulse φqand the deformation-thickness ratioare expressed as follows:

whereIis the total impulse,Bis the panel width,Lis the panel length.σ0is the static yield stress of panel material,and σ0of 2024 aluminum is 260 MPa.

Fig.23.Impulse characteristics in different stages: (a) Comparison between RMPs and inert metal projectiles; (b) Impulse composition at CH1.

As mentioned above, since the HRAM pressure decreases significantly with distance, the corresponding impulse also varies with distance.Therefore,the total impulse at CH1 is chosen for the non-dimensional analysis, which is closer to the front panel and better represents the impulse characteristic in the vicinity of the front panel.The corresponding non-dimensional impulse and the deformation-thickness ratio of the damaged front panel is calculated and fitted, as shown in Fig.25.An empirical relation is obtained from the least squares analysis with a correlation coefficient of 0.976 (quadrangular plate, non-dimensional impulse range:194.9-767.6), which is expressed as:

A statistical analysis shows that the above empirical relation can reliably predict the deformation of the front panel subjected to the HRAM pressure loading with a probability of 90.2% within one panel thickness.This analysis result indicates that the deformation of the front panel is linearly correlated to the impulse, which is reliable for both the RMPs and the inert metal projectiles.Combined with the above analysis in subsubsection 4.2.2, the RMP is demonstrated to enhance the near-field impulse by its unique impact-induced deflagration, finally resulting in the enhanced structural damage.As analyzed in subsection 4.1,the reasons for the enhanced energy transfer level of the RMP include the more concentrated kinetic energy transfer process induced by the impact-induced fragmentation, as well as the additional chemical energy released by the impact-induced deflagration.However,limited by the experimental conditions presented in this paper,the relation between these two reasons and their detailed contribution to the enhanced energy transfer level are not clear yet, which require further study.

5.Conclusions

In this paper,a series of ballistic experiments were designed and performed to study the damage behavior of RMPs impacting liquidfilled tank.Through the transparent tank and pressure acquisition system,the complete process of high velocity water entry of RMPs,the corresponding HRAM pressure and structural damage characteristics were obtained.The main conclusions drawn are as follows:

(1) A unique ellipsoidal cavity with a conical front was formed when a high velocity RMP entered water.Compared to the conical cavity formed by the inert metal projectile,the radial size of this ellipsoidal cavity was larger but the axial size was smaller.The corresponding cavity evolution closely depended on the impact-induced fragmentation and deflagration characteristics of the RMP, thereby was significantly influenced by the initial kinetic energy and initiation ratio of the RMP.

(2) The RMP enhanced the amplitude of the initial impact wave and reduced its attenuation rate,which was closely related to its local deflagration in the vicinity of the front panel.Correspondingly,the near-field impulse induced by the RMP was also significantly increased than that of the inert metal projectile.Moreover,these enhanced effects involving HRAM pressure were enhanced as the initiation ratio of the RMP increased, but were weakened with distance.

Fig.24.Cross-section of the damaged front panel along the length direction: (a) h = 3 mm; (b) h = 6 mm.

Fig.25.Graph of deformation-thickness ratio versus non-dimensional impulse for the damaged front panel.

(3) The damaged front panel bulged outward with a plugging damage formed around the impact point, and its plastic deformation gradually decreased along the impact point to the edge.Compared to the inert metal projectiles, the RMPs with similar initial kinetic energies significantly enhanced the global deformation of the front panel.This enhanced structural damage effect of the RMP was well verified,which was closely related to the combined effect of kinetic energy impact and chemical energy release.

(4) The non-dimensional analysis with a correlation coefficient of 0.976 shows a significant linear correlation between the deformation-thickness ratio and the non-dimensional impulse.For the RMP,the impact-induced fragmentation leads to a more concentrated kinetic energy transfer process,while the impact-induced deflagration releases additional chemical energy.Therefore, the energy level transferred from the RMP to the liquid is significantly enhanced, further increasing the near-field impulse,and finally resulting in the enhanced structural damage.

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.

Acknowledgements

This work was supported by the Youth Foundation of State Key Laboratory of Explosion Science and Technology (Grant No.QNKT22-12),and the State Key Program of National Natural Science Foundation of China (Grant No.12132003).