Yuan-feng Zheng,Cheng-hai Su,Huan-guo Guo,Qing-bo Yu,Hai-fu Wang

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

Keywords:Reactive materials Reactive jet Chain damage Behind armor blast

ABSTRACT Chain damage is a new phenomenon that occurswhen a reactive jet impacts and penetrates multispaced plates.The reactive jet produces mechanical perforations on the spaced plates by its kinetic energy(KE),and then results in unusual chain rupturing effects and excessive structural damage on the spaced plates by its deflagration reaction.In the present study,the chain damage behavior is initially demonstrated by experiments.The reactive liners,composed of 26 wt%Al and 74 wt%PTFE,are fabricated through a pressing and sintering process.Three reactive liner thicknesses of 0.08 CD,0.10 CD and 0.12 CD(charge diameter)are chosen to carry out the chain damage experiments.The results show a chain rupturing phenomenon caused by reactive jet.The constant reaction delay time and the different penetration velocities of reactive jets from liners with different thicknesses result in the variation of the deflagration position,which consequently determines the number of ruptured plates behind the armor.Then,the finite-element code AUTODYN-3D has been used to simulate the kinetic energy only-induced rupturing effects on plates,based on the mechanism of behind armor debris(BAD).The significant discrepancies between simulations and experiments indicate that one enhanced damage mechanism,the behind armor blast(BAB),has acted on the ruptured plates.Finally,a theoretical model is used to consider the BAB-induced enhancement,and the analysis shows that the rupturing area on aluminum plates depends strongly upon the KE only-induced pre-perforations,the mass of reactive materials,and the thickness of plates.

1.Introduction

Behind armor damage effects have received increasing attention in the field of terminal effects,especially in the cases of anti-light/medium armor targets.The traditional shaped charge warhead,usually used to attack an armored target,is more likely to form a copper jet,which achieves a deep penetration but with insufficient behind armor damage.Although the copper jet partially forms a BAD(behind armor debris)cloud after perforation and subsequently enlarges the damage range,there are increasing demands and attempts for greater behind armor damage effects.Moreover,modern battle targets have better protective measures and complex inner structures.If the copper jet attacks a target that is equivalent to spaced plates,the copper debris behind the armor would be prevented by the first plate in all probability,leaving other plates intact except for small penetration holes.Accordingly,a new concept of chain damage,which indicates producing significant damage on each plate,is proposed.One of the promising approaches is to use a reactive liner instead of the traditional metal liner in a shaped charge.The reactive liner shaped charge produces a reactive jet,which is made of reactive materials,during the formation process.The reactive jet perforates the desired plates by its kinetic energy(KE),and distributes itself among the plates.Then the deflagration of reactive jet causes a field of high temperature and high pressure,which enhances the damage effects to all the perforated plates.Thus,the great chain damage could be achieved by incorporating the defeat mechanisms of KE and chemical energy(CE)into a unitary damage element[1,2].

Owing to the unique performance,intensive studies on reactive liner have been conducted over the last ten years,and one of the most studied is the polymer-based reactive liner.The polymerbased reactive liner is commonly composed of reactive metal powders,alloy powders or intermetallic compounds,and a polymer matrix(typically polytetrafluoroethylene,PTFE).The reactive liner is fabricated by means of uniformly mixing,cold pressing and sintering.Up to the present,significant progress has been made on polymer-based reactive liner formulation,preparation technologies,reactive jet formation mechanism,and penetration behavior to concrete and steel targets[3-5].However,there is no special research on chain damage effects of spaced plates by reactive jet.The limited relevant studies are discussed as follows:

Arnold[6]demonstrates that the conventional copper jet does not produce considerable blast pressure behind the armor,and the copper jet only generates BAD.However,a large behind armor blast(BAB)effect occurs as the aluminum jet impacting the steel plate,causing a considerable blast pressure behind the steel plate.

Xu F Y[7]carries out a study on damage effects of doublespaced aluminum plates by a reactive projectile impact.The results imply that the plugging damage to the front plate is caused by the KE impact of the reactive projectile.However,the rear plate is damaged by both the KE impact and the CE release.It should be stressed that the chain damage effects caused by the reactive jet are more complex than the damage effects of the double-spaced aluminum plates by the reactive projectile.First,the reactive jet with high velocity can perforate more plates to achieve chain damage.Second,the reactive jet is initiated completely.Due to the strong shock wave generated during the jet formation process,the reactive jet is more likely to be initiated completely under the shaped charge effects.However,the reactive projectile is mainly initiated by the impact behavior during penetration process,and it has been known that the impact process may provide insufficient interaction between projectile and target,usually causing partial initiation of reactive projectile[8].Third,the reaction delay time should be considered for the reactive jet,due to the long penetration process through the multi-spaced plates.However,this consideration is ignored for a reactive projectile.

Zhang X P[9]discusses the behind armor overpressure produced by the reactive liner shaped charge.The results show the behind armor overpressure decays with the armor thickness,and a model is developed to describe the behind armor overpressure.The work actually analyzes the behind armor energy release behavior of a reactive jet,without discussing behind armor damage.

Based on the discussion above,the present study begins with experiments of reactive liner shaped charges against multi-spaced plates in order to verify the chain rupturing phenomena and obtain the influence characteristics of liner thickness on chain damage.Then,simulations are presented to describe the KE-induced rupturing effects,based on the BAD phenomena.Lastly,a theoretical model,considering both the KE and CE effects,is used to analyze the rupturing areas on aluminum plates.

2.Experiments

2.1.Liners

The preparation process for the PTFE/Al reactive liner includes the following steps:first,the powders are mixed by a planetary mill machine for 3 h,with a small amount of absolute alcohol as a medium.Then,the powders are dried at 82°C in a vacuum drying oven for 24 h approximately.Second,well-mixed powder is weighed and placed in a pressing mold.A cold pressing pressure of 200 MPa is maintained for 30 s.Third,the pressed liner samples are sintered in a nitrogen atmosphere with a maximum temperature of 380°C.Then,the samples are cooled with the furnace and a reshape process is needed after sintering[10,11].The average sizes of the PTFE and aluminum powders are 100 nm and 44μm,respectively.A sketch and reactive liner samples are shown in Fig.1,and the reactive liner thicknessσvaries from 3.84 mm to 5.76 mm.Moreover,a copper liner with a thickness of 1.49 mm is also employed as a comparison,and it is noted that the copper liner mass is the same as the mass of the reactive liner with a thickness of 5.76 mm.

Fig.1.Reactive liners:(a)sketch;(b)3.84 mm thick reactive liner;(c)4.80 mm thick reactive liner;(d)5.76 mm thick reactive liner.

2.2.Shaped charges

The cylindrical shaped charges with boat-tails are obtained by pressing the JH-2 powder in a rigid mold with a pressure of 200 MPa.All the shaped charges should have a mass of 95.6 g theoretically.Then,the reactive liner,the shaped charge and the steel case are assembled together as the final reactive liner shaped charge warhead(RLSCW),and a diagram of warhead is shown in Fig.2.Additionally,the copper liner shaped charge warhead is assembled by simply replacing the reactive liner with a copper liner.

Fig.2.Diagram of reactive liner shaped charge warhead.

2.3.Setup

The experimental setup is shown in Fig.3.The warhead is placed on a 45# steel column,with the multi-spaced plates underneath.The 45#steel column has a size ofΦ130 mm×15 mm.The multispaced plates,designed to study the chain damage effect,consist of one steel plate and five aluminum plates.The steel plate with dimensions of 400 mm×400 mm×5 mm is used to prevent the influence of the steel column impact and detonation products.The multi-spaced aluminum plates are used to verify the behind armor effect.The dimensions of each aluminum plate are 400 mm×400 mm×1.5 mm,and the distance between adjacent aluminum plates is 70 mm.All the warheads would be initiated at a stand-off of 1.0 CD,as the optimal stand-off of the reactive jet is about 1.0 CD[5,12].

Fig.3.Experimental setup.

2.4.Results

The results of experiments 1# through 4# are presented in Tables 1-4,respectively.The hole areas on the aluminum plates Shole-exp,shown in Fig.4 and listed in Table 5,are evaluated from the projection direction,and the detailed measurement method is proposed by Lu G C[13].

Table 1 summarizes the typical chain damage effects of multispaced plates by a reactive jet.As can be seen,the jet perforates the steel column,steel plate and four aluminum plates.Moreover,the reactive jet generates a great rupture phenomenon on the spaced plates.It can be seen that all holes on the four front plates are considerably large,lips are bent outward significantly,and all four front plates are greatly deformed.It is also shown that the reactive jet fails to perforate the fifth aluminum plate.In addition,the significant dark mark on each plate indicates that a violent chemical reaction has occurred.Importantly,the experimental results also reveal that the damage effects of the RLSCW on multispaced plates are influenced significantly by the liner thickness.As the liner thickness increases from 3.84 mm to 4.80 mm,the reactive jet perforates the steel column,steel plate and three aluminum plates,as shown in Table 2.Concurrently,the hole areas decrease 5.3%,11.5% and 18.9% for the first,second and third aluminum plates respectively,compared with the corresponding plates shown in Table 1.If the liner thickness further increases to 5.76 mm,similar trends are also found in Table 3:the first aluminum plate is disintegrated thoroughly,the second aluminum plate is perforated with significant bulge,and the third aluminum plate bends to some extent.It is noted that a very small dark mark can be seen in the fourth aluminum plate,suggesting a few reactive fragments are likely to perforate the third plate and leave sometraces on the fourth plate.However,the traces on the fourth plate are insignificant,which can be neglected here.

Table 1Results of RLSCW against spaced plates(3.84 mm thick reactive liner).

If a copper liner replaces the reactive liner,the damage results are summarized in Table 4.The copper jet perforates the steel column,the steel plate and all the aluminum plates successively.The penetration process produces a ductile perforation on the steel plate,and results in a rupture perforation on the first aluminum plate.However,only small perforation holes are formed on the other aluminum plates.

Table 2Results of RLSCW against spaced plates(4.80 mm thick reactive liner).

Table 3Results of RLSCW against spaced plates(5.76 mm thick reactive liner).

Table 4Results of copper liner shaped charge warhead against spaced plates.

Based on the experimental results,it can be concluded that the reactive jet can produce a chain rupturing damage effect on multispaced plates.However,the copper jet can only cause rupturing damage on the first aluminum plate,leaving the other aluminum plates perforated without the enhanced damage effect.In fact,the copper jet mainly damages the multi-spaced plates by its KE in the form of BAD and residual penetrator.By contrast,the reactive jet produces chain damage effects by the KE penetration and the BAB.Accordingly,the following section focuses on these complex interaction mechanisms by a combination of experiment,simulation and theoretical analysis.

Fig.4.Measurement method for projected hole areas on aluminum plates.

Table 5Measurement results of projected hole areas in aluminum plates.

3.Simulation method

3.1.SPH model

Clearly,both the copper and reactive jets produce KE effects on the multi-spaced plates.Therefore,discussions on the KE-induced damage are carried out,based on numerical simulations.The numerical models are developed with the software AUTODYN-3D,which is particularly suitable for nonlinear dynamic problems.The software allows for the employment of the smoothed particle hydrodynamics(SPH)technique to solve the interaction problem.The simulation includes two steps of jet formation and penetration.The model of jet formation is shown in Fig.5(a),including the liner,the JH-2 explosive and the steel case.When the jet tip gets the stand-off,the JH-2 explosive and the steel case are both deleted,and the multi-spaced plates are added in the simulation(see Fig.5(b)).Owing to the symmetry,modeling one-fourth of the geometry is necessary to simplify the analysis and reduce the computational cost.The explosive,liner,case and the multi-spaced plates are all discretized by a set of particles assigned with a mass interacting among themselves.The shaped charge,liner,and steel case have the same particle size as 0.25 mm,and the target particles have a size of 0.5 mm.

Fig.5.Simulation models:(a)model for jet formation;(b)model for penetration.

3.2.Material models and parameters

The Jones-Wilkins-Lee(JWL)equation of state(EOS)is used to describe the JH-2 explosive:

where P is the pressure;V=1/ρeis the specific volume;ρeis the density;E0is the specific internal energy per unit mass;A1,B1,R1,R2andωare material constants.The parameters of JH-2 are listed in Table 6[14].

The EOS of the steel column,steel plate,aluminum plate,aluminum case,copper liner and reactive liner are all based on the shock model.Their strength models are described by Johnson-Cook,which is used to represent the strength behavior of materials,subjected to large strains,high strain rates and high temperatures.Such behavior might arise in problems of intense impulsive loading due to high velocity impact.With this model,the yield stress varies depending on strain,strain rate and temperature.The model defines the yield stressσas:

Table 6Parameters of JH-2 explosive.

Table 7Parameters of copper,steel,PTFE/Al,and aluminum.

where A,B,C,n and m are material constants.εPis the effective plastic strain.˙ε0=1s-1is the reference plastic strain rate.Tmeltand Troomdenote the melting and room temperatures,respectively.

The parameters of different materials are listed in Table 7.It is noted thatρis the density,G is the shear modulus,Ca,S1are shock Hugoniot parameters,andΓis the Gruneisen coefficient.Moreover,there is no use of failure and erosion in the present paper,due to the SPH algorithm.The material parameters of copper,45#steel and PTFE/Al are all from Refs.[14-17].Moreover,the quasi-static and Hopkinson bar experiments are both conducted to acquire the parameters G,A,B,C,n of aluminum,and the corresponding curves are shown in Fig.6.The parameter m of aluminum is chosen as 1.0[18].

Fig.6.Quasi-static and Hopkinson bar curves of aluminum.

4.Formation of jets

The sequences of forming a reactive jet and a copper jet are schematically shown in Fig.7 and Fig.8,respectively.The influences of liner thickness on reactive jet characteristics and the comparison with a copper jet are summarized quantitatively in Table 8.

The simulation results show that both the reactive liner and the copper liner collapse under the shaped charge effects.The inner wall of the liner moves relatively fast and develops into the“jet”section,whereas the other part of the liner travels with a relatively low velocity and forms the“slug”.The simulation shows the jet coming out of pressed and sintered liner is more likely to expand,especially at the tip of the jet.Moreover,both the tip and the slug velocities decrease gradually with increasing reactive liner thickness,which would affect the coupled effects of KE penetration and CE release.However,the reactive liner thickness has no significant influence on reactive jet density and tip diameter.As for the copper jet,there is no significant expansion behavior,and the tip velocity decreases due to its high density.Fig.9 compares jet tip velocities between different jets.

5.BAD effect induced by copper jet

As a comparison,Fig.10 firstly gives the simulation process of a copper jet against a combined target.Fig.10(a)shows that only a small pit is produced on the surface of the steel target due to the small diameter of the jet tip.As the penetration proceeds,the contact area between the copper jet and the target increases because of the lateral flow of the jet head.Then,after perforating the steel plate,the debris from the copper jet head and the steel plate forms a fragmentation cloud behind the steel plate.In this case,the copper jet does not produce considerable blast pressures,and the jet only generates BAD.As such,it is reasonable to infer that the first aluminum plate in Table 4 is damaged by both the behindarmor fragments and the residual penetrator,resulting in a large hole on the first aluminum plate.After that,the jet continues to perforate the second aluminum plate.However,the fragmentation cloud behind the first aluminum plate has a weaker penetration capability compared with that behind the steel plate,due to the relatively lower jet velocity and the significantly lower density and strength of the aluminum plate.As such,the hole diameter on the second aluminum plate decreases considerably,and the hole is mainly produced by the residual penetrator.For the same reason,holes on the subsequent aluminum plates become gradually smaller.Fig.11 presents simulation results of holes on plates and their areas Shole-sim.Comparisons between simulation and experiment results of plate damage modes and hole areas show an acceptable agreement.

Fig.7.Typical formation process of reactive jet:(a)velocity view without a stand-off;(b)velocity view at a stand-off of 0.5CD;(c)velocity view at a stand-off of 1.0CD.

Fig.8.Typical formation process of copper jet:(a)velocity view without a stand-off;(b)velocity view at a stand-off of 0.5CD;(c)velocity view at a stand-off of 1.0CD.

Table 8Simulation results of the jet formation.

Fig.9.Comparison of jet tip velocities between different jets.

6.Combined effect induced by reactive jet

6.1.BAD-induced primary damage effect

The discussion on reactive jet against multi-spaced plates is more complex,due to the coupled mechanisms of KE penetration and CE release.Simulation can be a useful tool to illuminate this issue.What should be stressed is that the shock EOS used for reactive materials in the present study cannot describe the chemical reaction behavior.However,the simulation results are still meaningful for the analysis of jet formation,BAD,and jet penetration-induced damage.In fact,this new reactive material in the present study is very insensitive compared with traditional explosives,indicating that this new reactive material needs both high pressure and enough pressure duration time to be initiated[19].That is,although the highest pressure is obtained in the reactive liner during the collapse process,the pressure duration time is so short that most of the jet cannot react violently,except for a small localized reaction.Then,the local reaction heats the surrounding materials to the threshold temperature.Because the heat conduction process needs a relatively long time compared with the liner collapse time,the reactive jet has a delay time before violent reactions.In other words,the reaction is insignificant before the reaction delay time,and the chemical reaction in this stage can be ignored.If the time t0=0 is defined as the moment when the JH-2 explosive is initiated,the reaction delay time is normally denoted asτ.Thus,it is reasonable to neglect the chemical reaction behavior in the formation and penetration processes before the time ofτ,which is the basis of simulations in this study.Consequently,the chemical energy enhancement can be analyzed and discussed by comparing the simulations with experiments.

Fig.10.Simulation results of copper jet against multi-spaced plates:(a)the jet penetrating the steel plate at the time of 30.2μs;(b)the debris cloud and the damage behavior at the time of 44.0μs;(c)the debris cloud and the damage behavior at the time of 59.5μs;(d)the debris cloud and the damage behavior at the time of 110.5μs.

Fig.11.Partially enlarged view of copper jet impact-induced holes on plates by simulations:the hole areas are 7539 mm2,1186 mm2,576 mm2,333 mm2,and 113 mm2 for the plates by the order,respectively.

Typical simulation results are shown in Fig.12.Take the liner thickness of 3.84 mm for example,the corresponding reactive jet produces holes with the diameters of 27.2 mm and 36.8 mm on the steel column and steel plate,respectively.Then,the reactive jet continues to penetrate the spaced aluminum plates one by one.At the time of 147.0μs,the penetration hole diameters from the first to the fourth aluminum plates are 121.0 mm,81.2 mm,46.2 mm and 20.8 mm,respectively.There is no significant rupturing effect on each aluminum plate in the simulation,due to the absence of a deflagration material model in the penetration simulation.Furthermore,if the simulation is continued to conduct,the reactive jet can perforate the fifth aluminum plate at the time of 186.0μs,which is inconsistent with the experimental result that only four front aluminum plates are perforated.The difference between simulation and experiment indicates that the penetration termination is not due to the penetration capability of reactive jet,but the violent chemical reaction.In fact,the jet would be activated during the formation process.However,the jet produces a major and violent chemical reaction with a time delay.As such,it is reasonable to neglect the chemical reaction in the formation and penetration process before the time ofτ.Then,at the time ofτ,the reactive jet reacts violently and the penetration would be terminated,leading no further plate to be perforated.

Moreover,the significant contrast indicates the real reaction delay time should be in the range of t1≤τ≤t2,where,t1=147.0μs and t2=186.0μs are the moments when the reactive jet just perforates the fourth and the fifth aluminum plates respectively.Because the times t1and t2are so close,the average value of them is considered as the reaction delay timeτ≈166.5μs If the reactive liner thickness increases,the reactive jet obtains a lower tip velocity and may perforate fewer aluminum plates before the timeτ.Fig.13 shows simulation results corresponding to the second and the third experiments,respectively.Due to the same formulation and preparation method,the three reactive liners should have the same reaction delay time.As a result,the simulations in Fig.13 are terminated at the time of 166.5μs.

The results of simulation and experiment show a good agreement on the number of perforated plates.The data on rupture area is listed in Table 9 for comparison,based on the simulations.It is noted that the data in Table 9 can only indicate the KE effect of the reactive jet.On one hand,the results show the KE-only induced hole diameter varies with the liner thickness increasing from 3.84 mm to 5.76 mm,showing the KE penetration process determines the hole areas to some extent.On the other hand,the hole areas obtained by simulations are significantly smaller than the corresponding experimental values,showing that the reactivity effect-induced damage on the aluminum plates is significant.

Fig.13.Simulation results of kinetic energy-only induced damage on multi-spaced plates by reactive jets:(a)the jet from a liner with a thickness of 4.80 mm penetrating the multispaced plates at the time of 166.5μs;(b)the jet from a liner with a thickness of 5.76 mm penetrating the multi-spaced plates at the time of 166.5μs.

Table 9Partially enlarged view of KE only-induced holes on plates by reactive jets.Note:The data below each picture is the corresponding rupturing area induced by KE.

6.2.BAB-induced damage enhancement effect

Actually,the real interaction should include three stages as follows.

In the first stage of formation,the shock wave from the JH-2 explosive detonation propagates into the reactive liner,causing the liner to collapse.Meanwhile,the shock wave also activates the reactive liner.However,the reactive liner does not react violently in this stage because of the reaction delay time,which is discussed above.

Then,in the second stage of penetration,the reactive jet penetrates the steel column and the steel plate by its KE.Care has to be taken that only a portion of the reactive jet participates in the penetration and formation of the fragment cloud behind the steel plate.Moreover,the residual jet,which sustains shock loads during the jet formation process,would not form a fragment cloud but would remain as a jet in the second stage.It is noted that the fragment cloud and the residual jet only occur local chemical reaction at several scattered positions during the formation and penetration process.The major and violent chemical reaction of the reactive materials occurs with a significant time delay,due to the specific delayed reaction characteristic.Hence,the reactive materials flow out of the steel plate and continue to move forward to impact and penetrate the spaced aluminum plates by its KE.The simulation results show that if the reaction delay timeτtends to infinity,the reactive jet can perforate all the spaced aluminum plates.However,under actual conditions,the reactive jet only perforates four aluminum plates in Table 1,because the violent chemical reaction directly results in the reactive jet losing its penetration capacity.

Once the time t=τ,the reactive materials deflagrate violently and produce a blast front,and fields of high pressure and high temperature are produced in spaces.For mechanism considerations,the PTFE decomposes and releases much oxidants,which react with the aluminum particles.The main reactions may include:

As can be seen,the main gaseous products include AlF3,AlF2and AlF.In fact,the KE perforation provides a precondition for the formation of cracks,or directly induces initial cracks on the aluminum plates.This means the impact energy of jet has some contributions to the damage area.However,the single KE damage cannot maintain the further propagation of the cracks.Then,the deflagration of the reactive jet inside the spaced plates provides one damage enhancement mechanism to the aluminum plates.The rapid expansion of gaseous products and the chemical energy released further enlarge the pre-perforations on the aluminum plates and cause rupturing effects finally.

6.3.Analytical model for rupturing area

As discussed above,the lack of a material model for the chemical reaction in the present form results in the failure of the simulation to describe the chemical effects.As such,a theoretical model is used to predict the CE release enhancement behavior.

Actually,the chemical reaction of reactive materials can release much gaseous products and chemical energy,which produces consequential overpressures on the aluminum plates.As shown in Fig.14,the overpressure is equivalent to a linear distribution loading.The parameter 2aiis the KE-induced hole diameter,while parameter 2biis considered as the final hole diameter caused by the combined effects of KE and CE.Thus,the final ruptured area can be described as[20].

Fig.14.Equivalent deflagration overpressures on the spaced plates.

where,Δt is the duration,ρAlis the aluminum plate density,h is the aluminum plate thickness,E is the Young modulus,KICis the fracture toughness of the aluminum plate[21],meffis the effective mass of reactive materials,and F is a constant.

In equation(3),the constant F needs to be fitted based on the experimental results.For each aluminum plate,the parameters of meffand aican be obtained from simulation results,and the final areas on the aluminum plates are from the experiments.What should be emphasized is that the mass mefffor each plate is only relevant to the portion which is inside the space in front of the corresponding plate.In fact,reactive materials inside each space have enough macro-residual velocity forward,which may result in the chemical reaction products mainly flowing forward.Hence,only the portion in the space in front of the plate produces severe damage on the corresponding plate.The corresponding relationships among the three parameters are listed in Table 10.The durationΔt is chosen as 40 ms based on a previous study[8].Then,the termi s regarded as variable X.The fitted curve on variables X and S is shown in Fig.15,and the constant F is fitted as 0.0675 mm-2s-2.

Table 10Parameters used for the theoretical model.

Based on the fitted value of F,Fig.16 depicts the theoretical rupturing area by the combination of KE and CE.By comparing of lines with the same color,it shows the influences of the KE onlyinduced hole radius on the final rupturing area.Comparison of the lines with the same type,it can be seen that the rupturing area exhibits a remarkable decreasing behavior with the increasing of aluminum plate thickness.For any curve,it shows an upward trend with the increasing of effective mass of reactive materials.

7.Conclusions

The BAB-induced damage enhancement effects of reactive jets on spaced aluminum plates are studied.Conclusions are as follows:

(a)The experiments show that the reactive jet perforates the steel plate and produces significant BAB effects on spaced aluminum plates,resulting in great chain rupturing damage on these aluminum plates.However,the traditional metallic copper jet only produces BAD effects on the spaced aluminum plates.

(b)The experiments also show that the match of the reaction delay time and the KE penetration process is the primary determinant of the chain rupturing effects.With increasing reactive liner thickness,the reactive jet penetration velocity decreases and the corresponding behind armor effects cause fewer aluminum plates being ruptured.

(c)The theoretical model indicates that the rupturing area is decided by the mass of the effective reactive materials,the aluminum plate thickness and the KE only-induced hole radius.The rupturing area shows a positive relationship with the mass of reactive materials,while exhibits a negative relationship with the aluminum plate thickness.In addition,the KE only-induced hole radius is also an influencing parameter for the final rupturing area.

(d)The reactive jet is assumed to be completely inert in the simulation,and then the chemical reaction behavior is discussed based on a theoretical model.This method could deal with the interaction well in the present study.However,it should be mentioned that the interaction between reactive jet and target is a complicated process of dynamic response and chemical kinetics.As such,further work needs to be performed to complete the reaction model of reactive materials for simulations and reveal the coupled mechanism of KE and CE.

Fig.15.The fitted curve on variables X and S.

Fig.16.Theoretical rupturing areas by the combination of KE and CE.

Acknowledgment

This research is supported by the National Natural Science Foundation of China(No.U1730112).