Shock-induced reaction behaviors of functionally graded reactive material

Ying Yuan,Zhen-yang Liu,Suo He,Chao Ge,Qing-bo Yu,Yuan-feng Zheng,Hai-fu Wang

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

Keywords: Functionally graded reactive material PTFE/Al Reaction behavior Ballistic impact experiments Reaction efficiency

ABSTRACT In this paper,the ballistic impact experiments,including impact test chamber and impact double-spaced plates,were conducted to study the reaction behaviors of a novel functionally graded reactive material(FGRM),which was composed of polytetrafluoroethylene/aluminum (PTFE/Al) and PTFE/Al/bismuth trioxide (Bi2O3).The experiments showed that the impact direction of the FGRM had a significant effect on the reaction.With the same impact velocity,when the first impact material was PTFE/Al/Bi2O3,compared with first impact material PTFE/Al,the FGRM induced higher overpressure in the test chamber and larger damaged area of double-spaced plates.The theoretical model,which considered the shock wave generation and propagation,the effect of the shock wave on reaction efficiency,and penetration behaviors,was developed to analyze the reaction behaviors of the FGRM.The model predicted first impact material of the FGRM with a higher shock impedance was conducive to the reaction of reactive materials.The conclusion of this study provides significant information about the design and application of reactive materials.

1.Introduction

Reactive materials,as a class of special energetic materials,have been drawn extensive attention and have been widely applied [1].Among them,polytetrafluoroeth-ylene/aluminum(PTFE/Al)and its derivatives,are widely researched due to its unique reaction characteristics and has a wide application prospect in weapons.

The researches of PTFE/Al series materials mainly focused on the mechanical properties and reaction characteristics.Daniel T.Casem investigated the effect of strain rate and temperature on the mechanical characteristics and developed the Johnson-Cook and modified Johnson-Cook model to describe the PTFE/Al mechanical behaviors[2].The researchers conducted SHPB tests on PTFE/Al/W materials and provided an effective material model of PTFE/Al/W that can be used for simulation calculation[3-5].J.Cai performed the Quasi-static tests,Hopkinson bar tests,and Drop-weight tests to investigate the mechanical properties of PTFE/Al/W with changing the morphology of the particles.The results show that the mechanical strength of PTFE/Al/W containing fine W is higher than that of PTFE/Al/W containing coarse W [6].Wu investigated the effect of Al particle size on the mechanical properties of PTFE/Al by quasi-static compression.It indicated that,with the Al particle size increasing from 0.05 μm to 34 μm,the yield strength and hardening modulus decreased and the failure stress and toughness first increased and then decreased[7].The SHPB tests were performed,and the experiments showed that with the porosity increasing,the yield strength and compressive strength decreased [8].

Studies have shown that the reaction behavior of PTFE/Al is influenced by many factors,such as particle size,composition,impact velocity,and even target.Bin Feng investigated the effect of sintering temperature,Al mass ratio,and Al particle size of PTFE/Al on the sensitivity under the low-speed impact [9].Liu Wang investigated the effect of W percentage on reaction energy and the impact insensitivity of PTFE/Al/W.The insensitivity of W-PTFE-Al composites to impact loading shows an increasing tendency with the increased W content [10].Xu conducted the impact chamber tests to investigated the energy release behavior of PTFE/Al/W which were affected by impact velocity and plate thickness.The experiments indicated that the behind-plate overpressure effect by PTFE/Al/W is mainly determined by the projectile initiation rate and the reaction extent before perforating the plate[11].

The further studies on the reaction mechanism indicated that the reaction behavior was mainly codetermined by the strength of shock wave and the impact sensitivity[12-14].To order to improve the reaction characteristics of reactive materials,many energetic components were introduced into PTFE/Al materials,such as bismuth trioxide (Bi2O3) [15],copper oxide (CuO) [16],hydrogenated titanium (TiH2) [17,18] and nickel (Ni) [19].These additional components can improve the reaction characteristics and the impact sensitivity of traditional PTFE/Al materials to some extent.

However,the above studies all focus on the homogeneous PTFE/Al reactive materials,that is,the reaction characteristics of reactive materials at all positions are the same.Due to the attenuation of the shock wave in the impact ignition process of reactive materials,homogeneous reactive materials tend to fail to be fully ignited,which reduces the energy release rate of reactive materials.In order to further improve the reactive performance of reactive materials,the functionally graded material,whose property changes with the position [20],was introduced to optimize the structure of reactive materials.Mars,Jamel and their group have systematically studied the mechanical behavior of functionally graded materials [21-25].The numerical model for low-velocity impact response of functionally graded materials structures investigated and the simulation results are in good agreement with the experiments and theory,which is of great significance to the study of the mechanical behavior of functionally graded materials.

Considering the effect of Bi2O3content on the impact sensitivities of PTFE/Al/Bi2O3,Bi2O3was introduced into reactive materials to fabricate the heterogeneous PTFE/Al series reactive materials.In this paper,the novel functionally graded reactive material (FGRM)with positional Bi2O3content and heterogeneous reaction characteristics was designed and fabricated.The ballistic impact experiments,including impact test chambers and impact double-spaced plates,were conducted to investigate the reaction behavior of the FGRM.Moreover,a theoretical model was developed to analyze the reaction behavior of the FGRM and the influence of impact direction on reaction.The conclusions would provide a constructive guide to the design and application of reactive materials.

2.Experimental materials and procedures

2.1.Simple preparation

Raw materials:PTFE powder(2.2 g/cm3,DuPont PTFE,type MP 1000);Al powder(2.78 g/cm3,Hunan Goldsky Aluminum Industry High-Tech Co.,Ltd.,Changsha,China,FLQT2);Bi2O3powder (8.9 g/cm3,GooMoo Chemical,Changsha,China,average particle size:300 mesh).In this work,the sample consists of the two composites,PTFE/Al and PTFE/Al/Bi2O3,and Al could react with PTFE and Bi2O3,releasing a large amount of heat,respectively.The chemical reaction equations are as follows.

The two components of the FGRM were prepared respectively according to the stoichiometry ratio.The specific information on the two components is listed in Table 1.The size of the FGRM prepared in this study was φ 10 mm×10 mm,in which the size of PTFE/Al/Bi2O3and PTFE/Al were both φ 10 mm × 5 mm.

Table 1 The information of two components of the FGRM.

The preparation process of the FGRM mainly included powder mixture,multi-step cold pressing,and sintering.Firstly,the raw powders of a certain mass were added to the anhydrous ethanol solution and mixed by a blender for about 60 min,followed by a drying process at room temperature lasting 48 h.Then the PTFE/Al/Bi2O3mixed powders were placed in a mold with an inner diameter of 10 mm and cold uniaxial pressed at about 250 MPa.The semimanufactured sample after the first-step cold press were kept in the mold,and the PTFE/Al mixed powders were added in the mold,and cold uniaxial pressed at about 250 MPa.After two-step cold pressing,the FGRM was taken out from the mold and was placed in sintering oven.The oven temperature was raised to 370°C at a rate of 50°C/h,then holding at 370°C for 6 h,and cooling to ambient temperature naturally.

The FGRM fabricated in this work belong to PTFE-based composite material.In high temperature sintering process,with the temperature increasing,the fluidity of PTFE increases,and the crystal of PTFE transmits,promoting the integrity.However,the distribution of particles wrapped by PTFE matrix hardly changes during the sintering.Therefore,the FGRM with integrated structure and positional oxide content was prepared by multi-step pressing and high temperature sintering.

2.2.Experimental setup

In this study,the shock-induced reaction behavior of the FGRM was investigated by ballistic impact experiments,including impact test chamber and impact double-spaced plates.In the experiments,the FGRM encapsulated in nylon sabot was launched from the 12.7 mm ballistic gun.The impact velocities of the FGRM which were controlled by adjusting the mass of the propellant powder were low velocity(900 m/s～1000 m/s)and high velocity(1250 m/s～1350 m/s).Because of the axial difference of graded reactive materials,there were two optional directions of the FGRM when they impacted the test chamber or double-spaced plates.In the experiment,in order to distinguish the different impact directions of the FGRM,the one with PTFE/Al/Bi2O3first impact material was called G1,and the one with PTFE/Al/first impact material was called G2.

The physical photograph and the FGRM prepared in these experiments were presented in Fig.1.The schematic of the experimental setups was presented in Fig.2.The experimental systems including the arrangement for the impact test chamber and the impact double-spaced plates were similar in composition,mainly including the launching part (12.7 mm ballistic gun),the data acquisition part (velocity probes,high-speed photography,and pressure data acquisition system),and the target part(test chamber or double-spaced plates).

Fig.1.The physical photograph of experimental setups:(a)Experimental setup for impact test chamber;(b)Experimental setup for impact double-spaced plates;(c)The prepared FGRM.

As shown in Fig.2,the design of the test chamber is similar to that designed by Ames [26].The 2024-T3 aluminum plates with thicknesses of 3 mm were used as the front cover plate of the test chamber with a volume of 27.35 L.The pressure data acquisition part including pressure sensors and the data acquisition system.The pressure sensor sampling frequency was 10 KHz and the measuring range was 0-1 MPa.As shown in Fig.2,the doublespaced 2024-T3 Al plates with thicknesses of 3mm/3 mm were used in the experiments.The distance between the front and rear plates was 200 mm.The material,thickness and distance between the plates are selected in double-spaced plates experiments according to the practical application.

Fig.2.Schematic of ballistic impact experimental setup.

The Phantom V710 high-speed photography (Vision Research,Inc.,Wayne,NJ,USA) was applied to record the experiments.The selected frame rate was 10000 per second,so that a frame was taken every 100 μs.The resolution was 640 × 480 pixels and the exposure time was set to 15 μs.

2.3.Mechanical properties

The quasi-static mechanical properties were investigated by the WDT series Universal Materials Testing Machine controlled by a computer.In order to reduce the friction between the ends of the sample and the equipment in the compression test,the ends of the sample were coated with Vaseline for lubrication.In the quasistatic compression test,the moving down the speed of the crosshead was 0.6 mm/min,and the corresponding compression strain rate of the sample was 0.001/s.The true stress-strain curves as shown in Fig.3.Test 1 and Test 2 are the FGRM with PTFE/Al/Bi2O3part facing up and PTFE/Al part facing up respectively.It can be seen that due to the low strain rate,there is no significant directional effect on the quasi-static mechanical behavior of the FGRM.The materials show significant elastoplastic mechanical properties under quasi-static compression.The elastic modulus of the FGRG is 492.02 MPa,yield strength is 14.49 MPa,and failure strain is higher than 1.5.

3.Shock-induced reaction behavior of the FGRM

3.1.Typical shock-induced reaction behavior of the FGRM

Fig.3.True stress-strain curves of the FGRM.

Fig.4.Typical FGRM two-step impact reaction behavior.

When the FGRM is launched by the ballistic gun and impacts test chamber or the double-spaced plates at a certain velocity,a two-step impact occurs and a severe deflagration/detonation occurs,which causes the overpressure inside the test chamber or causes more serious damage to the double-spaced plates.For the typical two-step impact reaction behavior of the FGRM,it mainly includes four stages,as shown in Fig.4.Among them,according to whether the reactive material penetrates the plate,its reaction behavior can be divided into two types.

The first stage is presented in Fig.4(b).When the FGRM first impacts the plate,the shock wave is generated and it propagates from the head of FGRM to the tail.Because of the attenuation of the shock wave,the FGRM is usually ignited partly.There is some reactive debris near the front plate,which is formed by the head of the FGRM.

The second stage is shown in Fig.4(c).After the FGRM penetrates the front plate,the reactive material breaks up partly,and the residual material continues to move between the two plates,and debris cloud is formed between the two plates.The reactive debris formed in the first stage deflagrates in succession.

The third stage is shown in Fig.4(d).According to whether FGRM penetrates the rear plate,its energy release behavior can be divided into two types.When the residual material penetrates through the plate,its response behavior is roughly the same as that in the first stage,and the FGRM is reignited,forming reactive debris near the plate.When the residual material cannot penetrate the plate,most of the reactive materials are fragmented and the reactive debris is distributed between the two plates.

The fourth stage is shown in Fig.4(e).When FGRM penetrates the rear plate,deflagration of the residual FGRM mainly occurs near the perforation of the rear plate,and the overpressure formed by deflagration enhances the damage effect of the rear plate.If the FGRM could not penetrate the plate,the residual FGRM deflagration mainly occurred between the two plates,which increase the overpressure between the two plates.

As shown in Fig.4,there are two optional impact directions of the FGRM,when it impacts the target.Comparing with the ordinary homogeneous reactive materials,the impact direction of the FGRM has a significant influence on shock-induced reaction behavior due to the differences in properties of each part of the FGRM,such as strength,energy content,impact sensitivity,and shock wave impedance.

3.2.Shock wave distribution in the FGRM

Based on the one-dimensional shock wave theory,according to the conservation of mass at impact interface,the strength of the initial shock wave generated by the impact can be calculated as the following equation.

whereP0is the initial impact shock pressure,vis the sample impact velocity,UsandUt,are the shock wave velocity of the sample and the target,ρs0and ρc0are the initial density of the sample and the target,respectively.The relationship between shock velocity and particle velocity can be expressed as

whereCs,Cc,StandStare the Hugoniot parameters of the sample and the target,usanducare the particle velocity in the sample and target,respectively.

The Hugoniot parameters of the mixture can be estimated by the following equations.

whereiis the number of each component in the sample,miis the mass fraction of the numberedicomponent in the mixture.

The propagation of the shock wave in a homogeneous reactive material decays exponentially,and it can be expressed as

wherexis the distance from the impact interface,δ is the constant related to material property.

Due to the interface between different media in the functional graded reactive material,the shock wave will be transmitted in the FGRM.The intensity of the transmitted wave can be expressed as

wherePTis the transmitted pressure,xinterfaceis the distance between the first impact interface and interface of different media,ρ andCare the density and sound velocity,respectively.Subscripts A and B represent the media parameters of the incident wave and the transmitted wave respectively.The transmitted wave continues to propagate in the new medium with exponential attenuation,as shown in Eq.(6).

3.3.Reaction efficiency of the FGRM

Under the shock wave compression,the temperature of the reactive material increases,causing a chemical reaction.Because of the compression time of the shock wave is short,the process of material heating can be regarded as an adiabatic process.According to the Hugoniot curve and the law of thermodynamics,the relationship between the adiabatic temperature rise and shock pressure of reactive materials can be expressed as

whereTis the temperature,γ is the Gruneisen coefficient,Vis the specific volume,Cvis the heat capacity at constant volume,P(x) is the shock pressure,respectively.Subscript 0 represents the material parameters in the initial state,and subscript 1 represents the parameters after the shock wave compression state.

For PTFE/Al and PTFE/Al/Bi2O3reactive material,it is assumed that the chemical reaction rate and time are linear.According to reach of Ortega research [27],the relationship between reaction efficiency η and temperatureTof the reactive material can be expressed as

whereRuis the universal gas constant,Eais the apparent activation energy,nis the coefficient related to boundary conditions and reaction mechanisms.

3.4.Penetration behaviors of the FGRM

When the FGRM impact the front aluminum plates,leading to the velocity decreasing,the ballistic limit velocity could be estimated according to the following equation [28].

wherev50is the ballistic limit velocity (m/s),htis the thickness of plate(cm),Ais the sample average area of contact(cm2),mpis the sample mass (g).When the cylindrical FGRM penetrates the aluminum plate,plastic deformation occurs at the interface between the sample and the aluminum plate,forming a plug.The residual velocityvrof the reactive projectile can be expressed as

wherev0is the impact velocity(m/s),arandbare the coefficients,respectively,which could be expressed as the following equations.

whereDis the diameter of the reactive projectile.

In the penetration,with the shock wave,the reactive material is partially fragmented,and the fragmentation length can be assumed as 20% of the FGRM length [29].After penetrating the front plate,the remaining FGRM impact the rear plate at the residual velocity,and reacts violently again.

4.Results

4.1.Overpressure in the test chamber

The FGRM impacted the test chamber at a velocity of 902 m/s to 1282 m/s,inducing chemical reaction,causing overpressure in the chamber.The overpressure data in the test chamber were shown in Fig.5.Fig.5(a)illustrated the difference between original pressure data and quasi-static pressure data.As shown in Fig.5(a),it was noted that there was a like-detonation peak among the original data.The quasi-static pressure varying with time caused by the FGRM with two different impact directions were presented in Fig.5(b),which showed that the deflagration reaction was significantly influenced by the impact velocity and impact direction.The experimental results were listed in Table 2,including quasi-static pressure peak and impulse.

Table 2 Experimental results of the impact chamber.

It was noted that when the impact velocity was high,the impact direction of the FGRM had little influence on the pressurization characteristics.When impact velocities were 1253 m/s and 1282 m/s,the quasi-static pressure peak was about 0.24 MPa and the impulses were 11.15 kPa s and 10.65 kPa s.On the other hand,when the impact velocity was low,the pressurization characteristics were strongly dependent on the impact direction of the FGRM,especially the quasi-static pressure peak.

Fig.5.The original pressure data and quasi-static pressure in the test chamber:(a)Original pressure data and quasi-static pressure data;(b)The quasi-static pressure of the FGRM.

Fig.6 presented typical high-speed video frames of the FGRM impacting test chamber with different impact directions.The FGRM perforated the front cover plate of the test chamber,and the FGRM fragmented partly.The reactive material debris outside the test chamber reacted violently with a dazzling firelight.The residue FGRM entered the test chamber,and then a second impact occurred,intensifying the reaction and producing a bright flame.There were significantly different reaction characteristics of the FGRM impacting with different impact direction.

As shown in Fig.6(a)(b),when the impact velocity was low(900 m/s～ 950 m/s),compared with G1,the reaction flame of G2 was more violent and the lasted longer.According to the flame brightness outside the test chamber,it could be found that when G2 impact,more reactive materials reacted outside the test chamber.This indicated that compared with PTFE/Al/Bi2O3,PTFE/Al was more prone to fracture and deflagration in the first impact,presumably because the strength of PTFE/Al was lower than PTFE/Al/Bi2O3.This was also consistent with the experimental results in Table 2.Since there were fewer reactive materials for G2 entering the test chamber,the peak of quasi-static pressure was significantly lower than that caused by G1.As shown in Fig.6(c)(d),when the impact velocity was high(about 1250 m/s～1300 m/s),the reaction phenomena of G1 and G2 impact test chamber were similar.

It was worth noting that the impact velocity had little effect on the time of the most violent flame outside the test chamber when G1 impacted,which kept about 1.2 ms,but had a significant effect on that of G2.When G2 impacted,with the impact velocity increasing from 949 m/s to 1253 m/s,the time of most violent flame outside the test chamber was shortened from 1.8 ms to 1.2 ms.This indicated that the reaction delay time of PTFE/Al reactive material was significantly affected by the impact velocity,while the impact velocity had a blunt influence on the reaction delay time of PTFE/Al/Bi2O3reactive material.

4.2.Damage effect of double-spaced plates

The FGRM impacted the double-spaced plates at a velocity range from 939 m/s to 1338 m/s,and the chemical reaction was induced by the two-step impact,causing damage to the front and rear plates,as shown in Figs.7 and 8.The equivalent diameter of perforation was chosen to characterize the damage to the front plate.Because the damaged area of the rear plate was irregular,the damage of the rear plate was represented by the perforated area.The damage effects of double-spaced plates are listed in Table 3.

Table 3 Experimental results of impact double-spaced plates.

Table 4 Parameters involved in the calculation of the model [14,30].

Fig.6.Typical high-speed video frames of FGRMs impacting test chamber:(a) G1, v=902 m/s;(b) G2, v=949 m/s;(c) G1, v=1253 m/s;(d) G2, v=1282 m/s.

Fig.7.Damage effect of double-spaced plates with low velocity (900 m/s～ 1000 m/s):(a) G1,front plate;(b) G1,rear plate;(c) G2,front plate;(a) G2,rear plate.

Fig.7 showed the damage of the front and rear plates induced by G1 and G2 at a low impact velocity.As shown in Fig.7(a)(c),the front plate had regular circular perforation,with a plugging damage mode,and the equivalent diameter of perforation was roughly the same,18.56 mm and 19.02 mm,respectively.As shown in Fig.7(b)(d),the damaged area of the rear plate was significantly larger than that of the front plate,and there was obvious blackening near the damaged area,which was caused by an incomplete reaction of the FGRM.Compared with the damage of the front plate,there was more bulging in or near the damaged area.It was probably because with the two-step impact,the FGRM was ignited,and violent deflagration between the front and rear plates resulted in high overpressure,causing the regional bulge of the rear plate.In addition,due to the decrease of the FGRM velocity after penetrating the front plate,the damage mode of the rear plate gradually changed from the plunge mode to the ductile failure mode,which also led to the rear plate regional bulge.It was worth noting that when the impact velocities of G1 and G2 were low,the damage modes and damaged areas of the front and rear plates were roughly the same,indicating that the impact direction had little influence on the damage effect of such graded reactive materials.

As shown in Fig.8(a)(c),the damage of the rear plate was roughly the same as that of the front plate at a low velocity,which was shown as the plugging failure mode.The perforation equivalent diameters were 19.24 mm and 19.67 mm,respectively.As shown in Fig.8(b)and(d),the damaged area of the rear plate was irregular,and the damaged area was as high as 782.51 mm2and 629.59 mm2,respectively,which were 2.38 and 1.95 times of the damaged area at low velocity,and the blackening area of the rear plate was also wider.This indicated that,compared with the lowvelocity impact,there were more reactive materials involved in the reaction of the FGRM in the high-velocity impact,but the reaction was still incomplete.Besides,irregular pits could be found near the damaged area of the rear plate,which was speculated to be caused by the impact of reactive fragments formed by the fragmentation of the FGRM under the high-velocity impact.Compared with the low-velocity impact,the damage mode of the rear plate under high-velocity impact evolved from the plugging failure mode to the petal failure mode.This was mainly due to the violent chemical reaction of the FGRM in the process of penetrating the plate,and the high overpressure generated by the reaction increased the upheaval of the split plate.

Fig.8.Damage effect of double-spaced plates with high velocity (1300 m/s～ 1350 m/s):(a) G1,front plate;(b) G1,rear plate;(c) G2,front plate;(a) G2,rear plate.

The damaged area of the front plate was roughly the same,which was because the front plate is roughly with a plugging failure,and it was affected by the kinetic energy and diameter of the penetrator.It was worth noting that when the impact velocity was low(939 m/s～983 m/s),the damaged area of the rear plate of G1 and G2 was roughly the same.When the impact velocity was high(1305 m/s～1338 m/s),the damaged area of G1 to the rear plate was larger than that of G2.This indicated that,when the impact velocity was high,the impact direction of the FGRM had a significant influence on the damage effect,especially the rear plate.When the impact velocity was low,the damage effect of the FGRM had no significant influence on the damage effect.

Fig.9 presents the typical high-speed video frames of the FGRM impacting double-spaced plate behavior.When the FGRM impacted the double-spaced plates with a low velocity,the reactive material was partially ignited,and reactive material reacted around the front plate.The reactive material perforated the front plate and then impacted the rear plate.It could be seen from the intensity of the flame that the secondary impact made the gradient material react more violently.According to the frame after t=4 ms,when the impact velocity was about 950 m/s,the reactive material reaction was mainly between the front and rear plates.

When the FGRM impacted the double-spaced plates at the velocity of about 1321 m/s,the reactive material reaction was mainly located between the two plates and behind the rear plate,and the flame duration of behind the front plate was longer than that of between the two plates.The main reason was that the increase of the gradient material velocity increased the amount of remaining reactive materials penetrating the rear plate,so the reaction after the rear plate was more violent.With the increase of the impact velocity,the reaction time of gradient materials was shortened.This was because the reaction delay time of the reactive material was shortened and the reaction rate was increased with the increase of the impact velocity.In addition,when the FGRM impacted in different directions,the flame duration was slightly different,and the flame duration of G1 was slightly shorter than that of G2.

5.Discussion

Fig.10.Shock wave distributions within graded materials.

Based on the theoretical analysis model of the FGRM reaction behaviors,when the impact velocities are 925 m/s and 1268 m/s(standing for low and high velocity,respectively),the shock wave distributions within the FGRM as shown in Fig.10.The parameters involved in the calculation of the model are listed in Table 4.Because it is difficult to accurately measure the attenuation coefficient of reactive material,the attenuation coefficient,which will not subvert the analysis conclusion of this model,is assumed to be 0.2 in the calculation.As shown in Fig.10,the impact direction of the FGRM has two effects on the distribution of the shock wave in the FGRM.On the one hand,with the same impact velocity,the initial shock wave generated by the first impact of PTFE/Al/Bi2O3is higher than that of PTFE/Al.On the other hand,when the propagation of shock wave crosses the interface of two different materials,the shock wave strength sharply changes.When the shock wave propagates from PTFE/Al/Bi2O3into PTFE/Al,the shock wave strength increases,whereas the strength decreases.The above analysis shows that the shock wave strength is higher in the FGRM when PTFE/Al/Bi2O3impact first.

As shown in Fig.11,the reaction efficiency of the two reactive materials,PTFE/Al/Bi2O3and PTFE/Al,changes with the strength of the shock wave.It can be seen that the reaction efficiencies of PTFE/Al/Bi2O3and PTFE/Al change rapidly with the shock pressure ranging from 2 GPa to 12 GPa.Within this shock pressure range,with the same shock pressure,the reaction efficiency of PTFE/Al/Bi2O3is lower than that of PTFE/Al.

According to Eqs.(3)～(9),when the FGRM impact with different velocities and in different directions,the positional reaction efficiency of the FGRM is shown in Fig.12.It can be seen that the reaction efficiency of the reactive material decreases as the distance from the impact interface increases,and the reaction efficiency of the material changes suddenly at the interface of the two materials.

Fig.11.Reaction efficiency of reactive materials vary with shock pressure.

Fig.12.Reaction efficiency at each position of the gradient material.(a) Reaction efficiency after first impact (b) Reaction efficiency after second impact.

After the first impact,the velocity of the FGRM attenuated and partially fractured.According to Eqs.(10)～ (12),when the initial velocities of the impact are 925 m/s and 1268 m/s,the residual velocities of the FGRMs are 570.2 m/s and 975.0 m/s,respectively.The residual reactive materials with the residual velocity impact secondly and the graded materials react violently again.The reaction efficiency of the gradient material with the second impact is shown in Fig.12(b).The reaction efficiency induced by the second impact is similar to that induced by the first impact.

It is noted that the experimental phenomenon shows that,compared with the first impact,the flame of the FGRM induced by the second impact is more violent,but the theoretical analysis indicates that the chemical reaction efficiency of the second impact is lower than that of the first impact(as shown in Fig.12).The reason is that the temperature of the graded material will increase due to the first reaction,which will also increase the reaction efficiency of the reactive material in the second impact,making the reaction more violent.In addition,there is a delay time of the reaction induced by the first impact,resulting in the reaction occurring at the time of the second impact.

Fig.13.Overall chemical reaction efficiency of graded material.

Fig.13 presents the overall chemical reaction efficiency of the FGRM vary with the distance from impact interface after two impacts.As can be seen from Fig.13,the chemical reaction efficiency of the graded material changes sharply at the second impact interface and the interface of different media.The chemical reaction efficiency increases when the shock wave propagates from PTFE/Al/Bi2O3to PTFE/Al,but decreases when it propagates from PTFE/Al to PTFE/Al/Bi2O3.This is related to the shock mechanical properties of the two materials,which compose of the graded material.Since the shock impedance of PTFE/Al/Bi2O3wave is higher than that of PTFE/Al,the initial shock wave generated in the PTFE/Al/Bi2O3impact is higher than that of PTFE/Al.Moreover,through the interface of the two materials,transmission wave propagating from PTFE/Al to PTFE/Al/Bi2O3enhances,which is conducive to improving the chemical reaction efficiency of reactive materials.It is because of the difference in properties of graded materials,the impact direction of the FGRM has a significant influence on the reaction.The theoretical calculation indicates that the reaction efficiency of G1 is higher than that of G2,which is consistent with the test chamber experiment results that the overpressure induced by G1 is higher than that of G2.The higher reaction efficiency of G1 also results in the damaged area of G1 to the rear plate of the double-spaced plates is larger than that of G2.

It is worth noting that in the experiment,the impact direction has roughly little influence on the overpressure in the test chamber with the FGRM high-velocity impact,and the damaged area of the rear plate after the low-velocity impact is roughly the same,which is inconsistent with the theoretical analysis results.This is affected by the attenuation coefficientnof shock wave in the reactive material.Due to the imprecision of the attenuation coefficient,the theoretical model is not accurate enough to predict the reaction behavior of the reactive material under certain impact velocity conditions.However,this theoretical model can still predict the reaction behavior of FGRM to some extent with inaccurate coefficient.

6.Conclusion

In this paper,the shock-induced reaction behavior of FGRM which consisted of PTFE/Al/Bi2O3and PTFE/Al was investigated by experiments,including impact test chamber and double-spaced plates.The theoretical analysis model was developed to analyze the shock-induced reaction behaviors and the effect of impact direction.The main conclusion can be drawn as follows:

(1) The impact direction of FGRM has a significant effect on the reaction behaviors of reactive materials.Compared with G2(PTFE/Al impact first),G1(PTFE/Al/Bi2O3impact first)cause a larger damaged area of the rear plate of the double-spaced plates.

(2) Compared with G2 (PTFE/Al impact first),G1(PTFE/Al/Bi2O3impact first) induced higher overpressure in the test chamber,when impact with low velocity.Whatever the impact velocity is high or low,the impulse induced by G1 is higher than that induced by G2,or even twice as much as that of G2.

(3) The theoretical analysis model,considering the generation and propagation of shock wave within the FGRM,high temperature inducing chemical reaction,and penetration behavior,was developed to analyze the shock-induced reaction behavior of the FGRM.It indicates that the first impact material with higher shock impedance is conducive to improve the reaction efficiency of the FGRM.

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 was supported by National Natural Science Foundation of China [grant number U1730112],China.