A melt-cast Duan-Zhang-Kim mesoscopic reaction rate model and experiment for shock initiation of melt-cast explosives

Shu-rui Li,Zhuo-ping Duan,Lian-sheng Zhang,Zhuo-cheng Ou,Feng-lei Huang

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

Keywords: Melt-cast explosive Shock initiation Mesoscopic reaction rate model Hot-spot ignition Shock sensitivity

ABSTRACT A melt-cast Duan-Zhang-Kim(DZK)mesoscopic reaction rate model is developed for the shock initiation of melt-cast explosives based on the pore collapse hot-spot ignition mechanism.A series of shock initiation experiments was performed for the Comp B melt-cast explosive to estimate effects of the loading pressure and the particle size of granular explosive component,and the mesoscopic model is validated against the experimental data.Further numerical simulations indicate that the initial density and formula proportion greatly affect the hot-spot ignition of melt-cast explosives.

1.Introduction

Melt-cast explosives are composed of granular explosive components,matrix explosive components as well as some additives,and they have been widely used in munitions due to the advantage of low cost and easy shaping.In general,granular explosive components have high energy performance such as the hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX),and matrix explosive components have low melting points as liquid carriers such as the 2,4,6-trinitrotoluene (TNT).During preparations of melt-cast explosives,matrix components will suffer a phase transition from liquid to solid that accompanied with other physical processes,including the thermal conduction and volume contraction.It leads to mesoscopic defects (such as pores or cracks) that greatly affect the initiation sensitivity of melt-cast explosives and the safety performance of munitions [1,2].Therefore,it is essential to explore initiation mechanisms as well as effects of mesoscopic structures on the shock-to-detonation transition (SDT) process in melt-cast explosives.

Chemical reaction rate models constitute a key element of the shock initiation simulations of explosives.They are mainly divided into the macroscopic [3-7] and the mesoscopic [8-11] ones.At present,the so-called Lee-Tarver (L-T) macroscopic reaction rate model [3] has been widely used in SDT simulations of melt-cast explosives.For example,Urtiew et al.[12] have determined a set of L-T model parameters for Comp B-1 melt-cast explosive (containing 63 wt% RDX,36 wt% TNT and 1.0 wt% wax) by combining corresponding parameters of TNT with those of RDX-based C-4 explosive (containing 91 wt% RDX and 9 wt% additives).However,the simulated results of both shock arrival times and post-shock pressure evolution deviate greatly from the experimental data of Comp B-1.Moreover,to simulate the SDT processes with different initial densities,Vandersall et al.[13]had to propose two different sets of L-T parameters for Comp B-2 explosive (containing 61 wt%RDX,38 wt%TNT and 1.0 wt%wax).It indicates that the parameters of macroscopic reaction rate models are valid only in the state variables range where they were determined.Thus,to grapple with the weakness of macroscopic reaction rate models,several mesoscopic reaction rate models have been developed by considering the heterogeneity of plastic bonded explosives (PBXs) at the mesoscale [9,10].As the mesoscopic structures of melt-cast explosives are much different from those of PBXs due to their different preparation procedures,it is necessary to develop a mesoscopic reaction rate model incorporating the own mesoscopic characteristics of melt-cast explosives.

Abundant experimental SDT data provides the foundation for exploring shock initiation mechanisms and developing reaction rate models.In shock initiation measuring techniques,tested explosives are initiated by plane shock waves that generated by plate impacts or chemical explosions [14-20].Lagrangian gauges are utilized to measure the pressure histories or particle velocity histories in the SDT processes of tested explosives,such as the manganin piezoresistive pressure gauges [16,17,20-22] and the electromagnetic particle velocity gauges[23-27].Most of previous SDT experiments were conducted on PBXs[18,25,27-30]and those on melt-cast explosives mainly concerned the effect of loading pressures.For instance,Urtiew et al.[12] measured the pressure histories in SDT processes of Comp B-1 explosive by manganin piezoresistive pressure gauges under various impact velocities of aluminum flyers.Moreover,Gibson et al.[26] investigated the particle velocity histories of Comp B explosive(containing 59.5 wt%RDX,39.5 wt% TNT and 1.0 wax) under different loading pressures by using multiple electromagnetic particle velocity gauges and Kel-F81 polymer flyers.To the best of authors’ knowledge,the experimental SDT research on melt-cast explosives concerning the effects of mesoscopic characteristics has not been reported yet.

The purpose of this paper is therefore to develop a mesoscopic reaction rate model for the shock initiation of melt-cast explosives.A series of shock initiation experiments was performed to investigate the mesoscopic effects on shock initiation and validate the mesoscopic model.The paper is organized as follows.After this brief introduction,the mesoscopic reaction rate model (melt-cast Duan-Zhang-Kim model) is presented in Section 2.Section 3 describes the shock initiation experiments of Comp B explosive(containing 59.5 wt% RDX,39.5 wt% TNT and 1.0 wt% wax) with different particle sizes of RDX under various loading pressures.Section 4 presents the numerical simulations of the shock initiation processes of Comp B as well as the validation of the mesoscopic reaction rate model.Section 5 analyses the effects of initial density and formula proportion on the SDT process,and the ignition characteristics of melt-cast explosives together with some discussions are also presented in this section.Conclusions are given in Section 6.

2.Melt-cast Duan-Zhang-Kim mesoscopic reaction rate model

The viscosity of molten melt-cast explosives is constrained strictly to avoid sedimentation,so that the particle sizes of the granular explosive components are generally hundreds of micrometers.Fig.1 shows a scanning electron micrograph (SEM) of a melt-cast explosive(containing 60 wt%RDX and 40 wt%TNT)[31].Under shock wave loading,the pores induced in the cooling and solidification processes of the matrix explosive component will collapse,then lots of heat are generated by mechanical deformations and the high temperature areas(namely,hot-spots)are localized.Thus,the mesoscopic structure of the melt-cast explosive is simplified in this study as shown in Fig.2.

With assuming the granular explosive and the matrix explosive are both elastic-viscoplastic,a double-layered hollow sphere hotspot ignition model is constructed as shown in Fig.3.In the figure,the radiirpandrirepresent the average sizes of the granular explosive particle and the pore,respectively.rmis the interfacial radius between the granular explosive and the matrix explosive.P0is the loading shock pressure andPgis the gas pressure inside the pore.

Porosity β is defined as the volume ratio of the pores to the explosive components,and it satisfies the relation between the initial density ρ0and theoretical maximum density ρtas,

Volume ratio χ of the granular explosive to the matrix explosive is expressed as

where αpand ρpare respectively the mass fraction and the theoretical maximum density of the granular explosive,as well as αmand ρmare those of the matrix explosive.Then geometric parametersriandrmof the hot-spot ignition model could be obtained with a knownrp.

Under shock wave loading,the governing equations of the elastic-viscoplastic collapse motions of two explosive hollow spheres are [8,9].

wherej∈{p,m}.represent respectively the radial stresses,the tangential stresses and the radial velocities that are functions of the radius distancerand the timet.kj,Gjand γjare the yield strengths,the shear moduli and the viscosity coefficients,respectively.DefiningPmas the interfacial pressure atr=rm,the boundary conditions are given by,

Fig.2.Simplified mesoscopic structure of the melt-cast explosive.

Fig.3.Elastic-viscoplastic double-layered hollow sphere hot-spot ignition model for a melt-cast explosive.

With the interfacial velocity continuityvp(rm,t)=vm(rm,t)and the assumption of the elastic deformation is accomplished instantaneously att=0,the radial velocitiesare derived as,

All gaseous reaction products are assumed to fill into the pore.Thus,the volume of gaseous productsVgshould be the total volumes of the poreViand the reacted explosivesVsas,

whereTjare the explosive temperatures,and the relative volumesand

Temperature rises dTjof explosive hollow spheres created by the elastic-viscoplastic mechanical deformations in collapse motions are given by,

where ρjandare respectively the densities and the heat capacities.Neglecting the heat generated by elastic deformations,Eq.(3b) could be written as,

Then substituting Eqs.(5)and(9)into Eq.(8)with supposingP0?kj,the rates of temperature riseare derived as,

where γk=γmfor the granular explosive and γk=γpfor the matrix explosive.Apart from mechanical deformations,the chemical reactions and heat conduction also lead to temperature rises in collapse process[8,9],so the total rates of temperature rise(dT/dt)jare,

where the temperaturesTjare given by,

Therefore,the reacted explosive volumes of the two hollow spheres are derived as,

Defining the ignition degree of the hot-spot model as the ratio of the reacted explosive volumeto total explosive volumeVtotal,the ignition rate (dλ/dt)ignof the hot-spot model is obtained as,

As the reaction rates of the two explosive hollow spheres are derived as,

the ignition rate (dλ/dt)ignof the hot-spot model could be written as,

where χjare the volume fractions of the granular explosive and the matrix explosive components.

After ignition,hot spots will enter the first growth stage,which is called the slow burning stage because of its low pressure and low reaction rate.In this study,surface burning is supposed to propagate from inner to outer surfaces of the hot spot model and the burning rate obeys dr/dt=apn,wherepis the pressure,a and n are constants.Neglecting initial porosities,the reaction degree λ (volume fraction of the reacted explosive)could be expressed as λ=r3/Then the reaction rate of the slow burning stage is given by Refs.[8,9],

where a burn-up factor (1 -λ)bis introduced to incorporate the decrease of burning surface areas induced by growths of adjacent multiple hot spots [16].

With continual burning reactions and amalgamations of adjacent hot spots,the pressure and the reaction rate increase rapidly and the hot spots enter the second growth stage called the fast burning stage.Zhang et al.[32] have proposed a high-pressure reaction rate equation that could simulate the chemical reaction of heterogeneous explosives under high pressures,

whereG,zandxare constants.Coupling above ignition rate and reaction rate equations,the melt-cast Duan-Zhang-Kim (DZK)mesoscopic reaction rate model could be constructed with a threeterm reaction rate equation as,

The first term is the hot-spot ignition rate (dλ/dt)ignsimplified by Eq.(17)(j∈{p,m}),which is obtained by weighting the reaction rates of the two explosive hollow spheres by their volume fractions.Only thermodynamic parameters of the granular explosive and the matrix explosive are required for the first ignition term,and the six reaction rate constants(a,n,b,G,z,x)in the last two terms need to be calibrated by shock initiation data of melt-cast explosives.

3.Experimental set-up

Fig.4 shows the one-dimensional Lagrangian measuring system established with manganin piezoresistive pressure gauges and Fig.5 presents assembly parts of the experimental device.An explosive plane-wave lens and a TNT booster are combined to generate a plane detonation wave.The plane detonation wave is first attenuated by the air-gap and aluminum board before initiating the Comp B samples,thus the loading pressure on the upper surface of Comp B samples could be controlled by altering the thicknesses of the air-gap and aluminum board.To ensure the one-dimensional property of the experimental data,the φ80 mm plane-wave lens and the φ80 mm × 20 mm TNT booster are used,and all the Comp B samples are φ50 mm.As shown in Fig.5,a set of Comp B sample is composed of three thin discs with 3 mm or 5 mm in thickness and one thick disc with 25 mm in thickness.

Four manganin piezoresistive pressure gauges are used in each test.One is placed between the first explosive disc and the aluminum board to measure the loading pressure,and others are placed between the explosive discs to measure the pressure histories at different Lagrangian locations.Hence,the tested Lagrangian locations could be adjusted by assembling explosive discs with different thickness.All gauges are armored with thin Teflon insulation(0.1 mm or 0.2 mm in thickness)on both sides and packaged with silicone grease to prolong the measuring time.

The pressure gauges,oscilloscope and constant-current source constitute a constant-current circuit.When the shock wave arrives at the pressure gauge,the pressure increment leads to both the resistance variation and the voltage variation due to the piezoresistivity of manganin.Voltage histories of the four gauges are recorded by oscilloscope as shown in Fig.6(a),where the two signal leaps on each curve indicate respectively the trigger time at the moment of plane-wave lens exploding and the arrival time of shock wave.Then the voltage histories could be transformed into the pressure histories (see Fig.6(b)) by coupling the relation ΔR/R0=ΔU/U0of constant-current circuit and the pressure-resistance relation of the gauges expressed as follows [33],

wherePis the pressure,R0,U0and △R,△Uare respectively the initial values and increments of the resistance and voltage.Numbers at the bottom of Fig.6(b)represent the tested Lagrangian locations.

Four shock initiation experiments of Comp B were performed with different particle sizes of RDX under various loading pressures.Properties of the tested Comp B explosive are listed in Table 1 and concrete information of the four tests is listed in Table 2,where the loading pressure refers to the pressure on the leading wave measured by gauge 1.All the experimental data are presented in Section 4.

4.Verification of mesoscopic model

The melt-cast DZK mesoscopic reaction rate model is implemented into hydrodynamic software to simulate the shock initiation of Comp B explosive.To avoid modeling of the complex loading device (including the explosive plane-wave lens,the TNT booster,the air-gap and the aluminum board),the measured pressure history at the 0 mm Lagrangian location is taken as the input boundary condition.Fig.7 shows the one-dimensional numerical model for Comp B,in which a series of elements with 0.025 mm centroid distance is generated along thex-direction and all the elements only move along thex-direction in shock initiation.Moreover,for the manganin piezoresistive pressure gauges,the effect of Teflon films on the reaction flow fields is considered,while that of manganin foils is ignored due to their negligible thickness(～10 μm).h1-h4represent the Lagrangian locations of the four embedded pressure gauges.

Fig.4.Diagram of the one-dimensional Lagrangian test system.

Fig.5.Assembly parts of the experimental device.

The Grüneisen equation of state (EOS) is used to describe the mechanical behavior of Teflon films that given by,

whereeis the specific internal energy,γ0is the Grüneisen coefficient,μ=ρ/ρ0-1 is the compressive coefficient,andC,S1,S2,S3and a are constants.The EOS parameters for Teflon are listed in Table 3[35].The Jones-Wilkins-Lee (JWL) EOS in temperature dependent form is utilized for both the unreacted explosive and the detonation product of the Comp B explosive,which is expressed as

wherep,E,Tare respectively the pressure,the internal energy,the relative specific volume and the temperature,andA,B,R1,R2,ω andCvare constants.Parameters of JWL EOS for the unreacted explosive and the detonation product of Comp B are listed in Table 4.Here,the parameters for the unreacted explosive are determined by fitting the Rankine-Hugoniot relationship with genetic algorithm [34,36],and those for the detonation product are quoted from explosive handbook [37].

The geometric parameters of the hot-spot model for Comp B are calculated by Eqs.(1) and (2).Taking the Comp B sample with the fine RDX particles as an example,the particle sized50of RDX is 275.05 μm,then the parametersrp=137.525 μm,rm=104.141 μm andri=39.732 μm are obtained.The thermodynamic parameters of granular explosive RDX and matrix explosive TNT required for the first ignition term of the melt-cast DZK mesoscopic reaction rate model are listed in Table 5 [38].The six reaction rate parameters of the last two terms are calibrated by the shock initiation data of Comp B and listed in Table 6.

Table 1 Properties of the melt-cast Comp B explosive.

Table 2 Experimental conditions of each shock initiation test.

Table 3 Parameters of Grüneisen EOS for Teflon [35].

Table 4 Parameters of JWL EOS for the unreacted explosive and detonation product of Comp B.

Table 5 Thermodynamic parameters of RDX and TNT used in the first ignition term [38].

Table 6 Reaction rate parameters of Comp B used in the second and third terms.

Figs.8 and 9 present the experimental data (in solid lines) and simulated results (in dashed lines) of pressure histories in shock initiation of Comp B with different particle sizes of RDX under various loading pressures.The experimental and simulated results of leading wave trajectories are shown in Fig.10.The good agreement between the simulated results and the experimental data validates the ability of the melt-cast DZK mesoscopic reaction rate model to characterize the shock initiation behaviors as well as the effects of explosive particle size and loading pressure on the shock initiation of melt-cast explosives.

Fig.6.(a) Voltage histories recorded by oscilloscope;(b) Pressure histories transformed from voltage histories.

Fig.7.One-dimensional shock initiation numerical model of Comp B.

Fig.8.Experimental and simulated pressure histories of Comp B under various loading pressures:(a) P0=2.23 GPa;(b) P0=3.08 GPa.

Fig.9.Experimental and simulated pressure histories of Comp B with different particle sizes of RDX:(a) Coarse particle;(b) Fine particle.

Fig.10.Experimental and simulated leading wave trajectories of Comp B with different (a) loading pressures and (b) particle sizes of RDX.

It is found from the experimental data of Comp B that for a certain Lagrangian location,the pressure on the leading shock wave is low but the post-shock pressure grows remarkably.This phenomenon indicates the slow hot-spot ignition reaction near the leading shock wave and the rapid increase of post-shock reaction rate,which are verified by the reaction rate histories in the shock initiation of Comp B as shown in Fig.11.The reaction rate is found tobe low at first on the leading shock wave,but increase gradually and reach up to a peak value after a period.The remarkable increases of the post-shock reaction rate and post-shock pressure are induced by the subsequent ignition and reaction of potential hot-spots,which arise from the burning growth of the first ignited hot-spots on leading shock waves and then the significant rises of the pressure and temperature inside explosive.

Moreover,the pressure on the leading shock wave grows continually with the Lagrangian locations due to the pursuit of compressive waves generated by post-shock chemical reactions.It is also found that the higher the loading pressure or the smaller the particle size of RDX,the faster the leading shock wave propagates and the rapider the pressure growth.

Trajectories of the leading shock wave,the peak pressure,the peak particle velocity and the peak reaction rate in the shock initiation of Comp B are shown in Fig.12.It is found that after the leading shock wave,the particle velocity is the first to reach its peak,and then the reaction rate and the pressure successively.With the increase of Lagrangian locations,all the three trajectories gradually tend to the leading shock wave.When detonation is formed inside the Comp B explosive,the pressure,the particle velocity and the reaction rate reach their peak values simultaneously on the leading shock wave.Furthermore,it can be inferred that with the increase of loading pressure and the decrease of particle size of RDX,the three trajectories would tend faster to the leading shock wave,which implies a faster detonation growth and then a shorter run distance to detonation.

Fig.11.Histories of (a) reaction degree and (b) reaction rate in the shock initiation of Comp B.

Fig.12.Trajectories of leading shock wave,peak particle velocity,peak reaction rate and peak pressure in the shock initiation of Comp B.

Fig.13 present reaction degree histories of the total chemical reaction and hot-spot ignition at the 0 mm Lagrangian location under two different loading pressures of 2.23 GPa and 3.08 GPa.It is seen that the SDT process under a higher loading pressure is faster due to the ignition of more hot spots and a higher burning growth rate.

Fig.14 shows reaction degree histories of the total chemical reaction and hot-spot ignition at the 0 mm Lagrangian location with the fine and the coarse RDX particles.It is seen that the SDT process with fine RDX particles has a lower hot-spot ignition rate but a higher total chemical reaction rate than that with coarse RDX particles.That is the fine RDX particles have a larger burning surface area and consequently a larger burning reaction rate,although a smaller particle size of RDX leads to a smaller average pore size and a lower hot-spot ignition rate.It seems the Comp B explosive with fine RDX particles should be more difficult to be initiated.

5.Numerical simulations and discussions

Effects of the initial density (porosity) and formula proportion on the shock initiation as well as hot-spot ignition characteristics of melt-cast explosives are further simulated in this section.A onedimensional plane impact numerical model loaded by aluminum flyers is presented as Fig.15,whereVAlrepresents the initial impact speed of the flyer.In a similar way,a set of elements with 0.025 mm centroid distance is divided along thex-direction.The Grüneisen EOS parameters of the aluminum flyer are listed in Table 7 [35].

The SDT processes of Comp B with four different initial densities(1.67 g/cm3,1.69 g/cm3,1.71 g/cm3,and 1.73 g/cm3) and those of four common RDX/TNT melt-cast explosives in different proportions (listed in Table 8) are simulated to estimate respectively the effects of the porosity and the formula proportion.Particle sizes of RDX are selected as 275.05 μm.In addition,the parameters of JWL EOS listed in Table 4 are still utilized with neglecting the dependence of EOS parameters on both the initial density and the formula proportion.

Table 7 Parameters of Grüneisen EOS for aluminum [35].

Table 8 Proportions of four common RDX/TNT melt-cast explosives.

Fig.13.Degree histories of (a) total chemical reaction and (b) hot-spot ignition under various loading pressures in the shock initiation of Comp B.

Fig.14.Degree histories of (a) total chemical reaction and (b) hot-spot ignition with different particle sizes of RDX in the shock initiation of Comp B.

Fig.15.One-dimensional shock initiation numerical model impacted by the aluminum flyer.

With the same initial impact speed of 1050 m/s,the simulated hot-spot ignition degree histories at the 0 mm Lagrangian location of Comp B with different initial densities are shown in Fig.16(a)and those of the four RDX/TNT melt-cast explosives are shown in Fig.16(b).It is seen that inside the Comp B explosive with a lower initial density(or a higher porosity),the larger number of pores and the larger average pore size will result in more ignited hot spots and then a larger ignition rate.Moreover,the hot-spot ignition rate increases with the decrease of TNT mass fraction,which implies the melt-cast explosive becomes easier to be ignited and its shock sensitivity becomes higher.

Detailed ignition characteristics of melt-cast explosives are further explored by the calibrated hot-spot ignition model of Comp B.With the particle sized50,RDXof 275.05 μm and the initial density of 1.707 g/cm3,geometric parameters of the ignition model are obtained asrp=137.55 μm,rm=104.18 μm andri=39.99 μm.The two explosive hollow spheres of TNT and RDX are both divided into ten sub-hollow spheres and their spatial locations are represented by their inner radii at initial time.Then under the loading pressure of 4.93 GPa,temperature histories of the twenty sub-hollow spheres in the ignition are shown as Fig.17.The temperature distribution at a certain moment(e.g.t=0.032 μs)is shown as Fig.18,whereri?,rm?andrp?are respectively the inner,the interfacial and the outer radii at this moment.Moreover,reaction degree histories of the TNT and the RDX components are also presented in Fig.19.

Fig.16.Simulated hot-spot ignition degree histories at the 0 mm Lagrangian location of:(a)the Comp B with different initial densities;(b)the four RDX/TNT melt-cast explosives.

Fig.17.Temperature histories of sub-hollow spheres in the ignition:(a) TNT component;(b) RDX component.

Fig.18.Temperature distribution of the hot-spot ignition model at the moment of t=0.032μs.

Fig.19.Reaction degree histories of TNT and RDX components in the ignition.

Above simulated results show that in the ignition,the radial velocity and the rate of temperature rise are largest at the inner surface of TNT hollow sphere,and they both decrease with the increase of spatial locations.Thus,the maximum temperature is reached on the inner surface of the matrix hollow sphere.Moreover,the much lower temperature rise of the RDX hollow sphere induced by its slight mechanical deformation leads to a much lower ignition rate of the RDX component than the TNT component.Therefore,the TNT component contributes more reaction degree to the ignition of the hot-spot model than the RDX component.This might account for the experimental phenomenon that the shock sensitivity of a melt-cast explosive becomes lower while its matrix explosive component has a lower shock sensitivity [39].

Fig.20.Simulated run distances to detonation of Comp B with different particle sizes of RDX.

In addition,the run distances to detonation of Comp B are simulated with the two RDX particle sizes listed in Table 1.With the initial density of 1.707 g/cm3and four different initial impact speeds (i.e.1000 m/s,1150 m/s,1250 m/s and 1450 m/s),the pressure histories at different Lagrangian locations (equidistant spacing by 0.025 mm)are calculated and the first location that the stable detonation is formed is chosen as the run distance to detonation.The simulated run distances to detonation are compared with previous experimental data[12,26,38,40]as shown in Fig.20.It is seen that the Comp B explosive with fine RDX particles has a shorter run distance to detonation and a higher shock sensitivity.

6.Conclusion

A melt-cast DZK mesoscopic reaction rate model is constructed to describe the shock initiation behavior of melt-cast explosives with the pore collapse hot-spot ignition mechanism.Shock initiation experiments of the Comp B explosive were performed with different particle sizes of RDX under various loading pressures.The satisfactory agreement between the experimental data and simulated results validates the ability of the mesoscopic model to predict the effects of the loading pressure and the particle size of granular explosive component.The post-shock pressures in the shock initiation of Comp B are found to grow remarkably due to the gradual increases of the number of hot-spots and the ignition rates.Moreover,the pressure growth becomes faster under a higher loading pressure or with a smaller particle size of the granular explosive,and the hot-spot ignition rate increases with the decreases of both the initial density and the mass fraction of matrix explosive component.Furthermore,the matrix component is found to contribute more reaction degree to the ignition of the hot-spot model,which might account for the experimental phenomenon that the shock sensitivity of a melt-cast explosive becomes lower when its matrix explosive component has a lower shock sensitivity.

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.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No.11772056),the NSAF Joint Fund(Grants No.U1630113) and the Innovative Group of Material and Structure Impact Dynamics(Grant No.11521062).The authors also acknowledge the assistance with numerical simulations from Prof.Zhenyu Zhang and the experimental support from the Gansu Yinguang Chemical Industry Group Company Limited.