Peng-song Nie ,Sho-hu Jin ,Li-xio-song Du ,Li-jie Li ,Kun Chen ,Yu Chen ,Rui Yu

a School of Materials Science and Engineering,Beijing Institute of Technology,Zhongguancun South Street 5,Beijing,100081,China

b Xi'an Modern Control Technology Research Institute,Xi'an,710065,China

Keywords:NTO Shock initiation Hugoniot data JWL Ignition and growth reactive model

ABSTRACT 3-nitro-1,2,4-tri-azol-5-one(NTO)is a high energy insensitive explosive.To study the shock initiation process of NTO-based polymer bonded explosive JEOL-1(32%octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine(HMX),32% NTO,28% Al and 8% binder system),the cylinder test,the gap experiments and numerical simulation were carried out.Firstly,we got the detonation velocity(7746 m/s)and the parameters of Jones-Wilkins-Lee(JWL)equation of state(EOS)for detonation product by cylinder test and numerical simulation.Secondly,the Hugoniot curve of unreacted explosive for JEOL-1 was obtained calculating the data of pressure and time at different Lagrangian positions.Then the JWL EOS of unreacted explosive was obtained by utilizing the Hugoniot curve as the reference curve.Finally,we got the pressure growth history of JEOL-1 under shock wave stimulation and the parameters of the ignition and growth reaction rate equation were obtained by the pressure-time curves measured by the shockinitiation gap experiment and numerical simulation.The determined trinomial ignition and growth model(IG model)parameters can be applied to subsequently simulation analysis and design of insensitive ammunition with NTO-based polymer bonded explosive.

1.Introduction

3-nitro-1,2,4-tri-azol-5-one(NTO)[1]is a high energy insensitive explosive.Its performance of safety is close to TATB,but its detonation velocity is higher than that of TATB.As a warhead charge,it has stable performance,good formability and low level of response to external stimuli such as mechanical impact,shock waves and accidental ignition.It has high safety in production,storage and service processing.NTO-based polymer bonded explosives can effectively reduce the response level of the warheads when it is accidently stimulated on the battlefield,and greatly improve the safety of weapons and ammunition.Thus,NTO-based polymer bonded explosives have been widely used in insensitive warheads[2—7].The study of about initiation,deflagration and detonation process of explosives,which is a core issue to understand its initiation characteristics,the law of energy release and safety performance,has important theoretical and practical significance for the safe application of explosives.

The shock-to-detonation process of explosives is a very complex process involving the effects of chemistry,mechanics and heat.Many experimental and theoretical work on shock initiation of explosives had been conducted.Gittings[8]studied the shock initiation performance of PBX-9404 and found that the explosive initiation was related to the shock pressure and the width of shock wave.Through the gap experiments,Bernecker[9]studied the instantaneous detonation and delayed detonation of explosives by high-speed photography.Jiashan Ke[10]studied the shock initiation performance of JO-9159 explosive by the gap experiment,obtaining the threshold of initiation pressure and used the X-ray machine to study the delayed detonation phenomenon.In 1998,Massoni J and Saurel R[11]established an ignition growth model for shock initiations of solid explosives.It assumed that the ignition occurs in the cavity area inside the explosive,and the growth starts from the combustion inside the cavity.Khasainov[12]considered the influence of factors such as different nuclear gases,the mass conversion between gas-solid phase materials and the chemical decomposition of solid explosives under shock loading.But the experiment of explosive initiation and warhead explosion is costly and risky.At the same time,it cannot measure all the physical andchemical information and the mechanism cannot be fully described.In order to make up for the shortcomings of detonation experiment,numerical simulation has become an important method for explosive initiation and detonation research.The numerical simulation of the shock-to-detonation process requires a complete set of detonation reaction flow models,including basic nonlinear fluid dynamics equations,reaction rate equations,unreacted explosives EOS and detonation products EOS.Lee and Tarver[13]of the LLNL laboratory in the United States have done a lot of work on the study of explosive reaction rate models.The trinomial ignition and growth model(IG model)proposed by them is still the most commonly used models for simulating the shock initiation and detonation growth process of explosives.IG model parameters of many composite explosives have been studied and reported,such as TATB-based explosives[14],HMX-based explosives[15]and B explosive[16].In 2002,J.K.Clutter[17]used the ignition growth model to simulate the shock-to-detonation of explosives and the simulated curves were in good agreement with the experimental curves.In addition,he also simulated the interaction between detonation waves.Guoping Jiang[18]used twodimensional Lagrangian experiments to study the shock initiation of press-packed TNT and gave the parameters of the IG model of the explosive.Lefrancois[19]used the ls-dyna software to simulate the diameter effect of the LX-16 explosive.The explosive with larger diameter at the bottom adopts the JWL EOS and the explosive with smaller diameter adopts the IG model,and the critical diameter is calculated by the simulation model.

Because of the demand for high-value weapon platforms,this article uses NTO-based polymer bonded explosive JEOL-1(32%octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine(HMX),32% 3-nitro-1,2,4-triazole-5-one(NTO),28% Al and 8% binder system)as the research object.Through the gap experiments[20]and the cylinder test,the JWL EOS and reaction rate equation of the JEOL-1 are obtained.It provides support for the numerical simulation and engineering application in shock initiation and detonation of NTObased polymer bonded explosives,and provides a certain technical reference for the development of insensitive ammunition and insensitive warhead technology.

2.Experiments

2.1.Cylinder test

Fig.1.Diagrams of cylinder test.

The cylinder test device was shown in Fig.1.The history of the expansion speed of the cylinder wall is measured by the DISAR test system,and the result is recorded by the oscilloscope.The density of JEOL-1 explosive sample is 1.917 g/cm3.The size of cylinder is φ50 mm×500 mm,the size of TNT detonator is φ50 mm×20 mm,and the size of transition grain is φ50 mm×50 mm.The experiment uses 3 laser probes to measure the velocity of cylinder wall.Among them,two are 300 mm away from the upper end of the cylinder,one is 350 mm away from the upper end of the cylinder.The wavelength of the laser probes is 1550 nm.The diameter of the laser probes used for testing is 3.2 mm,and the diameter of the laser focal spot is less than 0.3 mm.At the same time,a copper foil probe with a thickness of about 0.2 mm is placed on both ends of the cylinder to measure the detonation velocity of the tested explosive.The uncertainty of the cylinder test is mainly determined by the uncertainty of the measured data by laser probes and the uncertainty caused by the installation of the cylinder and the probes.

2.2.The gap experiments

The gap experiments equipment chart was shown in Fig.2.The initiation system was made of electric detonator,trigger probe,explosive plane wave generator(φ80mm)and main TNT charge(φ80mm×20 mm).The measurement system structures included such parts:Aluminium gap,JEOL-1 sample,manganese-copper pressure gauge and steel socket.The signal collection system consisted of a high speed pulse constant current source and an oscilloscope.The uncertainty of the gap experiments is mainly determined by the uncertainty caused by the installation of manganese-copper pressure gauge and the uncertainty in reading the data of oscilloscope.

The parameters and experiment conditions of the JEOL-1 explosive sample are shown in Table 1.In order to maintain the manganese-copper pressure gauge for a relative long time to record as many voltage signals as possible,0.1 mm PTFE films were used to encapsulate the surface of gauge.When the plane wave generator was initiated,the plane wave was generated and the signal collection system was triggered.When the shock wave reached the explosive,the oscilloscope recorded the voltage change signals of manganese-copper gauges at different positions and the voltage signals recorded was converted into the pressure-time curve.

Table 1The detailed experimental parameters.

3.Methods

3.1.JWL EOS of detonation product

Note:P,pressure of detonation product(GPa);V,the relative volume of the detonation product;C,constant-volume specific heat capacity;T,temperature;A,B,R,Rand ωare coefficients.

3.1.1.Determination of initial estimated value of detonation product JWL EOS

The composition,density and enthalpy of formation of the explosive are used as the input parameters of the EXPLO5 software,and then the BKW equation of state is used to calculate the detonation parameters and isentropic curves of the explosive.Finally the PV data(the pressure of detonation product(GPa)and the relative volume of the detonation product)is fitted into the JWL EOS form by a nonlinear fitting method to obtain the initial estimated value of the parameters of the JWL EOS of detonation product.The pressure of detonation product and detonation heat of JEOL-1 explosive measured by other experiments are 28.85 GPa and6790 kJ/kg.

Fig.2.Equipment chart of gap experiment.

3.1.2.Simulation of cylinder test

Using LS-DYNA software,a two-dimensional cylinder model was established according to the actual size of the cylinder test(Fig.3).The models of explosives and copper wall adopt elastoplastic hydrodynamic models,and the parameters are shown in Table 2.The equation of state of copper is described by the Grüneisen equation(Table 3).

Table 2The modle parameters of copper[21]and explosive.

Table 3The equation of state parameters of copper[21].

Table 4The modle parameters of manganese-copper and PTFE[21].

The estimated value of the parameters of the JWL EOS of detonation product is used to simulate the cylinder test.Then we can obtain the data such as the relationship between the expansion distance and expansion time and the velocity of cylinder wallthrough the post-processing calculation.

Fig.3.Simulation model of cylinder test.

3.1.3.Comparison of simulation and experiment

By comparing the error between the simulated value and the experimental value of cylinder wall velocity measured by cylinder test,if the error is within the acceptable range,the parameters of the JWL EOS of detonation product are considered the final calibration result.If the error is too large,fine-tuning R,Rand ω on the basis of the estimated parameters of the JWL EOS of detonation product and the new values of A,B and C can be obtained by solving the linear Eqs.(2).Using this as the estimated value of the new round of the JWL EOS of detonation product and repeat steps 2)and 3)until the error between the simulated value and the experimental value is within the allowable range.

Note:V＝γ/(1＋γ),E＝ρQ;the units are cm,g and μs when calculating.

3.2.JWL EOS of unreacted explosive

According to Eqs.(3)—(5),we got Eq.(6):

3.2.1.Determination of hugoniot curve of the unreacted explosive

Reading the data of pressure and time of gap experiments when the shock wave arrive the different Lagrangian positions of 1,2,and 4,and subtracting the propagation time of the shock wave in the PTFE film,we would get the actual time of shock wave arriving at each Lagrangian position.Then the average velocity of the shock wave between two adjacent Lagrangian positions was obtained,and the interpolation method is used to obtain the velocity of the shock wave at each position of manganese-copper pressure gauge.The same interpolation method is also used for pressure,so that a set of pressure and shock wave velocity data were obtained.Using the conservation of momentum of shock wave front,the shock wave velocity and particle velocity data of the unreacted explosive at the corresponding position can be obtained.Generally,there is approximately a linear relationship between shock velocity(D)and particle velocity(u),as described in Eq.(7).

where a and b are the undetermined coefficients of Hugoniot relationship.

3.2.2.Comparison of two curves

According to Eq.(7)of the unreacted explosive on the(D,u)plane,Eq.(8)of the unreacted explosive on the(p,v)plane can be obtained as:

where Vand V were initial specific volume and specific volume,respectively.

And the e(specific internal energy)could be obtained by the equation of conservation of energy(Eq.(9)):

Taking the initial internal energy of the explosive(except chemical energy)e＝0,we can obtain Eq.(10)from Eq.(6)and Eq.(9):

Appropriately select the parameters A,B,R,Rand ω in Eq.(10).Until the curve of Eq.(10)is consistent with the curve of Eq.(8),the parameters of JWL EOS for unreacted explosive can be determined.

3.3.Reaction rate equation

Note:F,the reaction fraction of explosive;P,pressure;ρ/ρ,the relative density;Iabcdegxy and z,fitting constant;F、Fand F,cutoff of corresponding reaction term.

At present,reaction rate equation is generally an empirical model.It contains some parameters,which are mainly determined by the fitting of numerical simulation calculation to experimental data.The DYNA2D program was used to simulate gap experiments(Fig.4).In the calibration process,we mainly focused on the first jump pressure of different position to determine the I,Gand G.And by adjusting the x,y and z,we matched the calculated pressure curves to corresponding experimental curves as similarly as possible.Until the curves of simulation are consistent with the curves of gap experiments,the parameters of reaction rate equation can be determined.

Fig.4.Numerical model.

As shown in Fig.4,the pressure-time curve at the 0 mm position measured by the experiment is used as the initial boundary condition.In addition,considering the manganese-copper pressure gauge and PTFE film embedded in the explosive during the experiments,during the modeling,the manganese-copper pressure gauge material and the PTFE material properties are also set at the Lagrangian positions inside the explosive.

The material models of manganese-copper pressure gauge and PTFE adopt elastoplastic hydrodynamic model,and the EOS adopts the Grüneisen equation of state.The parameters are shown in Table 4 and Table 5,respectively.

Table 5The EOS parameters of manganese-copper and PTFE[21].

Table 6The final calibration result.

4.Results and discussions

4.1.Cylinder test

The detonation velocity of JEOL-1 explosive measured by copper foil probes at both ends of the cylinder is 7746 m/s(Fig.5),and the velocity of cylinder wall-time curve is shown in Fig.6.

4.2.Gap experiments

The loading pressure history of the experiments were shown in Fig.7(a)-(c).

From Fig.7(a),the initial input shock pressure in 1and 2were of 8.32 GPa and 6.17 GPa.The 4are repeatability experiments.From Fig.7(b),it can be seen clearly that the results are alsoconsistent,indicating that the experiment system is stable and reliable,and verifying the repeatability of the experiment at the same time.Within the range of 0—4 mm positions,the pressure was not changed obviously.After shock wave arriving at 8 mm and 12 mm positions,the pressure rose obviously because of the shock initiated reaction.From Fig.7(c),the pressure-time history at the 0 mm position of 3、4are also consistent.Changing the other 3positions can enriches the pressure data of shock ignition and detonation growth process.

Fig.5.The signal of copper foil probe.

Fig.6.The v-t curves of cylinder.

Fig.7.Pressure-time curves.

Fig.8.The v-t curves of cylinder test and simulation.

4.3.Parameters of IG model

4.3.1.Parameters of detonation product JWL EOS

The parameters of the JWL EOS of the JEOL-1 detonation product determined by the combination of simulation and calculation are shown in Table 6.

From Fig.8,we can see that the numerical simulation curve and the experimental curve are basically coincide.In summary,the parameters of the JWL EOS for JEOL-1 detonation product finally calibrated in Table 6 are reasonable and reliable.

4.3.2.Parameters of unreacted expolsive JWL EOS

Through reading data of the gap experiments and calculating,shock wave velocity and particle velocity data were shown in Table 7.

The Hugoniot relationship of the unreacted explosive is obtained by fitting the data in Table 7:

In equation(12),21.3 m/s≤u≤2009.1 m/s,the fitting curve and each test point are shown in Fig.9.

Then we can obtain parameters of unreacted expolsive JWL EOS by utilizing the Hugoniot curve as the reference curve.The final calibration result was shown in Table 8.

4.3.3.Parameters of reaction rate equation

Finally,The final calibration result by a combination of experiment and numerical simulation was shown in Table 9.

Table 8Parameters of JWL EOS for unreacted explosive.

Table 9The parameters of reaction rate equation.

Fig.9.Hugoniot relationship of the unreacted explosive.

Table 7Shock wave velocity and particle velocity of the unreacted explosive.

From Fig.10(a)-10(d),we can see that simulated pressure-time curve and the experimental curve are basically coincide.As seen in Fig.10(a),after shock wave arrived 8.533 mm position,the pressure was 28.12 GPa.It approached to the C-J detonation pressure(28.85 GPa)of JEOL-1.In summary,the parameters of reaction rate equation finally calibrated in Table 9 are reasonable and reliable.

5.Conclusions

In this study,the shock-initiation characteristics of JEOL-1 polymer bonded explosive were investigated by cylinder test and gap experiments.The detonation velocity of JEOL-1 explosive was 7746 m/s and the JWL EOS of the detonation products for JEOL-1 was calibrated by cylinder test and numerical simulation.And the shock hugoniot relationship of the unreacted explosive was calculated from the data of pressure and time by oscilloscope when the shock wave arrive the different Lagrangian positions.Then we got the parameters of JWL EOS for the unreacted explosive.We used the pressure-time curves measured by the shock-initiation gap experiment and numerical simulation to accurately parameterize the ignition and growth reaction rate equation.Finally,we got the whole parameters of trinomial ignition and growth model for JEOL-1.It would provide great support for the application of NTO-based explosives in the warhead and greatly improve the safety of ammunition.

Fig.10.Experimental and simulated pressure-time curves.(a)In chronological order,from left to right,it is 0 mm,4.31 mm,8.533 mm,12.753 mm(b)In chronological order,from left to right,it is 0 mm,4.437 mm,8.66 mm,12.88 mm(c)In chronological order,from left to right,it is 0 mm,3.463 mm,6.796 mm,10.096 mm.(d)In chronological order,from left to right,it is 0 mm,4.32 mm,8.58 mm,12.813 mm.

The data that support his study are available from the corresponding author for reasonable request.

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.

The authors would like to thank the Fundamental Research Funds for the Central University in China.