Numerical Study on Deformation and Ignition Process of Impacting Granular HMX Explosive in Drop Hammer Test

YIN Lu, LIU Zhi-yue, WANG Li-qiong

(State Key Laboratory of Explosion Science and Technology & School of Mechatronical Engineering Beijing Institute of Technology, Beijing 100081, China)

1 Introduction

Drop hammer apparatus is widely used to test the impact sensitivities of energetic materials. Until present, there is just a little research work toward the quantitative analysis for the ignition process in the tests. Experimentally, Bowden and Yoffe[1]conducted drop hammer test and first proposed the concept of hot spots inside explosive under impact. They thought that the internal gas adiabatic compression, crystal surface frictions and viscous heat caused by turbulence are the main reasons for hot spot formation. Field[2]modified drop hammer test equipment to get the detailed knowledge of hot spot formation. Through observations, he concluded that the adiabatic bubble temperature, adiabatic shear band and surface or the internal friction are the main reasons for the ignition of explosives. Considering the factor of the grain effectiveness, Gonthier[3]studied the compaction ignition process using impact speed from 10 m·s-1to 100 m·s-1. He studied the effect of viscous elastic-plastic contribution to the ignition in grain explosives. Yushi Wen et al[4]conducted a drop weight tests on three samples including crystal powders of RDX, tetryl, and PBX powder to probe the correlation between the explosion probabilities and the sample dose. And they found that the explosion probability will firstly increase and then decrease when the mass of sample reduces from 50 mg to 1.1 mg, under drop height of 25 cm and a 10 kg hammer. They explained the increasing part by proposing that the less mass the more energy the explosive sample absorbs and the easier the explosions occur, leading to higher explosion probability. The other part is a little complicated, they used a dual-factor-competition model to explain in their paper. To a block of PBX-9501 explosive (plastic bonded explosives with HMX mass fraction of 95%) under the impact with a medium speed, Bennett[5]simulated the dynamic response of impact test by using the DYNA3D software. He revealed that the main ignition mechanism is due to the friction on the shear fracture surfaces. However, it is difficult to present the hot spot formation and the meso-size process development owing to the small size of the hot spot (0.1-100 μm magnitude) and the short time to ignition (0.1 μs-1ms magnitude). In this paper, we utilize the numerical simulation method to study the deformation processes of explosive particles under the low-speed (<10 m·s-1) impact of drop hammer in the practical drop hammer device. The plastic energy in the particles was investigated to examine its role in the formation of hot spots in HMX explosive. The temperature rises in HMX particles were calculated and compared with the critical ignition temperature from other experimental measurement.

2 Numerical Simulation

2.1 Brief Description of Drop Hammer Apparatus

Drop hammer apparatus is a device to be utilized to measure the impact sensitivity of explosives as shown in Fig.1. The hammer drops along a guide rail. From a certain height, the hammer falls freely and hits on the striker. The explosive material is placed between the striker and the anvil. The drop hammer, striker, anvil, guide sleeve and the base are generally made of steel cylinders. Fig.2 illustrates the tester part of the device in detail. Our simulation model will be established from it.

Fig.1 Schematic diagram of drop hammer apparatus

Fig.2 Schematic diagram of impact tester

1—guide sleeve, 2—strikers, 3—explosive samples, 4—base

2.2 Computational Model

Based on the actual drop hammer apparatus, it is assumed that the hammer directly impacts onto the striker with an initial speed. The stresses and strains in the striker, particles, the hammer and the anvil are investigated. The computational model system consists of drop hammer, striker, anvil, guide sleeve and explosives particles. The ANSYS Design Modeler software is employed to draw the computational shapes of the components given in Fig.2. The gained configuration is shown in Fig.3. The configuration in simulation contains five parts of drop hammer, striker, HMX particles, anvil, and guide sleeve. In the calculations, the anvil and the guide sleeve are assumed to be stationary. Area-1 in Fig.3 is the location of the HMX particles and the detailed particle distribution is amplified in Fig.4. The dimension of HMX particle is chosen from the practical characteristic scale size. For the computational convenience, the shape of the particle is simplified as a circle. The particles are evenly stacked in layer by layer. There are 25 particles at the bottom layer in half of the configuration (Fig.4). Considering the fact of the symmetry of the model, half of the configuration is selected to calculate during simulation.

In the model, both the diameters of striker and anvil are 10 mm and their heights are 10 mm. The outer diameter of guide sleeve is 40 mm, the inner diameter is 10 mm and the height is 16 mm. The drop hammer is 5 kg, the diameter is 40 mm and the height is 127 mm. The HMX particles have single diameter of 200 μm. The materials steel and HMX follow an elastic-plastic deforming behavior. Their materials parameters are listed in Table 1 and Table 2, respectively.

Fig.3 Simulation diagram of impact structure(1-sample area)

Fig.4 The amplification of impact structure schematic diagram

Table 1 Parameters of steel material[6]

materialdensity/kg·m-3elasticmodulus/GPaspecificheatcapacity/J·kg-1·K-1yieldstrength/GPaPoissonratiosteel78302104600.310.30

Table 2 Material parameters of HMX[3]

materialdensity/kg·m-3elasticmodulus/GPaspecificheatcapacity/J·kg-1·K-1yieldstrength/GPaPoissonratioHMX190324.015000.26[6]/0.13[7] 0.20

In the experimental tests for HMX particle samples, it is found that using 5 kg hammer the impact drop heightH50is 33 cm, from which letting the hammer fall, the probability of the ignition occurs is about 50%. According to this data, in the simulation,H50is used to get initial velocity for drop hammer. The velocity is calculated to be 2.543 m·s-1, at which the hammer will hit the striker. Accounting for the influence of the gravity, the system is subjected to the gravitational acceleration of 9.806 m·s-2. In the calculation, the time step is automatically controlled by the program, roughly being 3.1×10-10s.

Assuming that the HMX particles are suitable for the elastic-plastic constitutive model and the simulation uses the dynamic software AUTODYN in the ANSYS products. Before the calculations, the model needs to be meshed. The quadrilateral mesh is used for all parts of the model system. The HMX particles are meshed by general quadrilateral with the characteristic length of 1.5 μm. The other parts are of a square grid, with a typical size of 40 μm. Fig.5 shows the overall grid partition of the impact system. For the sake of better viewing, Fig.6 gives a magnification of the mesh of HMX particles.

Fig.5 Mesh partition diagram of impact structure

Fig.6 Magnification of mesh of HMX particles

3 Results and Discussions

3.1 Calculation Method of Temperature Rise

Since the simulation software does not provide a package for calculating the temperature rise accompanying the deformation, we have to establish a method to calculate it using the stresses and strains obtained from simulation. We already known that the deformation of HMX particles under stress including elastic and plastic deformations. However, the elastic behavior does not produce work to cause temperature rise, so we only discuss the calculation method of plastic work. The calculation formula for plastic work is according to Eq.(1).

(1)

Whereσis the stress, MPa,εis the strain. In calculating plastic work, an approximate method is taken. Since the stress and the strain are known at any time from the simulation results, the equivalent stress and the equivalent strain at each time can be calculated. The product of these two terms can be thought as equivalent plastic work. Summing the equivalent plastic work at all time phases, the total plastic work is obtained. At each time phase, the averaging stress is calculated according to Eq.(2).

(2)

Δεi=εi-εi-1

(3)

Whereεiis the difference of two plastic strains between two adjacent time-steps of Δti-1and Δti;εiis the plastic strain at time-step of Δti. In the beginning of the calculation, let Δε0=0. The total plastic work is gained by Eq.(4).

(4)

WhereW(J), is the work done during the plastic deformation of some specific element in all time-steps Δt1to Δtn.nis the number of the computational cycles from the beginning to the desired termination.

Setting the area of the specific element as unit value, the heat is transformed by the partial plastic workWs(J). We assume that the total plastic work is converted into heat energy, denoted byQs(J). AndCV(J/(kg·K)) is the volumetric specific heat of HMX material . The temperature rise ΔT(℃), due to the accumulation of heat can be determined by the following Eq.(5).

(5)

3.2 Effect of HMX Particle Inhomogeneity on Temperature Rise

In order to investigate the effect of particle inhomogeneity on the local heat formation, the arrangement of HMX particles are constructed into two cases: regular arrangement in which all particles are of the same circular shape and irregular arrangement in which at some locations there are replacements by smaller particles. Furthermore, owing to the fact that there is ambiguity on the yield strength value for HMX particle, two yield strength values are considered. Dick and Menikoff[7]gives a 0.26 GPa value by tests, however, Palmer and Field[8]present the value of 0.13 GPa. At first, a 0.26 GPa value for yield strength of HMX is used in the calculations to analyze the effect on temperature rise for both regular and irregular particle arrangements.

Firstly, we carry out simulations on the case of the regular arrangement. In the calculation of the plastic work, the plastic stress and plastic strain are two important physical variables. Those values should be correctly obtained and kept. Fig.7 shows stress distribution in HMX particles att=25 μs,t=50 μs,t= 75 μs andt=100 μs, for the knowledge of the changing process of the particles stress. In Fig.7, the different colors represent different ranges of the stress magnitude (unit-MPa). Fig.8 shows plastic strain diagram of HMX particles correspondingly att=25 μs,t=50 μs,t=75 μs andt=100 μs. Here, the colors represent different ranges of the plastic strain magnitude. After impacted by the drop hammer, the particles still keep the original regular arrangement, but, the forces in particles are uneven. As time reaches 100 μs, there appears a location with the maximum of plastic work in the particle system. With yield strength of 0.26 GPa, the location designated asM1presents the maximum plastic work just as shown in Fig.7 and Fig.8. Fig.9 shows the varying curves of the local stress and plastic strain with time correspondingly.

Fig.7 Equivalent stress of HMX particles at different times in case of regular arrangement

Fig.8 Equivalent plastic strain of HMX particles at different times in case of regular arrangement

Fig.9 Stress and plastic strain atM1point versus time curve in case of regular arrangement

Next, the account is taken into the case of irregular arrangement of particles. In the irregular arrangement, the HMX particles randomly packed. The arrangement includes 206 circular particles with diameters ranging from 40 mm to 300 mm. Fig.10 and Fig.11 show the calculated stress and plastic strain distributions in HMX particles with irregular arrangement att=25 μs,t=50 μs,t=75 μs andt=100 μs, respectively. Based on the simulation results, it is found that at point M2there is the maximum plastic work. Correspondingly, the curves of the stress and the plastic strain versus time at that point are shown in Fig.12.

After the stress and plastic strain values of pointsM1andM2are obtained at different times, the temperature rise can be calculated by Eqs. (1) to (5). Table 3 presents the results of the temperature rises obtained in this way. As it can be seen from the table, in the irregular arrangement of particles there gives great influence on HMX particle temperature rise, corresponding to the temperature rise of 142.9 ℃. Rather, the temperature rise in the regular arrangement reaches 37.2 ℃ only. It indicates that the plastic work in the irregular arrangement of HMX particles has great contribution to the temperature rise. On the knowledge acquired from thermal test, the ignition temperature for HMX particles is 210 ℃, so it is more reasonable in the simulation by considering the factor of irregular arrangement of the particles.

Fig.10 Equivalent stress of HMX particles at different times in case of irregular arrangement

Fig.11 Equivalent plastic strains in HMX particles at different times in case of irregular arrangement

Fig.12 Stress and plastic strain at pointM2versus time in case of irregular arrangement

Table 3 Temperature rises at specific locations in two cases of HMX particle arrangement

pointM1M2ΔT/℃37.2142.9

From the numerical simulations as well as calculations for temperature rise, it is found that the irregular arrangement of HMX particles can provide higher temperature rise in the particles than the regular arrangement. The difference comes from the sizes of the gaps between the particles. In the irregular arrangement, the particles with random distributions can form larger voids. The distribution of stress is uneven. In the larger gap area there is greater local plastic work.

3.3 Effect of Dropping Height on Temperature Rise in Irregular Arrangement

The difference of dropping height gives the different initial speed of the hammer. Higher dropping height passes a greater speed to the hammer. Owing that the irregular arrangement of particles produces much higher temperature rise in particles, we mainly focus our study on the case of irregular arrangement of particles. Let the hammer fall from different heights more thanH50, we calculate the temperature rises. To three kinds of the dropping heights of 40, 50 cm and 60 cm, the changes of temperature rises at the location with maximum plastic work are calculated in the similar ways as given before. The obtained temperatures are presented in Table 4 for these situations.

As seeing from Fig.13, the temperature rise in the particles increases with the rising of the height of the drop hammer. When the drop height reaches 60 cm, the temperature at point with maximum strain is 178.3 ℃. This value is more closer to the ignition temperature of the HMX particles.

Table 4 Temperature rise values of HMX particles at different drop heights

H/cm33405060ΔT/℃142.9149.5165.3178.3

Fig.13 Histogram of temperature rises with changes in drop heights

3.4 Effect of Reducing Yield Strength on Temperature Rise

In the above sections, we have calculated the temperature rises in the particles as the yield strength is selected to be 0.26 GPa. Now reducing the yield strength to 0.13 GPa, the calculation is operated and the temperature rise is calculated. The drop height is stillH50and the particles are packed in the form of the irregular arrangement. The purpose is to examine how the value of the yield strength affects the temperature rise in particles.

After simulations, the equivalent stress distribution and equivalent plastic strain distribution are shown in Fig.14 and Fig.15. As before, a point with maximum plastic work is designated with labelling byM3in the figures. In accordance to the temperature rise calculation by Eq.(1) to Eq.(5), the temperature rise at pointM3is obtained to be 83.2 ℃.

In the calculations, the changes of the yield strength value of the HMX particle material affect the temperature rise in particles greatly. When the yield strength is of smaller value, the temperature rise in particles is low. The explanation for this result is that under the same loading, as the yield strength is reduced, the stress values in particles are also reduced. Hence, the lower stresses lead to smaller plastic work while plastic strains vary in the same range. The temperature is naturally low from the smaller heat energy.

Fig.14 Equivalent stresses of HMX particles at different times with 0.13 GPa yield strength

Fig.15 Equivalent plastic strains of HMX particles at different times with 0.13 GPa yield strength

4 Conclusions

Through numerical simulation of drop hammer test for granular HMX, the local temperature rises of the particles can be calculated from the plastic deformation work of the particles. To experimentalH50critical drop height for HMX, and particles being under irregular arrangement, the maximum temperature rise in particles is calculated to be 142.9 ℃. As the drop height is increased to 60 cm, the temperature rise reaches 178.3 ℃. These predicted temperatures tend to initiate chemical reaction. However, also, the simulation does not provide the proof on the existence of the obvious inter-particle friction. On the influence of yield strength for explosive particles, smaller yield strength value leads to a lower temperature rise. The result indicates that the yield strength for explosive particles is one of the important factors in the prediction of temperature rise in drop hammer test.

At present,the chemical reaction and the self-heating process of particles are not included in the analysis. Even so, the obtained results on the temperature rises are tend to reach the ignition temperature of HMX explosive measured via ther-mal analysis test. Regarding other factors that might cause the particle ignition will be studied in the future work.

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