Experiment and Numerical Prediction on Shock Sensitivity of HMX–Based Booster Explosive with Small Scale Gap Test at Low and Elevated Temperatures

Abstract

In order to analyze the effect of temperature changes on the shock initiation performance of HMX–based booster explosive, which consists of 95% HMX and 5% FPM₂₆₀₂ by weight, a temperature calibration test of acceptor was designed. The temperature changes in the booster at low and elevated temperatures under the constraint of steel sleeve were obtained. Based on the temperature calibration results, polymethyl methacrylate (PMMA) was selected as gap material to conduct a small scale gap test (SSGT) of HMX–based booster under different temperature conditions. The corresponding critical gap thickness was tested. Based on SSGT results at different temperatures, the shock initiation processes were simulated by adjusting parameters of ignition and growth reactive rate model. The critical gap thickness and critical initiation pressure of HMX–based booster at different temperatures were numerically predicted. By combining SSGT experimental data and simulation results, the attenuation law and fitting prediction formula of the critical initiation pressure of HMX–based booster were proposed. The mechanism of temperature effect on the shock sensitivity of HMX–based booster explosive was analyzed. The research results indicate that the critical gap thickness of HMX–based booster gradually increases with the rise in temperature, and the critical initiation pressure gradually decreases during the shock initiation process under the heating temperature conditions. In addition, the simulation results show that the heated HMX–based booster under steel constraints becomes more sensitive at high temperatures (>120 °C), while the cooled booster is more insensitive, but its critical initial pressure does not change significantly between 88 °C and 120 °C. The experimental and numerical prediction results are important for the shock initiation safety and design of an insensitive booster explosive.

1. Introduction

Booster explosives are an essential component in various types of warheads. They are applied in various industries, such as conventional weapons, aerospace, aviation, nuclear weapons, etc. All countries in the world attach great importance to the research and development of explosives and propellants. Booster explosives are the components in the explosive train that transfer and enhance the detonation energy of the initiating explosive, which ensure the reliable detonation of the main charge. The shock initiation performance and safety of booster explosive are important indicators in the low vulnerability assessment of weapon systems. There are various unexpected stimuli or environmental changes in the processes, such as production, handling, transportation, storage and use of weapons and equipment, that may lead to accidental explosions of ammunition caused by booster and catastrophic consequences. The safety of the booster explosive includes the comprehensive effects of many factors (shock, thermal stimuli, static electricity, light stimulation, etc.), which are complex responses integrating various effects. In recent years, with the deep study on the safety of booster, the shock response process and mechanism under different temperatures have become an important topic of booster safety research. At present, the thermal environment mainly comes from two aspects: the former refers to weapons in a harsh high–temperature combat environment, such as the production, use and transportation of ammunition and the aerodynamic heating situation of high–speed missiles; the latter is accidental thermal stimuli, including fire, frictional heat and strong radiation, during nuclear explosions. The JO–9C I booster explosive has stable performance, good safety and high heat resistance among high–energy explosives. It is a plastic-bonded explosive made of HMX and 2# Viton [1]. In foreign countries, the U.S. MIL–STD-1751MIL–STD1316C military standards allow for the use of JO–9C I explosives (PBXN–5) [2]. In China, North University of China (formerly North China Institute of Technology) stereotyped JO–9C I explosives [3].

In the past few decades, the shock sensitivity of boosters, such as PBX-9501(95% HMX, 2.5% estane and 2.5% nitro-plasticizer by weight), under various thermal conditions has been extensively studied. It is generally believed that, when boosters are exposed to high temperature, they may be more sensitive to shock or any other stimuli than when exposed to room temperature. When HMX crystal particles (5 µm) undergo phase transition of crystal form from β towards δ at 194 °C [4], the appearance of micro-defects and macroscopic cracks can lead to an increase in sensitivity and affect its thermal stability, making it more prone to explosion when subjected to external stimuli. Thermal stimuli may lead to accidental ignition, burning and even unexpected detonation of the booster, causing irreparable heavy losses of personnel and property [5,6,7]. A large number of experimental and numerical simulation studies have been conducted on shock sensitivity of the booster under various thermal conditions. For the booster at room temperature, SSGT experiments of American boosters had been conducted by the Naval Ordnance Laboratory (NOL) [8]. Tarver, C. M., Forbes, J. W., Urtiew, P. A. and Vandersall, K. S. et al. [9,10,11,12,13] quantitatively measured and simulated the effects of elevated temperatures on the shock sensitivity of HMX–based explosives, such as the commonly used PBX 9501 and LX–04 (85% HMX with 15% Viton binder). The results of the shock initiation experiments conducted with LX–04 preheated to 150 °C, 170 °C and 190 °C, respectively, as well as the PBX–9501 preheated to 20 °C, 50 °C and 150 °C for flyer impact or fragment impact were presented. Chakravarty, A. et al. [14] used the explosive load as a stimulus to mitigate the shock pulse by placing a layer between the charged material column and the high-energy material column of interest and carried out a gap test. Arnold, W. et al. [15] conducted research on sensitivity trends while changing the broad range of important parameters, providing insight into the quantitative shock of parameters. Keshavarz, M. H. et al. [16] introduced a new method for predicting the shock sensitivity of C_aH_bN_cO_d explosives without using any experimental data and determined the shock sensitivity based on small–scale gap tests. Chen, L. and Wang, C. [17,18] carried out flyer impact tests on an HMX/2,4,6–triamino–1,3,5–trinitrobenzene (TATB) composite explosive at different temperatures by an experimental detonation device designed for homogeneous heating of the explosive test sample and studied the effect of temperature and confinement on the shock initiation of PBXC10 (HMX/TATB)–based explosives. Chuzeville, V. et al. [19] studied the shock to detonation transition phenomenon of two melt-cast high-energy explosives (HE) and carried out plate impact tests on wedge specimens, measured the running distance and detonation time and established the Pop diagram relationship of several molten casting HEs.

In addition, relevant researchers conducted a numerical simulation analysis on SSGT used to heat the booster explosives. Sutherland, G. T. et al. [20] carried out CTH calculations on shock and particle velocities in large scale gap tests (LSGT) and extended large scale gap tests (ELSGT) to determine that PMMA and Pentolite material models available in CTH can best replicate the measured calibration data. Verbeek, R. et al. [21] measured the shock sensitivity of explosives using small–scale gap experiments and used the critical energy fluence criterion to evaluate the shock sensitivity of explosives. Moreover, the shock initiation process of SSGT process for boosters was simulated at room temperature by the dynamic reaction rate equation [22,23,24,25]. Tan, K.Y. et al. [26] conducted a numerical simulation of the shock initiation process of an HMX/TATB composite explosive and TATB-based insensitive high explosive (IHE) using the Lagrange analysis method, ignition and growth model. The results show that the shock sensitivity of the two explosives increases with the rise in ambient temperature. Kim, B. et al. [27] applied a multi-material hydrocode based on a mixed particle level set to quantitatively study the complex shock interaction, critical gap thickness, acoustic impedance and on/off characteristics of pyrotechnic systems. Sutherland, G.T. et al. [28] performed large scale gap tests and corrected gap tests on the explosive PBXN–103 (40% AP, 27% Al, 23% TMETN, 2.5% TEGDN, 6% NC, 1.3% EC and 0.2% Res) and obtained the reaction rate law parameters of Hugoniot. Lee Tarver. Yang, K. et al. [29] verified the accuracy of quantitative shock sensitivity prediction by comparing the shock sensitivity of ordinary explosives and the characteristics of anisotropic shock-induced response. Yang, Y. et al. [30] had built a new ignition growth reaction rate model, which can describe the shock initiation process of explosives with different initial density, particle size and loading pressure through only one set of model parameters.

In this work, the temperature calibration test was designed for HMX–based booster explosive, which consists of 95% HMX and 5% fluororubber by weight, and small scale gap tests of HMX–based booster were carried out under different temperature conditions. The corresponding critical gap thickness was obtained. By adjusting the parameters of the ignition and growth reaction rate model, the shock initiation processes of small scale gap tests at different temperatures were numerically simulated for HMX–based booster, and the critical gap thickness and critical initiation pressure of HMX–based booster at different heating temperatures were predicted. The effect of temperature changes on the shock initiation performance of typical booster explosives was analyzed, and the response characteristics of boosters under shock waves at different temperatures were studied. This has important practical significance and application value in reducing the occurrence of accidental explosion accidents caused by the shock of external temperature on the detonation performance of booster explosives in ammunition systems.

2. Materials and Methods

2.1. Experiment

2.1.1. Materials and Instruments

The chemicals and reagents used in these experiments, and their manufacturers are shown in

Table 1. Chemicals, reagents and their manufacturer.

Name	Specifications	Manufacturer
JO–9C	100~300 μm	Chinese weapons industry booster explosive performance testing center laboratory (Taiyuan, China)
ethyl acetate	500 mL	China National Pharmaceutical Group Chemical Reagent Co., Ltd. (Beijing, China)
Fluorine Rubber (FPM2602)	500 g	Liming Research Institute of Chemical Industry (Luoyang, China)
HMX	d50 = 50 μm	Gansu Yinguang Arms Group 805 Factory (Gansu, China)

.

Conventional instruments and various testing equipment were applied in SSGT experiment. The main instruments and their models used in these experiments are shown in

Table 2. Main instruments and their specifications used in SSGT experiment.

Name	Specifications	Manufacturer
electronic analytical balance	DT-100A; accuracy value 0.0001 g	Shanghai Jingke Electronics Co., Ltd. (Shanghai, China)
PLUS scanning electron microscope	SEM-30	Beijing Tianyao Technology Co., Ltd. (Beijing, China)
Transmission electron microscope	Tecnai 12	Shanghai Shengxi Hardware and Electromechanical Co., Ltd. (Shanghai, China)
Hydraulic presses	50 T	Woda Heavy Industry Company (Zaozhuang, China)
polymethyl methacrylate (PMMA)	Φ 40 mm	Suzhou Yilan Microelectronics Co., Ltd. (Suzhou, China)
Industrial Fire Detonator	24 V	Xi’an Northern Qinghua Electromechanical Group (Xi’an, China)
Steel Sleeve	Inner diameter: Φ 5.15 mm; Outer diameter 25.40; Height: 38.10 mm	Zibo Xinshengxin Pipe Industry Co., Ltd. (Zibo, China)
contact type industrial high-temperature thermometer based on K-type thermocouple	DT1311. measurement range: –50~100 °C, accuracy value: 0.1 °C	Wenzhou Hanbang Electronics Co., Ltd. (Wenzhou, China)
circulating water vacuum pump	SHZ–D(II) type	Henan Gongyi Yingyu Yuhua Instrument Factory (Gongyi, China)

.

2.1.2. Preparation and Characterization of HMX–Based Booster Explosives

The conventional water suspension method was used to prepare moulding powder granules of HMX–based booster [31]. The applicator columns were prepared by pressing in seven stages, while the primary explosives were pressed into individual columns, which were then prepared into small columns for the gap tests. As shown in Figure 1, scanning electron microscopy observation of the moulding powder particles indicates that the particle size ranges from 20 to 300 μm, and the shape of the particles is nearly spherical. Figure 1 also shows that the HMX explosive crystals are wrapped around the surface by Viton winding, forming a thin layer of gel-like binder. Such a wrapping method not only improves the mechanical properties of HMX–based booster but also improves the various sensitivities of HMX–based booster, such as the mechanical sensitivity, shock sensitivity, etc. HMX–based booster can be pre-pressed into a column with a size of Φ 5.09 mm × 5.45 mm and then loaded into the main steel sleeve, or it can be positioned in stages and then loaded into the main steel sleeve. HMX–based booster can be pre-pressed into pillars with dimensions of Φ 5.09 mm × 5.45 mm and then loaded into the receiving steel sleeve, or it can be pressed directly into the receiving steel sleeve using a split-positioning press. The formed columns are shown in Figure 2. The results of microscopic observation of the interface of the pressed columns show that the modelling powder particles are extruded and deformed under pressure and arranged tightly and the interface between the particles is obvious and there are tiny holes, i.e., the so-called pore defects of the charge, which is one of the important factors affecting the shock sensitivity. Under the effect of low or high temperature, the interface between the HMX explosive crystals and Viton inside the column charge will have a small shrinkage or debonding effect, which will cause the microstructure of the charge to change. On a macroscale, it shows that the shock wave susceptibility of HMX–based booster based on SSGT test will change accordingly.

2.1.3. Temperature Calibration Experiment

In the compilation of SSGT data by the NOL laboratory, it was mentioned that it was desirable not to change the temperature of the witness plate or the donor, and a method was needed for initiating SSGT acceptors at non-ambient temperatures. During SSGT of HMX–based booster at non-ambient temperature, HMX–based booster acceptor with a steel sleeve was preheated or cooled for a certain period of time to keep the temperature of the acceptor charge stable. Due to the time required for the assembly and startup of SSGT devices and the heat exchange between the acceptor charge and air during this time, the temperature deviation of HMX–based booster acceptor is caused. Therefore, the temperature change calibration experiment of HMX–based booster acceptor charge should be carried out.

Due to the unpredictable weather conditions and the time required for the preparation, each group of SSGTs under different temperatures is needed to carry out the corresponding temperature calibration experiments. The time interval between SSGT and its temperature calibration test should not be too far, and the ambient temperature should be in the same range. Firstly, 3~4 HMX–based booster pellets were placed inside the empty steel sleeve; then, the temperature probe of the thermocouple thermometer was suspended above the stacked pellets. Aluminum foil paper was used to tightly wrap the top of the steel sleeve to simulate the internal environment of HMX–based booster pellets in SSGT to prevent the effect of outside air. The temperature loss of the inner pellets of the steel sleeve was measured in the ambient environment, and the corresponding temperature curve and temperature attenuation law equation were obtained. The temperature calibration experimental assembly drawings are shown in Figure 3.

2.1.4. SSGT Set Up

HMX–based booster was tested at different temperatures through SSGT to verify its shock sensitivity. After the detonator initiated the donor explosive, the detonation wave was attenuated by the gap and then acted on the acceptor explosive. A witness plate of steel material was installed at the bottom of the acceptor to facilitate the Go/No–go judgment by observing the dents of the steel witness plate and the fracture steel sleeve of the acceptor. The length of gap substance was varied to observe the 50% critical gap thickness, namely G₅₀, until the acceptor charge detonated under the condition of SSGT. SSGT method in this paper mainly adopted the national military standard GJB2178.1A–2005 (test method of safety for booster) [32]. The explosives were confined within a circular steel sleeve with an inner diameter of approximately 5.15 mm and a thickness of 10.125 mm. The donor explosive was cyclomethylenetrinitramine (RDX) with an initial density of 1.635 g/cm³, which was pressed directly into the steel sleeve seven times. The acceptor was HMX–based booster, and its initial density was 1.700 g/cm³. Seven HMX–based booster tablets with a size of Φ 5.09 mm×5.45 mm were pressed and filled into the steel sleeve. The height of the donor and acceptor should be kept the same at 38.1 mm, while the gap thickness was varied by stacking PMMA discs. SSGT configuration is shown in Figure 4.

During SSGT at non-ambient temperature, HMX–based booster acceptor charges were preheated or cooled firstly, and the detonator, donor charge, PMMA gap, and witness plate was assembled together in descending order and placed in the explosion box in advance. The position of the acceptor charge was first located in the empty steel sleeve. After that, the acceptor charge was quickly removed from the oven or refrigerator and placed in a proper position for assembly, and the detonator was quickly detonated.

2.2. SSGT Modeling and Simulation

2.2.1. Modeling

The simulation analysis of SSGT for HMX–based booster at different temperatures was carried out through AUTODYN software. In order to reduce the calculation time, the Lagrangian meshes were used to model SSGT device, and a two–dimensional axisymmetric model was established. Assuming that the explosive particle size was uniform, the charges were regarded as monolithic homogeneous blocks. For all models involved in SSGT, the grid size of the materials was set to 0.2 mm × 0.2 mm. SSGT experimental model had approximately 120,000 grids. The point detonation method provided by AUTODYN software was used to detonate the donor explosive RDX, thereby omitting the modeling of detonators used in the experimental process. The unit system adopted cm–g–μs. The model established in AUTODYN is shown in Figure 5.

2.2.2. Reactive Flow Modeling

The shock initiation process of the booster is usually described by the ignition and growth reactive rate equation and the JWL (Jones–Wilkins–Lee) equation of state (EOS). The ignition and growth reactive rate equation is given by the following [33]:

$${\displaystyle \frac{\partial F}{\partial t}}=I·{\left(1-F\right)}^b·{\left({\displaystyle \frac{\rho }{{\rho }_0}}-1-a\right)}^x+G_1·{\left(1-F\right)}^c·F^d·P^y+G_2·{\left(1-F\right)}^e·F^g·P^{yz}$$

(1)

where $F$ is the reaction ratio; $t$ is the time; $\rho$ is the density of the explosive; ${\mathsf{\rho }}_0$ is the initial density of the explosive; $p$ is the pressure; and $I$, $G_1$, $G_2$, $a$, $b$, $c$, $d$, $e$, $g$, $x$, $y$ and $z$ are constants.

The JWL EOS of the unreacted explosive and detonation product is, respectively, as follows [34]:

$$p_e=A·e^{-R_1{\upsilon }_e}+B·e^{-R_2{\upsilon }_e}+{\displaystyle \frac{w{c}_V{T}_e}{{\upsilon }_e}}$$

(2)

$$p_p=A·e^{-R_1{\upsilon }_p}+B·e^{-R_2{\upsilon }_p}+{\displaystyle \frac{w{c}_V{T}_p}{{\upsilon }_p}}$$

(3)

where $p_e$ and $p_p$ are the pressure (unreacted explosive denoted with the subscript “$e$”, and reaction products denoted with the subscript “$p$”); ʋ is the relative volume; $c_V$ is the specific heat capacity; $T$ is the thermodynamic temperature; and $A$, $B$, $R_1$ and $R_2$ are constants.

3. Results and Discussion

3.1. Experimental Results at Low and Elevated Temperatures

The criterion for the Go/No–go judgment depended on the damage potential of HMX–based booster in the experimental test. A dent more than half the depth of the average dent produced by HMX–based booster, initiated with no gap between the donor and the acceptor, is regarded as a “go”. A smaller dent is a “no–go”. Three SSGTs without gaps were tested at room temperature.

Table 3. SSGT results with no gap at 25 °C.

Exp/num	Depth of Dent/mm
1	1.90
2	1.74
3	1.81

lists SSGT results with no gap, and we take half of the average dent of 0.91 mm as the criterion.

Tian Xiuqi et al. [35] conducted SSGT tests on HMX–based boosters at 25 °C with different gap thicknesses of PMMA. Nine tests were conducted, and according to the experimental data, the critical gap thickness was between 7.2 and 7.3 mm.

3.2. Experimental Results at Non-Ambient Temperature

The assembled acceptor charge was put into the freezer for at least 5 h under the seven gears mode of quick freezing, and then, it was taken out and placed outdoors to monitor the temperature change. According to the data recorded by the temperature sensor, the change temperature curves of the current outdoor and HMX–based booster inside the steel sleeve were drawn by Origin software, and the temperature fitting curve of HMX–based booster inside the steel sleeve was fitted, as shown in Figure 6.

The law equation of the temperature change in HMX–based booster inside the steel sleeve was obtained:

$$\mathrm{T}=10.68-37.52e^{-0.068t}$$

(4)

where $T$ is the ambient temperature, °C; and $t$ is the measurement time, min. The coefficient of correlation is ${\mathrm{R}}^2$ = 0.9988, indicating that the measured temperature curve is in good agreement with the fitting curve. Due to the closed wrapping of aluminum foil paper over the steel sleeve, the temperature of HMX–based booster is not affected by outdoor temperature, so its temperature changing curve shows more regularity. Because the outdoor temperature is higher than the inner temperature of the steel sleeve, the change trend of HMX–based booster temperature increases exponentially.

The same cooling method was used to carry out SSGT of HMX–based booster. The outdoor temperature measured by the thermometer during the test was within the range of Equation (4). The time from taking out the acceptor charge from the refrigerator to ignition was controlled at 42–46 s. Equation (4) was used to calculate that the temperature of the acceptor charge when initiating the donor was −25.1~−24.9 °C, approximately −25 °C. A total of five tests were carried out, and

Table 4. Experimental results of SSGT at −25 °C.

Exp/num	PMMA Gap Thickness/mm	Depth of Dent/mm	Go/No Go
1	6.8	0.22	No go
2	5.9	1.46	Go
3	6.5	0.44	No go
4	6.3	1.68	Go
5	6.4	0.34	No go

lists SSGT experimental results at −25 °C. The critical thickness was found to be between 6.3 and 6.4 mm based on the experimental data.

Tian Xiuqi et al. [35] conducted SSGT of HMX–based accelerants at 88 °C. A total of six tests were conducted, and the obtained critical gap thickness of PMMA based on HMX–based booster detonation was approximately between 7.5 and 7.8 mm.

Table 5. Experimental results of SSGT at 88 °C.

Exp/num	PMMA Gap Thickness/mm	Depth of Dent/mm	Go/No Go
1	9.4	0.02	No go
2	9.1	0.04	No go
3	8.4	0.44	No go
4	8.0	0.20	No go
5	7.5	1.76	Go
6	7.8	0.36	No go

lists SSGT experimental results at 88 °C.

The acceptor charge was put into the oil bath oven and heated at 130 °C for 4 h. The temperature fitting curve of HMX–based booster inside steel sleeve is shown in Figure 7.

The law equation of the temperature change of HMX–based booster inside the steel sleeve was obtained:

$$\mathrm{T}=33.27+91.12e^{-0.061\mathrm{t}}$$

(5)

where $T$ is the ambient temperature, °C; and $t$ is the measurement time, min. The coefficient of correlation is ${\mathrm{R}}^2$ = 0.9987. The same heating method was used to carry out SSGT of HMX–based booster. The time from taking out the acceptor charge from the refrigerator to ignition was controlled at 48–55 s. Equation (6) was used to calculate that the temperature of the acceptor charge when initiating the donor was 119.1~121.1 °C, approximately 120 °C. A total of six tests were carried out.

Table 6. Experimental results of SSGT at 120 °C.

Exp/num	PMMA Gap Thickness/mm	Depth of Dent/mm	Go/No Go
1	9.0	0.16	No go
2	8.0	0.06	Go
3	8.5	1.76	No go
4	8.2	1.76	Go
5	8.3	1.48	Go
6	8.4	0.38	No go

lists SSGT results at 120 °C. The critical thickness was found to be between 8.3 and 8.4 mm according to the experimental data.

Based on the published ignition and growth model parameters of HMX–based booster, the parameters in the simulation calculation were adjusted to make the simulated results consistent with the test results so as to obtain the modeling parameters of HMX–based booster at normal temperature [36]. Referring to the rule of the JWL state equation and reactive rate equation for other explosives with changing temperature, it can be observed that most of the model constants remain unchanged; only a few of them require a small change depending on the temperature [5,6,7,9,10,11,12,17,37]. According to the test results of HMX–based booster at non-ambient temperature, the shock initiation equation parameters for the booster were optimized by changing two parameters: $B$ in the JWL equation of state and ${\mathrm{G}}_1$ in the ignition and growth reactive rate equation. The state equation parameters of HMX–based booster at non-ambient temperatures could be obtained.

Table 7. Ignition and growth model parameters of HMX–based booster at 25 °C.

UNREACTED JWL		REACTED JWL
$A$ (GPa)	95,220	$A$ (GPa)	614
$B$ (GPa)	–5.944	$B$ (GPa)	10.89
$R_1$	14.1	$R_1$	4.41604
$R_2$	1.41	$R_2$	1.19
$\mathsf{\omega }$	0.8867	$\mathsf{\omega }$	0.33
${\mathrm{T}}_0\left(\mathrm{K}\right)$	298 K	${\mathrm{E}}_0\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	9.08
Shear Modulus (GPa)	5	$D$ (m/s)	8212.5
Yield Stress (GPa)	0.2	${\mathrm{P}}_{\mathrm{C}\mathrm{J}}$ (GPa)	30.4
$\mathsf{\rho }(\mathrm{g}/{\mathrm{c}\mathrm{m}}^3)$	1.700
REACTION RATES
$I$$({\mathsf{\mu }\mathrm{s}}^{-1}$)	4 × 105	$g$	1.0
$b$	0.667	$z$	3.0
$a$	0.113	${\mathrm{F}}_{\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}}$	0.1
$x$	4.0	${\mathrm{F}}_{\mathrm{G}1\mathrm{m}\mathrm{a}\mathrm{x}}$	0.5
$c$	0.667	${\mathrm{F}}_{\mathrm{G}2\mathrm{m}\mathrm{a}\mathrm{x}}$	0.5
$d$	0.667	${\mathrm{G}}_1$ (GPa/μs)	100,000
$y$	2.0	${\mathrm{G}}_2$ (GPa/μs)	32,000
$e$	0.333

where ${\mathrm{E}}_0$ is heat of reaction, Mbar; $D$ is detonation velocity, cm/μs; ${\mathrm{P}}_{\mathrm{C}\mathrm{J}}$ is pressure, Mbar; ${\mathrm{F}}_{\mathrm{i}\mathrm{g}\mathrm{m}\mathrm{a}\mathrm{x}}$ is maximum F for ignition term; ${\mathrm{F}}_{\mathrm{G}1\mathrm{m}\mathrm{a}\mathrm{x}}$ is maximum F for growth term; ${\mathrm{F}}_{\mathrm{G}2\mathrm{m}\mathrm{a}\mathrm{x}}$ is maximum F for completion term; and $I$, $b$, $a$, $x$, $c$, $d$, $y$, $e$, $g$, $z$, ${\mathrm{G}}_1$ and ${\mathrm{G}}_2$ are constants.

contains the adjusted model parameters for HMX–based booster.

The complete shock initiation process simulation of the Go/No–go response is shown in Figure 8. Simulation results of shock initation process and detonation pressure progress for SSGT: (a) Go case at 7.2 mm PMMA thickness; (b) No-go case at 7.3 mm PMMA thickness.when the shock wave passes through the PMMA and reaches the acceptor. In order to distinguish the Go/No–go response and the generation of transmitted and reflected waves, the pressure change process of simulation calculation was observed under different gap thicknesses. As the explosion proceeds, the pressure of the product gas changes the shape of the steel sleeve, but it does not affect the progress of the explosion. The detonation wave front of the donor reaches the upper interface of the PMMA after initiation, and the energy loss is converted into a pressure decrease. Pressure attenuation occurs through the PMMA. When the shock wave pressure at the bottom of the PMMA is greater than the critical initiation pressure of the acceptor, the transmitted wave into the acceptor causes ignition and detonation. When the reflected wave reaches the bottom of the PMMA, its pressure is greater than the actual critical initiation pressure of the acceptor. If the acceptor is not detonated, the reflected wave produced has little effect on the PMMA.

There are calculated shock pressure profiles at various depths of SSGT for the Go case of 7.20 mm and No–go case of 7.30 mm PMMA gaps shown in Figure 9. At 4.60 μs, the donor explosive RDX reacted completely, and the stable detonation pressure was approximately 21.7 GPa. The theoretical detonation velocity of the donor RDX is approximately 8200 m/s. The time for the shock wave running in the depth of the RDX was approximately 4.65 μs. It was consistent with the actual situation. Due to the deformation of the PMMA and the different impedance of the contact material, the detonation wave is attenuated when it contacts the top of the PMMA, and it is transmitted to the acceptor. The critical initiation pressure of HMX–based booster is approximately 3.6 GPa at 25 °C.

The ignition and growth simulation of the shock initiation for HMX–based booster at −25, 88 and 120 °C is illustrated in Figure 10, respectively. The calculation SSGT results of the booster were consistent with the actual situation. From Figure 10, it is quite evident that the ignition and growth model simulates experimental records quite well and can be reliably used to describe the shock ignition process involving HMX–based booster at a temperature range from −25 to 120 °C.

While most of the modeling constants remain unchanged, only a few of them require a change depending on the temperature. The parameters of the shock initiation equation for HMX–based booster with non-ambient temperature were optimized by changing two parameters: $B$ in the JWL equation of state and ${\mathrm{G}}_1$ in the ignition and growth reactive rate equation. These constants are shown in

Table 8. Ignition and growth parameter change for HMX–based booster at different temperatures.

${\mathit{T}}_0$ (°C)	$\mathbf{Unreacted} \mathit{B}$ (GPa)	${\mathit{G}}_1$ (GPa/μs)
−25	–5.0750 ± 0.104	95,000 ± 2058
25	–5.9440 ± 0.128	100,000 ± 3359
88	–7.0384 ± 0.136	112,500 ± 4740
120	–7.5425 ± 0.141	145,000 ± 5061

.

Contrary to the experiments, which provide limited data on critical gap thickness G₅₀ at only four temperature positions of HMX–based booster shock sensitivity test, the numerical simulations provide more detailed information on the shock initiation processes. Figure 8 shows the calculated shock pressure profiles at various depths of HMX–based booster for −25, 88 and 120 °C conditions. As the temperature increases, the critical initiation pressure of HMX–based booster gradually decreases, which is approximately 4.6 GPa (−25 °C), 2.7 GPa (88 °C) and 2.2 GPa (120 °C), respectively.

3.3. Prediction of Shock Sensitivity of HMX–Based Booster at Different Temperatures

Once the relationship between $B$, $G_1$ and temperature is determined, the ignition and growth rate equation parameters of HMX–based booster at different temperatures can be obtained. The change curve of $B$ and $G_1$ in the temperature range of −25~120 °C can be obtained by exponential fitting, as shown in Figure 11. The fitting empirical formulas for $B$ and $G_1$ are applicable until the phase transition temperature of the HMX explosive crystals reaches 195 °C. Therefore, the applicable range of the fitting formula can be between −25 °C and 180 °C. The experiential formulas obtained are as follows:

$$B=-5.51-0.0171\mathrm{T},R^2=0.9996\hspace{1em}\hspace{1em}\hspace{1em}(-25\le T\le 180°\mathrm{C})$$

(6)

$$G_1=96023.43+933.71e^{0.0329T},R^2=0.9886 (-25\le T\le 180 °C)$$

(7)

where $B$ is the modeling parameter of unreacted explosive; $G_1$ is the constant of reacted explosive, GPa/μs; and T is the temperature, °C. The relationships are well-fitted.

According to the change rule of equation parameters, the critical gap thickness G₅₀ and critical initiation pressure value of HMX–based booster at 150 °C and 180 °C were estimated. It could be found that the simulated values of the critical gap thickness G₅₀ of HMX–based booster were within the range of 9.1–9.2 mm (150 °C) and 9.6–9.8 mm (180 °C). The fitting curves of G₅₀ and P_cr based on the experimental data and numerical prediction results were shown in Figure 12.

The exponential formula was obtained according to the fitted curve of the critical initiation pressure with temperature, which provides a theoretical basis for later research on the influence of temperature on other boosters:

$$G_{50}=6.67+0.0157\mathrm{T},R^2=0.9926 (-25\le T\le 180 °C)$$

(8)

where $G_{50}$ is the critical gap thickness, mm; and T is the temperature, °C. The linear formula obtained is well-fitted.

The exponential formula was obtained according to the fitted curve of the critical initiation pressure with temperature, which provides a theoretical basis for later research on the influence of temperature on other boosters:

$$P_{cr}=-0.25+4.31e^{-0.00469T},R^2=0.9986 (-25\le T\le 180 °C)$$

(9)

where $P$ is the critical initiation pressure, GPa; and $T$ is the temperature, °C. The exponential formula obtained is well-fitted.

3.4. Mechanism Analysis of Temperature Effect on Shock Sensitivity of HMX–Based Booster

The acceptor explosive HMX–based booster is composed of 95% HMX and 5% FPM₂₆₀₂, of which the main component is HMX; the melting point of HMX is 267~280 °C, and the thermal decomposition temperature of HMX is approximately 278 °C [38]. The results of SSGT show that, in a low-temperature environment, the gap value of the JO–9C detonation booster charge decreases and the shock sensitivity decreases; on the contrary, in a high-temperature environment, the gap value of HMX–based booster detonation booster charge increases, and the shock sensitivity increases. The following is a discussion of different ambient temperatures on the mechanism of HMX–based booster detonating charge shock initiation performance.

In a low-temperature environment, the HMX explosive volume of HMX–based booster transmissive charge may contract, resulting in an increase in internal density so that the size of the HMX crystal hole spacer decreases or disappears, making it difficult to form an effective hotspot at this location on the shockwave front [39]. In addition, the column itself is in a low-temperature state, and the conditions for hotspot formation are more demanding than those at room temperature, resulting in the inability of hotspots to form and expand in large numbers inside the column. Therefore, the low-temperature environment of the charge density increases, the crystal cavity reduction and the column of the macroscopic cryogenic effect, so that HMX–based booster in the impact of shock waves cannot generate a large number of hotspots and is easy to extinguish, resulting in a reduction in HMX–based booster detonating charge shock sensitivity.

In the existing studies on HMX–based explosives, it is known that the internal pores of the explosive particles, the HMX crystal-binder interface and the HMX crystals encapsulated by the binder are visible when observed at room temperature. When the explosives are heated, the internal pores and interfaces become blurred, indicating that the binder undergoes thermal decomposition and fills the original pores between the interfaces [38,40,41,42]. The fluidity inherent in the binder when heated also increases the irregularity of the arrangement of the HMX crystals, leading to a sharp increase in the number of voids with temperature and a significant increase in the sensitivity to explosives [39]. The heat generated by the decomposition reaction within the explosive is greater than the heat it conducts to the outside, leaving the explosive itself in an unstable state [38] and leading to an increase in sensitivity.

The main component of HMX–based booster is HMX, which is known to exist in α, β, γ and δ as well as phase transitions between them, where β→δ may be a phase transition that occurs at certain temperatures or pressures [43]. β–HMX is the most stable state at room temperature and has the maximum energy and density and minimum sensitivity of the HMX crystals. The β→δ phase transition significantly improves the effect of HMX explosion sensitivity. And when β–HMX and δ–HMX coexist, HMX explosives have greater shock sensitivity [44]. When HMX–based explosives are at 195 °C, the β→δ phase transition may be a key factor in influencing their shock sensitivity [40]. Experiments were carried out to observe the morphology of HMX crystals at different temperatures, and the surface morphology of HMX crystals under the action of external temperatures between 30 °C and 150 °C did not change, and no damage occurred; however, when the temperature was increased to 180 °C, which exceeded the temperature at which the β→δ phase transition occurs, the HMX crystals underwent cracking, and some of them were even completely broken. It is known that the β→δ phase transition of HMX crystals leads to a reduction in their partial load-bearing capacity, which has a greater effect on the shock sensitivity of HMX–based explosives themselves [45]. The crystal transformation of HMX explosives at high temperatures causes a significant increase in their blast sensitivity [5,46,47,48]. In addition, due to the β→δ phase transition in HMX explosives, there is a 6% volume expansion [11], which reduces the density of HMX explosives and increases the number of hotspots formed in shock compression.

There is also a theory that, in a high-temperature environment, as the HMX cell volume increases compared to room temperature, the relative amplitude of its internal intermolecular vibration increases, and the vibration frequency also accelerates, resulting in a reduction in the strength of the valence bond of the atoms in the HMX particles, which are more prone to conformational changes, leading to an increase in the shock wave susceptibility of the HMX explosives [48,49].

Therefore, in a high-temperature environment of HMX–based booster, the explosive charge will be subjected to thermal expansion, and the internal porosity of the explosive and crystal cavities will increase, resulting in a decrease in its own density and a corresponding increase in shock sensitivity. In addition, as the ambient temperature rises to the HMX phase transition temperature, the changes in the charge structure of HMX explosives, such as crystalline phase transition, crystal cracking or fragmentation and the coexistence of β and δ HMX crystals, may not only lead to the generation of more hot spots within the pyrotechnic charge but also promote a faster growth rate of the internal hot spot reaction so that the hot spot grows more rapidly into the surrounding preheated particles [17,18,47,50], leading to an increase in the shock sensitivity of the explosive.

4. Conclusions

The temperature calibration test was designed for the main charge of HMX–based booster in this paper. Based on the temperature calibration results, small scale gap tests were conducted on HMX–based booster at low and elevated temperatures, and the corresponding critical gap thickness G₅₀ was obtained. A numerical simulation of the shock initiation process of SSGT for HMX–based booster at different temperatures was conducted to predict the critical gap thickness G₅₀ and critical initiation pressure. The effects of different temperatures on the shock sensitivity of HMX–based booster were analyzed. The following conclusions are drawn:

Under the same assembly conditions, the low and elevated temperature calibration experiments were conducted separately. The temperature change equation inside the steel sleeve was established for HMX–based booster charge. The temperature change trend of HMX–based booster under low–temperature conditions showed an exponential increase, while under high-temperature conditions, it showed an exponential decrease. The temperature calibration test results of the booster charge provide an experimental basis for temperature changes in SSGT.

According to the results of the temperature calibration experiments, small scale gap tests were conducted on HMX–based boosters at −25 °C, 25 °C, 88 °C and 120 °C. The critical gap thickness prediction formula with temperature as the independent variable was constructed. The critical gap thickness G₅₀ of HMX–based booster under corresponding temperature conditions was obtained to be 6.3~6.4 mm, 7.2~7.3 mm, 7.5~7.8 mm and 8.3~8.4 mm, respectively. From the experimental results of SSGT, it can be observed that the critical gap thickness G₅₀ of HMX–based booster increases gradually with the rise of the initial heating temperature. And the gap prediction formula for the shock sensitivity of HMX–based booster explosive was established.

Based on SSGT test data under different temperature conditions, the pressure variation processes with different gap thicknesses were simulated for HMX–based booster. The simulated prediction results of SSGT show that the critical initiation pressure of HMX–based booster is 4.6 GPa (−25 °C), 3.6 GPa (25 °C), 2.7 GPa (88 °C) and 2.2 GPa (120 °C), respectively. On the basis of the simulation test data, a prediction formula of the critical initiation pressure with temperature as the independent variable was constructed. The critical initiation pressure decreases gradually with the increase in temperature and shows exponential decay. This indicates that temperature has a significant effect on the shock sensitivity of HMX–based booster.

The shock sensitivity of HMX–based booster explosive charge in the low and elevated temperature conditions has undergone significant changes and its mechanism have been analyzed. The main mechanism by which temperature affects shock sensitivity of HMX–based booster explosive is that the microstructure and mechanical properties of the booster charge undergo corresponding changes when the external temperature changes. These situations result in the shock initiation of booster charge not easily generating hotspots at low temperatures, but relatively easily forming hotspots at high temperatures. Therefore, HMX–based booster explosive at low temperature and elevated temperature become sensitive to insensitive. The research results provide a theoretical basis for the design of booster explosive formula, as well as the reliability and safety of shock initiation.