## 3 Results and Discussion
### 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 \(-25\)-\(120\)\({}^{\circ}\)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 \(195\)\({}^{\circ}\)C. Therefore, the applicable range of the fitting formula can be between \(-25\)\({}^{\circ}\)C and \(180\)\({}^{\circ}\)C. The experiential formulas obtained are as follows:  
\[B=-5.51-0.0171T,R^{2}=0.9996\ \ \ (-25\leq T\leq 180^{\circ}\mathrm{C}) \tag{6}\]  
\[G_{1}=96023.43+933.71e^{0.0329T},R^{2}=0.9886\ \ \ \ \ \ \ \ \ \ (-25\leq T\leq 180\ ^{\circ}C) \tag{7}\]  
where \(B\) is the modeling parameter of unreacted explosive; \(G_{1}\) is the constant of reacted explosive, \(\mathrm{GPa/\SIUnitSymbolMicro}\)s; and T is the temperature, \({}^{\circ}\)C. The relationships are well-fitted.  
Figure 10: Pressure profiles at various depths of HMX–based booster with different gap thickness under non–ambient temperature: (**a**) \(-25\)\({}^{\circ}\)C vs. 6.3 mm gap; (**b**) \(-25\)\({}^{\circ}\)C vs. 6.4 mm gap; (**c**) \(88\)\({}^{\circ}\)C vs. 7.5 mm gap; (**d**) \(88\)\({}^{\circ}\)C vs. 7.8 mm gap; (**e**) \(130\)\({}^{\circ}\)C vs. 8.3 mm gap; (**f**) \(130\)\({}^{\circ}\)C vs. 8.4 mm gap.  
According to the change rule of equation parameters, the critical gap thickness G\({}_{50}\) and critical initiation pressure value of HMX-based booster at 150 \({}^{\circ}\)C and 180 \({}^{\circ}\)C were estimated. It could be found that the simulated values of the critical gap thickness G\({}_{50}\) of HMX-based booster were within the range of 9.1-9.2 mm (150 \({}^{\circ}\)C) and 9.6-9.8 mm (180 \({}^{\circ}\)C). The fitting curves of G\({}_{50}\) and P\({}_{\rm cr}\) 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:  
\[G_{50}=6.67+0.0157\rm{T},R^{2}=0.9926\qquad\left(-25\leq T\leq 180\ ^{\circ}C\right) \tag{8}\]  
where \(G_{50}\) is the critical gap thickness, mm; and T is the temperature, \({}^{\circ}\)C. The linear formula obtained is well-fitted.  
Figure 11: Change curves of \(B\) and \(G_{1}\) in the temperature range of \(-\)25-180 \({}^{\circ}\)C.  
Figure 12: (**a**) Fitted curve of critical gap thickness with temperature; (**b**) Fitted curve of critical initiation pressure with temperature.  
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:  
\[P_{cr}=-0.25+4.31e^{-0.004697},R^{2}=0.9986\qquad\left(-25\leq T\leq 180\,^{ \circ}C\right) \tag{9}\]  
where \(P\) is the critical initiation pressure, GPa; and \(T\) is the temperature, \({}^{\circ}\)C. The exponential formula obtained is well-fitted.