Optimization Development and Application of Lee-Tarver Reaction Rate Model
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摘要: 针对Lee-Tarver点火增长反应速率方程参数多且不易标定的问题，在三项式结构的基础上，引入半周期三角函数对模型进行优化。新速率方程优化了点火项的连续性，将增长项和完成项的形状因子最大数值限制为1，减弱了比例系数和形状因子的参数补偿，消除了三项式的反应度极限，将反应速率方程参数由15个降至10个，提高了参数标定的效率。基于LS-DYNA对改进的点火增长模型进行二次开发，对比计算了Lee-Tarver模型和优化模型的冲击起爆仿真结果，炸药内部压力和反应度高度一致，验证了模型开发的正确性。基于炸药驱动金属板试验结果，应用LS-OPT标定了优化的点火增长模型参数，并统计了反应速率方程参数的敏感度，提炼出了关键参数，可为进一步提高参数标定效率提供参考。仿真结果与炸药驱动金属板试验结果的相对误差小于3%，验证了标定参数的准确性。应用改进的点火增长模型，结合子弹/破片撞击弹药的安全性试验，研究了子弹/破片撞击下弹药的冲击起爆响应特性。子弹撞击弹药后66 μs内炸药内部峰值超压达到14.5 GPa（爆压的48.3%），表明炸药未发生爆轰反应；破片撞击条件下，炸药内部峰值超压仅为0.79 GPa，近撞击点的反应度大于其他区域，最大反应度仅为0.01，炸药未起爆。优化模型的仿真结果与试验测试结果的一致性较好，验证了优化开发的点火增长模型的工程应用性。Abstract: To address the short comings of the Lee-Tarver ignition and growth reaction rate equation, which comprises numerous parameters (15) and is difficult to calibrate, semi-periodic trigonometric functions were introduced to optimize the model. The new reaction rate equation enhances the continuity of the ignition term, restricts the maximum value of the shape factors for the growth and completion terms to 1, mitigates the parameter compensation between the proportional coefficients and the shape factors, eliminates the reaction degree limit of the trinomial structure, reduces the number of parameters in the reaction rate equation to 10, thereby improving parameter calibration efficiency. Based on LS-DYNA, a secondary development was conducted for the improved ignition and growth model. Comparative calculations were performed to assess the shock initiation simulation results from the Lee-Tarver model and the optimized model, revealing highly consistent results for the internal pressure and reaction degree of the explosive, validating the correctness of the model development. Utilizing test data from explosive-driven metal plates, the parameters of the optimized ignition and growth model were calibrated with LS-OPT, and the sensitivity of the rate equation parameters was statistically analyzed to identify key parameters, providing a reference for further improving parameter calibration efficiency. Comparisons between test and simulated results of explosive-driven metal plates showed a simulation error of less than 3%, confirming the engineering validity of the calibrated parameters. Applying the improved ignition and growth model with safety experiments, the impact initiation response characteristics of ammunition under bullet/fragment impact were investigated. Within 66 μs after bullet impact, the peak internal pressure of the explosive reached 14.5 GPa (48.3% of the detonation pressure), indicating no detonation reaction occurred. Under fragment impact conditions, the peak internal pressure of the explosive was only 0.79 GPa, with the reaction degree near the impact point being higher than in other regions, but the maximum reaction degree was merely 0.01, confirming no detonation. The simulation results of the optimized model exhibited good consistency with test results, validating the engineering applicability of the optimized and developed ignition and growth model.
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图 1 Lee-Tarver速率方程和优化速率方程的点火项对比
Figure 1. Comparison of the ignition terms of the Lee-Tarver reaction rate equation and the improved reaction rate equation
图 4 破片冲击裸炸药模型及测点分布
Figure 4. Model of fragment impact on bare explosive and distribution of gauge points
图 5 t=0 μs和t=6.0 μs时炸药反应度计算结果
Figure 5. Calculation results of reaction degree of explosive at t=0 μs and t=6.0 μs
图 6 830 m/s冲击速度下不同监测点处的压力变化
Figure 6. Pressure histories measured at different monitoring points under impact velocity of 830 m/s
图 12 破片撞击试验的高速摄影结果
Figure 12. High-speed camera recording images of fragment impact test
表 1 黄铜材料的Johnson-Cook本构模型参数[27]
Table 1. Parameters of the Johnson-Cook constitutive model for brass[27]
ρ0/(g·cm−3) AJC/MPa BJC/MPa CJC n m Tm/K cp/(J·kg−1·K−1) 8.52 112 505 0.009 0.42 1.68 1189 385 
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ρ0/(kg·m−3) pk/Pa Cμ/(Pa·s) 1.29 −3 1.68×10−5
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C0 C1 C2 C3 C4 C5 C6 E0/MPa V0 0 0 0 0 0.4 0.4 0 2.53 2
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表 4 LX-04的改进反应速率模型参数
Table 4. Parameters of the improved reaction rate model for LX-04
f F1 C1 E3 $ {G}_{1} $ E1 m $ {G}_{2} $ E2 n 0.5 6×104 0.075 7 220 0.67 2 320 0.888 2.0
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表 5 超压测试结果
Table 5. Shock wave overpressure test results
Gauge point Δpmax/kPa Δt+/ms 1 65.476 3.283 2 58.072 3.103 3 67.891 3.030 4 58.015 3.173
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表 6 铜的Johnson-Cook本构模型参数[30]
Table 6. Parameters of the Johnson-Cook constitutive model for copper[30]
ρ0/(g·cm−3) AJC/MPa BJC/MPa CJC n m Tm/K cp/(J·kg−1·K−1) 8.96 90 292 0.025 0.31 1.09 1356 383
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表 7 LS-OPT标定的优化模型参数
Table 7. Parameters of the improved model calibrated by LS-OPT
f F1 C1 E3 $ {G}_{1} $ E1 m $ {G}_{2} $ E2 n 0.31 3.13×104 0.042 8.49 570 1.34 1.76 442 1.37 0.68
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