Simulation Study on Influential Factors of EFP Underwater Forming
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摘要: 由于密度、压力等物理量存在差异，爆炸成型弹丸（EFP）在空气和水中的成型过程差别较大。为了优化水下EFP的设计方案，利用AUTODYN有限元软件开展仿真研究，详细讨论了装药、药型罩及弹前空气域3部分共7个变量对EFP水下成型过程的影响，最终得出适合水下EFP装药的设计参数。根据仿真结果，总质量为1 kg的EFP装药优化后的设计参数：炸药长径比为1.5，炸药种类选择爆速较高的HMX，药型罩材料为紫铜，切向锥角
$\alpha $ 为145°，壁厚$\delta $ 为2 mm，弹前空气域长度为3倍装药半径，起爆半径r为0.4倍装药半径。该方案对优化EFP速度、长径比及动能等有较好的效果。Abstract: Due to the difference in physical quantities such as density and pressure, the forming process of explosive formed projectile(EFP) in air and water is quite different. In order to optimize the design scheme of underwater EFP, the simulation study was carried out using AUTODYN finite element software and the specific effects of the seven variables of the charge were discussed in detail. A set of design parameters suitable for underwater EFP charge is produced. According to the simulation results, the optimized design parameters of the EFP charge with a total mass of 1 kg are: the aspect ratio of the explosive is 1.5, the type of explosive is HMX with a higher detonation speed, the material of the liner structure is copper, and the tangential cone angle is 145°, the wall thickness$\delta $ is 2 mm, the length of the air field is 3 times the charge radius, and the initiation radius r is 0.4 times the charge radius. This scheme has a good effect on optimizing EFP speed,aspect ratio and kinetic energy. -
图 12 不同
$\alpha $ 值对应的EFP形状Figure 12. EFP shapes corresponding to different
$\alpha$ values
图 13 不同
$\delta $ 值EFP的速度-时间曲线Figure 13. v-t curves of EFP with different
$\delta $ values
图 15 不同Lcavity/R值EFP的速度-时间曲线
Figure 15. v-t curves of EFP with different Lcavity/R values
表 1 原始模型参数
Table 1. Original model parameters
Type Material L/D $\alpha $/(°) $\delta $/mm Lcavity/R r/R TNT Copper 0.5 120 2 2 0 
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表 2 Polynomial方程的主要参数
Table 2. Main parameters of Polynomial equation
A1/GPa A2/GPa A3/GPa B0 B1 T1/GPa T2/GPa 2.20 9.54 14.57 0.28 0.28 2.20 0
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表 3 JWL方程主要参数
Table 3. Main parameters of Polynomial equation
Type A/GPa B/GPa R1 R2 $\omega $ $\,\rho$/kg·m−3 DCJ/(m·s−1) E/(GJ·m−3) pCJ/GPa TNT 373.77 3.75 4.15 0.90 0.35 1630 6930 6.0 21.0 B 524.23 7.68 4.20 1.10 0.34 1717 7980 8.5 29.5 PBX 581.45 6.80 4.10 1.00 0.35 1787 8390 9.0 34.0 H6 758.07 8.51 4.90 1.10 0.20 1760 7470 10.3 24.0 HMX 778.28 7.07 4.20 1.00 0.30 1891 9110 10.5 42.0
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表 4 Johnson-Cook方程的主要参数
Table 4. Main parameters of Johnson-Cook equation
Material A/MPa B/MPa n C m Steel 792 510 0.26 0.014 1.03 Copper 90 292 0.31 0.025 1.09 Tungsten alloy 1506 177 0.12 0.016 1.00 Tantalum 142 164 0.31 0.057 0.88
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表 5 试算工况
Table 5. Conditions of trial calculation
Case No. Computational
domain/（mm × mm）Grid size/
（mm × mm）Grid quantity Case No. Computational
domain/（mm × mm）Grid size/
（mm × mm）Grid quantity 1 1000 × 400 0.5 × 0.5 1600000 8 600 × 240 0.2 × 0.2 3600000 2 800 × 320 0.5 × 0.5 1024000 9 600 × 240 0.3 × 0.3 1600000 3 600 × 240 0.5 × 0.5 576000 10 600 × 240 0.4 × 0.4 900000 4 500 × 200 0.5 × 0.5 400000 11 600 × 240 0.5 × 0.5 576000 5 400 × 160 0.5 × 0.5 256000 12 600 × 240 0.6 × 0.6 400000 6 300 × 120 0.5 × 0.5 144000 13 600 × 240 0.7 × 0.7 293878 7 200 × 80 0.5 × 0.5 64000 14 600 × 240 0.8 × 0.8 225000
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表 6 变量取值情况
Table 6. Summary of variable values
L/D Type Material $\alpha $/(°) $\delta $/mm Lcavity/R r/R 0.5–3($\varDelta $ = 0.5) TNT Copper 120 2 2 0 1.5 TNT/B/H6/HMX Copper 120 2 2 0 1.5 HMX Steel/Copper/Tantalum/Tungsten 145 2 2 0 1.5 HMX Copper 120–160($\varDelta$ = 5) 2 2 0 1.5 HMX Copper 145 2–6($\varDelta $ = 0.5) 2 0 1.5 HMX Copper 145 2-6 1–4($\varDelta$ = 0.5) 0 1.5 HMX Copper 145 2-6 2 0–0.8($\varDelta$ = 0.2)
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表 7 优化后的EFP参数
Table 7. Optimized EFP parameters
L/D Type Material $\alpha $/（°） $\delta $/mm Lcavity/R r/R 1.5 HMX Copper 145 2 3 0.4
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