Study on Jet Formation and Penetration of Double-Layer Sub-Caliber Shaped

Proceedings of the 2019 Hypervelocity Impact Symposium HVIS2019 April 14-19, 2019, Destin, FL, USA HVIS2019-100

Study on jet formation and penetration of double-layer Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 sub-caliber shaped charge Yu-ting Wanga, Qiang-qiang Xiaoa *,Zheng-xiang Huanga, Xu-dong Zua, Bin Maa

aSchool of Mechanical Engineering, Nanjing University of Science & Technology, 210094, Jiangsu, China

Abstract

The ordinary shaped charge has a low kill-radius because of its structure. In order to adapt to the different battlefields, this paper proposed the double-layer sub-caliber shaped charge, which is modified from an ordinary shaped charge with insensitive explosive appended to its outer layer. In this paper, a study of the Ø56 mm shaped charge was conducted as a benchmark case. The simulations were carried out using AUTODYN for jet formation and penetration of different axial thicknesses of additional insensitive explosive and the additional height of the charge, with the aim to obtain the optimal size of double-layer sub-caliber shaped charge. The results show that the optimum axial thickness of additional insensitive explosive is R/R = 0.8, and the optimum size of the additional height of charge is / = 0.4.

0 0 Keywords: double-layer sub-caliber shaped charge; jet∆; formation; penetration ∆𝐿𝐿 𝐿𝐿

Nomenclature Axial thickness of additional insensitive explosive Radius of the benchmark shaped charge ∆𝑅𝑅 Additional height of charge 0 𝑅𝑅 Height of the benchmark shaped charge ∆𝐿𝐿 0 1.𝐿𝐿 Introduction

The ordinary shaped charge has a low kill-radius because of its structure. In order to adapt to the different battlefields, that is, to increase the kill-radius of shaped charge while also satisfying the penetration requirements of the armor-piercing index, double-layer sub-caliber shaped charge can be used. A double-layer sub-caliber shaped charge is a shaped charge with insensitive explosive appended to the outer layer of the shaped charge. Compared with the ordinary shaped charge, the double- layer sub-caliber shaped charge can increase the charge quantity and reduce the sensitivity of ammunition while the armor- piercing index is also satisfied. Researchers have carried out numerous studies on detonation wave propagation in double-layer charges [1-4]. Zhang X F [5] obtained characteristic parameters of the sandwich shaped charge using AUTODYN, conducted a numerical study on the jet forming of a typical shaped charge with a single structure charge and a sandwich charge, and calculated the parameters of the sandwiched shaped charge jets of different explosive. The results show that, compared with the single structure charge, the jet head speed of the sandwiched shaped charge is increased by 20%. Hussain T [6,7] compared the ballistic performance of Double-layer shaped charges (DLSC) with the ordinary shaped charge (OSC) by using the hydrodynamic software LS-DYNA, which found that OSC may have some advantages over DLSC, especially in smaller lengths. They also found that the shaped charges in which an explosive with higher Chapman-Jouguet pressure is utilized in the inner core, yield more penetration. Wang

* Corresponding author. Tel.: 13851796765. E-mail address: [email protected]. 104 V001T03A007 Z[8] performed a theoretical analysis on detonation wave propagation in a double-layer shaped charge (DLSC), and compared between jet formations in DLSC and OSC using AUTODYN. The results show that the improved detonation velocity ratio and radial charge percentage of outer-to-inner layer charges are conducive to the formation of a convergent detonation wave, which contributes to enhancement of jet top velocity in DLSC. The thickness and mass percentages of liner flowing into the jet in DLSC closely follows an exponential distribution along the radial direction, but the percentages in DLSC and the mass of the effective jet, which have a significant influence on the penetration depth, are lower than those in the OSC with the outer layer charge. Researchers have previously focused on the difference of jet formation and penetration between the ordinary shaped charges Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 and double-layer shaped charges whose calibres remain the same. The study of the double-layer sub-caliber shaped charge has not been conducted. In this paper, we research the jet formation and the penetration of double-layer sub-caliber shaped charges with different axial thickness of additional insensitive explosive and additional height of charges using the finite element code AUTODYN, and obtained the optimal size of a double-layer sub-caliber shaped charge.

2. Numerical Simulation Model

The structure of the double-layer sub-caliber shaped charge is shown in Fig2.1. The multi-material Euler solver AUTODYN was adopted to conduct the simulation of jet formation. The initiation point is located at the center of the end surface of the charge. The initiation mode is indirect to ensure that the detonation of the inner explosive triggers the initiation of the external explosive. The optimum thickness of the additional insensitive explosive was obtained through numerical simulations, with R/R = 0, 0.2, 0.4, 0.6, 0.8 and 1.0 respectively. To gain the optimum size of additional height of charge, we then simulated the working conditions of / with values of 0, 0.2, 0.4, 0.6, 0.8 and 1.0 respectively under the circumstances of the optimum 0 ∆axial thickness of additional insensitive explosives. ∆𝐿𝐿 𝐿𝐿0

Insensitive explosive

High-energy explosive

Liner

Fig 2.1 Double-layer sub-caliber shaped charge

3. Material Model and Parameters

The high-energy explosive used in this study is 8701, and the insensitive explosive is Composition B. The material model used is high explosive detonation, and the Jones-Wilkins-Lee (JWL) equation of state is used.

w−− ww pA=−(1 ) eRV12 +− B (1 ) eRV + E RV12RVV where is pressure, is the relative volume, is the internal energy, and are material parameters. , and are constants. Specific material parameters are shown in Table 3.1. 𝑝𝑝 𝑉𝑉 𝐸𝐸 𝐴𝐴 𝐵𝐵 𝑅𝑅1 𝑅𝑅2 𝑤𝑤 Table 3.1 The calculated parameters of 8701 and Composition B

3 Material ρ(g/cm ) D(m/s) e0(KJ/m3) PCJ(GP) A(GP) B(GP) ω R1 R2

8701 1.717 8350 8.5E+6 29.66 618.4 6.9 0.38 4.3 0.87

105 Composition B[9] 1.717 7980 8.5E+6 29.5 524.23 7.678 0.34 4.2 1.10

The material of the liner is copper, and the target material is carbon steel C45. The material model is Johnson-Cook and the equation of state is SHOCK.

 pHH+Γρ () ee −,0 u ≥ p  Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 ρ00cuu,0> With ρ cu2 ()1+ u 1 pu p = 00 e = H H 2 H 21ρ ()+ u 11−−()λ u , 0 where is the Grüneisen coefficient, is the initial density, = 1. and are constants, determined by the following shock wave experimental relationship: = + , is the shock wave velocity, is the velocity of the particle after the wave. 0 0 0 SpecificΓ material parameters of Cu𝜌𝜌 and 45 steel are shown𝜇𝜇 in Table𝜌𝜌⁄ 𝜌𝜌 3.2− 𝜆𝜆 𝑐𝑐 𝐷𝐷 𝜆𝜆𝜆𝜆 𝑐𝑐0 𝐷𝐷 𝜈𝜈 Table 3.2 The calculated parameters of Copper and 45#

3 Material ρ0（g/cm ） Green coefficient C1（m/s） S1 Ts（K） Shear modulus（GPa） Yield Strength（MPa） Tm（K） Cu 8.930 2.02 3940 1.489 383 47.7 120 1790 45 steel 7.83 2.17 4569 1.33 408 76.99997 352 1760

4. The influence of the axial thickness of additional insensitive explosive

4.1. Shaped charge jet forming

slug jet 0

slug jet 0.2

0 slug jet RR / 0.4 slug jet ∆ 0.6 slug jet 0.8 slug jet 1.0

50 100 150 200 250 The length of penetrator

Fig 4.1 The morphology of penetrator at 50us while the axial thickness of additional insensitive explosive varies

Table 4.1 The related data of penetrator while the axial thickness of additional insensitive explosive varies

R/R The jet top velocity (m/s) The jet tail velocity(m/s) The jet length (mm) The maximum energy of Cu(MJ)

∆ 0 0 6074 1273 183.5 0.125 0.2 6183 1972 160 0.167 0.4 6282 2717 140 0.190 0.6 6275 2998 132 0.197 0.8 6283 3022 134 0.198 1.0 6278 3023 130 0.199 106 Fig. 4.1 shows the penetrator morphology at 50us when the axial thickness of the additional insensitive explosive varies. The penetrator is composed of jet and slug, where the last collapse unit of the liner was regarded as the boundary of jet and slug, as shown at Fig4.1. It can be seen that with the increase of the axial thickness of the additional insensitive explosive the length of the jet decreases gradually, the length of slug increases, and the maximum diameter of the slug decreases. We can see that the slug of the double-layer sub-caliber shaped charge has tensile capacity, but the back segment of slug shows serious breakage. Figure 4.2 was drawn by using the related data of the jet while the axial thickness of additional insensitive explosive was

varied. As shown in Fig 4.2, the jet tip velocity increases with the axial thickness of additional insensitive explosive until Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 / = 0.4. The jet tail velocity and the maximum energy of copper increase with the axial thickness of additional insensitive explosive until / = 0.6. Initially the length of jet increases, when the axial thickness of additional insensitive 0 ∆𝑅𝑅explosive𝑅𝑅 increase between / = 0 and / = 0.6, then it is almost a constant value. ∆𝑅𝑅 𝑅𝑅 0 ∆𝑅𝑅 𝑅𝑅 0 ∆𝑅𝑅 𝑅𝑅 0

(a) (b)

Figure 4.2 (a) The parameters of jet (b) The energy of the copper

4.2. Penetration

In order to analyze the penetration ability of the penetrator when the axial thickness of additional insensitive explosive varies, numerical simulations were conducted at stand-off = 80 mm, 160 mm and 280 mm. It is well known that the slug of an ordinary shaped charge jet has no benefit to penetration because of its low velocity and bulky shape. But the slug of a double-layer sub- caliber shaped charge jet can increase the penetration depth because of the increase of the tail velocity of the jet and the velocity gradient of the front part of the slug, which shows that slug has certain stretching ability and penetration ability. The penetration ability of the jet decreases due to the decrease in the length of the jet. The penetration data is shown in Table 4.2.

Table 4.2 Data of Penetration

Penetration depth by Penetration depth by Penetration depth by jet Penetration depth by Penetration depth by jet R/R penetrator when stand- penetrator when stand- when stand- penetrator when stand- when stand- off=80mm off=160mm off=160mm off=280mm off=280mm ∆ 0 0 232.1mm 251.1mm 242.1mm 225.7mm 218.1mm 0.2 222.3mm 282.9mm 262.1mm 289.4mm 237.1mm 0.4 216.9mm 264.1mm 223.1mm 316.7mm 239mm 0.6 192.9mm 271.7mm 230mm 324.9mm 239.1mm 0.8 200.1mm 270.9mm 218.1mm 342.8mm 255.2mm 1.0 204.8mm 309.1mm 235.1mm 299.7mm 228.1mm The total penetration depth of the penetrator while axial thickness of the additional insensitive explosive varies is shown in Figure 4.3(a). It can be seen from the figure that the penetration depth of the double-layer sub-caliber shaped charge is smaller than the penetration depth of the ordinary shaped charge at stand-off = 80mm, and reaches minimum value at / = 0.6.

∆𝑅𝑅 𝑅𝑅0 107 The decrease in penetration depth can be attributed to the reduction in the length of jet and the slug not being fully stretched, therefore the slug cannot reach the bottom of the penetration hole so the slug has no contribution to the penetration depth. When stand-off = 160mm, the penetration depth of double-layer sub-caliber shaped charge is larger than the penetration depth of ordinary shaped charge, and it reaches the extreme value at / = 0.2, and maximum value at / = 1.0. The penetration depth of the double-layer sub-caliber shaped charge remains basically constant between / = 0.4 and / = 0 0 0.8, and it is higher than the penetration depth of ordinary shaped charge∆𝑅𝑅. 𝑅𝑅 ∆𝑅𝑅 𝑅𝑅 0 0 ∆𝑅𝑅 𝑅𝑅 / ∆𝑅𝑅 𝑅𝑅 While stand-off = 280mm, the penetration depth of double-layer sub-caliber shaped charge increases when increases, Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 and reaches maximum value at / = 0.8. The penetration depth increases most sharply at / = 0.2. 0 To find out the difference between the penetration process of the double-layer sub-caliber shaped charge ∆𝑅𝑅and 𝑅𝑅the ordinary 0 0 shaped charge, the penetration depth∆𝑅𝑅 𝑅𝑅 of the penetrator and the penetration depth of the jet were∆𝑅𝑅 both𝑅𝑅 considered, as shown in Fig. 4.3(b). It can be seen from the figure that the trend of the penetration depth of the jet is consistent with that of the penetration depth of the penetrator. The difference between the penetration depth of penetrator and the penetration depth of jet is the penetration ability of slug. The penetration ability of slug increases with / , until / = 0.6. The variation tendency of the jet tail velocity is the same as the penetration ability of slug. ∆𝑅𝑅 𝑅𝑅0 ∆𝑅𝑅 𝑅𝑅0

(a) (b)

Figure 4.3 Data of penetration (a) penetration depth of penetrator (b) Penetration depth of penetrator and jet at stand-off=160,280mm.

4.3. Summary

Table 4.3 penetration error to R/R = 0

∆ 0 Penetration error of Penetration error of Penetration d error of Penetration error of Penetration error of jet R/R penetrator when stand- penetrator when stand- jet when stand- penetrator when stand- when stand- off=80mm off=160mm off=160mm off=280mm off=280mm ∆ 0 0 / / / / / 0.2 -4.2% 12.7% 8.3% 28.2% 8.7% 0.4 -6.5% 5.2% -7.8% 40.3% 9.6% 0.6 -16.9% 8.2% -5.0% 44.0% 9.6% 0.8 13.8% 7.9% -9.9% 51.9% 17.0% 1.0 11.8% 23.1% 2.9% 32.8% 4.6% The penetration error for the penetration of R/R = 0 at different stand-off is shown at Table 4.3. It can be seen from Table 4.3 that, at stand-off = 80mm, the axial additional insensitive explosive is not conducive to increasing the penetration 0 depth. When stand-off = 160mm, the penetration depth∆ by the penetrator of the double-layer sub-caliber shaped charge reaches the maximum value at / = 1.0, resulting in an increase of 23.1% compared to the penetration depth by the penetrator of the ordinary shaped charge. While stand-off = 280mm, the penetration depth by the penetrator of the double-layer sub-caliber 0 shaped charge reaches the∆𝑅𝑅 maximum𝑅𝑅 value at / = 0.8, giving a 51.9% increase compared to the penetration depth of the ordinary shaped charge. The improvement in penetration for stand-off = 280mm is far greater than for stand-off = 160mm, and ∆𝑅𝑅 𝑅𝑅0

108 in this paper, we consider the penetration depth of the penetrator as the most important property of shaped charge jet. Therefore, the optimum axial thickness of the additional insensitive explosive is / = 0.8.

0 5. The influence of the additional height of charge ∆𝑅𝑅 𝑅𝑅

5.1. Shaped charge jet forming Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021

slug jet 0

slug jet 0.20.40.6 slug jet 0 LL

/ slug jet ∆ slug jet 0.81.0 slug jet

50 100 150 200 250 The length of penetrator

Fig 5.1 The morphology of penetrator at 50us when the additional height of charge varies

In this section, to determine the optimum size of the additional height of the charge, we simulated the working conditions of / with values of 0, 0.2, 0.4, 0.6, 0.8 and 1.0 respectively at the optimum additional thickness, that is / = 0.8. Fig. 5.1 shows the morphology of penetrator at 50us when the additional height of charge varies. The last collapse unit of the liner 0 0 wa∆𝐿𝐿s regard𝐿𝐿 as the boundary of jet and slug, as shown at Fig5.1. It can be seen from the figure that, while∆𝑅𝑅 the𝑅𝑅 height of the double-layer explosive charge increases, the length of the jet varies, the length of the penetrator decreases, the front segment of slug has tensile capability, the velocity of the front of slug varies and the phenomenon of necking occurs. Also, the back segment of the slug breaks seriously.

Table 5.1 The related data of the penetrator at 50us while the additional height of charge varies

L/ The jet top velocity(m/s) The jet tail velocity (m/s) The jet length(mm) The maximum energy of Cu(MJ)

∆ 0 𝐿𝐿0 6283 3022 134 0.198 0.2 6570 2956 143 0.225 0.4 6776 2984 139 0.249 0.6 6921 3194 132 0.266 0.8 7050 3148 118 0.276 1.0 7117 3232 124 0.292

(a) (b)

Figure 5.2 (a) The parameters of jet (b) The energy of the copper 109 Figure 5.2 was drawn by using the related data of the jet while the additional height of the charge varies. It can be clearly seen from Fig 5.2 that the jet tip velocity and the maximum energy of Cu increase when the additional height of charge increases. The jet tail velocity increases while the additional height of charge increases, and the jet tail velocity reaches the maximum value at / = 0.6, then the tail velocity of the jet decreases slightly. The length of the jet varies with the additional height of charge, and it reaches the maximum value at / = 0.4. In addition, the length of the jet reaches the 0 minimum value at ∆𝐿𝐿/ 𝐿𝐿 = 0.8. ∆𝐿𝐿 𝐿𝐿 0 0 Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 5.2. Penetration ∆𝐿𝐿 𝐿𝐿

In order to analyze the penetration ability of the penetrator while the additional height of the charge varies with the axial thickness of additional insensitive explosive held constant at / = 0.8, numerical simulations were conducted at stand-off = 80 mm, 160 mm and 280 mm. The penetration data is shown in Table 5.2. Since the penetrator has not been fully stretched, only 0 the penetration depth of penetrator was collected when stand-∆𝑅𝑅off=80mm.𝑅𝑅

Table 5.2 Data of Penetration

Penetration depth by Penetration depth by Penetration depth by Penetration depth by jet Penetration depth by jet L penetrator when stand- penetrator when stand- penetrator when stand- when stand-off=160mm when stand-off=280mm off=80mm off=160mm off=280mm ∆ ⁄𝐿𝐿0 0 200.1mm 270.9mm 218.1mm 342.8mm 255.2mm 0.2 204mm 294.5mm 219.2mm 359.6mm 268mm 0.4 208.8mm 310.4mm 216mm 355.4mm 282.7mm 0.6 200mm 305.5mm 188.3mm 365.7mm 277.8mm 0.8 198.7mm 270mm 170.7mm 375.4mm 217.8mm

1.0 214mm 276mm 194mm 394.7mm 270mm The penetration depth of the penetrator for varying additional heights of the charge is shown in Figure 5.3(a). It can be seen from the figure that the change in total penetration depth is not obvious when the additional height of the double-layer sub- caliber explosive charge varies at stand-off = 80mm. The penetration depth reaches the extreme value at / = 0.4 and the maximum value at / = 1.0. 0 When stand-off = 160mm, the penetration depth of the double-layer sub-caliber shaped charge increase∆𝐿𝐿s with𝐿𝐿 the height of 0 the additional charge∆𝐿𝐿 between𝐿𝐿 / = 0 and / = 0.4, and it decreases with the height of the additional charge between / = 0.6 and / = 0.8, then it increases at / = 1.0. 0 0 When stand-off = 280mm, the∆𝐿𝐿 penetration𝐿𝐿 depth∆𝐿𝐿 𝐿𝐿 increases when / increases. 0 0 0 ∆𝐿𝐿 The𝐿𝐿 penetration∆𝐿𝐿 depth𝐿𝐿 of the penetrator and the ∆𝐿𝐿penetration𝐿𝐿 depth of the jet are shown in Fig. 5.3(b). It can be seen from the 0 figure that the changing trend of the penetration depth of the jet is∆𝐿𝐿 consistent𝐿𝐿 with that of the total penetration depth of the penetrator, except when / = 0.8 at stand-off = 160mm. When stand-off = 160mm, the penetration ability of slug increase with / until / = 0.6, then it begins to decrease. When stand-off = 280mm, the penetration ability of slug decreases 0 with / until / ∆𝐿𝐿= 0.4𝐿𝐿 , then it begins to increase, and slug has greatest penetration ability at / = 0.8. ∆𝐿𝐿 𝐿𝐿0 ∆𝐿𝐿 𝐿𝐿0 ∆𝐿𝐿 𝐿𝐿0 ∆𝐿𝐿 𝐿𝐿0 ∆𝐿𝐿 𝐿𝐿0

(a) (b)

Figure 5.3 Data of penetration (a) penetration depth of penetrator (b) Penetration depth of penetrator and jet at stand-off=160,280mm 110 5.3. Summary

Table 5.3 penetration error to L = 0

∆ ⁄𝐿𝐿0 Penetration error of Penetration error of Penetration d error of Penetration error of Penetration error of jet L penetrator when stand- penetrator when stand- jet when stand- penetrator when stand- when stand- off=80mm off=160mm off=160mm off=280mm off=280mm 0

∆ ⁄𝐿𝐿 Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 0 / / / / / 0.2 1.9% 8.7% 0.5% 4.9% 5.0% 0.4 4.3% 14.6% -1.0% 3.7% 10.8% 0.6 0% 12.8% -13.7% 6.7% 8.9% 0.8 -0.7% -0.3% -21.7% 9.5% -14.7% 1.0 6.9% 1.9% -11.1% 15.1% 5.8% The penetration error for the penetration with / = 0 at different stand-off distances is collected in Table 5.3. Based on a comprehensive analysis of Table 5.3, at stand-off = 80mm the additional height of double-layer sub-caliber explosive charge can 0 hardly change the penetration depth. When stand-∆𝐿𝐿off 𝐿𝐿= 160mm, the penetration depth of the penetrator for the double-layer sub- caliber shaped charge reaches the maximum value at L/L = 0.4, and it increases by 14.6%. When stand-off = 280mm, the penetration depth of the penetrator increases when / increases, and it increase by 15.1% at / = 1.0 . The 0 improvement in penetration depth of the penetrator when∆ stand-off = 160mm and 280mm is almost the same. Considering the 0 0 utilization of the explosive, we think the optimum additional∆𝐿𝐿 height𝐿𝐿 of the charge is / = 0.4. ∆𝐿𝐿 𝐿𝐿

0 6. Experiments ∆𝐿𝐿 𝐿𝐿

Fig 6.1 Double flash X-ray exposures of the shaped charge jet at 30 and 50 us after initiation

To verify the validity of the simulations described in this paper, we compared experimental results with simulation results for the benchmarked shaped charge. As Fig. 6.1 illustrates, the jet tip and tail velocity were measured by the X-ray system. The jet tip velocity was 6510 m/s, and jet tail velocity was 1189 m/s. The length of the jet was approximately 167.5 mm at 30 us and 291.5 mm at 50 us after initiation. [10] Depth of penetration (DOP) experiments at stand-off = 80 mm, 160 mm and 280 mm were executed to analyze the jet penetration ability of 56mm. [11]

∅

(a) (b) (c)

Fig 6.2 Target of DOP experiment at different stand-off (a) stand-off=80mm, (b) stand-off=160mm, (c) stand-off=280mm 111 Table 6.1 Data of experiment and simulation of 56 mm shaped charge jet

Data of jet ∅ Data of penetration The jet tip The jet tail The jet length Stand-off Stand-off Stand-off velocity (m/s) velocity(m/s) at 50us(mm) =80mm =160mm =280mm experiment 6510 1189 219.2 201 246 217

simulation 6109.5 1298 183.5 232.1 251.1 225.7 Downloaded from http://asmedigitalcollection.asme.org/hvis/proceedings-pdf/HVIS2019/883556/V001T03A001/6551043/v001t03a001-hvis2019-100.pdf by guest on 27 September 2021 error 6.15% 9.16% 16.28% 15.47% 2.07% 4.01% A comparison of the data from the experiments and simulations for the 56 mm shaped charge jet is shown in Table 6.1. In the table, both the jet tip and the jet tail velocity are the averages between 30us and 50us because of the measurement method employed in the experiment. From Table 6.1, it can be seen that the simulation∅ s described in this paper can produce accurate jet velocities and penetration depths at stand-off=160 and 280mm. For stand-off=80mm a deviation of the jet length and penetration depth can be seen between the simulation and the experiment, but the difference is still within an acceptable range. The measured penetrations of 56 mm shaped charge at stand-off=80mm, 160 mm, 280mm, as well as the X-ray radiographs of the jets formed by 56 mm shaped charge, demonstrate that the research of this article is credible. ∅ 7. Conclusion ∅

In this paper, we research the influence of the axial thickness of additional insensitive explosive and the additional height of charge on the jet formation and the penetration depth of a double-layer sub-caliber shaped charge using the finite element code AUTODYN. According to the simulation results, it can be shown that, for the benchmarked Ø56 mm shaped charge, the optimum axial thickness of additional insensitive explosive for the double-layer sub-caliber shaped charge is / = 0.8, and the optimum size of the additional height of the double-layer sub-caliber shaped charge is / = 0.4. ∆𝑅𝑅 𝑅𝑅0 0 Acknowledgements ∆𝐿𝐿 𝐿𝐿 This study is supported by the National Natural Science Foundation of China (Grant Nos. 11702144).

References

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