Influence of the Medium and Structural Parameters on the Formation Effect of Linear Explosively Formed Projectiles

Abstract

The linear explosively formed projectile (LEFP) is a special type of linear shaped charge (LSC) and is developed on the basis of the explosively formed projectile. Known for their excellent penetration performance and directional destruction capacity, LEFPs are widely utilized in explosion dismantlement, petroleum exploration, concrete crushing, metal cutting, and penetrator interception. LEFPs can also induce multimode damage—combining penetrator impact, shock waves, and bubble effects—during underwater detonations. Thus, they are employed in applications including subsea pipeline disruption and effective neutralization of underwater vehicles. Adequate formation effect is a criterion for a desirable penetration performance of shaped charges. Therefore, investigating the formation characteristics of LEFPs in different media and optimizing the structural parameters are important tasks. In this study, the arbitrary Lagrangian—Eulerian (ALE) method is adopted for numerical simulation, and the efficacy of the ALE method is verified by the consistency between numerical and experimental results. Then, the formation effects of LEFPs in pure air medium, water medium, and water with air cavity are investigated separately. The results show that the stabilized velocity of the penetrator in air is 1 355 m/s, while the velocity is only 423.6 m/s in water. Furthermore, the liner cannot be completely closed in water and cannot form a slender penetrator as in air. After the addition of the air cavity, the stabilized velocity of the penetrator increases to 966.6 m/s, and its morphology is significantly enhanced. Moreover, explosive material, liner material, and liner thickness are chosen as the primary factors for orthogonal optimization. The optimized factor combination is RDX—Copper—1 mm. The peak velocity of the penetrator, the velocity before penetration, the velocity after penetration, and the length of penetration increase by 50.8%, 44.9%, 26%, and 10.3%, respectively.

• The formation characteristics of linear explosively formed projectiles (LEFPs) are explored through 3D numerical simulations based on the arbitrary Lagrangian—Eulerian method.

Keywords

Linear explosively formed projectile / ALE / Penetrator formation / Underwater explosion / Orthogonal optimization

References

[1] Agu HO, Hameed A, Appleby-Thomas GJ. Application of shell jetting analysis to determine the location of the virtual origin in shaped charges. International Journal of Impact Engineering, 2018, 122: 175-181.

[2] Ahmed M, Malik AQ. A review of works on shaped charges. Engineering, Technology & Applied Science Research, 2017, 7(5): 2098-2103.

[3] Barras G, Souli M, Aquelet N, Couty N. Numerical simulation of underwater explosions using an ALE method. The pulsating bubble phenomena. Ocean Engineering, 2012, 41: 53-66.

[4] Cao C, Wang JX, Kong LQ, Tang K, Xiao YJ, Gu YC, Yang M, Wang J. Study on the formation characteristics of underwater hemispherical shaped charge jet and its penetration performance into concrete. Defence Technology, 2024

[5] Cardoso D, Teixeira-Dias F. Modelling the formation of explosively formed projectiles (EFP). International Journal of Impact Engineering, 2016, 93: 116-127.

[6] Cheng X, Huang GY, Liu CM, Feng SS. Design of a novel linear shaped charge and factors influencing its penetration performance. Applied Sciences, 2018, 8(10): 1863.

[7] Deng H, Li G, Liang Z, Ren X, Guo H. Study on forming control and penetration performance of tantalum in linear explosively formed penetrators (LEFP) warhead. The International Journal of Multiphysics, 2022, 16(3): 261-272

[8] Ding L, Jiang JW, Men JB, Wang SY, Li M. Research on feasibility of several high density materials for EFP liner and material selection criteria. Propellants, Explosives, Pyrotechnics, 2017, 42(4): 360-369.

[9] Dobratz BMProperties of chemical explosives and explosive simulants, 1974

[10] Duan WY, Du ZH. Orthogonal Design Research on Shaping Factors of LEFP Warhead. Journal of Projectiles, Rockets, Missiles and Guidance, 2010, 30(02): 123-125

[11] Elbeih A, Elshenawy T, Zeman S, Akstein Z. Application of BCHMX in shaped charges against RHA targets compared to different nitramine explosives. Central European Journal of Energetic Materials, 2018, 15(1): 3-17.

[12] Feng DL, Liu MB, Li HQ, Liu GR. Smoothed particle hydrodynamics modeling of linear shaped charge with jet formation and penetration effects. Computers & Fluids, 2013, 86: 77-85.

[13] Fu JP, Chen ZG, Hou XC, Li SQ, Li SC, Wang JW. Simulation and experimental investigation of jetting penetrator charge at large stand-off distance. Defence Technology, 2013, 9(2): 91-97.

[14] Gou RJ. Numerical Simulation of Liner Curvature Radius on Formation of LEFP. Advanced Materials Research, 2014, 941: 2305-2308.

[15] Gou RJ, Zhang SH. Formation mechanism of linear explosive formed penetrator by midpoint initiating manner. Advanced Materials Research, 2011, 295: 1643-1646.

[16] Gou RJ, Zhang SH. The Bifurcate Fracture Analysis of Linear Red Copper Penetrator. Advanced Materials Research, 2011, 189: 213-216.

[17] Gou RJ, Zhang SH, Fan K. Numerical simulation of linear explosive formed penetrator by endpoint initiating manner. Advanced Materials Research, 2012, 538: 534-537.

[18] Gu YC, Wang JX, Li H, Tang K, Liu LT. Formation characteristics and penetration performance of an underwater shaped charge jet. Ocean Engineering, 2022, 258: 111695.

[19] Gu YC, Wang JX, Li H, Liu LT, Tang K, Ma T, Lin SJ. Comparative study on the forming characteristics and penetration effects of shaped charge jet in water and air. Journal of Applied Physics, 2023, 258: 111695

[20] Hu F, Wu H, Fang Q, Liu JC. Numerical simulations of shaped charge jet penetration into concrete-like targets. International Journal of Protective Structures, 2017, 8(2): 237-259.

[21] Johnston M, Lim S. Numerical observation of the jet flight patterns of linear shaped charges. Applied Sciences, 2012, 2(3): 629-640.

[22] Joo J, Choi J, Koo MH, Kim D. Numerical analysis on penetration reduction of a WHA penetrator by an impact of linear explosively formed penetrator (LEFP). Journal of the Korea Institute of Military Science and Technology, 2017, 20(3): 384-392

[23] Kim JH, Shin HC. Application of the ALE technique for underwater explosion analysis of a submarine liquefied oxygen tank. Ocean Engineering, 2008, 35(8–9): 812-822.

[24] Li YB, Wang JX, Liu ZT, Tang K, Wang HF, Chen XW. Orthogonal optimization design and experiments on explosively formed projectiles with fins. International Journal of Impact Engineering, 2023, 173: 104462.

[25] Lim S. Jet velocity profile of linear shaped charges based on an arced liner collapse. Journal of Energetic Materials, 2013, 31(4): 239-250.

[26] Liu J, Du ZH, Liu RZ, Dong YC. The Study of LEFP Based on One Part of Semicircle Liner. Advanced Materials Research, 2013, 753: 1625-1629.

[27] Liu YK, Yin JP, Wang ZJ, Zhang XP, Bi GJ. The EFP formation and penetration capability of double-layer shaped charge with wave shaper. Materials, 2020, 13(20): 4519.

[28] Ma TB, Liu J, Wang Q. Influence of shaped charge structure parameters on the formation of linear explosively formed projectiles. Defence Technology, 2022, 18(10): 1863-1874.

[29] Ma TB, Liu J, Wang Q. Structural Design and Parameter Optimization of Linear Explosive Forming Projectile. Propellants, Explosives, Pyrotechnics, 2022, 47(4): e202100348.

[30] Mao X, Ma TB, Liu J. Structure optimization of linear shaped charge based on different explosives. Propellants, Explosives, Pyrotechnics, 2024, 49(5): e202300321.

[31] Mehmannavaz H, Ramezani A, Nabakhteh MA, Liaghat G. A practical review study on shaped charge in the last two decades (2000–2020). International Journal of Protective Structures, 2021, 12(4): 665-693.

[32] Nobile F, Formaggia LA. Stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements. East-West Journal of Numerical Mathematics, 1999, 7(2): 105-132

[33] Pishevar AR, Amirifar R. An adaptive ALE method for underwater explosion simulations including cavitation. Shock Waves, 2010, 20: 425-439.

[34] Steinberg DJSpherical explosions and the equation of state of water, 1987.

[35] Journal of Applied Physics, 2023, 134(4

[36] Tian XY, Zhao SW, Liang ZY, Xiong F, Xu XD, Li QG, Guo YJ. Numerical simulation of shaped jet penetrating granite based on S-ALE method. Journal of Ordnance Equipment Engineering, 20251-7

[37] Vigil MGDesign and development of precision linear shaped charges, 1989Albuquerque, NM (United States)Sandia National Lab. (SNL-NM)

[38] Defence Science Journal, 2015, 65(4

[39] Wang W, Wang YP, Yang JC, Wang JH. Investigation on air blast resistance of POZD-coated composite steel plates: Experiment and numerical analysis. Composites Part B: Engineering, 2022, 237: 109858.

[40] Wu SZ, Gu WB, Li XF. Study on the Orthogonal Optimization Design of Structured Parameters of the Linear Shaped Charge with Oval Cover. Engineering Blasting, 2013, 41(05): 12-16

[41] Yang G, Han X, Hu DA. Computer simulation of two-dimensional linear-shaped charge jet using smoothed particle hydrodynamics. Engineering Computations, 2011, 28(1): 58-75.

[42] Yu ZR, Ni BY, Wu QG, Wang ZC, Liu P, Xue YZ. Numerical Simulation of Icebreaking by Underwater-Explosion Bubbles and Compressed-Gas Bubbles Based on the ALE Method. Journal of Marine Science and Engineering, 2023, 12(1): 58.

[43] Physics of Fluids, 2023, 35(3

[44] Zhang AM, Li SM, Xu RZ, Pei SC, Li S, Liu YL. A theoretical model for compressible bubble dynamics considering phase transition and migration. Journal of Fluid Mechanics, 2024, 999: A58.

[45] Zhang XW, Xiao QQ, Huang ZX, Zu XD, Jia X, Ma B. Influence of liner material on penetration capability by jet into high strength concrete. J. Proj. Rocket. Missiles Guid, 2020, 40: 1-4

[46] Zhang ZF, Wang C, Xu WL, Hu HL, Guo YC. Application of a new type of annular shaped charge in penetration into underwater double-hull structure. International Journal of Impact Engineering, 2022, 159: 104057.

[47] Zhang ZF, Wang LK, Silberschmidt VV. Damage response of steel plate to underwater explosion: Effect of shaped charge liner. International Journal of Impact Engineering, 2017, 103: 38-49.

[48] Zhang ZF, Yang SX, Zhang SH, Wang LK, Sui YT, Li T, Zhang GY. Experimental study of damage to double-hull structure by underwater explosions of three charge types-blasting, shaped, and linear shaped charges. International Journal of Impact Engineering, 2025, 2025: 105369.

[49] Physics of Fluids, 2025, 37(2

[50] Physics of Fluids, 2024, 36(12

[51] Zu XD, Huang ZX, Zhu CS, Xiao QQ. Study of detonation wave contours in EFP warhead. Defence technology, 2016, 12(2): 129-133.

RIGHTS & PERMISSIONS

The Author(s)

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.