Equivalent Strength of Armour Steel against High-velocity Penetration of Long-rod Projectile

doi:10.12382/bgxb.2023.0619

Abstract

Abstract:

Armour grade steel is one of the main components of composite armour. A 3D SPH-FEM coupling model is developed to investigate the equivalent strength of armour grade steel against the penetration of long-rod projectile. On the basis of verifying the reliability of the model, a simulation study on tungsten alloy long-rod projectiles penetrating a semi-infinite 300-600HBW armour steel in the initial velocity range of 1000-1800m/s is carried out. The equivalent strength of armour steel under high strain rate-adiabatic conditions is explored based on the resistance force and Walker-Anderson model. The calculated results show that the penetration process of tungsten long-rod projectiles into semi-infinite steel targets can be divided into three stages: initial transient, quasi-steady and residual penetration. In most conditions, Walker-Anderson model can be used to accurately calculate the depth of penetration and head velocity of quasi-steady stage. the diameter of rod body and the equivalent strength of target are approximately constant in the quasi-steady stage, thus the penetration resistance can be described by the Poncelet formula. According to the above analysis, a nonlinear conversion model for the equivalent strength and hardness of armour steel is developed. Combined with Walker-Anderson model, it can accurately predict the depth of penetration of long-rod projectiles against semi-infinite targets. The model shows that equivalent strength is positively related to hardness, but its increase slows down due to the enhancement of thermal softening and the weakening of strain rate hardening.

Key words: long-rod projectile, semi-fluid penetration, semi-infinite target, high-hardness armour steel, smoothed particle hydrodynamics

CLC Number:

O347

WANG Jirui, WANG Chengxin, WANG Yini, TANG Kui, BO Qile. Equivalent Strength of Armour Steel against High-velocity Penetration of Long-rod Projectile[J]. Acta Armamentarii, 2023, 44(12): 3755-3770.

Figures/Tables 25

Table 1 Parameters of Johnson-Cookmodel of projectile and target

材料	A/MPa	B/MPa	n	C	m	D₁	D₂	D₃	D₄	D₅
钨合金^[20]	1275	624	0.12	0.016	0.94	2	1.77	-3.4	0	0
4340钢^[8]	719	456	0.093	0.008	1.03	-0.8	2.1	-0.5	0.002	0.61
Mars 190^[21]	1193	500	0.676	0.00435	1.17	0.21	7.2	-5.44	0	0
Armox 500^[22]	1470	702	0.199	0.00549	0.811	0.068	5.382	-2.554	0	0
Armox 600^[23]	1580	958	0.175	0.00877	0.712	-0.4	1.5	-0.5	0	0

Table 2 Equation of state parameters of projectile and target

材料	ρ_i/ (kg·m^-3)	C₀/ (m·s^-1)	S₁	γ	a
钨合金^[20,25]	17700	4029	1.44	1.58	0.011
钢^[20,25]	7850	4578	1.33	1.93	0.47

Fig.1 True stress vs true strain of materials

Fig.2 Maximum stress and hardness of armour steels

Table 3 Comparison of strength estimation methods

H_t/ HBW	σ_JCmax/ MPa	σ_fit/ MPa	σ_m/ MPa	δ_fit/ %	δ_m/ %
300	1152	1139	1144	1.1	9.2
400	1450	1492	1370	2.9	5.5
500	1888	1845	1716	2.3	9.1
600	2182	2197	2180	0.7	0.1

Fig.3 SPH-FEM model of tungsten rod and semi-infinite target

Table 4 Influence of mesh size on simulation results

粒子间距/mm	侵彻深度/mm	侵彻深度误差/%	背面变形量/mm	背面拉伸不稳定
0.80	34.3	14.3	3.9	无
0.61	36.8	8.0	4.7	无
0.47	39.9	0.25	6.1	弱
0.40	40.6	1.5	7.2	强
0.35	41.4	3.5	7.8	强

Fig.4 Influence of mesh size on penetration process

Fig.5 Johnson-Cook damage of projectile and target with different mesh sizes

Fig.6 Johnson-Cook damage of 300HBW semi-infinite target penetrated by 1615m/s long rod projectile

Fig.7 Simulated results of 1000-1800m/s tungsten rod projectile penetrating 300HBW target

Fig.8 Relationship between head velocity and resistance force

Fig.9 Head shape changing during penetration of tungsten long rod projectile into 300HBW target at 1600m/s

Fig.10 Johnson-Cook damage of target at 1600m/s

Fig.11 Maximum effective stress of target during penetration of tungsten dart into 300HBW RHA at 1000-1800m/s

Fig.12 Maximum effective stress of tungsten long rod projectile during its penetration into 300HBW RHA at 1000-1800m/s

Fig.13 Maximum effective stresses of 400~600HBW targets

Table 5 Fitting result of resistance force of armour steels

H_t/HBW	S_r	k_r	k_σ	σ_t/MPa
300	4.08	2.79	1.00	1152
400	4.16	2.48	0.89	1288
500	4.11	2.42	0.87	1637
600	4.07	2.30	0.82	1799

Fig.14 Resistance force fitting result of 300~600HBW

Fig.15 Head and tail velocities of simulation and W-A model of penetrating 300HBW target

Table 6 Comparison of W-Amodel and simulated results of 300HBW target

v_i/ (m·s^-1)	中点头部速度/(m·s^-1)			侵彻深度/mm
v_i/ (m·s^-1)	仿真值	计算值	相对偏差/%	仿真值	计算值	相对偏差/%
1000	358	297	17.0	35.3	34.6	2.0
1200	497	463	6.8	57.9	59.7	3.1
1400	630	624	0.9	80.1	82.3	2.7
1600	776	776	0.1	101.0	101.0	0.5
1800	928	924	0.4	118.0	115.0	2.5

Fig.16 Comparison of head velocities of simulation and W-A model of 300~600HBW target

Fig.17 Comparison of simulated and fitting results of equivalent strength of armor steel

Fig.18 Comparison of experimental and calculated P/L

Table 7 Comparison of calculation methods of equivalent strength

H_t/HBW	σ_t/MPa
H_t/HBW	仿真值	Tate^[13]结果	Recht^[12]结果
300	1152	1260	1176
400	1288	1680	1568
500	1637	2100	1960
600	1799	2520	2352

References 56

[1]	唐群轶. 长杆弹超高速流体侵彻理论模型研究[D]. 绵阳: 西南科技大学, 2021.
	TANG Q Y. Study on the theoretical model of hypervelocity fluid penetration of long-rod projectile[D]. Mianyang: Southwest University of Science and Technology, 2021. (in Chinese)
[2]	ZAKI S, UDDIN E, MUBASHAR A. Experimental investigation of impact of long rod eroding projectiles against rolled homogeneous armour[J]. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2020, 234(10): 1335-1342.
[3]	张清源. 长杆弹斜侵彻模型及仿真技术研究[D]. 长沙: 国防科技大学, 2020.
	ZHANG Q Y. Oblique penetration model of long rod projectile and simulation technology research[D]. Changsha: National University of Defense Technology, 2020. (in Chinese)
[4]	门建兵, 蒋建伟, 王树有. 爆炸冲击数值模拟技术基础[M]. 北京: 北京理工大学出版社, 2015.
	MEN J B, JIANG J W, WANG S Y. Fundamentals of numerical simulation for explosion and shock problems[M]. Beijing: Beijing Institute of Technology Press, 2015. (in Chinese)
[5]	BOJANOWSKI C. Numerical modeling of large deformations in soil structure interaction problems using FE, EFG, SPH, and MM-ALE formulations[J]. Archive of Applied Mechanics, 2014, 84: 743-755. doi: 10.1007/s00419-014-0830-5 URL
[6]	SU H, ZHANG C, YAN Z F, et al. Numerical simulation of penetration process of depleted uranium alloy based on an FEM-SPH coupling algorithm[J]. Metals, 2023, 13(1): 79. doi: 10.3390/met13010079 URL
[7]	曲禹同. 基于绝热剪切机制的细晶钨合金弹芯自锐行为研究[D]. 沈阳: 沈阳理工大学, 2022.
	QU Y T. Study on self-sharpening behavior of fine grain tungsten alloy projectile core based on adiabatic shear mechanism[D]. Shenyang: Shenyang Ligong University, 2022. (in Chinese)
[8]	GOH W L, ZHENG Y, YUAN J, et al. Effects of hardness of steel on ceramic armour module against long rod impact[J]. International Journal of Impact Engineering, 2017, 109: 419-426. doi: 10.1016/j.ijimpeng.2017.08.004 URL
[9]	唐奎, 王金相, 刘亮涛, 等. 长杆弹二次侵彻机理及影响因素研究[J/OL]. 兵工学报, 2023(2023-04-29)[2023-05-12].
	TANG K, WANG J X, LIU L T, et al. Study on the mechanism of secondary penetration of long rod and its influencing factors[J/OL]. Acta Armamentarii, 2023(2023-04-29)[2023-05-12]. (in Chinese)
[10]	TANG K, WANG J X, SONG H P, et al. Investigation on the penetration of jacketed rods with striking velocities of 0.9-3.3km/s into semi-infinite targets[J]. Defence Technology, 2022, 18(3): 476-489. doi: 10.1016/j.dt.2021.03.003 URL
[11]	DANESHJOU K, SHAHRAVI M. The role of simulation in long-rod ricochet phenomenon[J]. Journal of Mechanical and Aerospace Engineering, 2008, 3(4): 69-86.
[12]	RECHT R F. Taylor ballistic impact modelling applied to deformation and mass loss determinations[J]. International Journal of Engineering Science, 1978, 16(11): 809-827. doi: 10.1016/0020-7225(78)90067-8 URL
[13]	TATE A. Long rod penetration models—Part II. Extensions to the hydrodynamic theory of penetration[J]. International Journal of mechanical sciences, 1986, 28(9): 599-612. doi: 10.1016/0020-7403(86)90075-5 URL
[14]	ROSENBERG Z, DEKEL E. A computational study of the relations between material properties of long-rod penetrators and their ballistic performance[J]. International journal of impact engineering, 1998, 21(4): 283-296. doi: 10.1016/S0734-743X(97)00068-7 URL
[15]	ROSENBERG Z, KOSITSKI R, MALKA-MARKOVITZ A. The effective strength of metallic plates perforated by rigid projectiles[J]. International Journal of Impact Engineering, 2018, 121: 35-43.
[16]	ALEKSEEVSKII V P. Penetration of a rod into a target at high velocity[J]. Combustion, explosion and shock waves, 1966, 2(2): 63-66. doi: 10.1007/BF00749237 URL
[17]	TATE A. A theory for the deceleration of long rods after impact[J]. Journal of the Mechanics and Physics of Solids, 1967, 15(6): 387-399. doi: 10.1016/0022-5096(67)90010-5 URL
[18]	ROSENBERG Z, MARMOR E, MAYSELESS M. On the hydrodynamic theory of long-rod penetration[J]. International Journal of Impact Engineering, 1990, 10(1/2/3/4): 483-486. doi: 10.1016/0734-743X(90)90081-6 URL
[19]	WALKER J D, ANDERSON C E. A time-dependent model for long-rod penetration[J]. International Journal of Impact Engineering, 1995, 16(1): 19-48. doi: 10.1016/0734-743X(94)00032-R URL
[20]	ZHU F L, CHEN Y, ZHU G L. Numerical simulation study on penetration performance of Depleted Uranium (DU) alloy fragments[J]. Defence Technology, 2021, 17(1): 50-55. doi: 10.1016/j.dt.2020.01.002
[21]	FRAS T, MURZYN A, PAWLOWSKI P. Defeat mechanisms provided by slotted add-on bainitic plates against small-calibre 7.62mm×51 AP projectiles[J]. International Journal of Impact Engineering, 2017, 103: 241-253. doi: 10.1016/j.ijimpeng.2017.01.015 URL
[22]	SKOGLUND P, NILSSON M, TJERNBERG A. Fracture modelling of a high performance armour steel[J]. Journal de Physique Ⅳ, 2006, 134: 197-202.
[23]	BADUROWICZ P, PACEK D. Determining ricocheting projectiles’ temperature using numerical and experimental approaches[J]. Materials, 2022, 15(3): 928. doi: 10.3390/ma15030928 URL
[24]	SONG W J, CHEN X W, CHEN P. Effect of compressibility on the hypervelocity penetration[J]. Acta Mechanica Sinica, 2018, 34: 82-98. doi: 10.1007/s10409-017-0688-1 URL
[25]	孔繁家. 并联组合式LEFP对杆式穿甲弹的毁伤仿真研究[D]. 太原: 中北大学, 2023.
	KONG F J. Simulation research on damage of parallel combined LEFP to rod armor-piercing projectiles[D]. Taiyuan: North University of China, 2023. (in Chinese)
[26]	HOLMQUIST T J, JOHNSON G R, GOOCH W A. Modeling the 14.5mm BS 41 projectile for ballistic impact computations[M]//SYNGELLAKIS S. Projectile Impact:Modelling Techniques and Target Performance Assessment. Ashurst Lodge, Southampton, UK: WIT Press, 2014: 73-87.
[27]	LITTLE D, BURKINS M, PARAS J.Evaluation of surrogate 14. 5-mm BS41 armor-piercing projectiles: ARL-TN-1046[R]. Adelphi, MD, US: DEVCOM Army Research Laboratory, 2020.
[28]	BARÉNYI I, MAJERÍK J, BEZÝECN J, et al. Material and technological aspects while processing of selected ultra high strength steel[J]. Manufacturing Technology, 2019, 19(2): 184-189. doi: 10.21062/ujep/267.2019/a/1213-2489/MT/19/2/184 URL
[29]	FRUEH P, HEINE A, RIEDEL W. Assessment of the protective properties of two different UHA steels based on material testing and numerical simulation[J]. Procedia engineering, 2017, 197: 119-129. doi: 10.1016/j.proeng.2017.08.088 URL
[30]	WALKER J D, ANDERSON C E. The influence of initial nose shape in eroding penetration[J]. International journal of impact engineering, 1994, 15(2): 139-148. doi: 10.1016/S0734-743X(05)80027-2 URL
[31]	HEDJERES S, TRIA D E, BOUDIAF A, et al. The influence of plasma nitriding hardness treatment on the dynamic compressive behavior of the Hardox 400 at a wide temperature range[J]. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2023, 237(4): 867-885.
[32]	NIEZGODA T, MORKA A. On the numerical methods and physics of perforation in the high-velocity impact mechanics[J]. World Journal of Engineering, 2009, 6: 414-416.
[33]	TRIA D E, TREBIŃSKI R. Methodology for experimental verification of steel armour impact modelling[J]. International Journal of Impact Engineering, 2017, 100: 102-116. doi: 10.1016/j.ijimpeng.2016.10.011 URL
[34]	TRAJKOVSKI J, KUNC R, PEPEL V, et al. Flow and fracture behavior of high-strength armor steel PROTAC 500[J]. Materials & Design, 2015, 66: 37-45. doi: 10.1016/j.matdes.2014.10.030 URL
[35]	BØRVIK T, DEY S, CLAUSEN A H. Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles[J]. International Journal of Impact Engineering, 2009, 36(7): 948-964. doi: 10.1016/j.ijimpeng.2008.12.003 URL
[36]	ZHANG R, HAN B, LI L, et al. Influence of prestress on ballistic performance of bi-layer ceramic composite armors: experiments and simulations[J]. Composite Structures, 2019, 227: 111258. doi: 10.1016/j.compstruct.2019.111258 URL
[37]	XU J, HU W, REN B, et al. Adaptive smoothed particle hydrodynamics and higher order kernel function in LS-DYNA®[C]//Proceedings 16th international LS-DYNA users’ conference. Detroit, MI, US: DYNAmore GmbH, 2020.
[38]	王猛, 杨明川, 荣光, 等. 穿甲过程中钨合金杆式弹失效模式及数值模拟[J]. 稀有金属材料与工程, 2015, 44(9):2170-2174.
	WANG M, YANG M C, RONG G, et al. Failure model and numerical simulation of the tungsten alloy long rod when piercing into armor target[J]. Rare Metal Materials and Engineering, 2015, 45(9):2170-2174. (in Chinese)
[39]	王晓东, 王江波, 徐立志, 等. 异型截面长杆弹侵彻半无限厚金属靶板实验研究[J]. 爆炸与冲击, 2021, 41(3):37-46.
	WANG X D, WANG J B, XU L Z, et al. Experimental study on penetration of non-circular cross-section long-rod projectiles into semi-infinite metal target[J]. Explosion and Shockwaves, 2021, 41(3): 37-46. (in Chinese)
[40]	刘铁磊, 徐豫新, 王晓锋, 等. 钨合金球形破片侵彻低碳钢的弹道极限速度计算模型[J]. 兵工学报, 2022, 43(4):768-779.
	LIU T L, XU Y X, WANG X F, et al. Ballistic limit calculation model of tungsten alloy spherical fragments penetrating into low carbon steel plate[J] Acta Armamentarii, 2022, 43(4): 768-779. (in Chinese) doi: 10.12382/bgxb.2021.0448
[41]	焦文俊, 陈小伟. 长杆高速侵彻问题研究进展[J]. 力学进展, 2019, 49(1):201904.
	JIAO W J, CHEN X W. Review on long-rod penetration at hypervelocity[J]. Advances in Mechanics, 2019, 49(1): 201904. (in Chinese)
[42]	KEELE M J, RAPACKI E J, BRUCHEY W J. High velocity performance of a uranium alloy long rod penetrator: BRL-TR-3236[R]. Aberdeen Proving Ground, MD, US: Army Ballistic Research Laboratory, 1989.
[43]	ANDERSON C E, MORRIS B L, LITTLEFIELD D L. A penetration mechanics database: AD-A246 351[R]. San Antonio, TX, US: Southwest Research Institute, 1992.
[44]	DOWDING R J, TAUER K J, WOOLSEY P, et al. The metallurgical and ballistic characterization of quarter-scale tungsten alloy penetrators: AD-A223 998[R]. Watertown, MA, US: US Army materials Technology Laboratory, 1990.
[45]	TRIA D E, TREBIŃSKI R. On the influence of fracture criterion on perforation of high-strength steel plates subjected to armour piercing projectile[J]. Archive of mechanical engineering, 2015, 62(2): 157-179. doi: 10.1515/meceng-2015-0010 URL
[46]	CHOUDHARY S, SINGH P K, KHARE S, et al. Ballistic impact behaviour of newly developed armour grade steel: an experimental and numerical study[J]. International Journal of Impact Engineering, 2020, 140: 103557. doi: 10.1016/j.ijimpeng.2020.103557 URL
[47]	RYAN S, LI H, EDGERTON M, et al. The ballistic performance of an ultra-high hardness armour steel: an experimental investigation[J]. International journal of impact engineering, 2016, 94: 60-73. doi: 10.1016/j.ijimpeng.2016.03.011 URL
[48]	MA D, GIGLIO M, MANES A. Numerical investigation on the uniaxial compressive behaviour of an epoxy resin and a nanocomposite[J]. European Journal of Mechanics-A/Solids, 2022, 92: 104500. doi: 10.1016/j.euromechsol.2021.104500 URL
[49]	NEUKAMM F, FEUCHT M, HAUFE A, et al. On closing the constitutive gap between forming and crash simulation[C]//Proceedings of the 10th International LS-DYNA Users Conference. Detroit, MI, US: DYNAmore GmbH, 2008: 12-21.
[50]	MEYER H W, KLEPONIS D S. An analysis of parameters for the Johnson-Cook strength model for 2-in-thick Rolled Homogeneous Armor: ARL-TR-2528[R]. Adelphi, MD, US: Army Research Laboratory, 2001.
[51]	ANDERSON C E, HOHLER V, WALKER J D, et al. Time-resolved penetration of long rods into steel targets[J]. International Journal of Impact Engineering, 1995, 16(1): 1-18. doi: 10.1016/0734-743X(94)E0030-Y URL
[52]	WANG X, JIANG J W, SUN S J, et al. Investigation on the spatial distribution characteristics of behind-armor debris formed by the perforation of EFP through steel target[J]. Defence Technology, 2020, 16(1): 119-135. doi: 10.1016/j.dt.2019.05.016
[53]	BERGS T, HARDT M, SCHRAKNEPPER D. Determination of Johnson-Cook material model parameters for AISI 1045 from orthogonal cutting tests using the Downhill-Simplex algorithm[J]. Procedia Manufacturing, 2020, 48: 541-552. doi: 10.1016/j.promfg.2020.05.081 URL
[54]	林莉, 支旭东, 范锋, 等. Q235B钢Johnson-Cook模型参数的确定[J]. 振动与冲击, 2014, 33(9):153-158, 172.
	LIN L, ZHI X D, FAN F, et al. Determination of parameters of Johnson-Cook models of Q235B steel[J]. Journal of Vibration and Shock, 2014, 33(9): 153-158, 172. (in Chinese)
[55]	BUCHAR J, VOLDRICH J, ROLC S, et al. Ballistic performance of dual hardness armor[C]//Proceedings of the 20th International Symposium on Ballistics. Orlando, FL, US: International Ballistics Society, 2002: 23-27.
[56]	BOYCE B L, DILMORE M F. The dynamic tensile behavior of tough, ultrahigh-strength steels at strain-rates from 0.0002s^-1 to 200s^-1[J]. International Journal of Impact Engineering, 2009, 36(2): 263-271. doi: 10.1016/j.ijimpeng.2007.11.006 URL