Cavity Forming Characteristics of Ballistic Soap Penetrated by Sub-millimeter Particles and Injury Threshold

doi:10.12382/bgxb.2023.1017

Abstract

Abstract:

Ballistic soap is widely used in the field of wound ballistics, as an equivalent target of biological target, to observe the damage characteristics of wound channels for assessing the potential damage of ammunition. However, there is still a lack of damage standards for sub-millimeter particle damage elements of low collateral damage munitions to the biological targets. The dimensional analysis method is used to determine the forming characteristics of penetrating cavity, and the actual wound trajectory of soap target is obtained through the particle driving test. The evolution law of penetrating cavity of sub-millimeter particles is analyzed by numerical simulation, and the critical damage conditions of sub-millimeter particles on the soap target equivalent target are established. The conical cavity produced by sub-millimeter particles penetrating the soap target is represented by inlet diameter and cavity depth. The results show that the cavities caused by sub-millimeter particles with different densitues, sizes and velocities are significantly different, and the cavity characteristics are related to specific kinetic energy. The volume of the cavity produced by penetrating the soap target increases with the increase in the the density, size and velocity of particle material. The larger the particle size is, the deeper the penetration into the soap target is, and the inlet diameter expand to 2.0-2.5 times of the particle size. According to the fragment killing criteria, the injury thresholds of sub-millimeter particles with different particle sizes to the soap target are determined. The energy density of particle penetration should exceed 0.83J/cm² to cause damage to the soap target. The numerically simulated, test and theoretically analyzed results agree well with each other, and the the influence law of penetration effect is consistent. The results can provide theoretical reference for the structural design of low collateral damage warhead and the effect evaluation.

Key words: soap target, low collateral damage, sub-millimeter particle, cavity evolution, injury threshold

CLC Number:

TJ410.1

WANG Shaohong, FAN Ruijun, WANG Jinying, LI Haijie, PI Aiguo. Cavity Forming Characteristics of Ballistic Soap Penetrated by Sub-millimeter Particles and Injury Threshold[J]. Acta Armamentarii, 2024, 45(11): 3868-3878.

Figures/Tables 23

Fig.1 Plasma driving device and principle[25]

Fig.2 Heavy metal particles embedded charge structure

Fig.3 Experimental site layout

Fig.4 Cavity morphology of soap target penetrated by sub-millimeter particles

Fig.5 The position of the penetration end point of particles relative to the expansion of soap cavity

Fig.6 Microscopic observation of penetrating cavity under different conditions

Table 1 Test results at different impact speeds

试验序号	飞行时长/ ms	侵彻深度/ mm	开坑直径/ mm	是否贯穿
01	16.3	12	0.600
02	22.0	3	0.520
03	13.0	22	0.811
04	11.5	24	0.865	否
05	15.5	10	0.687
06	14.0	20	0.763
07	20.0	3.5	0.520

Fig.7 Dimensionless relationship between penetration depth and particle velocity

Fig.8 Dimensionless relationship between inlet diameter and particle velocity

Fig.9 Finite element model

Table 2 Material parameters of tungsten alloy particles

ρ/(g·cm^-3)	E/GPa	v	σ/GPa
17	117	0.35	1.506

Table 3 Material parameters of ballistic soap[26]

ρ/ (g·cm^-3)	E/ GPa	σ/ MPa	E_H/ Pa	C₁/ Pa	C₂/ Pa	C₃/ Pa	C₄/ Pa
1.2	1	1	1×10³	0.0	0.0	2.93×10¹⁰	0.0

Fig.10 Equivalent stress cloud map at different moments and velocity decay curve of particles at different moments

Fig.11 Comparison of simulated and experimental results(left:cavity depth,right:cavity inlet diameter)

Fig.12 Finite element models of particles with different sizes

Fig.13 Simulated results of penetration depth of particles with different particle sizes

Table 4 Cavity characteristics generated by particles with different sizes

入口直径与深度	粒径/μm
入口直径与深度	200	300	400	500
入口直径/mm	0.522	0.673	0.867	1.061
深度/mm	6.441	12.171	18.734	21.962

Table 5 Cavity characteristics produced by particle penetration of different materials

入口直径与深度	铝	陶瓷	钢	镍	钨合金
入口直径/mm	0.981	1.001	1.072	1.065	1.061
深度/mm	4.031	5.434	9.599	11.261	21.962

Fig.14 Velocity decay curves in the particle penetration processes of different materials

Fig.15 Simulated results of inlet diameter of cavity penetrated by particles at different initial velocities

Table 6 Cavity characteristics generated by particles penetrating the soap target at different initial velocities

入口直径与深度	颗粒初速度/(m·s^-1)
入口直径与深度	400	600	800	1000
入口直径/mm	1.061	1.451	1.593	1.810
深度/mm	21.962	26.453	28.266	29.391

Table 7 Critical velocity of particle penetration m/s

侵彻深度/mm	粒径/μm
侵彻深度/mm	100	300	500	700	900
1	305	225	195	178	166
5	477	352	305	278	260
10	578	426	370	337	314

Fig.16 Critical energy-density of particles during penetration

References 26

[1]	刘俊. 低附带弹药毁伤元抛撒机理研究[D]. 南京: 南京理工大学, 2015.
	LIU J. Study on the mechanism of dispersive damage element of LCD[D]. Nanjing: Nanjing University of Science and Technology, 2015. (in Chinese)
[2]	李兵仓. 低附带毁伤弹药概况及其对人体杀伤特点[J]. 创伤外科杂志, 2022, 24(7): 486-489.
	LI B C. General information of low collateral damage ammunition and its killing characteristics to human body[J]. Journal of Traumatic Surgery, 2022, 24(7): 486-489. (in Chinese)
[3]	FROST D L, ORNTHANALAI A C, ZAREI Z. Particle momentum effects from the detonation of heterogeneous explosive[J]. Journal of Applied Physics, 2007, 87(4):639-671.
[4]	ZHANG F, FROST D L, THIBAULT P A, et al. Explosive dispersal of solid particles[J]. Shock Waves, 2001, 10(6): 431-443.
[5]	XUE K, LI F F, BAI C H. Explosively driven fragmentation of granular materials[J]. European Physical Journal, 2013, 36(8):1-16.
[6]	XUE K. Formation mechanism of the shock-induced particle jetting[C]// Proceedings of the 17th APS March Meeting.New Orleans, LA, US: Bulletin of the American Physical Society, 2016.
[7]	刘意. 高密度惰性金属炸药爆轰驱动与粒子流形成过程研究[D]. 北京: 北京理工大学, 2010.
	LIU Y. Detonation of dense inert metal explosive and the formation of particles flow[D]. Beijing: Beijing Institute of Technology, 2010. (in Chinese)
[8]	ALEXANDER L, MICHAEL S. Armed conflict injuries to the extremities[M]. New York,NY, US: Springer, 2011.
[9]	王辛桐, 汪送. 防暴动能弹终点效应测试靶标研究进展[J]. 测试技术学报, 2022, 36(6):468-478, 485.
	WANG X T, WANG S. Review on target of anti-riot Kinetic energy projectiles blunt ballistic impact[J]. Journal of Test and Measurement Technology, 2022, 36(6):468-478, 485. (in Chinese)
[10]	KAZMIRSKA A S, BARZDO M, JURCZYK A P, et al. Penetration depth of projectiles fired from a replica of colt navy of 1851 in 20% gelatin blocks correlated with fatal injuries assessed in an autopsy of a 78-year-old man[J]. Journal of Forensic Sciences, 2015, 60(5): 1365-1368.
[11]	SALISBURY C P, CRONIN D S. Mechanical properties of ballistic gelatin at high deformation rates[J]. Experimental Mechanics, 2009, 49(6): 829-840.
[12]	MENG S S. Numerical modeling of impacts at high velocities by a meshfree method Smoothed particles Hydrodynamics. Application to micro-impacts in soft tissues[D]. Belfort, France: Université de Technology de Belfort-Montbéliard, 2021.
[13]	PIRLOT M, DYCKMANS G, BASTIN I. Soap and gelatin for simulating human body tissue: an experimental and numerical evaluation[C]// Proceedings of the 19th International Symposium of Ballistics. Interlaken, Switzerland: Joe Carleoni, Dennis Orphal, 2001:1011-1018.
[14]	SHEPHERD C J, APPLEBY-THOMAS G J, WILGEROTH J M, et al. On the response of ballistic soap to one-dimensional shock loading[J]. International Journal of Impact Engineering, 2011, 38(12):981-988.
[15]	贾骏麒, 王敬夫, 马秦, 等. 柱形钢质破片侵彻肥皂靶的弹道特征研究[J]. 创伤外科杂志, 2017, 19(6):462-465.
	JIA J Q, WANG J F, MA Q, et al. Study on the ballistic characteristics of cylindrical steel fragments penetrating soap target[J]. Journal of Traumatic Surgery, 2017, 19(6): 462-465. (in Chinese)
[16]	李冠桦, 张良潮, 翁昌梅, 等. 超高速钢球打击肥皂与生物靶标的创伤弹道特点研究[J]. 兵工学报, 2022, 43(9): 2399-2407. doi: 10.12382/bgxb.2022.0536
	LI G H, ZHANG L C, WENG C M, et al. Study of traumatic ballistic characteristics of ultra-high speed steel balls striking soap and biological targets[J]. Acta Armamentarii, 2022, 43(9): 2399-2407. (in Chinese) doi: 10.12382/bgxb.2022.0536
[17]	HILL R. Cavitation and the influence of headshape in attack of thick targets by nondeforming projectiles[J]. Journal of the Mechanics and Physics of Solids, 1980, 28(5):249-263.
[18]	STURDIVAN L M. A mathematical model of penetration of chunky projectiles in a gelatin tissue simulant[M]. US: Defense Technical Information Center, 1978.
[19]	SEGLETS S B. Modeling the penetration behavior of rigid spheres into ballistic gelatin[R]. MD, US: Army Research Laboratory, 2008.
[20]	SWAIN M V, KIESER D C, SHAH S, et al. Projectile penetration into ballistic gelatin[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2014, 29: 385-392. doi: 10.1016/j.jmbbm.2013.09.024 pmid: 24184862
[21]	刘丽. 弹道明胶的冲击与侵彻动力学研究[D]. 杭州: 浙江大学, 2014.
	LIU L. Study on impact and penetration in ballistic gelatin[D]. Hangzhou: Zhejiang University, 2014. (in Chinese)
[22]	梁化鹏. 低侵彻弹的侵彻特性研究[D]. 南京: 南京理工大学, 2018.
	LIANG H P. Study on penetration characteristics of low penetration projectile[D]. Nanjing: Nanjing University of Science and Technology, 2018. (in Chinese)
[23]	李向东, 杜忠华. 目标易损性[M]. 北京: 北京理工大学出版社, 2021.
	LI X D, DU Z H. Target vulnerability[M]. Beijing: Beijing Institute of Technology Press, 2021. (in Chinese)
[24]	张先锋, 李向东, 沈培辉, 等. 终点效应学[M]. 北京: 北京理工大学出版社, 2017.
	ZHANG X F, LI X D, SHEN P H, et al. Terminal effects[M]. Beijing: Beijing Institute of Technology Press, 2017. (in Chinese)
[25]	李宏伟. 微小空间碎片撞击效应研究[D]. 北京: 中国科学院, 2010.
	LI H W. Research of small space debris impact effect[D]. Beijing: Chinese Academy of Sciences, 2010. (in Chinese)
[26]	HÖRMANN M, STELZMANN U, MCCARTHY M A, et al. Horizontal tailplane subjected to impact loading[C]// Proceeding of the 8th International LS-DYNA Conference. Dearborn, MI,US, 2004: 11-30.