Calculation of Impact Energy Release Based on Fragment Size Distribution for Reactive Materials

doi:10.12382/bgxb.2024.0545

Abstract

Abstract:

Aiming at the dynamic fragmentation characteristics of reactive material and its effect on the impact energy release behavior,two types of reactive materials,Al/Ti and Al/Ti/W,are selected as the research subjects.Dynamic fragment soft-recovery test is conducted to obtain the fragment size distribution characteristics of reactive material at different impact velocities.Additionally,the impact-induced energy release test is performed to analyze the impact pressure characteristics and reaction processes of Al/Ti and Al/Ti/W.Based on these investigations,a calculation method for impact pressure,which considers material fragmentation characteristics and the critical size of the reaction,is proposed.The results indicate that the fragmentation characteristics of reactive material are crucial in influencing its impact energy release behavior.The cumulative size distribution of fine fragments formed after the impact fragmentations of both Al/Ti and Al/Ti/W materials can be described using a Logistic distribution function.The impact reaction process of reactive material in a reaction chamber can be divided into primary and secondary reaction stages.The calculation error of the proposed calculation method is less than 15% when calculating the quasi-static pressure during the primary reaction stage.

Key words: Al/Ti-based reactive material, impact fragmentation, fragment distribution, energy release calculation, secondary reaction

CLC Number:

TJ012.4

ZHOU Jie, ZHAO Xufeng, PI Aiguo. Calculation of Impact Energy Release Based on Fragment Size Distribution for Reactive Materials[J]. Acta Armamentarii, 2025, 46(6): 240545-.

Figures/Tables 21

Fig.1 Sintered reactive material samples

Table 1 Basic parameters of reactive material samples

试样类型	平均质量/g	理论密度 /(g·cm^-3)	实际密度 /(g·cm^-3)
Al/Ti	2.73	4.03	3.48
Al/Ti/W	5.11	6.88	6.51

Fig.2 Micrographs of raw materials (left)and reactive material samples (right)

Fig.3 Schematic diagram of soft-recovery experimental layout

Fig.4 Schematic diagram of the soft-recovery chamber and its photograph

Fig.5 Schematic diagram of the test chamber and its photograph

Table 2 Typical photographs of recovered fragments

试样材料	速度/ (m·s^-1)	大碎片	中等碎片	小碎片	细小碎片
Al/Ti	662
Al/Ti/W	633

Fig.6 Recovered fragment masses of the samples at different impact velocities

Fig.7 Statistical results of the recovered fragments with different sizes

Fig.8 Normalized probability density distributions of fine fragments

Fig.9 The fitting results of recovery rate and impact velocity

Fig.10 The fitting results of mass fraction and impact velocitie of fine fragments

Fig.11 Normalized cumulative distribution functions (CDF) of fine fragment

Fig.12 Quasi-static pressure traces inside the reaction chamber at different impact velocities

Fig.13 The impact reaction process of Al/Ti reactive materials at 991m/s

Fig.14 The impact reaction process of Al/Ti/W reactive materials at 1022m/s

Fig.15 The processes of impact fragmentation and energy release reaction of reactive materials

Fig.16 XRD patterns of the reaction residues

Fig.17 Schematic representation of the pressure calculation model for the impact-induced energy release of reactive materials

Fig.18 Micromorphology of debris from the impact of Al/Ti reactive materials

Fig.19 Comparation of the calculated results and the measured results

References 35

[1]	杨素兰, 张皓瑞, 聂洪奇, 等. Al/Ti基纳米复合燃料热反应性及燃烧性能[J]. 兵工学报, 2023, 44(4):1118-1125.
	YANG S L, ZHANG H R, NIE H Q, et al. Thermal reactivity and combustion performances of Al /Ti-based nano-composite fuels[J]. Acta Armamentarii, 2023, 44(4):1118-1125. (in Chinese)
[2]	徐瑞泽, 肖建光, 马俊杨, 等. 活性破片高速撞击产生等离子体的毁伤效应[J]. 兵工学报, 2023, 44(12):3733-3742.
	XU R Z, XIAO J G, MA J Y, et al. Damage effect of plasma produced by high-velocity impact of reactive fragments[J]. Acta Armamentarii, 2023, 44(12):3733-3742. (in Chinese)
[3]	王在成, 徐祎, 姜春兰, 等. 钨锆钛活性破片对间隔靶的毁伤效应[J]. 兵工学报, 2023, 44(12):3862-3871.
	WANG Z C, XU Y, JIANG C L, et al. Damage effect of W/Zr/Ti reactive fragments on spaced targets[J]. Acta Armamentarii, 2023, 44(12):3862-3871. (in Chinese)
[4]	HE B, HAN Z W, WANG J Y, et al. Construction of Al@PTFE composites with excellent ignition and combustion properties through mechanical and thermal activation[J]. Journal of Alloys and Compounds, 2024, 987:174178.
[5]	MAO Y F, HE Q Q, WANG J, et al. Tuning energy output of PTFE/Al composite materials through gradient structure[J]. Defence Technology, 2023, 26:134-142.
[6]	AMES R. Energy release characteristics of impact-initiated energetic materials[J]. MRS Proceedings, 2005, 896:0896-H03-08.
[7]	AMES R. Vented chamber calorimetry for impact-initiated energetic materials[C]// Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit.Reno,NV,US:AIAA, 2005:AIAA2005-279.
[8]	CHEN C, TANG E L, ZHU W J, et al. Modified model of Al/PTFE projectile impact reaction energy release considering energy loss[J]. Experimental Thermal and Fluid Science, 2020, 116:110132.
[9]	XIONG W, ZHANG X F, TAN M T, et al. The energy release characteristics of shock-induced chemical reaction of Al/Ni composites[J]. The Journal of Physical Chemistry C, 2016, 120(43):24551-24559.
[10]	DING L L, ZHOU J Y, TANG W H, et al. Impact energy release characteristics of PTFE/Al/CuO reactive materials measured by a new energy release testing device[J]. Polymers, 2019, 11(1):149.
[11]	WANG S, KLINE J, MILES B, et al. Reactive fragment materials made from an aluminum-silicon eutectic powder[J]. Journal of Applied Physics, 2020, 128(6):065903.
[12]	HOU X W, ZHANG X F, XIONG W, et al. Study on energy release characteristics and penetration effects to concrete targets of Hf-based amorphous alloys[J]. Journal of Non-Crystalline Solids, 2022, 581:121438.
[13]	ZHOU J, ZHAO X F, WANG S H, et al. An approach to distinguish chemical and kinetic energy of reactive materials:PTFE/LiF as an inert substitute to PTFE/Al[J]. Propellants,Explosives,Pyrotechnics, 2024, 49(5):e202300307.
[14]	LIU S B, ZHENG Y F, YU Q B, et al. Interval rupturing damage to multi-spaced aluminum plates impacted by reactive materials filled projectile[J]. International Journal of Impact Engineering, 2019, 130:153-162.
[15]	XU F Y, GENG B Q, ZHANG X P, et al. Experimental study on behind-plate overpressure effect by reactive material projectile[J]. Propellants,Explosives,Pyrotechnics, 2017, 42(2):192-197.
[16]	XU F Y, YU Q B, ZHENG Y F, et al. Damage effects of double-spaced aluminum plates by reactive material projectile impact[J]. International Journal of Impact Engineering, 2017, 104:13-20.
[17]	XU F Y, ZHENG Y F, YU Q B, et al. Experimental study on penetration behavior of reactive material projectile impacting aluminum plate[J]. International Journal of Impact Engineering, 2016, 95:125-132.
[18]	YUANG Y, CAI Y Q, GUO H G, et al. Time-sequenced damage behavior of reactive projectile impacting double-layer plates[J]. Defence Technology, 2023, 27:263-272.
[19]	WANG C T, HE Y, JI C, et al. Investigation on shock-induced reaction characteristics of a Zr-based metallic glass[J]. Intermetallics, 2018, 93:383-388.
[20]	JI C, HE Y, WANG C T, et al. Effect of dynamic fragmentation on the reaction characteristics of a Zr-based metallic glass[J]. Journal of Non-Crystalline Solids, 2019, 515:149-156.
[21]	TANG M G, HOOPER J P. Impact fragmentation of a brittle metal compact[J]. Journal of Applied Physics, 2018, 123(17):175901.
[22]	KLINE J, HOOPER J P. The effect of annealing on the impact fragmentation of a pure aluminum reactive material[J]. Journal of Applied Physics, 2019, 125(20):205901.
[23]	ZHANG F, GAUTHIER M, COJOCARU C V. Dynamic fragmentation and blast from a reactive material[J]. Propellants,Explosives,Pyrotechnics, 2017, 42(9):1072-1078.
[24]	KLINE J, MASON B P, HOOPER J P. Energy release and fragmentation of brittle aluminum reactive material cases[J]. Propellants,Explosives,Pyrotechnics, 2021, 46(8):1324-1333.
[25]	BLAISDELL G L, MELENDY T D, BLAISDELL M N. Ballistic protection using snow[J]. International Journal of Impact Engineering, 2021, 155:103903.
[26]	PALMER S. Three-dimensional fragment tracking and size estimation using stereo focused shadowgraphy[D]. Socorro,NM,US: New Mexico Institute of Mining and Technology, 2022.
[27]	YOUNGBLOOD S, PALMER S, VIOLANTE D A, et al. In situ measurement of the fragmentation behavior of Al/PTFE reactive materials subjected to explosive loading,Part 1:fragment size measurements[J]. Propellants,Explosives,Pyrotechnics, 2023, 48(1):e202200103.
[28]	PALMER S, YOUNGBLOOD S, KIMBERLEY J, et al. In situ measurement of the fragmentation behavior of Al/PTFE reactive materials subjected to explosive loading,Part 2:fragment velocity and trajectory measurements[J]. Propellants,Explosives,Pyrotechnics, 2023, 48(1):e202200104.
[29]	李航. 统计学习方法[M]. 第2版. 北京: 清华大学出版社, 2019.
	LI H. Statistical learning method[M]. 2nd ed. Beijing: Tsinghua University Press, 2019. (in Chinese)
[30]	ZHAO K X, ZHANG X H, GU X R, et al. Tungsten combustion in impact initiated W-Al composite based on W(Al) super-saturated solid solution[J]. Defence Technology, 2022, 25:112-120.
[31]	GROMOV A A, PAUTOVA Y I, LIDER A M, et al. Interaction of powdery al,Zr and Ti with atmospheric nitrogen and subsequent nitride formation under the metal powder combustion in air[J]. Powder Technology, 2011, 214(2):229-236.
[32]	DREIZIN E L, SCHOENITZ M. Correlating ignition mechanisms of aluminum-based reactive materials with thermoanalytical measurements[J]. Progress in Energy and Combustion Science, 2015, 50:81-105.
[33]	WANG S, KLINE J, MILES B, et al. Reactive fragment materials made from an aluminum-silicon eutectic powder[J]. Journal of Applied Physics, 2020, 128(6):065903.
[34]	VOJTECH D, CIZOVA H, JUREK K, et al. Influence of silicon on high-temperature cyclic oxidation behaviour of titanium[J]. Journal of Alloys and Compounds, 2005, 394(1):240-249.
[35]	DEBSKI A, GASIOR W, SYPIEN A, et al. Enthalpy of formation of intermetallic phases from Al-Ni and Al-Ni-Ti systems[J]. Intermetallics, 2013, 42:92-98.