Modelling of spall damage evolution and fragment distribution for melted metals under shock release

Zhang Feng-Guo; Liu Jun; He An-Min; Zhao Fu-Qi; Wang Pei

doi:10.7498/aps.71.20221340

Abstract

A strong shock-wave, produced by plate impact, explosive detonation or laser irradiation, can induce metal materials to melt. Reflection of the triangular pressure wave from the free surface generates a strong tensile stress in the liquid state, resulting in the creation of an expanding cloud of liquid debris. This phenomenon is called micro-spalling. The understanding of spall damage evolution and dynamic fragmentation of melted metal under shockwave loading and subsequent releasing is an issue of considerable importance for both basic and applied science, to predict the evolution of engineering structures subjected to explosive detonation in implosive dynamics or inertial confinement fusion, the latter involving high energy laser irradiation of thin metallic shells. For dynamic failure processes, spall fracture in solid material has been extensively studied for many years, while scarce data can be found about how such a phenomenon can evolve after being melted partially or fully when being compressed or released. In this paper, by studying the physical laws of void evolution in melted metals, we expect to reveal the mode and criterion of void coalescence, inertial and temperature effects on void distribution and evolution, and the relationship between fragment distribution and characteristics of breakup of damaged material. According to these physical laws, we can develop theoretical model to describe the damage evolution and fragment distribution of metal that melts when shock releases. This model is implemented as a failure criterion in a one-dimensional hydrocode. The experimental results and computational results are in fairly good agreement with each other. Some discrepancies are explained by using both experimental uncertainties and model limitations which are carefully pointed out and discussed. We believe that these results can deepen our physical understanding of the damage evolutions of metals and improve the credibility of numerical simulation on the damage and fragmentation of materials under implosive loading.

Keywords:

Authors and contacts

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Corresponding author: Zhang Feng-Guo, zhang_fengguo@iapcm.ac.cn

Funds: Project supported by the Science Challenge Project (Grant No. TZ2018001) and the National Natural Science Foundation of China (Grant No. 12271054).

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References

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[41]	Wu X Y, Ramesh K T, Wright T W 2003 J. Mech. Phys. Solids 51 1 Google Scholar
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[43]	Czarnota C, Jacques N, Mercier S, Molinari A 2008 J. Mech. Phys. Solids 56 1624 Google Scholar
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[47]	张凤国, 刘军, 王裴, 胡晓棉, 周洪强, 邵建立, 冯其京 2018 爆炸与冲击 38 659 Google Scholar Zhang F G, Liu J, Wang P, Hu X M, Zhou H Q, Shao J L, Feng Q J 2018 Explos. Shock Waves 38 659 Google Scholar

Cited By

图 1 材料的卸载熔化损伤/破碎　(a)波系示意图(U_s为冲击压缩波, P为冲击压缩波峰值压力, U_T为反射稀疏波); (b)损伤/破碎过程MD模拟图; (c)熔化破碎实验结果

Figure 1. Spall damage evolution and fragment distributing for melted metals under shock release: (a) Schematic of the shock wave; (b) MD simulation of damage/fragment development; (c) abel inverted volume densities of tin target.

DownLoad: Full-Size Img PowerPoint

图 2 破碎颗粒回收实验统计结果及理论计算结果　(a) 破碎颗粒回收; (b)回收破碎颗粒统计结果及理论计算结果; (c) 现有破碎理论示意图

Figure 2. Cumulative number distribution of fragments size: (a) Three-dimensional reconstruction of tin fragments; (b) comparison between simulations and experiments; (c) schematic illustration of fragments.

DownLoad: Full-Size Img PowerPoint

图 3 含两个孔洞的六面体微单元

Figure 3. A cuboid unit cell with tow void for onset of voids coalescence.

DownLoad: Full-Size Img PowerPoint

图 4 靶板内部的压力分布

Figure 4. Pressure profiles inferred from simulations of Signo’s and our work.

DownLoad: Full-Size Img PowerPoint

图 5 自由面速度

Figure 5. Free surface velocity.

DownLoad: Full-Size Img PowerPoint

图 6 靶板内损伤分布的计算结果

Figure 6. Damage distribution in target from simulations.

DownLoad: Full-Size Img PowerPoint

图 7 材料内部的损伤、温度变化曲线

Figure 7. Evolutions of damage and temperature in target.

DownLoad: Full-Size Img PowerPoint

图 8 材料卸载熔化破碎颗粒分布的实验和模拟计算结果

Figure 8. Comparison between simulation and experimental results of decreasing cumulative number distribution of fragments size.

DownLoad: Full-Size Img PowerPoint

[1]	Shao J L, Wang C, Wang P, He A M, Zhang F G 2019 Mech. Mater. 131 78 Google Scholar
[2]	Holtkamp D B, Clark D, Rerm E, Gallegos R A, Hammon D, Hemsing W F, Hogan G E, Holmes V H, King N S P, Liljestrand R, Lopez R P, Merrill F E, Morris C L, Morley K B, Murray M M, Pazuchanics P D, Prestridge K P, Quintana J P, Saunders A, Schafer T, Shinas M A, Stacy H L 2003 AIP Conference Proceeding Shock Compression Condensed Matter, Melville, New York, July 20–25, 2003 pp477–482
[3]	Lescoute E, de Rességuier T, Chevalier J M, Loison D, Cuq-Lelandais J P, Boustie M, Breil J, Maire P H, Schurtz G 2010 J. Appl. Phys. 108 093510 Google Scholar
[4]	张林, 李英华, 张祖根, 李雪梅, 胡昌明, 蔡灵仓 2017 爆炸与冲击 37 692 Google Scholar Zhang L, Li Y H, Zhang Z G, Li X M, Hu C M, Cai L C 2017 Explos. Shock Waves 37 692 Google Scholar
[5]	陈永涛, 任国武, 汤铁钢, 胡海波 2013 物理学报 62 116202 Google Scholar Chen Y T, Ren G W, Tang T G, Hu H B 2013 Acta Phys. Sin. 62 116202 Google Scholar
[6]	陈永涛, 洪仁楷, 陈浩玉, 胡海波, 汤铁钢 2017 爆炸与冲击 37 61 Google Scholar Chen Y T, Hong R K, Chen H Y, Hu H B, Tang T G 2017 Explos. Shock Waves 37 61 Google Scholar
[7]	de Rességuier T, Signor L, Dragon A, Severin P, Boustie M 2007 J. Appl. Phys. 102 073535 Google Scholar
[8]	Signo L, de Rességuier T, Dragon A, Roy G, Fanget A, Faessel M 2010 Int. J. Impact Engi. 37 887 Google Scholar
[9]	de Rességuier T, Signor L, Dragon A, Boustie M, Berthe L 2008 Appl. Phys. Lett. 92 131910 Google Scholar
[10]	Luo S N, An Q, Germann T C, Han L B 2009 J. Appl. Phys. 106 013502 Google Scholar
[11]	Wang K, Zhang F G, He A M, Wang P 2019 J. Appl. Phys. 125 155107 Google Scholar
[12]	Zhou T T, He A, Wang P 2020 J. Nucl. Mater. 542 152496 Google Scholar
[13]	Wang X X, Sun Z Y, Zhao F Q, He A M, Zhou T T, Zhou H Q, Zhang F G, Wang P 2021 J. Appl. Phys. 130 205901 Google Scholar
[14]	Seppala E T, Belak J, Rudd R E 2004 Phys. Rev. Lett. 93 245503 Google Scholar
[15]	Strachan A, Çağın T, William A. Goddard I I I 2001 Phys. Rev. B 63 060103 Google Scholar
[16]	Durand O, Soulard L 2013 J. Appl. Phys. 114 194902 Google Scholar
[17]	张凤国, 王裴, 胡晓棉, 邵建立, 周洪强, 冯其京 2017 高压物理学报 31 280 Google Scholar Zhang F G, Wang P, Hu X M, Shao J L, Zhou H Q, Feng Q J 2017 Chin. J. High Pres. Phys. 31 280 Google Scholar
[18]	Grady D E 1988 J. Mech. Phys. Solids 36 353 Google Scholar
[19]	李英华, 张祖根, 李俊, 李牧, 张林 2014 强激光与粒子束 26 031003 Google Scholar Li Y H, Zhang Z G, Li J, Li M, Zhang L 2014 High Power Laser Particle Beams 26 031003 Google Scholar
[20]	Curran D R, Seaman L 1996 Simplified Models of Fracture and Fragmentation (New York: Springer-Verlag) pp340—365
[21]	Seaman L, Curran D R, Shockey D A 1976 J. App. Phys. 47 4814 Google Scholar
[22]	Gurson A L 1977 J. Eng. Mater. Technol. 99 2 Google Scholar
[23]	Johnson J N 1981 J. App. Phys. 52 2812 Google Scholar
[24]	Tonks D L, Thissell W R, Schwartz D S 2003 AIP Shock Compression of Condensed Matter—2003: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter Portland, Oregon, USA, July 20–25, 2003 pp507–510
[25]	Jacques N, Czarnota C, Mercier S, Molinari A 2010 Int. J. Fract. 162 159 Google Scholar
[26]	Bai Y L, Ke F J, Xia M F 1991 Acta Mech. Sin. 7 59 Google Scholar
[27]	Videau L, Combis P, Laffite S, Lescoute E, Jadaud J P, Chevalier J M, Raffestin D, Ducasse F, Patissou L, Geille A, de Resseguier T 2012 AIP Conference Proceeding 1426 1011
[28]	翟少栋, 李英华, 彭建祥, 张祖根, 叶想平, 李雪梅, 张林 2016 爆炸与冲击 36 767 Google Scholar Zhai S D, Li Y H, Peng J X, Zhang Z G, Ye X P, Li X M, Zhang L 2016 Explos. Shock Waves 36 767 Google Scholar
[29]	Chen X, Asay J R, Dwivedi S K, Field D P 2006 J. Appl. Phys. 99 023528 Google Scholar
[30]	Wilkerson J W 2017 Int. J. Plasticity 95 21 Google Scholar
[31]	Thomason P F 1999 Acta Matter. 47 3633 Google Scholar
[32]	Tonks D L, Zurek A K, Thissell W R 2003 J. De Physique IV 110 893 Google Scholar
[33]	张凤国, 周洪强, 胡晓棉, 王裴, 邵建立, 冯其京 2016 爆炸与冲击 36 596 Google Scholar Zhang F G, Zhou H Q, Hu X M, Wang P, Shao J L, Feng Q J 2016 Explos. Shock Waves 36 596 Google Scholar
[34]	Dekel E, Eliezer S, Henis Z, Moshe E 1998 J. Appl. Phys. 84 4851 Google Scholar
[35]	Cortes R 1992 Int. J. Solids Struct. 29 1339 Google Scholar
[36]	张凤国, 赵福祺, 刘军, 何安民, 王裴 2022 物理学报 71 034601 Google Scholar Zhang F G, Zhao F Q, Liu J, He A M, Wang P 2022 Acta Phys. Sin. 71 034601 Google Scholar
[37]	Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498 Google Scholar
[38]	李茂生, 陈栋泉 2001 高压物理学报 15 24 Google Scholar Li M S, Chen D Q 2001 Chin. J. High Pres. Phys. 15 24 Google Scholar
[39]	Trumel H, Hild F, Roy G, Pellegrini Y P, Denoual C 2009 J. Mech. Phys. Solids 57 1980 Google Scholar
[40]	张凤国, 周洪强, 张广财, 洪滔 2011 物理学报 60 074601 Google Scholar Zhang F G, Zhou H Q, Zhang G C, Hong T 2011 Acta Phys. Sin. 60 074601 Google Scholar
[41]	Wu X Y, Ramesh K T, Wright T W 2003 J. Mech. Phys. Solids 51 1 Google Scholar
[42]	Zhang F G, Zhou H Q, Hu J, Shao J L, Zhang G C, Hong T, He B 2012 Chin. Phys. B 21 094601 Google Scholar
[43]	Czarnota C, Jacques N, Mercier S, Molinari A 2008 J. Mech. Phys. Solids 56 1624 Google Scholar
[44]	Jacques N, Mercier S, Molinari A 2012 Int. J. Fract. 173 203 Google Scholar
[45]	Venkert A, Gudurn P R, Ravichandran G 2001 J. Eng. Mater. Technol. 123 261 Google Scholar
[46]	祁美兰, 贺红亮 2008 武汉理工大学学报 30 23 Google Scholar Qi M L, He H L 2008 J. Wuhan Univ. Technol. 30 23 Google Scholar
[47]	张凤国, 刘军, 王裴, 胡晓棉, 周洪强, 邵建立, 冯其京 2018 爆炸与冲击 38 659 Google Scholar Zhang F G, Liu J, Wang P, Hu X M, Zhou H Q, Shao J L, Feng Q J 2018 Explos. Shock Waves 38 659 Google Scholar

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