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).

FullText HTML : translate this paragraph

References

[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 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 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 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 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 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

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

map

[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 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 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 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 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 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

[1]	Zhang Feng-Guo, Zhao Fu-Qi, Liu Jun, He An-Min, Wang Pei. Dependence of spallstrength on temperature, grain size and strain rate in pure ductile metals. Acta Physica Sinica, 2022, 71(3): 034601. doi: 10.7498/aps.71.20210702
[2]	. Spall strength dependence on temperature, grain size and strain rate in pure ductile metals. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20210702
[3]	Lin Qian, Xie Pu-Chu, Hu Jian-Bo, Zhang Feng-Guo, Wang Pei, Wang Yong-Gang. Numerical simulation on dynamic damage evolution of high pure copper with different grain sizes. Acta Physica Sinica, 2021, 70(20): 204601. doi: 10.7498/aps.70.20210726
[4]	Xie Wen-Tao, Li Ruo-Ru, Peng Zheng, Jiang Yi-Min. Maximum ceasing angle of inclination andflux formula for granular orifice flow in water. Acta Physica Sinica, 2020, 69(10): 104501. doi: 10.7498/aps.69.20200217
[5]	Zhang Feng-Guo, Liu Jun, He An-Min, Wang Pei, Wang Kun, Zhou Hong-Qiang, Zhao Fu-Qi. Method of determining parameters of void growth damage model and its application to simulation of spall test. Acta Physica Sinica, 2020, 69(20): 204601. doi: 10.7498/aps.69.20200527
[6]	Zhou Yi-Xian. Analysis of the granular pressure and velocity field of hourglass flow based on the local constitutive law. Acta Physica Sinica, 2019, 68(13): 134701. doi: 10.7498/aps.68.20182205
[7]	Xu Min, Shen Jin, Huang Yu, Xu Ya-Nan, Zhu Xin-Jun, Wang Ya-Jing, Liu Wei, Gao Ming-Liang. Weighting inversion of dynamic light scattering based on particle-size information distribution character. Acta Physica Sinica, 2018, 67(13): 134201. doi: 10.7498/aps.67.20172377
[8]	Xin Jian-Ting, Zhao Yong-Qiang, Chu Gen-Bai, Xi Tao, Shui Min, Fan Wei, He Wei-Hua, Gu Yu-Qiu. Experimental investigation of tin fragments mixing with gas subjected to laser driven shock. Acta Physica Sinica, 2017, 66(18): 186201. doi: 10.7498/aps.66.186201
[9]	Pei Xiao-Yang, Peng Hui, He Hong-Liang, Li Ping. Discussion on the physical meaning of free surface velocity curve in ductile spallation. Acta Physica Sinica, 2015, 64(3): 034601. doi: 10.7498/aps.64.034601
[10]	Peng Hui, Pei Xiao-Yang, Li Ping, He Hong-Liang, Bai Jin-Song. Micro-damage characteristics of incipient spall in high-purity copper. Acta Physica Sinica, 2015, 64(21): 216201. doi: 10.7498/aps.64.216201
[11]	Zhang Feng-Guo, Zhou Hong-Qiang. Effects of grain size on the dynamic tensile damage of ductile polycrystalline metall. Acta Physica Sinica, 2013, 62(16): 164601. doi: 10.7498/aps.62.164601
[12]	Chen Yong-Tao, Ren Guo-Wu, Tang Tie-Gang, Hu Hai-Bo. Experimental diagnostic of melting fragments under explosive loading. Acta Physica Sinica, 2013, 62(11): 116202. doi: 10.7498/aps.62.116202
[13]	Tan Ye, Yu Yu-Ying, Dai Cheng-Da, Yu Ji-Dong, Wang Qing-Song, Tan Hua. Release melting of bismuth. Acta Physica Sinica, 2013, 62(3): 036401. doi: 10.7498/aps.62.036401
[14]	Sun Zhan-Feng, He Hong-Liang, Li Ping, Li Qing-Zhong. The spall strength and shock compressive damage of AD95 ceramics. Acta Physica Sinica, 2012, 61(9): 096201. doi: 10.7498/aps.61.096201
[15]	Yu Quan-Zhi, Yin Wen, Liang Tian-Jiao. Calculation and analysis of DPA in the main components of CSNS target station. Acta Physica Sinica, 2011, 60(5): 052501. doi: 10.7498/aps.60.052501
[16]	Wang Yong-Gang, Hu Jian-Dong, Qi Mei-Lan, He Hong-Liang. Simulation of incipient spallation experiments of high purity aluminum based on a single void growth model. Acta Physica Sinica, 2011, 60(12): 126201. doi: 10.7498/aps.60.126201
[17]	Peng Zheng, Jiang Yi-Min. Maximum ceasing angle of inclination and flux formula for granular orifice flow. Acta Physica Sinica, 2011, 60(5): 054501. doi: 10.7498/aps.60.054501
[18]	Zhang Feng-Guo, Zhou Hong-Qiang, Zhang Guang-Cai, Hong Tao. Inertial and elastic-plastic effect on spallationdamage of ductile metals. Acta Physica Sinica, 2011, 60(7): 074601. doi: 10.7498/aps.60.074601
[19]	Xiong Jun－jiang, Gao Zhen－tong, Liu Xian－bin, Sun Xun－fang. On Stochastic Bifurcation Behavior of the Atom Movement at the Tip of a Crack in Fatigue Damage System. Acta Physica Sinica, 2000, 49(1): 49-53. doi: 10.7498/aps.49.49
[20]	ZI JIAN, ZHANG KAI-MING. THE VIBRATIONAL PROPERTIES AND MELTING TEMPERATURES OF SMALL Si CLUSTERS. Acta Physica Sinica, 1989, 38(2): 343-348. doi: 10.7498/aps.38.343

Catalog

Vol. 71, Issue 24 - 2022-12-20

Metrics

Abstract views: 3186
PDF Downloads: 65
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板