Molecular dynamics simulation of effect of temperature on void nucleation and growth of single crystal iron at a high strain rate

Wang Yun-Tian; Zeng Xiang-Guo; Yang Xin

doi:10.7498/aps.68.20190920

Abstract

In this work, we investigate the triaxial deformation of single crystal iron at a strain rate of 5 × 10^–9 s^–1 by using molecular dynamics simulation through the embedded atomic method, and thus study the temperature effect on the void nucleation and growth, and we also discuss the applicability of nucleation and growth (NAG) model in single crystal iron. The molecular dynamics model size is 28.55 nm × 28.55 nm × 28.55 nm and contains 2 × 10⁶ atoms. The results show that the maximum tensile stress of single crystal iron decreases with temperature increasing. The maximum tensile stress reduces 35.9% when temperature rises from 100 K to 1100 K. We find that at 100−700 K temperatures, there are two peaks in the tensile stress-time profile. To ascertain the origin of the double-peak in the stress-time profile, we compute the void volume fraction evolution. In addition, we conduct the dislocation analysis, radial distribution function analysis and common neighbor analysis. The analysis results show that the relaxation of tensile stress in the first peak of stress-time profile takes place through the structural change and the body-centered cubic crystal structure transforming into face-centered cubic crystal structure, hexagonal close packed crystal structure and other structures. We find that there are no voids’ nucleation in the first peak of stress-time profile. The second-peak of stress-time profile proceeds through the nucleation and growth of voids. And the rapid increase of the void volume fraction corresponds to the rapid decline of the tensile stress. The void volume evolution can be divided into three stages. With the increase of temperature, the double peak characteristic of the tensile stress-time profile disappears at 900−1100 K. While at 900−1100 K the nucleation and growth of voids are the only way to release the built-up stress. It is shown that the nucleation and growth of voids are more preferred at high temperature than at low temperature. The nucleation and growth of voids in single iron under high strain rate follow the NAG model. We calculate the best-fit NAG parameters at 100−1100 K, and analyze the sensitivity of NAG parameters to temperature. It is shown that the nucleation and growth threshold of the single crystal iron are much higher than those of mild steel. The results can be useful for developing the fracture models of iron at high strain rate to describe the dynamic damage on a continuum length scale.

Keywords:

Authors and contacts

MOE Key Laboratory of Deep Earth Science and Engineering, College of Architecture and Environment, Sichuan University, Chengdu 610065, China

Corresponding author: Zeng Xiang-Guo, xiangguozeng@scu.edu.cn

Funds: Project supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant Nos. U1430119, U1530140)

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References

[1]	朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400 Google Scholar Zhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400 Google Scholar
[2]	Remington T P, Hahn E N, Zhao S, Flanagan R, Mertens J C E, Sabbaghianrad S, Langdon T G, Wehrenberg C E, Maddox B R, Swift D C, Remington B A, Chawla N, Meyers M A 2018 Acta Mater. 158 313 Google Scholar
[3]	Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253 Google Scholar
[4]	Kanel G I, Razorenov S V, Utkin A V, Fortov V E, Baumung K, Karow H U, Rusch D, Licht V, Davison L, Graham R A 1993 J. Appl. Phys. 74 7162 Google Scholar
[5]	Antoun T, Curran D R, Razorenov S, Seaman L, Kanel G I, Utkin A V 2003 Spall Fracture (New York: Springer) pp217– 220
[6]	Molinari A, Wright T W 2005 J. Mech. Phys. Solids 53 1476 Google Scholar
[7]	席涛, 范伟, 储根柏, 税敏, 何卫华, 赵永强, 辛建婷, 谷渝秋 2017 物理学报 66 040202 Google Scholar Xi T, Fan W, Chu G B, Shui M, He W H, Zhao Y Q, Xin J T, Gu Y Q 2017 Acta Phys. Sin. 66 040202 Google Scholar
[8]	白清顺, 张凯, 沈荣琦, 张飞虎, 苗心向, 袁晓东 2018 物理学报 67 234401 Google Scholar Bai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401 Google Scholar
[9]	Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143 Google Scholar
[10]	Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663 Google Scholar
[11]	Murphy W J, Higginbotham A, Kimminau G, Barbrel B, Bringa E M, Hawreliak J, Kodama R, Koenig M, McBarron W, Meyers M A, Nagler B, Ozaki N, Park N, Remington B, Rothman S, Vinko S M, Whitcher T, Wark J S 2010 J. Phys. Condens. Matter 22 065404 Google Scholar
[12]	Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177 Google Scholar
[13]	Ashitkov S I, Komarov P S, Agranat M B, Kanel G I, Fortov V E 2013 JETP Lett. 98 384 Google Scholar
[14]	Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901 Google Scholar
[15]	Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402 Google Scholar
[16]	Gurson A L 1977 J. Eng. Mater. Technol. 99 2
[17]	Johnson J N 1981 J. Appl. Phys. 52 2812 Google Scholar
[18]	Remington B A, Bazan G, Belak J, Bringa E, Colvin J D, Edwards M J, Glendinning S G, Kalantar D H, Kumar M, Lasinski B F, Lorenz K T, McNaney J M, Pollaine S M, Rowley D, Stölken J S, Weber S V, Wolfer W G, Caturla M, Ivanov D S, Zhigilei L V 2004 Metall. Mater. Trans. A 35 2587 Google Scholar
[19]	Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393 Google Scholar
[20]	Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12 Google Scholar
[21]	Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313 Google Scholar
[22]	Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104 Google Scholar
[23]	Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401 Google Scholar
[24]	Gao N, Gao F, Wang Z G 2017 Chin. Phys. Lett. 34 172
[25]	Mayer A E 2014 Mech. Solids 49 649 Google Scholar
[26]	Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401 Google Scholar
[27]	马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404 Google Scholar Ma W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404 Google Scholar
[28]	Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113 Google Scholar
[29]	Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007 Google Scholar
[30]	Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98 Google Scholar
[31]	Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148 Google Scholar
[32]	Ikkurthi V R, Hemani H, Sugandhi R, Rawat S, Pahari P, Warrier M, Chaturvedi S 2017 Procedia Eng. 173 1177 Google Scholar
[33]	Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philos. Mag. 83 3977 Google Scholar
[34]	Zhao K, Ringdalen I G, Wu J Y, He J Y, Zhang Z L 2016 Comput. Mater. Sci. 125 36 Google Scholar
[35]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236 Google Scholar
[36]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[37]	Stukowski A 2010 Modell. Simul. Mater. Sci. Eng. 18 015012
[38]	Hemani H, Warrier M, Sakthivel N, Chaturvedi S 2014 J. Mol. Graphics Modell. 50 134 Google Scholar
[39]	Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007 Google Scholar
[40]	Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021 Google Scholar
[41]	Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55 Google Scholar
[42]	Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201 Google Scholar
[43]	Yuan F 2012 Sci. China, Ser. G 55 1657
[44]	Jensen B J, Gray G T, Hixson R S 2009 J. Appl. Phys. 105 103502 Google Scholar
[45]	Smith R F, Eggert J H, Swift D C, Wang J, Duffy T S, Braun D G, Rudd R E, Reisman D B, Davis J P, Knudson M D, Collins G W 2013 J. Appl. Phys. 114 223507 Google Scholar
[46]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681 Google Scholar
[47]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120 Google Scholar
[48]	Wang J, Yip S, Phillpot S, Wolf D 1993 Phys. Rev. Lett. 71 4182
[49]	Patriarca L, Abuzaid W, Sehitoglu H, Maier H J, Chumlyakov Y 2013 Mater. Charact. 75 165 Google Scholar
[50]	Rudd R E 2009 Philos. Mag. A 89 3133 Google Scholar
[51]	Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608 Google Scholar
[52]	Chase M W 1998 NIST-JANAF Thermochemical Tables 4th (Washington DC: American Chemical Society and American Institute of Physics for the National Institute of Standards and Technology) p1221
[53]	Seaman L, Curran D R, Shockey D A 1976 J. Appl. Phys. 47 4814 Google Scholar
[54]	Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275 Google Scholar

Cited By

图 1 单晶铁三轴拉伸模型

Figure 1. Model of single crystal iron under triaxial tension (atoms are colored by CNA).

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图 2 100—1100 K温度下拉应力随时间的变化

Figure 2. Tensile stress as a function of time at 100–1100 K.

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图 3 拉应力峰值随温度的变化

Figure 3. Relationship of peak pressure and temperature.

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图 4 100—1100 K温度下孔洞体积分数随时间的变化

Figure 4. Void volume fraction as a function of time at 100–　1100 K.

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图 5 100—1100 K温度下孔洞成核时间

Figure 5. Void nucleation time at 100–1100 K.

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图 6 100—1100 K温度下内部孔洞分布(孔洞体积分数为0.1时)

Figure 6. Distribution of voids at 100–1100 K (void volume fraction is 0.1).

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图 7 100−1100 K温度下孔洞体积分数与拉应力的关系　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 7. Void volume fraction as a function of time at 100−700 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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图 8 100−700 K温度下拉应力时程曲线第二峰值点孔洞分布

Figure 8. Void distribution on the second-peak of tensile stress at 100−700 K.

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图 9 100−1100 K温度下位错密度变化情况　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 9. Evolution of dislocation density as a function of time at 100−1100 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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图 10 100−1100 K温度下径向分布函数变化情况　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 10. Radial distribution function of the system at 100−1100 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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图 11 100−1100 K温度下内部结构变化　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 11. Snapshots for the structural changes at 100−1100 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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图 12 100−1100 K温度下内部晶体结构占比　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 12. Crystal structure fraction as a function of time at 100−1100 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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图 13 300 K温度下系统内部结构变化

Figure 13. Structural changes at different time at 300 K.

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图 14 300−1100 K温度下铁原子键能

Figure 14. Bond energy of iron at 300−1100 K.

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图 15 100−1100 K温度下系统势能

Figure 15. Potential energy of the system at 100−1100 K.

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图 16 100−1100 K温度下NAG与MD的孔洞体积分数结果的对比　(a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K

Figure 16. Comparison of void volume fraction between the NAG model and MD at 100−1100 K: (a) 100 K; (b) 300 K; (c) 500 K; (d) 700 K; (e) 900 K; (f) 1100 K.

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表 1 100—700 K温度下四个特征点时间

Table 1. Four characteristic points time at 100– 700 K.

温度/K	时间/ps
温度/K	A	B	C	D
100	15.7	16.5	17.5	19.1
300	13.4	14.5	15.4	17.9
500	12.6	13.8	14.9	17.7
700	13.1	13.9	14.6	17.6

DownLoad: CSV

表 2 100−1100 K温度下NAG模型最佳拟合参数

Table 2. Best-fit NAG parameters at 100−1100 K.

	P_n0/Pa	P₁/Pa	${\dot N_0}$/m^–3·s^–1	P_g0/Pa	η/Pa·s	R_n/m	Σ
100 K	1.61 × 10¹⁰	1.42 × 10⁷	7.10 × 10¹⁵	2.75 × 10⁹	1.72 × 10^–1	3.1 × 10^–10	0.15
300 K	1.55 × 10¹⁰	2.35 × 10⁷	1.22 × 10¹⁵	2.48 × 10⁹	2.20 × 10^–1	3.1 × 10^–10	0.18
500 K	1.51 × 10¹⁰	1.18 × 10⁷	5.91 × 10¹⁴	2.15 × 10⁹	1.83 × 10^–1	3.1 × 10^–10	0.14
700 K	1.50 × 10¹⁰	3.31 × 10⁷	1.37 × 10¹⁶	2.02 × 10⁹	2.17 × 10^–1	3.1 × 10^–10	0.17
900 K	1.46 × 10¹⁰	2.76 × 10⁷	3.29 × 10¹⁵	1.98 × 10⁹	2.53 × 10^–1	3.1 × 10^–10	0.12
1100 K	1.33 × 10¹⁰	1.87 × 10⁷	1.88 × 10¹⁴	1.95 × 10⁹	2.11 × 10^–1	3.1 × 10^–10	0.17
低碳钢^[54]	1.12 × 10⁹	1.0 × 10⁸	2.5 × 10¹⁴	2.0 × 10⁸	2.778 × 10²	3.0 × 10^–5

DownLoad: CSV

[1]	朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400 Google Scholar Zhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400 Google Scholar
[2]	Remington T P, Hahn E N, Zhao S, Flanagan R, Mertens J C E, Sabbaghianrad S, Langdon T G, Wehrenberg C E, Maddox B R, Swift D C, Remington B A, Chawla N, Meyers M A 2018 Acta Mater. 158 313 Google Scholar
[3]	Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253 Google Scholar
[4]	Kanel G I, Razorenov S V, Utkin A V, Fortov V E, Baumung K, Karow H U, Rusch D, Licht V, Davison L, Graham R A 1993 J. Appl. Phys. 74 7162 Google Scholar
[5]	Antoun T, Curran D R, Razorenov S, Seaman L, Kanel G I, Utkin A V 2003 Spall Fracture (New York: Springer) pp217– 220
[6]	Molinari A, Wright T W 2005 J. Mech. Phys. Solids 53 1476 Google Scholar
[7]	席涛, 范伟, 储根柏, 税敏, 何卫华, 赵永强, 辛建婷, 谷渝秋 2017 物理学报 66 040202 Google Scholar Xi T, Fan W, Chu G B, Shui M, He W H, Zhao Y Q, Xin J T, Gu Y Q 2017 Acta Phys. Sin. 66 040202 Google Scholar
[8]	白清顺, 张凯, 沈荣琦, 张飞虎, 苗心向, 袁晓东 2018 物理学报 67 234401 Google Scholar Bai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401 Google Scholar
[9]	Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143 Google Scholar
[10]	Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663 Google Scholar
[11]	Murphy W J, Higginbotham A, Kimminau G, Barbrel B, Bringa E M, Hawreliak J, Kodama R, Koenig M, McBarron W, Meyers M A, Nagler B, Ozaki N, Park N, Remington B, Rothman S, Vinko S M, Whitcher T, Wark J S 2010 J. Phys. Condens. Matter 22 065404 Google Scholar
[12]	Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177 Google Scholar
[13]	Ashitkov S I, Komarov P S, Agranat M B, Kanel G I, Fortov V E 2013 JETP Lett. 98 384 Google Scholar
[14]	Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901 Google Scholar
[15]	Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402 Google Scholar
[16]	Gurson A L 1977 J. Eng. Mater. Technol. 99 2
[17]	Johnson J N 1981 J. Appl. Phys. 52 2812 Google Scholar
[18]	Remington B A, Bazan G, Belak J, Bringa E, Colvin J D, Edwards M J, Glendinning S G, Kalantar D H, Kumar M, Lasinski B F, Lorenz K T, McNaney J M, Pollaine S M, Rowley D, Stölken J S, Weber S V, Wolfer W G, Caturla M, Ivanov D S, Zhigilei L V 2004 Metall. Mater. Trans. A 35 2587 Google Scholar
[19]	Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393 Google Scholar
[20]	Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12 Google Scholar
[21]	Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313 Google Scholar
[22]	Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104 Google Scholar
[23]	Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401 Google Scholar
[24]	Gao N, Gao F, Wang Z G 2017 Chin. Phys. Lett. 34 172
[25]	Mayer A E 2014 Mech. Solids 49 649 Google Scholar
[26]	Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401 Google Scholar
[27]	马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404 Google Scholar Ma W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404 Google Scholar
[28]	Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113 Google Scholar
[29]	Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007 Google Scholar
[30]	Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98 Google Scholar
[31]	Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148 Google Scholar
[32]	Ikkurthi V R, Hemani H, Sugandhi R, Rawat S, Pahari P, Warrier M, Chaturvedi S 2017 Procedia Eng. 173 1177 Google Scholar
[33]	Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philos. Mag. 83 3977 Google Scholar
[34]	Zhao K, Ringdalen I G, Wu J Y, He J Y, Zhang Z L 2016 Comput. Mater. Sci. 125 36 Google Scholar
[35]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236 Google Scholar
[36]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[37]	Stukowski A 2010 Modell. Simul. Mater. Sci. Eng. 18 015012
[38]	Hemani H, Warrier M, Sakthivel N, Chaturvedi S 2014 J. Mol. Graphics Modell. 50 134 Google Scholar
[39]	Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007 Google Scholar
[40]	Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021 Google Scholar
[41]	Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55 Google Scholar
[42]	Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201 Google Scholar
[43]	Yuan F 2012 Sci. China, Ser. G 55 1657
[44]	Jensen B J, Gray G T, Hixson R S 2009 J. Appl. Phys. 105 103502 Google Scholar
[45]	Smith R F, Eggert J H, Swift D C, Wang J, Duffy T S, Braun D G, Rudd R E, Reisman D B, Davis J P, Knudson M D, Collins G W 2013 J. Appl. Phys. 114 223507 Google Scholar
[46]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681 Google Scholar
[47]	Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120 Google Scholar
[48]	Wang J, Yip S, Phillpot S, Wolf D 1993 Phys. Rev. Lett. 71 4182
[49]	Patriarca L, Abuzaid W, Sehitoglu H, Maier H J, Chumlyakov Y 2013 Mater. Charact. 75 165 Google Scholar
[50]	Rudd R E 2009 Philos. Mag. A 89 3133 Google Scholar
[51]	Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608 Google Scholar
[52]	Chase M W 1998 NIST-JANAF Thermochemical Tables 4th (Washington DC: American Chemical Society and American Institute of Physics for the National Institute of Standards and Technology) p1221
[53]	Seaman L, Curran D R, Shockey D A 1976 J. Appl. Phys. 47 4814 Google Scholar
[54]	Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275 Google Scholar

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Vol. 68, Issue 24 - 2019-12-20

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