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				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:
										
- single crystal iron /
- void nucleation and growth /
- temperature effect /
- molecular dynamics
 [1] 朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400  Google Scholar Google ScholarZhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400  Google Scholar 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 Google Scholar[3] Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253  Google Scholar 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 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 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 Google ScholarXi 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 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 Google ScholarBai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401  Google Scholar Google Scholar[9] Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143  Google Scholar Google Scholar[10] Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663  Google Scholar 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 Google Scholar[12] Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177  Google Scholar 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 Google Scholar[14] Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901  Google Scholar Google Scholar[15] Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402  Google Scholar 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 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 Google Scholar[19] Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393  Google Scholar Google Scholar[20] Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12  Google Scholar Google Scholar[21] Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313  Google Scholar Google Scholar[22] Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104  Google Scholar Google Scholar[23] Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401  Google Scholar 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 Google Scholar[26] Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401  Google Scholar Google Scholar[27] 马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404  Google Scholar Google ScholarMa W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404  Google Scholar Google Scholar[28] Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113  Google Scholar Google Scholar[29] Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007  Google Scholar Google Scholar[30] Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98  Google Scholar Google Scholar[31] Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148  Google Scholar 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 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 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 Google Scholar[35] Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236  Google Scholar Google Scholar[36] Plimpton S 1995 J. Comput. Phys. 117 1  Google Scholar 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 Google Scholar[39] Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007  Google Scholar Google Scholar[40] Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021  Google Scholar Google Scholar[41] Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55  Google Scholar Google Scholar[42] Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201  Google Scholar 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 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 Google Scholar[46] Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681  Google Scholar Google Scholar[47] Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120  Google Scholar 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 Google Scholar[50] Rudd R E 2009 Philos. Mag. A 89 3133  Google Scholar Google Scholar[51] Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608  Google Scholar 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 Google Scholar[54] Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275  Google Scholar Google Scholar
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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 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 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. Pn0/Pa P1/Pa ${\dot N_0}$/m–3·s–1 Pg0/Pa η/Pa·s Rn/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 
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[1] 朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400  Google Scholar Google ScholarZhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400  Google Scholar 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 Google Scholar[3] Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253  Google Scholar 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 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 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 Google ScholarXi 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 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 Google ScholarBai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401  Google Scholar Google Scholar[9] Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143  Google Scholar Google Scholar[10] Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663  Google Scholar 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 Google Scholar[12] Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177  Google Scholar 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 Google Scholar[14] Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901  Google Scholar Google Scholar[15] Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402  Google Scholar 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 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 Google Scholar[19] Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393  Google Scholar Google Scholar[20] Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12  Google Scholar Google Scholar[21] Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313  Google Scholar Google Scholar[22] Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104  Google Scholar Google Scholar[23] Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401  Google Scholar 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 Google Scholar[26] Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401  Google Scholar Google Scholar[27] 马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404  Google Scholar Google ScholarMa W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404  Google Scholar Google Scholar[28] Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113  Google Scholar Google Scholar[29] Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007  Google Scholar Google Scholar[30] Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98  Google Scholar Google Scholar[31] Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148  Google Scholar 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 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 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 Google Scholar[35] Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236  Google Scholar Google Scholar[36] Plimpton S 1995 J. Comput. Phys. 117 1  Google Scholar 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 Google Scholar[39] Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007  Google Scholar Google Scholar[40] Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021  Google Scholar Google Scholar[41] Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55  Google Scholar Google Scholar[42] Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201  Google Scholar 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 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 Google Scholar[46] Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681  Google Scholar Google Scholar[47] Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120  Google Scholar 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 Google Scholar[50] Rudd R E 2009 Philos. Mag. A 89 3133  Google Scholar Google Scholar[51] Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608  Google Scholar 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 Google Scholar[54] Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275  Google Scholar Google Scholar
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