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高应变率下温度对单晶铁中孔洞成核与生长影响的分子动力学研究

王云天 曾祥国 杨鑫

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高应变率下温度对单晶铁中孔洞成核与生长影响的分子动力学研究

王云天, 曾祥国, 杨鑫

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
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  • 采用嵌入原子势的分子动力学模拟方法, 研究了5 × 109 s–1应变率下, 温度效应对单晶铁中孔洞成核与生长的影响, 并对NAG (nucleation and growth)模型在单晶铁中的适用性进行了探讨. 结果表明: 随着温度的升高, 单晶铁的抗拉强度峰值降低, 1100 K温度下单晶铁抗拉强度峰值比100 K温度下降低了35.9%. 在100—700 K温度下, 拉应力时程曲线表现出双峰值特点, 分析表明, 第一峰值是由于拉应力升高引起内部结构发生相变而产生, 第二峰值则是因发生孔洞成核与生长而产生; 900—1100 K温度下, 拉应力时程曲线表现为单峰值, 孔洞成核与生长是拉应力下降的主要原因. 分析发现, 孔洞在高温下更容易成核, 高应变率下单晶铁中孔洞成核与生长和NAG模型有较好的符合度, 单晶铁中孔洞成核阈值与生长阈值都远高于低碳钢, 并且孔洞成核阈值与生长阈值随着温度的升高而逐渐降低. 研究结果可为建立高应变率下金属材料动态损伤演化模型提供借鉴.
    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.
      通信作者: 曾祥国, xiangguozeng@scu.edu.cn
    • 基金项目: 国家自然科学基金委员会-中国工程物理研究院联合基金(批准号: U1430119, U1530140)资助的课题
      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)
    [1]

    朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400Google Scholar

    Zhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400Google 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 313Google Scholar

    [3]

    Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253Google 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 7162Google 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 1476Google 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 040202Google 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 040202Google 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 234401Google Scholar

    Bai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401Google Scholar

    [9]

    Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143Google Scholar

    [10]

    Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663Google 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 065404Google Scholar

    [12]

    Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177Google Scholar

    [13]

    Ashitkov S I, Komarov P S, Agranat M B, Kanel G I, Fortov V E 2013 JETP Lett. 98 384Google Scholar

    [14]

    Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901Google Scholar

    [15]

    Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402Google Scholar

    [16]

    Gurson A L 1977 J. Eng. Mater. Technol. 99 2

    [17]

    Johnson J N 1981 J. Appl. Phys. 52 2812Google 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 2587Google Scholar

    [19]

    Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393Google Scholar

    [20]

    Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12Google Scholar

    [21]

    Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313Google Scholar

    [22]

    Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104Google Scholar

    [23]

    Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401Google Scholar

    [24]

    Gao N, Gao F, Wang Z G 2017 Chin. Phys. Lett. 34 172

    [25]

    Mayer A E 2014 Mech. Solids 49 649Google Scholar

    [26]

    Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401Google Scholar

    [27]

    马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404Google Scholar

    Ma W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404Google Scholar

    [28]

    Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113Google Scholar

    [29]

    Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007Google Scholar

    [30]

    Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98Google Scholar

    [31]

    Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148Google Scholar

    [32]

    Ikkurthi V R, Hemani H, Sugandhi R, Rawat S, Pahari P, Warrier M, Chaturvedi S 2017 Procedia Eng. 173 1177Google Scholar

    [33]

    Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philos. Mag. 83 3977Google Scholar

    [34]

    Zhao K, Ringdalen I G, Wu J Y, He J Y, Zhang Z L 2016 Comput. Mater. Sci. 125 36Google Scholar

    [35]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236Google Scholar

    [36]

    Plimpton S 1995 J. Comput. Phys. 117 1Google 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 134Google Scholar

    [39]

    Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007Google Scholar

    [40]

    Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021Google Scholar

    [41]

    Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55Google Scholar

    [42]

    Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201Google 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 103502Google 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 223507Google Scholar

    [46]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681Google Scholar

    [47]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120Google 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 165Google Scholar

    [50]

    Rudd R E 2009 Philos. Mag. A 89 3133Google Scholar

    [51]

    Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608Google 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 4814Google Scholar

    [54]

    Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275Google Scholar

  • 图 1  单晶铁三轴拉伸模型

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

    图 2  100—1100 K温度下拉应力随时间的变化

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

    图 3  拉应力峰值随温度的变化

    Fig. 3.  Relationship of peak pressure and temperature.

    图 4  100—1100 K温度下孔洞体积分数随时间的变化

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

    图 5  100—1100 K温度下孔洞成核时间

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

    图 6  100—1100 K温度下内部孔洞分布(孔洞体积分数为0.1时)

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

    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

    Fig. 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.

    图 8  100−700 K温度下拉应力时程曲线第二峰值点孔洞分布

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

    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

    Fig. 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.

    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

    Fig. 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.

    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

    Fig. 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.

    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

    Fig. 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.

    图 13  300 K温度下系统内部结构变化

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

    图 14  300−1100 K温度下铁原子键能

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

    图 15  100−1100 K温度下系统势能

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

    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

    Fig. 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.

    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
    ABCD
    10015.716.517.519.1
    30013.414.515.417.9
    50012.613.814.917.7
    70013.113.914.617.6
    下载: 导出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.

    Pn0/PaP1/Pa${\dot N_0}$/m–3·s–1Pg0/Paη/Pa·sRn/mΣ
    100 K1.61 × 10101.42 × 1077.10 × 10152.75 × 1091.72 × 10–13.1 × 10–100.15
    300 K1.55 × 10102.35 × 1071.22 × 10152.48 × 1092.20 × 10–13.1 × 10–100.18
    500 K1.51 × 10101.18 × 1075.91 × 10142.15 × 1091.83 × 10–13.1 × 10–100.14
    700 K1.50 × 10103.31 × 1071.37 × 10162.02 × 1092.17 × 10–13.1 × 10–100.17
    900 K1.46 × 10102.76 × 1073.29 × 10151.98 × 1092.53 × 10–13.1 × 10–100.12
    1100 K1.33 × 10101.87 × 1071.88 × 10141.95 × 1092.11 × 10–13.1 × 10–100.17
    低碳钢[54]1.12 × 1091.0 × 1082.5 × 10142.0 × 1082.778 × 1023.0 × 10–5
    下载: 导出CSV
  • [1]

    朱建士, 胡晓棉, 王裴, 陈军, 许爱国 2010 力学进展 40 400Google Scholar

    Zhu J S, Hu X M, Wang P, Chen J, Xu A G 2010 Adv. Mech. 40 400Google 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 313Google Scholar

    [3]

    Curran D R, Seaman L, Shockey D A 1987 Phys. Rep. 147 253Google 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 7162Google 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 1476Google 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 040202Google 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 040202Google 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 234401Google Scholar

    Bai Q S, Zhang K, Shen R Q, Zhang F H, Miao X X, Yuan X D 2018 Acta Phys. Sin. 67 234401Google Scholar

    [9]

    Lee O S, Choi H B, Kim H M 2011 J. Mech. Sci. Technol. 25 143Google Scholar

    [10]

    Minich R W, Cazamias J U, Kumar M, Schwartz A J 2004 Metall. Mater. Trans. A 35 2663Google 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 065404Google Scholar

    [12]

    Li Y, Guo Y, Hu H, Wei Q 2009 Int. J. Impact Eng. 36 177Google Scholar

    [13]

    Ashitkov S I, Komarov P S, Agranat M B, Kanel G I, Fortov V E 2013 JETP Lett. 98 384Google Scholar

    [14]

    Zaretsky E B, Kanel G I 2015 J. Appl. Phys. 117 195901Google Scholar

    [15]

    Chen Y T, Tang X J, Li Q Z 2010 Chin. Phys. B 19 056402Google Scholar

    [16]

    Gurson A L 1977 J. Eng. Mater. Technol. 99 2

    [17]

    Johnson J N 1981 J. Appl. Phys. 52 2812Google 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 2587Google Scholar

    [19]

    Rawat S, Raole P M 2018 Comput. Mater. Sci. 154 393Google Scholar

    [20]

    Liao Y, Xiang M, Zeng X, Chen J 2015 Mech. Mater. 84 12Google Scholar

    [21]

    Hahn E N, Germann T C, Ravelo R, Hammerberg J E, Meyers M A 2017 Acta Mater. 126 313Google Scholar

    [22]

    Wang H, Gao N, Lv G H, Yao Z W 2018 Chin. Phys. B 27 066104Google Scholar

    [23]

    Wang Y C, Zhang Y, Kawazoe Y, Shen J, Cao C D 2018 Chin. Phys. B 27 116401Google Scholar

    [24]

    Gao N, Gao F, Wang Z G 2017 Chin. Phys. Lett. 34 172

    [25]

    Mayer A E 2014 Mech. Solids 49 649Google Scholar

    [26]

    Shao J L, Wang P, Zhang F G, He A M 2018 J. Phys. Condens. Matter 30 255401Google Scholar

    [27]

    马文, 祝文军, 张亚林, 经福谦 2011 物理学报 60 066404Google Scholar

    Ma W, Zhu W J, Zhang Y L, Jing F Q 2011 Acta Phys. Sin. 60 066404Google Scholar

    [28]

    Sugandhi R, Warrier M, Chaturvedi S 2015 Appl. Soft Comput. 35 113Google Scholar

    [29]

    Rawat S, Warrier M, Chaturvedi S, Chavan V M 2011 Modell. Simul. Mater. Sci. Eng. 19 025007Google Scholar

    [30]

    Yang X, Zeng X G, Wang J, Wang J B, Wang F, Ding J 2019 Mech. Mater. 135 98Google Scholar

    [31]

    Rudd R E, Belak J F 2002 Comput. Mater. Sci. 24 148Google Scholar

    [32]

    Ikkurthi V R, Hemani H, Sugandhi R, Rawat S, Pahari P, Warrier M, Chaturvedi S 2017 Procedia Eng. 173 1177Google Scholar

    [33]

    Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philos. Mag. 83 3977Google Scholar

    [34]

    Zhao K, Ringdalen I G, Wu J Y, He J Y, Zhang Z L 2016 Comput. Mater. Sci. 125 36Google Scholar

    [35]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2006 AIP Conf. Proc. 845 236Google Scholar

    [36]

    Plimpton S 1995 J. Comput. Phys. 117 1Google 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 134Google Scholar

    [39]

    Stukowski A, Bulatov V V, Arsenlis A 2012 Modell. Simul. Mater. Sci. Eng. 20 085007Google Scholar

    [40]

    Stukowski A 2012 Modell. Simul. Mater. Sci. Eng. 20 045021Google Scholar

    [41]

    Dingley D J, Hale K F 1966 Proc. R. Soc. London, Ser. A 295 55Google Scholar

    [42]

    Xie H, Yu T, Fang W, Yin F, Khan D F 2016 Chin. Phys. B 25 126201Google 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 103502Google 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 223507Google Scholar

    [46]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2002 Science 296 1681Google Scholar

    [47]

    Kadau K, Germann T C, Lomdahl P S, Holian B L 2005 Phys. Rev. B 72 064120Google 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 165Google Scholar

    [50]

    Rudd R E 2009 Philos. Mag. A 89 3133Google Scholar

    [51]

    Eberhart J G, Horner S 2010 J. Chem. Educ. 87 608Google 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 4814Google Scholar

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    Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Eng. 30 275Google Scholar

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出版历程
  • 收稿日期:  2019-06-14
  • 修回日期:  2019-10-09
  • 上网日期:  2019-11-27
  • 刊出日期:  2019-12-01

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