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Law and mechanism of impact velocity on spalling and fracture behavior of single crystal nickel

Wang Lu-Sheng Luo Long Liu Hao Yang Xin Ding Jun Song Kun Lu Shi-Qing Huang Xia

Citation:

Law and mechanism of impact velocity on spalling and fracture behavior of single crystal nickel

Wang Lu-Sheng, Luo Long, Liu Hao, Yang Xin, Ding Jun, Song Kun, Lu Shi-Qing, Huang Xia
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  • In order to reveal the influence of impact velocity (Up) on the spalling and fracture behavior of single crystal nickel, a non-equilibrium molecular dynamics approach is adopted to investigate the free surface velocity curve, radial distribution function, atomic crystal structures, dislocations, and void evolution process. The results show that the critical impact velocity Up for spalling behavior in single crystal nickel is 1.5 km/s, and when Up ≤ 1.5 km/s the spallation mechanism is classical spallation damage and when Up >1.5 km/s it behaves as micro-spallation damage. The pore number and distribution area, and stress distribution area under micro-spallation damage are much higher than those under classical spallation damage. The influence of impact velocity on the classical spalling damage behavior (Up ≤ 1.5 km/s) is analyzed and the corresponding spalling strength is obtained, indicating that an accident of spalling strength occurs when Up is 1.3 km/s. The spalling strength of single crystal nickel is influenced by the combined effects of stacking faults, phase transformation, and dislocation. As the nucleation and emission of dislocations increase, the spalling strength decreases. When Up < 1.3 km/s, the spalling damage is mainly due to stacking faults. When Up = 1.3 km/s, the spalling strength is mainly affected by the competition between stacking faults and phase transformation. When Up > 1.3 km/s, spalling strength is predominantly influenced by the body-centered cubic (BCC) phase transformation mechanism (transformation path: FCC → BCT → BCC). This study reveals the impact velocity-dependent patterns, mechanisms, and effects on spalling damage and fracture, providing a theoretical basis for realizing the protective application of nickel-based materials under extreme impact conditions.
      Corresponding author: Huang Xia, huangxia@cqut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12202081), the National Natural Science Foundation of Chongqing, China (Grant No. CSTB2023NSCQ-MSX0363), and the Science and Technology Research Program of Chongqing Municipal Education Commission, China (Grant No. KJQN202301117).
    [1]

    Tang Y, Wang R X, Xiao B, Zhang Z R, Li S, Qiao J W, Bai S X, Zhang Y, Liaw P K 2023 Prog. Mater. Sci. 135 101090Google Scholar

    [2]

    Arcade S, Paul J H, Juan P E, Wang H X, Oromiehie E, Prusty G B, Phillips A W, John N A S 2023 Compos. Part A-Appl. S 173 107674Google Scholar

    [3]

    Wang P F, Xu S L 2022 Advances in Experimental Impact Mechanics (Elsevier) pp41–74

    [4]

    余文韬, 黄佩珍 2018 力学学报 50 828Google Scholar

    Yu W T, Huang P Z 2018 Chin. J. Theor. Appl. Mech. 50 828Google Scholar

    [5]

    Mukherjee T, Elmer J W, Wei H L, Lienert T J, Zhang W, Kou S, DebRoy T 2023 Prog. Mater. Sci. 138 101153Google Scholar

    [6]

    Ogorodnikov V A, Mikhaĭlov A L, Burtsev V V, Lobastov S A, Erunov S V, Romanov A V, Rudnev A V, Kulakov E V, Bazarov Y B, Glushikhin V V, Kalashnik I A, Tsyganov V A, Tkachenko B I 2009 J. Exp. Theor. Phys. 109 530Google Scholar

    [7]

    Huang L Q, Wang J, Momeni A, Wang S F 2021 Trans. Nonferrous Met. Soc. China 31 2116Google Scholar

    [8]

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

    [9]

    Ren K R, Liu H Y, Ma R, Chen S, Zhang S Y, Wang R X, Chen R, Tang Y, Li S, Lu F Y 2023 J. Mater. Sci. Tech. 161 201Google Scholar

    [10]

    Luo Q S, Kitchen M, Li J B, Li W B, Li Y Z 2023 Wear 523 204779Google Scholar

    [11]

    Zhang W L, Kennedy G B, Muly K, Li P J, Thadhani N N 2020 Int. J. Impact Eng. 146 103725Google Scholar

    [12]

    Cheng J C, Chai H W, Fan G L, Li Z Q, Xie H L, Tan Z Q, Bie B X, Huang J Y, Luo S N 2020 Carbon 170 589Google Scholar

    [13]

    Ren Y, Li Z, Zhang Z Y, Zhang Z Y, Chen R, Li Z Y, Tan C W, Chen P W 2022 Mater. Sci. Eng. A 860 144320Google Scholar

    [14]

    Molinari A, Wright T W 2005 J. Mech. Phys. Solids 53 1476Google Scholar

    [15]

    Luo S N, An Q, Germann T C, Han L B 2009 J. Appl. Phys. 106 013502Google Scholar

    [16]

    Liao Y, Xiang M Z, Li G M, Wang K, Zhang X Y, Chen J 2018 Mech. Mater. 126 13Google Scholar

    [17]

    Wang Y T, Zeng X G, Yang X, Xu T L 2022 Comput. Mater. Sci. 201 110870Google Scholar

    [18]

    Liao Y, Xiang M Z, Zeng X G, Chen J 2014 Comput. Mater. Sci. 95 89Google Scholar

    [19]

    Schuler H, Mayrhofer C, Thoma K 2006 Int. J. Impact Eng. 32 1635Google Scholar

    [20]

    Li P, Wang L S, Yan S L, Meng M, Zhou Y F, Xue K M 2021 Int. J. Refract. Met. H. 94 105376Google Scholar

    [21]

    Xiang M Z, Hu H B, Chen J, Long Y 2013 Modell. Simul. Mater. Sci. Eng. 21 055005Google Scholar

    [22]

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

    [23]

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

    [24]

    Li W H, Yao X H 2016 Comput. Mater. Sci. 124 151Google Scholar

    [25]

    He L, Wang F, Zeng X G, Yang X, Qi Z P 2020 Mech. Mater. 143 103343Google Scholar

    [26]

    Chen B, Li Y L, Şopu D, Eckert J, Wu W P 2023 Int. J. Plasticity 162 103539Google Scholar

    [27]

    Jiang D D, Shao J L, Wu B, Wang P, He A M 2022 Scripta Mater. 210 114474Google Scholar

    [28]

    Xie H C, Ma Z C, Zhang W, Zhao H W, Ren L Q 2024 J. Mater. Sci. Tech. 175 72Google Scholar

    [29]

    程志达, 朱静, 孙铁昱 2011 物理学报 60 037504Google Scholar

    Cheng Z D, Zhu J, Sun T Y 2011 Acta Phys. Sin. 60 037504Google Scholar

    [30]

    徐送宁, 张林, 张彩碚, 祁阳 2007 金属学报 43 379

    Xu S N, Zhang L, Zhang C B, Qi Y 2007 Acta Metall. Sin. 43 379

    [31]

    Liu B B, Chen Y C, Guo L, Li X F, Wang K, Deng H Q, Tian Z, Hu W Y, Xiao S F, Yuan D W 2023 Int. J. Mech. Sci. 250 108330Google Scholar

    [32]

    杜欣, 袁福平, 熊启林, 张波, 阚前华, 张旭 2022 力学学报 54 2152Google Scholar

    Du X, Yuan F P, Xiong Q L, Zhang B, Kan Q H, Zhang X 2022 Chin. J. Theor. Appl. Mech. 54 2152Google Scholar

    [33]

    Chen B, Wu W P, Chen M X 2022 Comput. Mater. Sci. 202 111015Google Scholar

    [34]

    Zhou X W, Johnson R A, Wadley H N G 2004 Phys. Rev. B 69 144113Google Scholar

    [35]

    Kedharnath A, Kapoor R, Sarkar A 2021 Comput. Struct. 254 106614Google Scholar

    [36]

    Potirniche G P, Horstemeyer M F, Wagner G J, Gullett P M 2006 Int. J. Plasticity 22 257Google Scholar

    [37]

    Wang W D, Yi C L, Fan K Q 2013 Trans. Nonferrous Met. Soc. China 23 3353Google Scholar

    [38]

    周延, 蔡洋, 卢磊 2022 实验力学 37 183

    Zhou Y, Cai Y, Lu L 2022 J. Exp. Mech. 37 183

    [39]

    Jian W R, Xie Z C, Xu S Z, Yao X H, Beyerlein I J 2022 Scripta Mater. 209 114379Google Scholar

    [40]

    王云天, 曾祥国, 陈华燕, 杨鑫, 王放, 祁忠鹏 2021 爆炸与冲击 41 139Google Scholar

    Wang Y T, Zeng X G, Chen H Y, Yang X, Wang F, Qi Z P 2021 Explo. Shock Waves 41 139Google Scholar

    [41]

    杨鑫, 赵晗, 高学军, 陈臻林, 王放, 曾祥国 2023 爆炸与冲击 43 29Google Scholar

    Yang X, Zhao Han, Gao X J, Chen Z L, Wang F, Zeng X G 2023 Explo. Shock Waves 43 29Google Scholar

    [42]

    Zhou T T, He A M, Wang P, Shao J L 2019 Comput. Mater. Sci. 162 255Google Scholar

    [43]

    Thürmer D, Zhao S T, Deluigi O R, Stan C, Alhafez I A, Urbassek H M, Meyers M A, Bringa E M, Gunkelmann N 2022 J. Alloys Compd. 895 162567Google Scholar

    [44]

    王嘉楠, 伍鲍, 何安民, 吴凤超, 王裴, 吴恒安 2021 高压物理学报 35 4Google Scholar

    Wang J N, Wu B, He A M, Wu F C, Wang P, Wu H A 2021 Chin. J. High Pressure Phys. 35 4Google Scholar

    [45]

    Mescheryakov Y I, Divakov A K, Zhigacheva N I 2000 Shock Waves 10 43Google Scholar

    [46]

    Tang J F, Xiao J C, Deng L, Li W, Zhang X M, Wang L, Xiao S F, Deng H Q, Hu W Y 2018 Phys. Chem. Chem. Phys. 20 28039Google Scholar

    [47]

    Wang K, Zhu W J, Xiang M Z, Xu Y, Li G M, Chen J 2019 Modell. Simul. Mater. Sc. 27 015001Google Scholar

    [48]

    Tuler F R, Butcher B M 1984 International Journal of Fracture 26 322Google Scholar

    [49]

    裴晓阳, 彭辉, 贺红亮, 李平 2015 物理学报 64 034601Google Scholar

    Pei X Y, Peng H, He H L, Li P 2015 Acta Phys. Sin. 64 034601Google Scholar

    [50]

    Davison L, Stevens A L 1972 J. Appl. Phys. 43 988Google Scholar

    [51]

    Kanel G I, Rasorenov S V, Utkin A V 1996 High-Pressure Shock Compression of Solids II (New York: Springer-Verlag) pp1–24

    [52]

    白以龙, 柯孚久, 夏蒙棼 1991 力学学报 23 290Google Scholar

    Bai Y L, Ke F J, Xia M F 1991 Chin. J. Theor. Appl. Mech. 23 290Google Scholar

    [53]

    Qiu T, Xiong Y N, Xiao S F, Li X F, Hu W Y, Deng H Q 2017 Comput. Mater. Sci. 137 273Google Scholar

    [54]

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

  • 图 1  单晶镍冲击加载模型

    Figure 1.  Impact loading model of single crystal nickel.

    图 2  数值模拟和实验获得的单晶镍的冲击波速度Us与加载速度Up的线性关系

    Figure 2.  Linear relationship between the shock wave velocity Us and the loading velocity Up of single crystal nickel.

    图 3  不同冲击速度下单晶镍的孔洞演化过程

    Figure 3.  Void evolution of single crystal nickel at different impact velocities.

    图 4  不同冲击速度下单晶镍自由面的速度随时间演化曲线

    Figure 4.  Time evolution between simulation time and free surface velocity for the single crystal nickel under different impact velocities.

    图 5  不同冲击速度下单晶镍对应初始时刻、压缩时刻、拉伸时刻的RDF

    Figure 5.  RDF of single crystal nickel corresponding to the initial time, compression time and tensile time at different impact velocities.

    图 6  冲击速度为Up = 1.0—1.5 km/s时的自由面速度曲线和层裂强度

    Figure 6.  Free surface velocity curve and spalling strength when the impact velocity is Up = 1.0–1.5 km/s.

    图 7  模拟时间t = 5 ps时, 不同冲击速度(Up = 1.0—1.5 km/s)下单晶镍的截面微观原子构型(CNA表征)

    Figure 7.  Microscopic atomic configuration (colored by CNA) of single crystal nickel at different impact velocities (Up = 1.0–1.5 km/s) at simulation time t = 5 ps.

    图 8  模拟时间t = 5 ps时, 不同冲击速度(Up = 1.0—1.5 km/s)下单晶镍晶体结构的原子数目定量统计

    Figure 8.  Number of crystal structure atoms for the single crystal nickel under different impact velocity (Up = 1.0–1.5 km/s) at simulation time of 5 ps.

    图 9  不同冲击速度(Up = 1.0—1.5 km/s)下冲击波到达单晶镍自由面时的原子晶体构型和位错构型

    Figure 9.  Atomic crystal configuration and dislocation configuration when the shock wave reaches the free surface of single crystal nickel at different impact velocities (Up = 1.0–1.5 km/s).

    图 10  不同冲击速度(Up = 1.0—1.5 km/s)下单晶镍的位错演化过程

    Figure 10.  Dislocation evolution of single crystal nickel at different impact velocities (Up = 1.0–1.5 km/s).

    图 11  不同冲击速度(Up = 1.0—1.5 km/s)下的孔洞成核与断裂微观图

    Figure 11.  Micrographs of void nucleation and fracture under different impact velocities (Up = 1.0–1.5 km/s).

    图 12  冲击速度分别为0.9 km/s和1.25 km/s时的孔洞成核与断裂微观图

    Figure 12.  Micrographs of void nucleation and fracture at impact velocities of 0.9 km/s and 1.25 km/s.

    图 13  冲击速度为1 km/s时, 单晶镍的原子构型演化过程(CNA表征)

    Figure 13.  Evolution of atomic configuration of single crystal nickel at impact velocity of 1 km/s (CNA characterization).

    图 14  冲击作用下单晶镍中FCC→BCT→ BCC晶体转变原理

    Figure 14.  Principle of FCC→BCT→ BCC crystal transition in single crystal nickel under impact loading.

    表 1  冲击速度为Up = 1.0—1.5 km/s时的加载应力和断裂时间

    Table 1.  Loading stress and fracture time under the impact velocity of Up = 1.0–1.5 km/s.

    冲击速度 Up/(km·s–1) 加载应力 P/GPa 断裂时间 tf/ps
    1.0 53.67 3.8
    1.1 60.46 3.2
    1.2 67.49 2.4
    1.3 74.78 1.8
    1.4 82.33 1.4
    1.5 90.13 1.2
    DownLoad: CSV

    表 2  冲击速度分别为0.9 km/s和1.25 km/s时的加载应力和断裂时间

    Table 2.  Loading stress and fracture time under the impact velocity of 0.9 km/s and 1.25 km/s.

    冲击速度 Up (km/s)加载应力P/GPa断裂时间tf/ps
    0.947.135.2
    1.2569.932.0
    DownLoad: CSV
  • [1]

    Tang Y, Wang R X, Xiao B, Zhang Z R, Li S, Qiao J W, Bai S X, Zhang Y, Liaw P K 2023 Prog. Mater. Sci. 135 101090Google Scholar

    [2]

    Arcade S, Paul J H, Juan P E, Wang H X, Oromiehie E, Prusty G B, Phillips A W, John N A S 2023 Compos. Part A-Appl. S 173 107674Google Scholar

    [3]

    Wang P F, Xu S L 2022 Advances in Experimental Impact Mechanics (Elsevier) pp41–74

    [4]

    余文韬, 黄佩珍 2018 力学学报 50 828Google Scholar

    Yu W T, Huang P Z 2018 Chin. J. Theor. Appl. Mech. 50 828Google Scholar

    [5]

    Mukherjee T, Elmer J W, Wei H L, Lienert T J, Zhang W, Kou S, DebRoy T 2023 Prog. Mater. Sci. 138 101153Google Scholar

    [6]

    Ogorodnikov V A, Mikhaĭlov A L, Burtsev V V, Lobastov S A, Erunov S V, Romanov A V, Rudnev A V, Kulakov E V, Bazarov Y B, Glushikhin V V, Kalashnik I A, Tsyganov V A, Tkachenko B I 2009 J. Exp. Theor. Phys. 109 530Google Scholar

    [7]

    Huang L Q, Wang J, Momeni A, Wang S F 2021 Trans. Nonferrous Met. Soc. China 31 2116Google Scholar

    [8]

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

    [9]

    Ren K R, Liu H Y, Ma R, Chen S, Zhang S Y, Wang R X, Chen R, Tang Y, Li S, Lu F Y 2023 J. Mater. Sci. Tech. 161 201Google Scholar

    [10]

    Luo Q S, Kitchen M, Li J B, Li W B, Li Y Z 2023 Wear 523 204779Google Scholar

    [11]

    Zhang W L, Kennedy G B, Muly K, Li P J, Thadhani N N 2020 Int. J. Impact Eng. 146 103725Google Scholar

    [12]

    Cheng J C, Chai H W, Fan G L, Li Z Q, Xie H L, Tan Z Q, Bie B X, Huang J Y, Luo S N 2020 Carbon 170 589Google Scholar

    [13]

    Ren Y, Li Z, Zhang Z Y, Zhang Z Y, Chen R, Li Z Y, Tan C W, Chen P W 2022 Mater. Sci. Eng. A 860 144320Google Scholar

    [14]

    Molinari A, Wright T W 2005 J. Mech. Phys. Solids 53 1476Google Scholar

    [15]

    Luo S N, An Q, Germann T C, Han L B 2009 J. Appl. Phys. 106 013502Google Scholar

    [16]

    Liao Y, Xiang M Z, Li G M, Wang K, Zhang X Y, Chen J 2018 Mech. Mater. 126 13Google Scholar

    [17]

    Wang Y T, Zeng X G, Yang X, Xu T L 2022 Comput. Mater. Sci. 201 110870Google Scholar

    [18]

    Liao Y, Xiang M Z, Zeng X G, Chen J 2014 Comput. Mater. Sci. 95 89Google Scholar

    [19]

    Schuler H, Mayrhofer C, Thoma K 2006 Int. J. Impact Eng. 32 1635Google Scholar

    [20]

    Li P, Wang L S, Yan S L, Meng M, Zhou Y F, Xue K M 2021 Int. J. Refract. Met. H. 94 105376Google Scholar

    [21]

    Xiang M Z, Hu H B, Chen J, Long Y 2013 Modell. Simul. Mater. Sci. Eng. 21 055005Google Scholar

    [22]

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

    [23]

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

    [24]

    Li W H, Yao X H 2016 Comput. Mater. Sci. 124 151Google Scholar

    [25]

    He L, Wang F, Zeng X G, Yang X, Qi Z P 2020 Mech. Mater. 143 103343Google Scholar

    [26]

    Chen B, Li Y L, Şopu D, Eckert J, Wu W P 2023 Int. J. Plasticity 162 103539Google Scholar

    [27]

    Jiang D D, Shao J L, Wu B, Wang P, He A M 2022 Scripta Mater. 210 114474Google Scholar

    [28]

    Xie H C, Ma Z C, Zhang W, Zhao H W, Ren L Q 2024 J. Mater. Sci. Tech. 175 72Google Scholar

    [29]

    程志达, 朱静, 孙铁昱 2011 物理学报 60 037504Google Scholar

    Cheng Z D, Zhu J, Sun T Y 2011 Acta Phys. Sin. 60 037504Google Scholar

    [30]

    徐送宁, 张林, 张彩碚, 祁阳 2007 金属学报 43 379

    Xu S N, Zhang L, Zhang C B, Qi Y 2007 Acta Metall. Sin. 43 379

    [31]

    Liu B B, Chen Y C, Guo L, Li X F, Wang K, Deng H Q, Tian Z, Hu W Y, Xiao S F, Yuan D W 2023 Int. J. Mech. Sci. 250 108330Google Scholar

    [32]

    杜欣, 袁福平, 熊启林, 张波, 阚前华, 张旭 2022 力学学报 54 2152Google Scholar

    Du X, Yuan F P, Xiong Q L, Zhang B, Kan Q H, Zhang X 2022 Chin. J. Theor. Appl. Mech. 54 2152Google Scholar

    [33]

    Chen B, Wu W P, Chen M X 2022 Comput. Mater. Sci. 202 111015Google Scholar

    [34]

    Zhou X W, Johnson R A, Wadley H N G 2004 Phys. Rev. B 69 144113Google Scholar

    [35]

    Kedharnath A, Kapoor R, Sarkar A 2021 Comput. Struct. 254 106614Google Scholar

    [36]

    Potirniche G P, Horstemeyer M F, Wagner G J, Gullett P M 2006 Int. J. Plasticity 22 257Google Scholar

    [37]

    Wang W D, Yi C L, Fan K Q 2013 Trans. Nonferrous Met. Soc. China 23 3353Google Scholar

    [38]

    周延, 蔡洋, 卢磊 2022 实验力学 37 183

    Zhou Y, Cai Y, Lu L 2022 J. Exp. Mech. 37 183

    [39]

    Jian W R, Xie Z C, Xu S Z, Yao X H, Beyerlein I J 2022 Scripta Mater. 209 114379Google Scholar

    [40]

    王云天, 曾祥国, 陈华燕, 杨鑫, 王放, 祁忠鹏 2021 爆炸与冲击 41 139Google Scholar

    Wang Y T, Zeng X G, Chen H Y, Yang X, Wang F, Qi Z P 2021 Explo. Shock Waves 41 139Google Scholar

    [41]

    杨鑫, 赵晗, 高学军, 陈臻林, 王放, 曾祥国 2023 爆炸与冲击 43 29Google Scholar

    Yang X, Zhao Han, Gao X J, Chen Z L, Wang F, Zeng X G 2023 Explo. Shock Waves 43 29Google Scholar

    [42]

    Zhou T T, He A M, Wang P, Shao J L 2019 Comput. Mater. Sci. 162 255Google Scholar

    [43]

    Thürmer D, Zhao S T, Deluigi O R, Stan C, Alhafez I A, Urbassek H M, Meyers M A, Bringa E M, Gunkelmann N 2022 J. Alloys Compd. 895 162567Google Scholar

    [44]

    王嘉楠, 伍鲍, 何安民, 吴凤超, 王裴, 吴恒安 2021 高压物理学报 35 4Google Scholar

    Wang J N, Wu B, He A M, Wu F C, Wang P, Wu H A 2021 Chin. J. High Pressure Phys. 35 4Google Scholar

    [45]

    Mescheryakov Y I, Divakov A K, Zhigacheva N I 2000 Shock Waves 10 43Google Scholar

    [46]

    Tang J F, Xiao J C, Deng L, Li W, Zhang X M, Wang L, Xiao S F, Deng H Q, Hu W Y 2018 Phys. Chem. Chem. Phys. 20 28039Google Scholar

    [47]

    Wang K, Zhu W J, Xiang M Z, Xu Y, Li G M, Chen J 2019 Modell. Simul. Mater. Sc. 27 015001Google Scholar

    [48]

    Tuler F R, Butcher B M 1984 International Journal of Fracture 26 322Google Scholar

    [49]

    裴晓阳, 彭辉, 贺红亮, 李平 2015 物理学报 64 034601Google Scholar

    Pei X Y, Peng H, He H L, Li P 2015 Acta Phys. Sin. 64 034601Google Scholar

    [50]

    Davison L, Stevens A L 1972 J. Appl. Phys. 43 988Google Scholar

    [51]

    Kanel G I, Rasorenov S V, Utkin A V 1996 High-Pressure Shock Compression of Solids II (New York: Springer-Verlag) pp1–24

    [52]

    白以龙, 柯孚久, 夏蒙棼 1991 力学学报 23 290Google Scholar

    Bai Y L, Ke F J, Xia M F 1991 Chin. J. Theor. Appl. Mech. 23 290Google Scholar

    [53]

    Qiu T, Xiong Y N, Xiao S F, Li X F, Hu W Y, Deng H Q 2017 Comput. Mater. Sci. 137 273Google Scholar

    [54]

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

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Metrics
  • Abstract views:  1459
  • PDF Downloads:  45
  • Cited By: 0
Publishing process
  • Received Date:  04 February 2024
  • Accepted Date:  07 July 2024
  • Available Online:  17 July 2024
  • Published Online:  20 August 2024

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