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Stability analysis of interfacial Richtmyer-Meshkov flow of explosion-driven copper interface

Yin Jian-Wei Pan Hao Wu Zi-Hui Hao Peng-Cheng Duan Zhuo-Ping Hu Xiao-Mian

Stability analysis of interfacial Richtmyer-Meshkov flow of explosion-driven copper interface

Yin Jian-Wei, Pan Hao, Wu Zi-Hui, Hao Peng-Cheng, Duan Zhuo-Ping, Hu Xiao-Mian
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  • In this paper, a stability analysis is given to study the unstable mechanism of the Richtmyer-Meshkov flow of explosion-driven copper interface. The Richtmyer-Meshkov flow refers as an interfacial instability growth under shockwave incident loading. Numerical investigations are performed to check the applicability of the two-dimensional hydrocode, which is named AFE2D, and the physical models of detonation waves propagating in the high explosives, equations of state and the constitutive behaviors of solids in the analysis of Richtmyer-Meshkov flow problems. Here we theoretically analyze the two key issues of the unstable mechanism in Richtmyer-Meshkov flow in solids. The unstable mechanism includes temperature related melting mechanism and the plastic evolution related tensile fracture mechanism. In the analysis of the temperature related unstable mechanisms, the calculated temperature increase during the shockwave compression from the shock Hugoniot data in the shockwave physics is not enough to melt the material near the perturbed interface. On the other hand, the temperature increase from the translation of plastic work during perturbation growth which relats to the distribution of the cumulative effective plastic strain is also not enough to supply the thermal energy which is needed to melt the crystal lattice of solid, either. Therefore, the temperature related melting mechanism is not the main factor of the unstable growth of copper interface under explosion driven. In the analysis of the plastic tensile fracture related unstable mechanism, a scaling law between the maximum cumulative effective plastic strain and the scaled maximum amplitude of spikes is proposed to describe the relationship between the plastic deformation of material and the perturbation growth of interface. Combined with a critical plastic strain fracture criterion, the unstable condition of the scaled maximum amplitude of spikes is given. If the spikes grow sufficiently to meet the unstable condition, the interfacial growth will be unstable. Numerical simulations with varying initial configurations of perturbation and yield strength of materials show good agreement with the theoretical stability analysis. Finally, a criterion to judging whether the growth is stable is discussed in the form of competition between the temperature related unstable mechanism and the tensile fracture unstable mechanism.
      Corresponding author: Hu Xiao-Mian, hu_xiaomian@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11602029).
    [1]

    Brouillette M 2002 Annu. Rev. Fluid Mech. 34 445

    [2]

    Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297

    [3]

    Meshkov E E 1969 Sovit. Fluid Dyn. 4 151

    [4]

    Rajan D, Oakley J, Bonazza 2011 Annu. Rev. Fluid Mech. 43 117

    [5]

    Luo X S, Guan B, Zhai Z G, Si T 2016 Phys. Rev. E 93 023110

    [6]

    Jacobs J W 1993 Phys. Fluids A 5 2239

    [7]

    Luo X S, Zhai Z G, Si T, Yang J M 2014 Adv. Mech. 44 201407 (in Chinese)[罗喜胜, 翟志刚, 司廷, 杨基明2014力学进展44 201407]

    [8]

    Zou L Y, Liu J H, Liao S F, Zheng X X, Zhai Z Z, Luo X S 2017 Phys. Rev. E 95 013107

    [9]

    Lindl J D, Landen O, Edwards J, Moses E, NIC Team 2014 Phys. Plasmas 21 020501

    [10]

    Plohr J N, Plohr B J 2005 J. Fluid Mech. 537 55

    [11]

    Mikaelian K O 2013 Phys. Rev. E 87 031003

    [12]

    Piriz A R, Lopez Cela J J, Tahir N A, Hoffmann D H H 2008 Phys. Rev. E 78 056401

    [13]

    Yin J W, Pan H, Wu Z H, Hao P C, Hu X M 2017 Acta Phys. Sin. 66 074701 (in Chinese)[殷建伟, 潘昊, 吴子辉, 郝鹏程, 胡晓棉2017物理学报66 074701]

    [14]

    Dimonte G, Terrones G, Cheren F J, Germann T C, Dunpont V, Kadau K, Buttler W T, Oro D M, Morris C, Preston D L 2011 Phys. Rev. Lett. 107 264502

    [15]

    Buttler W T, Or D M, Preston D L, Mikaelian K O, Cherne F J, Hixson R S, Mariam F G, Morris C, Stone J B, Terrones G, Tupa D 2012 J. Fluid Mech. 703 60

    [16]

    Jensen B J, Cheren F J, Prime M B, Fezzaa K, Iverson A J, Carlson C A, Yeager J D, Ramos K J, Hooks D E, Cooley J C, Dimonte G 2015 J. Appl. Phys. 118 195903

    [17]

    Dimonte G, Terrones G, Cherne F J, Ramaprabhu P 2013 J. Appl. Phys. 113 024905

    [18]

    Buttler W T, Or D M, Olsen R T, Cheren F J, Hammerberg J E, Hixson R S, Monfared S K, Pack C L, Rigg P A, Stone J B, Terrones G 2014 J. Appl. Phys. 116 103519

    [19]

    Karkhanis V, Ramaprabhu P, Buttler W T, Hammerberg J E, Cherne F J, Andrews M J 2017 J. Dynamic Behavior Mater. 3 265

    [20]

    Chen Y T, Hong R K, Chen H Y, Ren G W 2016 Acta Phys. Sin. 65 026201 (in Chinese)[陈永涛, 洪仁楷, 陈浩玉, 任国武2016物理学报65 026201]

    [21]

    Rousculp C L, Or D M, Griego J R, Turchi P J, Reinovsky R E, Bradley J T Ⅲ, Cheng B L, Freeman M S, Patten A R 2016 Los Alamos National Laboratory Report No. LA-UR-16-21901

    [22]

    Benson D J 1992 Comput. Methods Appl. Mech. Engrg. 99 235

    [23]

    Wilkins M L 1999 Computer Simulation of Dynamic Phenomena (Berlin Heidelberg:Springer-Verlag)

    [24]

    Sun Z F, Xu H, Li Q Z, Zhang C Y 2010 Chin. J. High Pressure Phys. 24 55 (in Chinese)[孙占峰, 徐辉, 李庆忠, 张崇玉2010高压物理学报24 55]

    [25]

    Liu H F, Song H F, Zhang Q L, Zhang G M, Zhao Y H 2016 Matter Radiat. Extrem. 1 123

    [26]

    Wouchuk J G, Sano T 2015 Phys. Rev. E 91 023005

    [27]

    Mikaelian K O 1994 Phys. Fluids 6 356

    [28]

    Monfared S K, Or D M, Hammerberg J E, LaLone B M, Park C L, Schauer M M, Stevens G D, Stone J B, Turley W D, Buttler W T 2014 J. Appl. Phys. 116 063504

    [29]

    Chen Y T, Ren G W, Tang T G, Hu H B 2013 Acta Phys. Sin. 62 116202 (in Chinese)[陈永涛, 任国武, 汤铁钢, 胡海波2013物理学报62 116202]

    [30]

    Steinberg D J 1996 Lawrence Livermore National Laboratory Report No. UCRL-MA-106439

    [31]

    Marsh S P 1980 LASL Shock Hugoniot Data (Berkeley:University of California Press)

    [32]

    Tang W H, Zhang R Q 2008 Introduction to Theory and Computational of Equation of State (2nd Ed.) (Beijing:Higher Education Press) p237(in Chinese)[汤文辉, 张若棋2008物态方程理论及计算概论(第二版) (北京:高等教育出版社)第237页]

    [33]

    Gao C Y, Zhang L C 2012 Int. J. Plast. 32-33 121

    [34]

    Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498

    [35]

    Johnson G R, Cook W H 1985 Eng. Fract. Mech. 21 31

    [36]

    Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Engrg. 30 275

  • [1]

    Brouillette M 2002 Annu. Rev. Fluid Mech. 34 445

    [2]

    Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297

    [3]

    Meshkov E E 1969 Sovit. Fluid Dyn. 4 151

    [4]

    Rajan D, Oakley J, Bonazza 2011 Annu. Rev. Fluid Mech. 43 117

    [5]

    Luo X S, Guan B, Zhai Z G, Si T 2016 Phys. Rev. E 93 023110

    [6]

    Jacobs J W 1993 Phys. Fluids A 5 2239

    [7]

    Luo X S, Zhai Z G, Si T, Yang J M 2014 Adv. Mech. 44 201407 (in Chinese)[罗喜胜, 翟志刚, 司廷, 杨基明2014力学进展44 201407]

    [8]

    Zou L Y, Liu J H, Liao S F, Zheng X X, Zhai Z Z, Luo X S 2017 Phys. Rev. E 95 013107

    [9]

    Lindl J D, Landen O, Edwards J, Moses E, NIC Team 2014 Phys. Plasmas 21 020501

    [10]

    Plohr J N, Plohr B J 2005 J. Fluid Mech. 537 55

    [11]

    Mikaelian K O 2013 Phys. Rev. E 87 031003

    [12]

    Piriz A R, Lopez Cela J J, Tahir N A, Hoffmann D H H 2008 Phys. Rev. E 78 056401

    [13]

    Yin J W, Pan H, Wu Z H, Hao P C, Hu X M 2017 Acta Phys. Sin. 66 074701 (in Chinese)[殷建伟, 潘昊, 吴子辉, 郝鹏程, 胡晓棉2017物理学报66 074701]

    [14]

    Dimonte G, Terrones G, Cheren F J, Germann T C, Dunpont V, Kadau K, Buttler W T, Oro D M, Morris C, Preston D L 2011 Phys. Rev. Lett. 107 264502

    [15]

    Buttler W T, Or D M, Preston D L, Mikaelian K O, Cherne F J, Hixson R S, Mariam F G, Morris C, Stone J B, Terrones G, Tupa D 2012 J. Fluid Mech. 703 60

    [16]

    Jensen B J, Cheren F J, Prime M B, Fezzaa K, Iverson A J, Carlson C A, Yeager J D, Ramos K J, Hooks D E, Cooley J C, Dimonte G 2015 J. Appl. Phys. 118 195903

    [17]

    Dimonte G, Terrones G, Cherne F J, Ramaprabhu P 2013 J. Appl. Phys. 113 024905

    [18]

    Buttler W T, Or D M, Olsen R T, Cheren F J, Hammerberg J E, Hixson R S, Monfared S K, Pack C L, Rigg P A, Stone J B, Terrones G 2014 J. Appl. Phys. 116 103519

    [19]

    Karkhanis V, Ramaprabhu P, Buttler W T, Hammerberg J E, Cherne F J, Andrews M J 2017 J. Dynamic Behavior Mater. 3 265

    [20]

    Chen Y T, Hong R K, Chen H Y, Ren G W 2016 Acta Phys. Sin. 65 026201 (in Chinese)[陈永涛, 洪仁楷, 陈浩玉, 任国武2016物理学报65 026201]

    [21]

    Rousculp C L, Or D M, Griego J R, Turchi P J, Reinovsky R E, Bradley J T Ⅲ, Cheng B L, Freeman M S, Patten A R 2016 Los Alamos National Laboratory Report No. LA-UR-16-21901

    [22]

    Benson D J 1992 Comput. Methods Appl. Mech. Engrg. 99 235

    [23]

    Wilkins M L 1999 Computer Simulation of Dynamic Phenomena (Berlin Heidelberg:Springer-Verlag)

    [24]

    Sun Z F, Xu H, Li Q Z, Zhang C Y 2010 Chin. J. High Pressure Phys. 24 55 (in Chinese)[孙占峰, 徐辉, 李庆忠, 张崇玉2010高压物理学报24 55]

    [25]

    Liu H F, Song H F, Zhang Q L, Zhang G M, Zhao Y H 2016 Matter Radiat. Extrem. 1 123

    [26]

    Wouchuk J G, Sano T 2015 Phys. Rev. E 91 023005

    [27]

    Mikaelian K O 1994 Phys. Fluids 6 356

    [28]

    Monfared S K, Or D M, Hammerberg J E, LaLone B M, Park C L, Schauer M M, Stevens G D, Stone J B, Turley W D, Buttler W T 2014 J. Appl. Phys. 116 063504

    [29]

    Chen Y T, Ren G W, Tang T G, Hu H B 2013 Acta Phys. Sin. 62 116202 (in Chinese)[陈永涛, 任国武, 汤铁钢, 胡海波2013物理学报62 116202]

    [30]

    Steinberg D J 1996 Lawrence Livermore National Laboratory Report No. UCRL-MA-106439

    [31]

    Marsh S P 1980 LASL Shock Hugoniot Data (Berkeley:University of California Press)

    [32]

    Tang W H, Zhang R Q 2008 Introduction to Theory and Computational of Equation of State (2nd Ed.) (Beijing:Higher Education Press) p237(in Chinese)[汤文辉, 张若棋2008物态方程理论及计算概论(第二版) (北京:高等教育出版社)第237页]

    [33]

    Gao C Y, Zhang L C 2012 Int. J. Plast. 32-33 121

    [34]

    Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498

    [35]

    Johnson G R, Cook W H 1985 Eng. Fract. Mech. 21 31

    [36]

    Ikkurthi V R, Chaturvedi S 2004 Int. J. Impact Engrg. 30 275

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  • Received Date:  25 April 2017
  • Accepted Date:  27 May 2017
  • Published Online:  05 October 2017

Stability analysis of interfacial Richtmyer-Meshkov flow of explosion-driven copper interface

    Corresponding author: Hu Xiao-Mian, hu_xiaomian@iapcm.ac.cn
  • 1. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China;
  • 2. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
  • 3. Graduate School of China Academy Engineering Physics, Beijing 100088, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11602029).

Abstract: In this paper, a stability analysis is given to study the unstable mechanism of the Richtmyer-Meshkov flow of explosion-driven copper interface. The Richtmyer-Meshkov flow refers as an interfacial instability growth under shockwave incident loading. Numerical investigations are performed to check the applicability of the two-dimensional hydrocode, which is named AFE2D, and the physical models of detonation waves propagating in the high explosives, equations of state and the constitutive behaviors of solids in the analysis of Richtmyer-Meshkov flow problems. Here we theoretically analyze the two key issues of the unstable mechanism in Richtmyer-Meshkov flow in solids. The unstable mechanism includes temperature related melting mechanism and the plastic evolution related tensile fracture mechanism. In the analysis of the temperature related unstable mechanisms, the calculated temperature increase during the shockwave compression from the shock Hugoniot data in the shockwave physics is not enough to melt the material near the perturbed interface. On the other hand, the temperature increase from the translation of plastic work during perturbation growth which relats to the distribution of the cumulative effective plastic strain is also not enough to supply the thermal energy which is needed to melt the crystal lattice of solid, either. Therefore, the temperature related melting mechanism is not the main factor of the unstable growth of copper interface under explosion driven. In the analysis of the plastic tensile fracture related unstable mechanism, a scaling law between the maximum cumulative effective plastic strain and the scaled maximum amplitude of spikes is proposed to describe the relationship between the plastic deformation of material and the perturbation growth of interface. Combined with a critical plastic strain fracture criterion, the unstable condition of the scaled maximum amplitude of spikes is given. If the spikes grow sufficiently to meet the unstable condition, the interfacial growth will be unstable. Numerical simulations with varying initial configurations of perturbation and yield strength of materials show good agreement with the theoretical stability analysis. Finally, a criterion to judging whether the growth is stable is discussed in the form of competition between the temperature related unstable mechanism and the tensile fracture unstable mechanism.

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