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The effect of window acoustic impedance on the wave profile of phase transition of zirconium under ramp wave compression is investigated in experiment and simulation. In the experiments, a ramp wave driven by magnetic pressure is applied to the zirconium samples backed windows with different acoustic impedances such as LiF, sapphire and free surface based on the compact pulsed power generator CQ-4. The experimental wave profiles measured by an advanced laser interference velocimeter show that the characteristic particle velocity of the onset phase transition from to is about 331.0 m/s in the conditions of LiF widow and free surface with low acoustic impedance, and it is approximately 301.9 m/s for the sapphire window with higher acoustic impedance. The corresponding onset pressure of phase transition varies from about 9.14 GPa to 8.27 GPa. The result shows that this onset pressure of phase transition, which is affected by diverse factors, is not the inherent value of phase transition belonging to the material properties. In order to describe these dynamic responses in experiment well, the numerical simulation of phase transition dynamics of zirconium is conducted in one-dimensional hydrodynamic code, in which included are the muti-phase equation of state based on Helmholtz free energy, the equation of non-equilibrium phase transition dynamics, and Steinberg constitutive relationship. The simulated results show that they can reflect the physical processes of elasto-plastic transition and - phase transition as well, which are excellently consistent with the experimental data. The relaxation times of - phase transition in three different acoustic impedance experiments are nearly the same (30 ns), and their finishing times of phase transition are all about 100 ns. The calculated quasi-isentrope of zirconium below 20 GPa in the pressure-volume and temperature-pressure thermodynamic planes shows that the isentrope and shock adiabat exhibit tiny difference before phase transition, and then separate gradually with the increase of pressure. The isentrope lies below the shock adiabat after the onset of phase transition. At about 20 GPa, the temperature of zirconium under ramp wave loading is bout 100 K lower than that under shock loading. Meanwhile, the abrupt change of volume at phase transition causes the Lagrange sound speed to reduce about 7% and then comes back to the bulk sound speed again after the phase transition has been finished.
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Keywords:
- multiphase equation of state /
- phase transition /
- ramp wave compression /
- acoustic impedance
[1] Xiao D W 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [肖大武2008 博士学位论文(合肥: 中国科学技术大学)]
[2] Bridgman P W 1952 Proceedings of the American Academy of Arts Sciences 81 165
[3] Jamieson J C 1963 Science 140 72
[4] Zilbershtein V A, Nosova G I, Estrin E I 1973 Phys. Met. Metallogr. 35 29
[5] Xia H, Parthasarathy G, Luo H, Vohra Y K, Ruoff A L 1990 Phys. Rev. B 42 6736
[6] Xia H, Duclos S J, Ruoff A L, Vohra Y K 1990 Phys. Rev. Lett. 64 204
[7] Al'Tshuler L V, Bakanova A A, Dudoladov I P 1967 Zh. Eksp. Teor. Fiz. 53 1967
[8] Al'Tshuler L V, Bakanova A A, Dudoladov I P, Dynin E A, Trunin R F, Chekin B S 1981 J. Appl. Mech. Tech. Ph. 22 145
[9] McQueen R G, Marsh S P, Taylor J W, Fritz J N, Carter W J 1970 High Velocity Impact Phenomena (New York: Academic) pp293-417
[10] Kutsar A R, Pavlovskii M N, Kamissarov V V 1982 Jetp. Lett. 39 1
[11] Greeff C W 2005 Model. Simul. Mater. Sc. 13 1015
[12] Cerreta E, Iii G T G, Hixson R S, Rigg P A, Brown D W 2005 Acta Mater. 53 1751
[13] Gray G T, Bourne N K 2000 Shock Compression of Condensed Matter (Vol. 505) (American Institute of Physics) p509
[14] Rigg P A, Greeff C W, Knudson M D, Iii G T G, Hixson R S 2009 J. Appl. Phys. 106 245
[15] Li Y H 2006 M. S. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [李英华 2006 硕士学位论文(绵阳: 中国工程物理研究院)]
[16] Chong T, Wang G J, Tan F L, Luo B Q, Zhang X P, Wu G, Zhao J H 2014 Sci. Sin.: Phys. Mech. Astron. 44 1 (in Chinese) [种涛, 王桂吉, 谭福利, 罗斌强, 张旭平, 吴刚, 赵剑衡 2014 中国科学: 物理学 力学 天文学 44 1]
[17] Wang G J, Luo B Q, Zhang X P, Zhao J H, Sun C W, Tan F L, Chong T, Mo J J, Wu G, Tao Y H 2013 Rev. Sci. Instrum. 84 015117
[18] Hall C A, Asay J R, Knudson M D, Stygar W A, Hall C A, Asya J R, Knudson M D 2001 Rev. Sci. Instrum. 72 3587
[19] Chong T 2012 M. S. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [种涛 2012 硕士学位论文(绵阳: 中国工程物理研究院)]
[20] Tang Z P 2008 Phase Transition under Shock Compression (Beijing: Science Press) p130 (in Chinese) [唐志平 2008 冲击相变 (北京: 科学出版社) 第130页]
[21] Hayes D B 1975 J. Appl. Phys. 46 3438
[22] Zuo Q H, Harstad E N, Addessio F L, Greeff C W 2006 Model. Simul. Mater. Sci. 14 1465
[23] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
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[1] Xiao D W 2008 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [肖大武2008 博士学位论文(合肥: 中国科学技术大学)]
[2] Bridgman P W 1952 Proceedings of the American Academy of Arts Sciences 81 165
[3] Jamieson J C 1963 Science 140 72
[4] Zilbershtein V A, Nosova G I, Estrin E I 1973 Phys. Met. Metallogr. 35 29
[5] Xia H, Parthasarathy G, Luo H, Vohra Y K, Ruoff A L 1990 Phys. Rev. B 42 6736
[6] Xia H, Duclos S J, Ruoff A L, Vohra Y K 1990 Phys. Rev. Lett. 64 204
[7] Al'Tshuler L V, Bakanova A A, Dudoladov I P 1967 Zh. Eksp. Teor. Fiz. 53 1967
[8] Al'Tshuler L V, Bakanova A A, Dudoladov I P, Dynin E A, Trunin R F, Chekin B S 1981 J. Appl. Mech. Tech. Ph. 22 145
[9] McQueen R G, Marsh S P, Taylor J W, Fritz J N, Carter W J 1970 High Velocity Impact Phenomena (New York: Academic) pp293-417
[10] Kutsar A R, Pavlovskii M N, Kamissarov V V 1982 Jetp. Lett. 39 1
[11] Greeff C W 2005 Model. Simul. Mater. Sc. 13 1015
[12] Cerreta E, Iii G T G, Hixson R S, Rigg P A, Brown D W 2005 Acta Mater. 53 1751
[13] Gray G T, Bourne N K 2000 Shock Compression of Condensed Matter (Vol. 505) (American Institute of Physics) p509
[14] Rigg P A, Greeff C W, Knudson M D, Iii G T G, Hixson R S 2009 J. Appl. Phys. 106 245
[15] Li Y H 2006 M. S. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [李英华 2006 硕士学位论文(绵阳: 中国工程物理研究院)]
[16] Chong T, Wang G J, Tan F L, Luo B Q, Zhang X P, Wu G, Zhao J H 2014 Sci. Sin.: Phys. Mech. Astron. 44 1 (in Chinese) [种涛, 王桂吉, 谭福利, 罗斌强, 张旭平, 吴刚, 赵剑衡 2014 中国科学: 物理学 力学 天文学 44 1]
[17] Wang G J, Luo B Q, Zhang X P, Zhao J H, Sun C W, Tan F L, Chong T, Mo J J, Wu G, Tao Y H 2013 Rev. Sci. Instrum. 84 015117
[18] Hall C A, Asay J R, Knudson M D, Stygar W A, Hall C A, Asya J R, Knudson M D 2001 Rev. Sci. Instrum. 72 3587
[19] Chong T 2012 M. S. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [种涛 2012 硕士学位论文(绵阳: 中国工程物理研究院)]
[20] Tang Z P 2008 Phase Transition under Shock Compression (Beijing: Science Press) p130 (in Chinese) [唐志平 2008 冲击相变 (北京: 科学出版社) 第130页]
[21] Hayes D B 1975 J. Appl. Phys. 46 3438
[22] Zuo Q H, Harstad E N, Addessio F L, Greeff C W 2006 Model. Simul. Mater. Sci. 14 1465
[23] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
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