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Porous material contains a large number of pores, and once the pore space collapses, it changes into a dense material with the great increase of temperature because of the energy deposition by porosity collapsing. In the process of shock compression, the temperature is extremely increased, which influences the thermodynamic state of porous material significantly. Therefore, the calculation of temperature is important for the shock compression of porous material, yet it has not been solved well in the literature. In this paper, based on the study of Grneisen general function v(v), the Debye temperature function of solid material is extended to the region of porous material, and the equivalent Debye temperature function (v) of porous material is formulated, from which the isentropic temperature function Ts(v) of porous material is obtained. Furthermore, a computation model is established, in which the isentropic work of porous is assumed to be equal to that of compact material under the same pressure at 0 K. With this model, the isentropic pressure function ps(v) of the porous material is acquired. Hence, the reference equation for calculating temperature and pressure of porous material, i.e., Ts(v) and ps(v), is completed. To demonstrate this method, the p-v and T-v curves of the Hgoniot state of porous copperare computed, and the values of porosity are m 1.13, 1.22, 1.41, 1.56 and 1.98, respectively. The calculated results are in good agreement with the experimental data. A comparison with other calculation is also made, indicating a better reliability of the present method.
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Keywords:
- porous material /
- porosity /
- Debye temperature /
- isentropic equation
[1] Liu P S 2004Introduction to Porous Materials(Beijing:Tsinghua University Press)(in Chinese) p16[刘培生2004多孔材料引论(北京:清华大学出版社)第16页]
[2] Gibson L J, Ashby M F 1999Cellular Solids:Structure and Properties(Cambridge:Cambridge University Press) p8
[3] Zhao X F, Fang Y 2006Acta Phys.Sin. 55 3785(in Chinese)[赵信峰, 方炎2006 55 3785]
[4] Zhang H W, Li Y X 2007Acta Phys.Sin. 56 4846(in Chinese)[张华伟, 李言祥2007 56 4864]
[5] Rosa M E 2008Phil.Mag.Lett. 88 637
[6] Tan H 2007Introduction to Experimental Shock-Wave Physics(Beijing:National Defence Industry Press) p56(in Chinese)[谭华2007实验冲击波物理导引(北京:国防工业出版社)第56页]
[7] Jing F Q 1986Introduction to Experimental Equation of State(Beijing:Science Press) p134(in Chinese)[经福谦1986实验物态方程导引(北京:科学出版社)第134页]
[8] Li X J, Gong Z Z, Liu F S 2001J.of High Press.Phys. 15 221(in Chinese)[李西军, 龚自正, 刘福生2001高压 15 221]
[9] Li X J, Gong Z Z, Jing F Q 2001Chin.Phys.Lett. 18 1632
[10] Wu Q, Jing F Q 1996J.Appl.Phys. 80 4343
[11] Chen J X, Yu J D, Li P, He H L 2015Acta Phys.Sin. 64 086401(in Chinese)[陈俊祥, 于继东, 李平, 贺红亮2015 64 086401]
[12] Boshoff-Mostert L, Viljoen H J 1999J.Appl.Phys. 86 1245
[13] Marsh S P 1980LASL Shock Hugoniot Data(Berkekeley American:University of California Press) p62
[14] Wang G J, Luo B Q, Zhang X P, Zhao J H, Che S W, Tan F L, Chong T, Mo J J, Wu G, Tao Y H 2013The Review of Scientific Instruments 84 015117
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[1] Liu P S 2004Introduction to Porous Materials(Beijing:Tsinghua University Press)(in Chinese) p16[刘培生2004多孔材料引论(北京:清华大学出版社)第16页]
[2] Gibson L J, Ashby M F 1999Cellular Solids:Structure and Properties(Cambridge:Cambridge University Press) p8
[3] Zhao X F, Fang Y 2006Acta Phys.Sin. 55 3785(in Chinese)[赵信峰, 方炎2006 55 3785]
[4] Zhang H W, Li Y X 2007Acta Phys.Sin. 56 4846(in Chinese)[张华伟, 李言祥2007 56 4864]
[5] Rosa M E 2008Phil.Mag.Lett. 88 637
[6] Tan H 2007Introduction to Experimental Shock-Wave Physics(Beijing:National Defence Industry Press) p56(in Chinese)[谭华2007实验冲击波物理导引(北京:国防工业出版社)第56页]
[7] Jing F Q 1986Introduction to Experimental Equation of State(Beijing:Science Press) p134(in Chinese)[经福谦1986实验物态方程导引(北京:科学出版社)第134页]
[8] Li X J, Gong Z Z, Liu F S 2001J.of High Press.Phys. 15 221(in Chinese)[李西军, 龚自正, 刘福生2001高压 15 221]
[9] Li X J, Gong Z Z, Jing F Q 2001Chin.Phys.Lett. 18 1632
[10] Wu Q, Jing F Q 1996J.Appl.Phys. 80 4343
[11] Chen J X, Yu J D, Li P, He H L 2015Acta Phys.Sin. 64 086401(in Chinese)[陈俊祥, 于继东, 李平, 贺红亮2015 64 086401]
[12] Boshoff-Mostert L, Viljoen H J 1999J.Appl.Phys. 86 1245
[13] Marsh S P 1980LASL Shock Hugoniot Data(Berkekeley American:University of California Press) p62
[14] Wang G J, Luo B Q, Zhang X P, Zhao J H, Che S W, Tan F L, Chong T, Mo J J, Wu G, Tao Y H 2013The Review of Scientific Instruments 84 015117
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