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## Temperature and pressure calculation of porous materials

Chen Jun-Xiang, Yu Ji-Dong, Geng Hua-Yun, He Hong-Liang
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• #### 摘要

多孔材料内部含有大量孔隙，孔隙一旦塌陷就回归为密实物质.但孔隙塌陷沉积的能量将提升基体材料的温度，导致热力学状态量发生变化.尤其是在冲击波压缩下，多孔材料的温升很高，温度变化对其他热力学状态量的变化影响很大，因此解决多孔材料的温度计算是不可回避的问题.本文在研究Grneisen通用函数v（v）的基础上，将密实材料的德拜温度函数通过数学的方法，延拓到多孔材料的密度范围，建立了多孔材料的等效德拜温度函数（v）；并据此推导出了多孔材料的等熵温度函数Ts（v）.再借鉴多孔材料0 K等熵功相等的假设，建立了多孔材料与密实材料在相等压强下等熵功相等的计算模型，给出了多孔材料的等熵压强函数ps（v）.于是，齐备了冲击波压缩下多孔材料温度和压强计算的参考方程，即温度方程Ts（v）和压强方程ps（v）.为了检验本文方法的有效性，以Cu为例计算了孔隙度m=1.13，1.22，1.41，1.56，1.98等5种多孔材料的冲击压强和冲击温度，计算结果与实验数据相符较好.同时，用其他方法做了计算，两种方法计算结果的比较，显示出本文计算方法的可靠性.

#### Abstract

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.

#### 作者及机构信息

###### 通信作者: 陈俊祥, cjx621@163.com
• 基金项目: 国家自然科学基金（批准号：11302202）和中国工程物理研究院科学技术发展基金（批准号：201402084）资助的课题.

#### Authors and contacts

###### Corresponding author: Chen Jun-Xiang, cjx621@163.com
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11302202) and the Foundation of President of China Academy of Engineering Physics (Grant No. 201402084).

#### 参考文献

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#### 施引文献

•  [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物理学报55 3785] [4] Zhang H W, Li Y X 2007Acta Phys.Sin. 56 4846(in Chinese)[张华伟, 李言祥2007物理学报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高压物理学报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物理学报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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##### 出版历程
• 收稿日期:  2016-10-11
• 修回日期:  2016-12-06
• 刊出日期:  2017-03-05

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