Review on Evaluation of Temperature-Pressure Equation of State of Porous Materials
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摘要: 多孔材料是一种重要的结构和功能材料，在过滤、催化、屏蔽和冲击防护等重要工程领域具有广泛的应用。多孔材料的物理力学行为极其复杂，虽然经过多年研究，但是仍未完全理解其在极端条件下的响应行为。以冲击加载下多孔材料的压力和温度变化特点为例，对目前常用的几种具有代表性的以密实材料Hugoniot为参照线的多孔材料物态方程模型进行深入分析，并对多种模型的优劣进行比较，在此基础上提出了一种分段处理多孔材料冲击波数据的方法。以多孔Cu为例，展示了该方法的有效性。这种方法将为发展更为精细严格的多孔材料状态方程理论提供有益的参考。Abstract: As an important structural and functional material, porous material has been widely used in the engineering fields such as filtration, catalysis, shielding and impact protection. Because of its complex physical-mechanical behavior, even with years of research, its response under extreme conditions still has not been fully understood. Taking the characteristics of pressure and temperature change of porous materials under shock loading as an example, this paper makes an in-depth analysis of several typical models of equation of state for porous materials by choosing Hugoniot of the dense material as the reference line and compares them. On the basis of this analysis, an approach of piecewise processing the shock data of porous materials is proposed and its effectiveness is demonstrated for porous copper. This approach may be helpful in developing an accurate and rigorous theory of the equation of state of porous materials.
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Key words:
- porous materials /
- Debye temperature /
- equation of state /
- shock Hugoniot
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图 2 W-J方程计算多孔Cu与实验数据比较
Figure 2. Compression curve of porous Cu calculated by W-J equation of state compared to experimental data
图 3 通过推广的W-J方程计算多孔Cu压强与实验结果比较
Figure 3. Compression curve of porous Cu calculated by improved W-J equation of state compared to experimental data
图 4 通过推广的W-J方程计算多孔Cu温度与其他计算结果比较
Figure 4. Shock temperature of porous Cu calculated by improved W-J equation of state compared to other calculated data
图 8 低孔隙度Cu的冲击温度线
Figure 8. Calculated shock temperature curve of Cu with ultra-low porosity
图 10 低孔隙度多孔Cu的p-
$\rho $ 曲线Figure 10. The p-
$\rho $ curves of Cu with different ultra-low porosities
图 11 大孔隙度Cu冲击压缩T-p线
Figure 11. The calculated shock T-p curves of Cu with a high porosity
表 1 不同孔隙度Cu的D-u数据拟合参数
Table 1. The parameters for the D-u data of Cu with high porosity
${\rho _{00}}$/(g·cm–3) m c0/(km·s–1) $\lambda $ $\lambda $' 7.900 1.13 1.920 46 2.414 25 –0.146 04 7.315 1.22 1.168 50 2.684 83 –0.199 24 6.326 1.41 0.421 78 2.694 98 –0.183 45 5.742 1.56 0.247 99 2.476 93 –0.117 16 4.508 1.98 0.090 92 2.105 15 –0.080 52 
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表 2 低孔隙度Cu冲击固相温度与液相温度函数参数
Table 2. The parameters for the shock temperature in the solid and liquid phases of Cu with low porosity
${{\rho _{00}}}$/(g·cm–3) ${T_{\rm H}=a+b p_{\rm H}+c p_{\rm H}^2+d p_{\rm H}^3}$ ${T_{\rm L}=a+b p_{\rm L}+c p_{\rm L}^2+d p_{\rm L}^3}$ a b c d a b c d 7.900 722.153 20 –17.753 26 0.735 67 –0.002 68 5911.275 89 –84.108 46 0.597 35 –8.591 44×10–4 7.315 868.336 33 –26.095 54 1.312 99 –0.006 91 3603.769 33 –55.517 72 0.537 68 –9.226 82×10–4 6.326 1195.581 88 –61.546 11 4.200 98 –0.044 56 –1936.853 58 54.373 03 –0.072 41 2.025 16×10–4 5.742 1342.781 34 –71.452 26 6.891 94 –0.107 30 –519.446 31 45.078 97 –0.040 80 1.391 05×10–4 4.508 –150.530 72 52.113 33 –0.158 49 5.409 68×10–4
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表 3 高孔隙度Cu的D-u数据处理参数
Table 3. The fitted parameters to the D-u experimental data of porous Cu with different porosities
${\rho _{00}}$/(g·cm–3) m c0/(km·s–1) $\lambda $ $\lambda'$ 3.5720 2.5 0.04 1.645 0.01 2.9767 3 0.041 1.456 8 0.026 5 2.073 32 1.182 42 10–9 2.5514 3.5 0.068 1.344 8 0.035 1 2.2325 4 0.112 1.3 0.023 2.966 17 0.866 16 0.015 61 1.6388 5.45 0.225 1.141 31 0.038 64 1.2403 7.2 0.346 83 0.993 52 0.052 32
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