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Applied Physics 2024
理想线弹性体的等温物态方程
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Abstract:
固体的物态方程多为经验公式，少量为基于微观力学的扩展，方程复杂且有效性低，建立有效的理论性的物态方程，一直是业内的梦想。本研究从材料力学角度出发，建立了一种理想线弹性体的2参数等温物态方程，该方程具有Bridgman方程的形式，方程参数仅为弹性模量和泊松比；对75中物质的弹性段数据进行了验证，发现新方程的符合性良好，可靠性佳，拟合精度可控制在3.72%以内。同时得出体积模量的一阶导数是泊松比的单一函数，揭示了这两个参数之间的深刻联系。
The equations of state for solids are mostly empirical formulas, with a small number being extensions based on micromechanics. The equations are complex and have low effectiveness. Establishing effective theoretical equations of state has always been a dream in the industry. This study establishes a 2-parameter isothermal equation of state for an ideal linear elastic body from the perspective of material mechanics. The equation takes the form of the Bridgman equation, with only elastic modulus and Poisson’s ratio as its parameters; The elastic segment data of 75 substances were validated, and it was found that the new equation has good consistency, reliability, and fitting accuracy can be controlled within 3.72%. At the same time, the first-order derivative of the bulk modulus is a single function of Poisson’s ratio, revealing the profound connection between these two parameters.
| [1] | 温原. 固态高分子等温物态方程的适用性[J]. 上海塑料, 2023, 51(1): 44-53. |
| [2] | Norman, E. 工程材料力学行为[M]. 北京: 机械工业出版社, 2016: 124-154. |
| [3] | 温原. 理想线弹性体的泊松比[J]. 力学研究, 2022, 11(2): 29-34. |
| [4] | Bridgman, P.W. (1958) The Physics of High Pressure. Bell and Sons Press, London. |
| [5] | 魏宇杰. 固体工程科学-工程材料的应用力学理论与实践[M]. 北京: 高等教育出版社, 2021: 16. |
| [6] | 许德美. 多晶Be的室温脆性研究[D]: [博士学位论文]. 沈阳: 东北大学, 2017. |
| [7] | 刘畅. 金刚石在复杂应变下的应力响应及物理性质[D]: [博士学位论文]. 长春: 吉林大学, 2020. |
| [8] | Gschneidner, K.A. (1964) Physical Properties and Interrelationships of Metallic and Semimetallic Elements. Solid State Physics, 16, 275-426. https://doi.org/10.1016/S0081-1947(08)60518-4 |
| [9] | Datchi, F., Dewaele, A., Godec, Y.L., et al. (2007) Equation of State of Cubic Boron Nitride at High Pressures and Temperatures. Physical Review B, 75, Article ID: 214104. https://doi.org/10.1103/PhysRevB.75.214104 |
| [10] | Vaidya, S.N. and Kennedy, G.C. (1972) Compressibility of 22 Elemental Solids to 45 KB. Journal of Physics and Chemistry of Solids, 33, 1377-1389. https://doi.org/10.1016/S0022-3697(72)80432-3 |
| [11] | Armentrout, M.M. and Kavner, A. (2015) A New High Pressure and Temperature Equation of State of Fcc Cobalt. Journal of Applied Physics, 118, Article ID: 194904. https://doi.org/10.1063/1.4935087 |
| [12] | Cynn, H., Klepeis, J.E., Yoo, C.S., et al. (2002) Osmium Has the Lowest Experimentally Determined Compressibility. Physical Review Letters, 88, Article ID: 135701. https://doi.org/10.1103/PhysRevLett.88.135701 |
| [13] | Li, D., Jaglinski, T., Stone, D.S., et al. (2012) Temperature Insensitive Negative Poisson’s Ratios in Isotropic Alloys Near a Morphotropic Phase Boundary. Applied Physics Letters, 101, 823-837. https://doi.org/10.1063/1.4772940 |
| [14] | Ma, C., Dou, Z.Y., Zhu, H.Y., et al. (2016) Structure Phase Transformation and Equation of State of Cerium Metal under Pressures Up to 51 GPa. Chinese Physics B, 25, Article ID: 046401. https://doi.org/10.1088/1674-1056/25/4/046401 |
| [15] | Anzellini, S., Burakovsky, L., Turnbull, R., et al. (2021) P-V-T Equation of State of Iridium up to 80 GPa and 3100 K. Crystals, 11, Article 452. https://doi.org/10.3390/cryst11040452 |
| [16] | Christensen, R.M. (2022) Perspective on the Bond Bending and Bond Stretching Effects at the Atomic Scale and Their Relationship to Ductile Versus Brittle Materials Failure. Journal of the Mechanics and Physics of Solids, 167, Article ID: 104984. https://doi.org/10.1016/j.jmps.2022.104984 |
| [17] | 简单, 朱燮刚, 刘瑜, 等. U和UO2状态方程研究进展[J]. 材料导报, 2021, 35(1): 82-95. |
| [18] | Barroso, D.E.G. (2015) Equation of State of Uranium and Plutonium. arXiv: 1502.00497. |
| [19] | 毛华杰, 何博, 郭巍, 等. 基于LM-UGO算法改性PP材料黏度模型与PVT模型拟合和试验验证[J]. 塑料科技, 2018, 46(12): 37-42. |
| [20] | 蔡天泽. 碳纤增强聚合物的PVT特性及其在制品精度控制中的应用[D]: [硕士学位论文]. 北京: 北京化工大学, 2017. |
| [21] | 李干, 李杰, 宋春明, 等. 花岗岩的动态力学性能、本构模型与状态方程研究[J]. 力学与实践, 2023, 45(5): 952-959. |
| [22] | 周梦, 陶应奇, 周晓云, 等. 新型含能离子盐TKX-50状态方程及热力学性质的第一性原理研究[J/OL]. 计算物理: 1-8. http://kns.cnki.net/kcms/detail/11.2011.O4.20230614.1058.002.html, 2024-03-05. |
