Skip to main content
SpringerLink
Log in

Macroscopic elastic constants of pure metal based on the interactions between microscopic particles

  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson’s ratio is the constant that is equal to 1–3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c 11 is 175.811 GPa, c 12 is 58.604 GPa, c 33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. WANG Yongjiang. The chang of the elastic constants of crystals due to vacancies[J]. Acta Physica Sinica, 1966, 22(2): 214–222. (in Chinese)

    Google Scholar 

  2. ZHAO Yijun, ZHANG Zhijie. Physical mechanical calculation of mechanical properties of metals I using Morse potential to calculate the elastic constants[J]. Journal of National University of Defense Technology, 1980(3): 51–79. (in chinese)

    Google Scholar 

  3. DING Yi. Numerical calculation of elastic constants of crystals[J]. Acta Acustica, 1989, 14(1): 68–72. (in Chinese)

    Google Scholar 

  4. GUO Lianquan, LI Daye, LIU Jiahui, et al. First principles calculation of lattice constant and elastic modulus of ZnO crystal[J]. Journal of Synthetic Crystals, 2010, 39(Supplement): 264–268. (in Chinese)

    Google Scholar 

  5. PANDA C V, VYAS P R, PANDYA T C, et al. An improved lattice mechanical model for FCC transition metals[J]. Physics B, 2001(307): 138–149.

    Article  Google Scholar 

  6. LI Jianying, CHEN Hongmei, CAO Qizhi, et al. First-principles calculation of elastic constants for Fe2P[J]. Journal of Guangxi University: Nat Sci Ed, 2009, 34(4): 565–570. (in Chinese)

    Google Scholar 

  7. LU Jianmin, HU Qingmiao, YANG Rui. A comparative study of elastic constants of NiTi and NiAl alloys from first-principle calculations[J]. J. Mater. Sci. Technol., 2009, 25(2): 215–218.

    Google Scholar 

  8. LIN Zheng, LIU Min. The elastic constants of polycrystalline materials with cubic system structural single crystals[J]. Acta Physica Sinica, 2009, 58(6): 4 096–4 012. (in Chinese)

    Google Scholar 

  9. LIU Qijun, LIU Zhengtang, FENG Liping, et al. First principles calculation of electronic structure and elastic constants of tetragonal HfO2 crystal[J]. Journal of Beijing Union University (Natural Sciences), 2009, 23(3): 76–80. (in Chinese)

    Google Scholar 

  10. LI Junwan, JIANG Wugui. Predictions of nanohardness and elastic modulus of thin film material with the quasicontinuum method[J]. Acta Metallurgica Sinica, 2007, 43(8): 851–856. (in Chinese)

    Google Scholar 

  11. XIE Genquan, LONG Shuyao. Calculation of the elastic modulus of metal nanorod based on small size effect[J]. Journal of University of Science and Technology of Suzhou: Engineering and Technology, 2005, 18(2): 27–31. (in Chinese)

    MATH  Google Scholar 

  12. ZHANG Ming, SHEN Jiang, HE Jiawen. Elastic constants of Al and TiN calculated by ab initio method[J]. Trans. Nonferrous Met. Soc. China, 2001, 11(2): 244–248.

    Google Scholar 

  13. CHEN Li. Calculation and applicability analysis for elastic constants of FCC crystal[J]. Chinese Journal of Mechanical Engineering, 2005, 41(9): 46–50. (in Chinese)

    Article  Google Scholar 

  14. CHEN Li. Applicability analysis for elastic constants of Ag and Au[J]. Journal of Xi’an Jiaotong University, 2005, 39(3): 325–328. (in chinese)

    Google Scholar 

  15. GUO Yundong, CHEN Xiangrong, YANG Xiangdong, et al. Elastic constants of superconducting MgB2 from molecular dynamics simulations with shell model[J]. Communications in Theoretical Physics (Beijing, China), 2005, 44(5): 936–940.

    Article  Google Scholar 

  16. ZHANG Kecong. The basis of modern crystallography (Volume 1)[M]. Beijing: Science Press, 1987: 157–162. (in Chinese)

    Google Scholar 

  17. WANG Junkui, DING Lizuo. Elasticity solid mechanics[M]. Beijing: China Railway Publishing House, 1990: 68–69. (in Chinese)

    Google Scholar 

  18. CHENG Changjun. Elastic mechanics[M]. Lanzhou: Lanzhou University Press, 1995: 93–96. (in Chinese)

    Google Scholar 

  19. SHI Zhendong, HAN Yaoxin. Elastic mechanics course[M]. Beijing: Beijing College of Aviation Press, 1987: 77–80. (in Chinese)

    Google Scholar 

  20. YI Xiangchu. Solid mechanics[M]. Beijing: Earthquake Publishing House, 1985: 68–70. (in chinese)

    Google Scholar 

  21. LI Tonglin, YIN Suiyu. Elasticity and plasticity mechanics[M]. Wuhan: China University of Geosciences Press, 2006: 50–51. (in Chinese)

    Google Scholar 

  22. CHEN Changle. Solid state physics[M]. Xi’an: Northwestern Polytechnical University Press, 1998: 1–37. (in Chinese)

    Google Scholar 

  23. VAINSHTEIN B K, FRIDKIN V M, INDENBOM V L. Modern crystallography: II[M]. Hefei: Press of University of Science and Technology of China, 1992: 75. (in Chinese)

    Google Scholar 

  24. YANG Shunhua. The theory basis of crystal dislocation: I[M]. Beijing: Science Press, 1998: 435. (in Chinese)

    Google Scholar 

  25. WAN Shumin. Solid interaction potential function between atoms and alkali metal, alkaline earth metal electron theory of elasticity[J]. Science in China: A Series, 1987(2): 176. (in Chinese)

    Google Scholar 

  26. XIE Youqing. A new potential energy function of solid multi-atom interaction[J]. Science in China: A Series, 1992(8): 887. (in Chinese)

    Google Scholar 

  27. YU Changfeng, YANG Xintie, YAN Kun, et al. Analytic expression dependent of microscopic parameters on the Young modulus of metallic single crystal[J]. Physics Experimentation, 2004, 24(8): 46. (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical & Electronic Engineering, Zhongyuan University of Technology, Zhengzhou, 450007, China

    Ming Lu, Yongsheng Niu & Rui Fan

Authors
  1. Ming Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongsheng Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming Lu.

Additional information

LU Ming, born in 1972, is currently a lecturer at School of Mechanical & Electronic Engineering, Zhongyuan University of Technology, China. He received his PhD degree from China Academy of Machinery Science & Technology, China, in 2009. His main research interests include super-small size transmission and computer-aided design.

NIU Yongsheng, born in 1959, is currently a professor and a master candidate supervisor at School of Mechanical & Electronic Engineering, Zhongyuan University of Technology, China. He received his bachelor degree from Chongqing University, China, in 1982. His main research interests include super-small size transmission and elasto-hydrodynamic lubrication.

FAN Rui, born in 1958, is currently a professor and a master candidate supervisor at School of Mechanical & Electronic Engineering, Zhongyuan University of Technology, China. She received her bachelor degree from Northeast Institute of Heavy Machinery, China, in 1982. Her research interests include mechanical design, transmission and distribution technology, fluid power transmission.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, M., Niu, Y. & Fan, R. Macroscopic elastic constants of pure metal based on the interactions between microscopic particles. Chin. J. Mech. Eng. 26, 356–364 (2013). https://doi.org/10.3901/CJME.2013.02.356

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2013.02.356

Key words

Search

Navigation