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Extraction on the Contact Forces Among the Opaque and Non-photoelastic Particles Under Electromagnetic Force

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Abstract

Contact force is related to the mechanical response of superconducting strands under a large electromagnetic body force, which is important for the safety of the international thermonuclear experimental reactor (ITER) magnet structure. Due to the complex structure of the cable-in-conduit conductor (CICC), the component unit of the ITER magnet, and the extreme operating environment, the research on the strand contact force caused by the electromagnetic force has been progressing slowly. In this study, a two-dimensional (2D) theoretical model based on the granular element method is constructed to compute the contact forces among some opaque and non-photoelastic ferromagnetic particles which are placed in a non-uniform magnetic field. In the experiment, the contact deformations of these particles may be obtained by the digital image correlation method. We also propose a method, which is similar to the least-squares method, to calculate the electromagnetic body forces of different particles. Subsequently, the distributional and statistical characteristics of the contact force chains and contact angles are presented. It is considered that the method proposed in this paper is suitable for the contact force analysis of the cross section of superconducting strands in the ITER CICC that is subjected to a transverse electromagnetic force. In the end, this 2D theoretical model is generalized to the three-dimensional (3D) case, and the concise mathematical framework is presented.

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References

  1. Nabara Y, Nunoya Y, Isono T, et al. Examination of Japanese mass-produced conductors for ITER toroidal field coils. IEEE Trans Appl Supercond. 2012;22(3):4804804.

    Article  Google Scholar 

  2. Nabara Y, Hemmi T, Kajitani H, et al. Examination of conductors for ITER central solenoids. IEEE Trans Appl Supercond. 2013;23(3):4801604.

    Article  Google Scholar 

  3. Yagai T, Kudo H, Hamano K, et al. Investigation of frictional force applied to strands surrounded by other strands and tribological analysis of contact surface in CIC conductor. IEEE Trans Appl Supercond. 2014;24(3):1–4.

    Article  Google Scholar 

  4. Yue Donghua, Zhang Xingyi, Zhou Youhe. Buckling behavior of Nb\(_{3}\)Sn strand caused by electromagnetic force and thermal mismatch in ITER cable-in-conduit conductor. IEEE Trans Appl Supercond. 2017;27:8400911.

    Article  Google Scholar 

  5. Brumfiel G. Cable test raised fears at fusion project. Nature. 2011;471:150.

    Article  Google Scholar 

  6. Devred A, Jong C, Mitchell N. Strain redistribution effects on current-sharing measurements on straight samples of large Nb\(_{3}\)Sn cable-in-conduit conductors. Supercond Sci Technol. 2012;25(5):054009.

    Article  Google Scholar 

  7. Devred A, Bessette D, Bruzzone P, et al. Status of conductor qualification for the ITER central solenoid. IEEE Trans Appl Supercond. 2013;23(3):6001208.

    Article  Google Scholar 

  8. Breschi M, Devred A, Casali M, et al. Results of the TF conductor performance qualification samples for the ITER project. Supercond Sci Technol. 2012;25(9):095004.

    Article  Google Scholar 

  9. Yue Donghua, Zhang Xingyi, Zhou Youhe. Theoretical analysis for the mechanical behavior caused by electromagnetic cycle in ITER Nb\(_{3}\)Sn cable-in-conduit conductors. Acta Mech Sin. 2018;34(4):614–22.

    Article  Google Scholar 

  10. Martovetsky N, et al. Test of the ITER central solenoid model coil and CS insert. IEEE Trans Appl Supercond. 2002;12(1):600.

    Article  Google Scholar 

  11. Mitchell N. Mechanical and magnetic load effects in Nb\(_{3}\)Sn cable-in-conduit conductors. Cryogenics. 2003;43(3–5):255–70.

    Article  Google Scholar 

  12. Mitchell N. Summary, assessment and implications of the ITER model coil test results. Fusion Eng Des. 2003;66–68(03):971–93.

    Article  Google Scholar 

  13. Mitchell N. Operating strain effects in Nb\(_{3}\)Sn cable-in-conduit conductors. Supercond Sci Technol. 2005;18(12):S396–404.

    Article  Google Scholar 

  14. Mitchell N. Assessment of conductor degradation in the ITER CS insert coil and implications for the ITER conductors. Supercond Sci Technol. 2006;20(1):25.

    Article  MathSciNet  Google Scholar 

  15. Nijhuis A, Ilyin Y. Transverse load optimization in Nb\(_{3}\)Sn CICC design; influence of cabling, void fraction and strand stiffness. Supercond Sci Technol. 2006;19(9):945–62.

    Article  Google Scholar 

  16. Nijhuis A. A solution for transverse load degradation in ITER Nb\(_{3}\)Sn CICCs: verification of cabling effect on Lorentz force response. Supercond Sci Technol. 2008;21(5):054011.

    Article  Google Scholar 

  17. Zhai Y, Bird MD. Florida electro-mechanical cable model of Nb\(_{3}\)Sn CICCs for high-field magnet design. Supercond Sci Technol. 2008;21(11):115010.

    Article  Google Scholar 

  18. Zhai Y. Electro-mechanical modeling of Nb\(_{3}\)Sn CICC performance degradation due to strand bending and inter-filament current transfer. Cryogenics. 2010;50(3):149–57.

    Article  Google Scholar 

  19. Zhu J, Luo W, Zhou Y, et al. Contact mechanical characteristics of Nb\(_{3}\)Sn strands under transverse electromagnetic loads in the CICC cross-section. Supercond Sci Technol. 2012;25(12):125011.

    Article  Google Scholar 

  20. Jia Shuming, Wang Dengming, Zheng Xiaojing. Numerical simulation of the mechanical properties of the Nb\(_{3}\)Sn CICCs under transverse cyclic loads. IEEE Trans Appl Supercond. 2014;24(1):8400706.

    Google Scholar 

  21. Jia Shuming, Wang Dengming, Zheng Xiaojing. Multi-contact behaviors among Nb\(_{3}\)Sn strands associated with load cycles in a CS1 cable cross section. Physica C. 2015;508(15):56–61.

    Article  Google Scholar 

  22. Shuming Jia, Dengming Wang, Xiaojing Zheng. Numerical investigation on transverse heat transfer properties in cross section of full size Nb\(_{3}\)Sn CICC ITER conductor. AIP Adv. 2015;5(5):057124.

    Article  Google Scholar 

  23. Cheng X, Zhang X, Liu C, et al. Experimental investigation on the contact mechanical characteristics of superconducting strands in the CICC cross-section. IEEE Trans Appl Supercond. 2017;27:8400806.

    Google Scholar 

  24. Andrade José E, Lim KW, Avila CF, et al. Granular element method for computational particle mechanics. Comput Methods Appl Mech Eng. 2012;241–244(3):262–74.

    Article  Google Scholar 

  25. Hurley R, Marteau E, Ravichandran G, et al. Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J Mech Phys Solids. 2014;63(1):154–66.

    Article  Google Scholar 

  26. Yamaguchi I. A laser-speckle strain gauge. J Phys E Sci Instrum. 2000;14(11):1270.

    Article  Google Scholar 

  27. Bing P. High-accuracy two-dimensional digital image correlation measurement system using a bilateral telecentric lens. Acta Opt Sin. 2013;33(4):0412004.

    Article  Google Scholar 

  28. Zhu G, Zhang R. Circle detection using Hough transform. Comput Eng Des. 2008;6:158–60.

    Google Scholar 

  29. Pan B, Xie H. Full-field strain measurement based on least-square fitting of local displacement for digital image correlation method. Acta Opt Sin. 2007;27(11):1980–6.

    Google Scholar 

  30. Gou XF, Yang Y, Zheng XJ. Analytic expression of magnetic field distribution of rectangular permanent magnets. Appl Math Mech. 2004;25:297–306.

    Article  Google Scholar 

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Acknowledgements

This work is supported by the fund of Natural Science Foundation of China (Nos. 11872196, 11902130).

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Authors and Affiliations

  1. Key Laboratory of Mechanics on Disaster and Environment in Western China Attached to the Ministry of Education of China, Lanzhou University, Lanzhou, 730000, China

    Shuaike Jiao, Cong Liu, Jun Zhou, Xingyi Zhang & You-He Zhou

  2. Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, China

    Shuaike Jiao, Cong Liu, Jun Zhou, Xingyi Zhang & You-He Zhou

Authors
  1. Shuaike Jiao
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  2. Cong Liu
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  3. Jun Zhou
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  4. Xingyi Zhang
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  5. You-He Zhou
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Correspondence to Xingyi Zhang.

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Jiao, S., Liu, C., Zhou, J. et al. Extraction on the Contact Forces Among the Opaque and Non-photoelastic Particles Under Electromagnetic Force. Acta Mech. Solida Sin. 35, 248–260 (2022). https://doi.org/10.1007/s10338-021-00293-1

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  • DOI: https://doi.org/10.1007/s10338-021-00293-1

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