Skip to main content
SpringerLink
Log in

A Theoretical Model for Characterizing the Internal Contact of the CICC Strands under Axial Strain

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

A theoretical model is proposed to calculate the internal contact distributions and contact forces of a 3×4×4×4 twisted Nb3Sn cable under applied axial strain. The critical current density reduction of the whole cable can be calculated. The thin rod theory is employed to analyze the mechanical behavior of each strand. According to the regular helical structure, the contact distribution of each strand is obtained, and the contact force in the cable is analyzed. At last, a prediction about the critical current density of the twisted cable is made. The results show that decreasing the pitch length can reduce the contact forces between strands.

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. Ciazynski, D., Review of Nb3Sn conductors for ITER. Fusion Engineering and Design, 2007, 82: 488–497.

    Article  Google Scholar 

  2. Mitchell, N., Summary, assessment and implications of the ITER model coil test results. Fusion Engineering and Design, 2003, 66: 971–993.

    Article  Google Scholar 

  3. Nijhuis, A., Ilyin, Y., Wessel, S., Krooshoop, E., Feng, L. and Miyoshi, Y., Summary of ITER TF strand testing under axial strain, spatial periodic bending and contact stress. Applied Superconductivity, IEEE Transactions on, 2009, 19: 1516–1520.

    Article  Google Scholar 

  4. Mitchell, N., Bessette, D., Gallix, R., Jong, C., Knaster, J., Libeyre, P., Sborchia, C. and Simon, F., The ITER magnet system. Applied Superconductivity, IEEE Transactions on, 2008, 18: 435–440.

    Article  Google Scholar 

  5. Nijhuis, A., van den Eijnden, N.C., IIyin, Y., van Putten, E.G., Veening, G.J.T., Wessel, W.A.J., den Ouden, A. and ten Kate, H.H.J., Impact of spatial periodic bending and load cycling on the critical current of a Nb3Sn strand. Superconductor Science and Technology, 2005, 18(12): S273.

    Article  Google Scholar 

  6. Shikov, A., Nikulin, A., Silaev, A., Vorobieva, A., Pantsyrnyi, V., Vedernikov, G., Salunin, N. and Sudiev, S., Development of the superconductors for ITER magnet system. Journal of Nuclear Materials, 1998, 258: 1929–1934.

    Article  Google Scholar 

  7. Ulbricht, A., Duchateau, J., Fietz, W., Ciazynski, D., Fillunger, H., Fink, S., Heller, R., Maix, R., Nicollet, S. and Raff, S., The ITER toroidal field model coil project. Fusion Engineering and Design, 2005, 73(2): 189–327.

    Article  Google Scholar 

  8. Zhu, J.Y., Luo, W., Zhou, Y.H. and Zheng, X.J., Contact mechanical characteristics of Nb3Sn strands under transverse electromagnetic loads in the CICC cross-section. Superconductor Science and Technology, 2012, 25(12): 125011.

    Article  Google Scholar 

  9. Mitchell, N., Operating strain effects in Nb3Sn cable-in-conduit conductors. Superconductor Science and Technology, 2005, 18(12): S396.

    Article  Google Scholar 

  10. Nijhuis, A., Ilyin, Y. and Abbas, W., Axial and transverse stress-strain characterization of the EU dipole high current density Nb3Sn strand. Superconductor Science and Technology, 2008, 21(6): 065001.

    Google Scholar 

  11. Nijhuis, A., Van Lanen, E.P.A. and Rolando, G., Optimization of ITER Nb3Sn CICCs for coupling loss, transverse electromagnetic load and axial thermal contraction. Superconductor Science and Technology, 2012, 25(1): 015007.

    Article  Google Scholar 

  12. Nijhuis, A., A solution for transverse load degradation in ITER Nb3Sn CICCs: verification of cabling effect on Lorentz force response. Superconductor Science and Technology, 2008, 21(5): 054011.

    Google Scholar 

  13. Mitchell, N., Mechanical and magnetic load effects in Nb3Sn cable-in-conduit conductors. Cryogenics, 2003, 43(3): 255–270.

    Article  Google Scholar 

  14. Nijhuis, A. and Ilyin, Y., Transverse load optimization in Nb3Sn CICC design; influence of cabling, void fraction and strand stiffness. Superconductor Science and Technology, 2006, 19(9): 945.

    Article  Google Scholar 

  15. Nijhuis, A. and Ilyin, Y., Transverse cable stiffness and mechanical losses associated with load cycles in ITER Nb3Sn and NbTi CICCs. Superconductor Science and Technology, 2009, 22(5): 055007.

    Article  Google Scholar 

  16. Nijhuis, A., Ilyin, Y., Abbas, W., ten Haken, B. and ten Kate, H.H.J, Performance of an ITER CS1 model coil conductor under transverse cyclic loading up to 40,000 cycles. Applied Superconductivity, IEEE Transactions on, 2004, 14(2): 1489–1494.

    Article  Google Scholar 

  17. Nijhuis, A., Noordman, N.H., ten Kate, H.H., Mitchell, N. and Bruzzone, P., Electromagnetic and mechanical characterisation of ITER CS-MC conductors affected by transverse cyclic loading. III. Mechanical properties. Applied Superconductivity, IEEE Transactions on, 1999, 9(2): 165–168.

    Article  Google Scholar 

  18. Ekin, J.W., Effect of stress on the critical current of Nb3Sn multifilamentary composite wire. Applied Physics Letters, 1976, 29(3): 216–219.

    Article  Google Scholar 

  19. Ekin, J., Filamentary A15 superconductors, Springer, 1980.

    Chapter  Google Scholar 

  20. Ekin, J., Effect of transverse compressive stress on the critical current and upper critical field of Nb3Sn. Journal of Applied Physics, 1987, 62(12): 4829–4834.

    Article  Google Scholar 

  21. Mitchell, N., Devred, A., Larbalestier, D.C., Lee, P.J., Sanabria, C. and Nijhuis, A., Reversible and irreversible mechanical effects in real cable-in-conduit conductors. Superconductor Science and Technology, 2013, 26(11): 114004.

    Google Scholar 

  22. Nijhuis, A., Pompe van Meerdervoort, R.P., Krooshoop, H.J.G., Wessel, W.A.J., Zhou, C., Rolando, G., Sanabria, C., Lee, P.J., Larbalestier, D.C., Devred, A., Vostner, A., Mitchell, N., Takahashi, Y., Nabara, Y., Boutboul, T., Tronza, V. and Park, S.H., The effect of axial and transverse loading on the transport properties of ITER Nb3Sn strands. Superconductor Science and Technology, 2013, 26(8): 084004.

    Article  Google Scholar 

  23. Mitchell, N., Analysis of the effect of Nb3Sn strand bending on CICC superconductor performance. Cryogenics, 2002, 42(5): 311–325.

    Article  Google Scholar 

  24. Zhai, Y.H. and Bird, M.D., Florida electro-mechanical cable model of Nb3Sn CICCs for high-field magnet design. Superconductor Science and Technology, 2008, 21(11): 115010.

    Article  Google Scholar 

  25. Qin, J.W., Wu, Y., Warnet, L.L. and Nijhuis, A.CORD, A Novel Numerical Mechanical Model for CICCs. Applied Superconductivity, IEEE Transactions on, 2011, 21(3): 2046–2049.

    Article  Google Scholar 

  26. Qin, J., Wu, Y., Warnet, L.L. and Nijhuis, A., A novel numerical mechanical model for the stress-strain distribution in superconducting cable-in-conduit conductors. Superconductor Science and Technology, 2011, 24(6): 065012.

    Article  Google Scholar 

  27. Zhao, Z.L., Zhao, H.P., Wang, J.S., Zhang, Z. and Feng, X.Q., Mechanical properties of carbon nanotube ropes with hierarchical helical structures. Journal of the Mechanics and Physics of Solids, 2014, 71: 64–83.

    Article  MathSciNet  MATH  Google Scholar 

  28. Hruska, F.H., Radial forces in wire ropes. Wire and Wire Products, 1952, 27(5): 459–463.

    Google Scholar 

  29. Hruska, F.H., Tangential forces in wire ropes. Wire and Wire Products, 1953, 28(5): 455–460.

    Google Scholar 

  30. Utting, W.S. and Jones, N., The response of wire rope strands to axial tensile loads—Part I. Experimental results and theoretical predictions. International Journal of Mechanical Sciences, 1987, 29(9): 605–619.

    Article  Google Scholar 

  31. Elata, D., Eshkenazy, R. and Weiss, M.P., The mechanical behavior of a wire rope with an independent wire rope core. International Journal of Solids and Structures, 2004, 41(5): 1157–1172.

    Article  MATH  Google Scholar 

  32. Raoof, M. and Hobbs, R.E., Analysis of multilayered structural strands. Journal of Engineering Mechanics, 1988, 114(7): 1166–1182.

    Article  Google Scholar 

  33. Jing, Z., Yong, Y.H. and Zhou, Y.H., Theoretical modeling for the effect of twisting on the properties of multifilamentary Nb3Sn superconducting strand. Applied Superconductivity, IEEE Transactions on, 2013, 23(11): 6000307.

    Google Scholar 

  34. Costello, G.A., Theory of Wire Rope. Springer Science & Business Media, 1997.

    Chapter  Google Scholar 

  35. Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, 2013.

  36. Thompson, J.M.T. and Hunt, G.W., A General Theory of Elastic Stability. John Wiley & Sons, 1973.

  37. Johnson, K.L., Contact Mechanics. Cambridge University Press, 1987.

  38. Li, Y., Yang, T., Zhou, Y. and Gao, Y., Spring model for mechanical-electrical properties of CICC in cryogenic-electromagnetic environments. Cryogenics, 2014, 62: 14–30.

    Article  Google Scholar 

  39. Xia, J., Yong, H. and Zhou, Y., A structural mechanics model for the 2-D mechanical characteristics of ITER cable-in-conduit conductor cable under transverse loads. Applied Superconductivity, IEEE Transactions on, 2013, 23: 8401209.

    Article  Google Scholar 

  40. Jia, S.M., Wang, D.M. and Zheng, X.J., Multi-contact behaviors among Nb3Sn strands associated with load cycles in a CS1 cable cross section. Physica C, 2015, 508: 56–61.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, and Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, 730000, Lanzhou, China

    Shuai Dong, Huadong Yong & Youhe Zhou

  2. School of Mechano-Electronic Engineering, Xidian University, 710071, Xi’an, China

    Ze Jing

Authors
  1. Shuai Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ze Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huadong Yong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Youhe Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huadong Yong.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11202087, 11472120 and 11421062), the National Key Project of Magneto-Constrained Fusion Energy Development Program (No. 2013GB110002), the National Key Project of Scientific Instrument and Equipment Development (No. 11327802), and New Century Excellent Talents in University of Ministry of Education of China (NCET-13-0266).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, S., Jing, Z., Yong, H. et al. A Theoretical Model for Characterizing the Internal Contact of the CICC Strands under Axial Strain. Acta Mech. Solida Sin. 29, 455–467 (2016). https://doi.org/10.1016/S0894-9166(16)30264-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(16)30264-6

Key Words

Search

Navigation