Skip to main content
Log in

Degradation of critical current in Bi2212 composite wire under compression load

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Since Bi2Sr2Ca1Cu2O8+x(Bi2212) wires are subject to mechanical loadings, degradation of critical current will occur. The effect of compressive loadings on the critical current of Bi2212 wire is studied by considering micro-buckling of filament. A Bi2212 wire is regarded as a unidirectional filament-reinforced composite in the theoretical analysis. By considering the influence of inclusion, the micro-buckling wavelength can be derived by using a two-dimensional model. Based on the experimental results, the critical current is fitted as a function of buckling wavelength. It is found that the decrease of the critical current is directly proportional to the reciprocal of square of the buckling wavelength. Change of micro-buckling wavelength with material parameters is discussed. A critical strain in the wire with a filament bridge is analyzed using the finite element method.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Miao, H., Kitaguchi, H., Kumakura, H., and Togano, K. Bi2Sr2CaCu2Ox/Ag multilayer tapes with Jc > 500 000 A/cm2 at 4.2 K and 10 T by using pre-annealing and intermediate rolling process. Physica C: Superconductivity, 303, 81–90 (1998)

    Article  Google Scholar 

  2. Shen, T., Ye, L., Turrioni, D., and Li, P. High-field quench behavior and dependence of hot spot temperature on quench detection voltage threshold in a Bi2Sr2CaCu2Ox coil. Superconductor Science and Technology, 28, 075014 (2015)

    Article  Google Scholar 

  3. Holesinger, T., Johnson, J., Coulter, J., and Safar, H. Isothermal melt processing of Bi2Sr2CaCu2Oy round wire. Physica C: Superconductivity, 253, 182–190 (1995)

    Article  Google Scholar 

  4. Cheggour, N., Lu, X. F., Holesinger, T. G., and Stauffer, T. C. Reversible effect of strain on transport critical current in Bi2Sr2CaCu2O8+x superconducting wires: a modified descriptive strain model. Superconductor Science and Technology, 25, 015001 (2012)

    Article  Google Scholar 

  5. Naderi, G., Liu, X., Nachtrab, W., and Schwartz, J. Understanding processing-microstructureproperties relationships in Bi2Sr2CaCu2Ox/Ag round wires and enhanced transport through sawtooth processing. Superconductor Science and Technology, 26, 105010 (2013)

    Article  Google Scholar 

  6. Godeke, A., Hartman, M. H. C., Mentink, M. G. T., and Jiang, J. Critical current of dense Bi-2212 round wires as a function of axial strain. Superconductor Science and Technology, 28, 032001 (2015)

    Article  Google Scholar 

  7. Shen, T., Ghosh, A., and Cooley, L. Role of internal gases and creep of Ag in controlling the critical current density of Ag-sheathed Bi2Sr2CaCu2Ox wires. Journal of Applied Physics, 113, 213901 (2013)

    Article  Google Scholar 

  8. Shin, J. K., Ochiai, S., Sugano, M., and Okuda, H. Analysis of the residual strain change of Bi2212, Ag alloy and Ag during the heating and cooling process in Bi2212/Ag/Ag alloy composite wire. Superconductor Science and Technology, 21, 075018 (2008)

    Article  Google Scholar 

  9. Shen, T., Li, P., Jiang, J., and Cooley, L. High strength kiloampere Bi2Sr2CaCu2Ox cables for high-field magnet applications. Superconductor Science and Technology, 28, 065002 (2015)

    Article  Google Scholar 

  10. Bjoerstad, R., Scheuerlein, C., Rikel, M. O., and Ballarino, A. Strain induced irreversible critical current degradation in highly dense Bi-2212 round wire. Superconductor Science and Technology, 28, 062002 (2015)

    Article  Google Scholar 

  11. Callaway, E. B., Naderi, G., van Le, Q., and Schwartz, J. Statistical analysis of the relationship between electrical transport and filament microstructure in multifilamentary Bi2Sr2CaCu2Ox/Ag/Ag-Mg round wires. Superconductor Science and Technology, 27, 044020 (2014)

    Article  Google Scholar 

  12. Dai, C., Liu, B., Qin, J., and Liu, F. The axial tensile stress-strain characterization of Ag-sheathed Bi2212 round wire. IEEE Transactions on Applied Superconductivity, 25, 6400304 (2015)

    Google Scholar 

  13. Lu, X., Goodrich, L., van der Laan, D., and Splett, J. Correlation between pressure dependence of critical temperature and the reversible strain effect on the critical current and pinning force in wires. IEEE Transactions on Applied Superconductivity, 22, 8400307 (2012)

    Article  Google Scholar 

  14. Ochiai, S., Hayashi, K., and Osamura, K. Influence of thermal cycling on critical current of superconducting silver-sheathed high Tc oxide wires. Cryogenics, 31, 954–961 (1991)

    Article  Google Scholar 

  15. Shin, J. K., Ochiai, S., Okuda, H., and Mukai, Y. Estimation of Young’s modulus, residual strain and intrinsic fracture strain of Bi2212 filaments in Bi2212/Ag/Ag alloy composite wire. Physica C: Superconductivity, 468, 1792–1795 (2008)

    Article  Google Scholar 

  16. Rosen, B. W. Mechanics of Composite Strengthening, NASA, United States (1965)

    Google Scholar 

  17. Aboudi, J. and Gilat, R. Buckling analysis of fibers in composite materials by wave propagation analogy. International Journal of Solids and Structures, 43, 5168–5181 (2005)

    Article  MATH  Google Scholar 

  18. Parnes, R. and Chiskis, A. Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling. Journal of the Mechanics and Physics of Solids, 50, 855–879 (2002)

    Article  MATH  Google Scholar 

  19. Andrianov, I. V., Kalamkarov, A. L., and Weichert, D. Buckling of fibers in fiber-reinforced composites. Composites Part B: Engineering, 43, 2058–2062 (2012)

    Article  Google Scholar 

  20. Kametani, F., Shen, T., Jiang, J., and Scheuerlein, C. Bubble formation within filaments of melt-processed Bi2212 wires and its strongly negative effect on the critical current density. Superconductor Science and Technology, 24, 075009 (2011)

    Article  Google Scholar 

  21. Jiang, J., Miao, H., Huang, Y., and Hong, S. Reduction of gas bubbles and improved critical current density in Bi-2212 round wire by swaging. IEEE Transactions on Applied Superconductivity, 23, 6400206 (2013)

    Article  Google Scholar 

  22. Zhang, G. and Latour, R. A. An analytical and numerical study of fiber microbuckling. Composites Science and Technology, 51, 95–109 (1994)

    Article  Google Scholar 

  23. Shen, T., Jiang, J., Kametani, F., and Trociewitz, U. P. Filament to filament bridging and its influence on developing high critical current density in multifilamentary Bi2Sr2CaCu2Ox round wires. Superconductor Science and Technology, 23, 025009 (2010)

    Article  Google Scholar 

  24. Lu, Y., Wang, Z., Yong, H., and Zhou, Y. Modeling effects of gas bubbles on the mechanical behaviors of Ag/Bi-2212 round wires using a double cantilever beam bridge model. Cryogenics, 77, 65–73 (2016)

    Article  Google Scholar 

  25. Le, Q. V., Chan, W. K., and Schwartz, J. Two-dimensional peridynamic simulation of the effect of defects on the mechanical behavior of Bi2Sr2CaCu2Ox round wires. Superconductor Science and Technology, 27, 115007 (2014)

    Article  Google Scholar 

  26. Kirchhoff, G. R. Über das gleichgewicht und die bewegung einer elastischen scheibe. Journal für die Reine und Angewandte Mathematik, 1850, 51–88 (1850)

    Article  Google Scholar 

  27. Latour, R. and Zhang, G. The Effect of Interfacial Bonding upon Compressive Strength and Fracture Energy of Carbon Fiber Reinforced Polymer (CFRP) Composite: a Theoretical Investigation, American Society for Testing and Materials, West Conshohocken (1993)

    Book  Google Scholar 

  28. Sun, Z., Gou, X., and Schwartz, J. A three-dimensional fractal-based study of the effects of the complex interface between Bi2Sr2CaCu2Ox filaments and the Ag matrix on the mechanical behavior of composite round wires. IEEE Transactions on Applied Superconductivity, 25, 6400808 (2015)

    Google Scholar 

  29. Hojo, M., Nakamura, M., Matsuoka, T., and Tanaka, M. Microscopic fracture of filaments and its relation to the critical current under bending deformation in (Bi, Pb)2Sr2Ca2Cu3O10 composite superconducting tapes. Superconductor Science and Technology, 16, 1043–1051 (2003)

    Article  Google Scholar 

  30. Liu, D., Yong H., and Zhou, Y. Analysis of critical current density in Bi2Sr2CaCu2O8+x round wire with filament fracture. Journal of Superconductivity and Novel Magnetism, 29, 2299–2309 (2016)

    Article  Google Scholar 

  31. Liu, D., Xia, J., Yong, H., and Zhou, Y. Estimation of critical current distribution in Bi2Sr2CaCu2Ox cables and coils using a self-consistent model. Superconductor Science and Technology, 29, 065020 (2016)

    Article  Google Scholar 

  32. Yong, H., Jing, Z., and Zhou, Y. Analysis of strain effect on critical current density in superconductors with a modified semiempirical Kim model. IEEE Transactions on Applied Superconductivity, 23, 8002806 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Huadong Yong.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11327802, 11472120, and 11421062), the National Key Project of Magneto-Constrained Fusion Energy Development Program (No. 2013GB110002), and the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-k18)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Yong, H. & Zhou, Y. Degradation of critical current in Bi2212 composite wire under compression load. Appl. Math. Mech.-Engl. Ed. 38, 1773–1784 (2017). https://doi.org/10.1007/s10483-017-2286-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-017-2286-8

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation