Skip to main content
SpringerLink
Log in

Nonlinear static and dynamic mechanical behaviors of Nb3Sn superconducting composite wire: experiment and analysis

Nb3Sn超导复合股线非线性力学行为研究

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, the nonlinear mechanical behaviors of Nb3Sn superconducting composite wires have been investigated by the quasi-static loading-unloading tensile and fatigue tests at the temperature of 77 and 300 K, respectively, which indicates that the quasi-static stress-strain curves and energy dissipations exhibit strong nonlinearity. Meanwhile, the nonlinear and linear unloading modulus are derived by considering the damage degradation, and the elastic-plastic constitutive is proposed to predict the quasi-static loading-unloading stress-strain responses and energy dissipation. Moreover, the damage evolution model has been conducted to elucidate the energy dissipation of fatigue tests for the Nb3Sn composite wire at the temperature of 77 and 300 K. The combination of experimental and theoretical results indicates that the nonlinearity of energy dissipation is caused by damage degradation during quasi-static loading and unloading tensile tests. Furthermore, the fatigue fracture modes of Nb3Sn composite wires also have been analyzed, which indicated that the Nb3Sn sub-elements show brittle fracture at the temperature of 77 K while ductile fracture at the temperature of 300 K. These findings provide novel insights into the nonlinear mechanical behaviors of Nb3Sn superconducting composite wires.

摘要

本文通过对Nb3Sn超导复合股线在77 K和300 K下进行准静态加卸载拉伸和疲劳实验, 研究了Nb3Sn超导复合股线的非线性力学行为, 结果表明: Nb3Sn超导复合股线的准静态应力-应变曲线和能量耗散具有很强的非线性. 同时, 考虑塑性应变产生的损伤退化,推导了卸载过程中非线性和线性卸载模量, 提出了考虑损伤的双曲面弹塑性本构模型来预测准静态加卸载应力-应变响应和能量耗散;通过疲劳损伤演化模型分析和预测Nb3Sn超导复合股线在77 K和300 K下疲劳过程中的能量耗散. 理论与实验结果对比表明: 准静态加卸载拉伸实验中损伤退化是能量损耗产生非线性的主要原因. 此外, 对Nb3Sn超导复合股线的疲劳断裂模式进行了分析, 结果表明: Nb 3Sn芯丝组在77 K时表现为脆性断裂, 在300 K时表现为韧性断裂. 这些新发现为研究Nb3Sn超导复合股线的非线性力学行为提供了新的视角.

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

References

  1. E. Gibney, Fuel for world’s largest fusion reactor ITER is set for test run, Nature 591, 15 (2021).

    Article  Google Scholar 

  2. Neutrino hunt resumes, ITER’s new confidence and Elsevier’s woes, Nature 566, 12 (2019).

    Article  Google Scholar 

  3. M. Breschi, D. Macioce, and A. Devred, Performance analysis of the toroidal field ITER production conductors, Supercond. Sci. Technol. 30, 055007 (2017).

    Article  Google Scholar 

  4. X. Xiao, D. Terentyev, H. Chu, and H. Duan, Theoretical models for irradiation hardening and embrittlement in nuclear structural materials: A review and perspective, Acta Mech. Sin. 36, 397 (2020).

    Article  Google Scholar 

  5. J. Qin, Y. Wu, J. Li, F. Liu, C. Dai, Y. Shi, H. Liu, Z. Mao, A. Nijhuis, C. Zhou, K. A. Yagotintsev, R. Lubkemann, V. A. Anvar, and A. Devred, New design of cable-in-conduit conductor for application in future fusion reactors, Supercond. Sci. Technol. 30, 115012 (2017).

    Article  Google Scholar 

  6. Z. Guo, C. Dai, J. Qin, C. Zhou, J. Li, W. Yu, F. Liu, D. Yang, C. Huang, L. Li, H. Zhang, T. Xue, A. Nijhuis, and A. Devred, Research on mechanical properties of high-performance cable-inconduit conductors with different design, Supercond. Sci. Technol. 33, 045002 (2020).

    Article  Google Scholar 

  7. G. De Marzi, B. Bordini, and D. Baffari, On the mechanisms governing the critical current reduction in Nb3Sn Rutherford cables under transverse stress, Sci. Rep. 11, 1 (2021).

    Article  Google Scholar 

  8. G. Brumfiel, Cable test raises fears at fusion project, Nature 471, 150 (2011).

    Article  Google Scholar 

  9. Y. He, Z. Shi, L. Qiao, G. Xiao, Z. Li, and L. Yang, Electromechanical coupling in high-pressured superconducting Nb3Sn: Analytical and simulation models, Int. J. Mech. Sci. 230, 107541 (2022).

    Article  Google Scholar 

  10. A. Godeke, A review of the properties of Nb3 Sn and their variation with A15 composition, morphology and strain state, Supercond. Sci. Technol. 19, R68 (2006).

    Article  Google Scholar 

  11. W. D. Markiewicz, Comparison of strain scaling functions for the strain dependence of composite Nb3Sn superconductors, Supercond. Sci. Technol. 21, 054004 (2008).

    Article  Google Scholar 

  12. J. E. Duvauchelle, B. Bordini, J. Fleiter, and A. Ballarino, Critical current measurements under transverse pressure of a Nb3 Sn Rutherford cable based on 1 mm RRP wires, IEEE Trans. Appl. Supercond. 28, 1 (2018).

    Article  Google Scholar 

  13. L. Gämperle, J. Ferradas, C. Barth, B. Bordini, D. Tommasini, and C. Senatore, Determination of the electromechanical limits of high-performance Nb3Sn Rutherford cables under transverse stress from a single-wire experiment, Phys. Rev. Res. 2, 013211 (2020).

    Article  Google Scholar 

  14. G. De Marzi, V. Corato, L. Muzzi, A. della Corte, G. Mondonico, B. Seeber, and C. Senatore, Reversible stress-induced anomalies in the strain function of Nb3 Sn wires, Supercond. Sci. Technol. 25, 025015 (2012).

    Article  Google Scholar 

  15. B. Seeber, C. Calzolaio, D. Zurmühle, V. Abächerli, M. Alessandrini, G. De Marzi, and C. Senatore, Reduced strain sensitivity of the critical current of Nb3 Sn multifilamentary wires, J. Appl. Phys. 126, 203905 (2019).

    Article  Google Scholar 

  16. G. Xiao, H. Jin, C. Zhou, H. Ma, D. Wang, F. Liu, H. Liu, A. Nijhuis, and A. Devred, Performance of highly flexible sub-cable for REBCO cable-in-conduit conductor at 5.8 T applied field, Superconductivity 3, 100023 (2022).

    Article  Google Scholar 

  17. N. N. Martovetsky, P. Bruzzone, B. Stepanov, R. Wesche, C. Gung, J. V. Minervini, M. Takayasu, L. F. Goodrich, J. W. Ekin, and A. Nijhuis, Effect of conduit material on CICC performance under high cycling loads, IEEE Trans. Appl. Supercond. 15, 1367 (2005).

    Article  Google Scholar 

  18. P. Bruzzone, A. M. Fuchs, B. Stepanov, and G. Vecsey, Performance evolution of Nb3Sn cable-in-conduit conductors under cyclic load [for Tokamaks], IEEE Trans. Appl. Supercond. 12, 516 (2002).

    Article  Google Scholar 

  19. N. Martovetsky, P. Michael, J. Minervini, A. Radovinsky, M. Takayasu, C. Y. Gung, R. Thome, T. Ando, T. Isono, K. Hamada, T. Kato, K. Kawano, N. Koizumi, K. Matsui, H. Nakajima, G. Nishijima, Y. Nunoya, M. Sugimoto, Y. Takahashi, H. Tsuji, D. Bessette, K. Okuno, N. Mitchell, M. Ricci, R. Zanino, L. Savoldi, K. Arai, and A. Ninomiya, Test of the ITER central solenoid model coil and CS insert, IEEE Trans. Appl. Supercond. 12, 600 (2002).

    Article  Google Scholar 

  20. C. Sanabria, P. J. Lee, W. Starch, T. Blum, A. Devred, M. C. Jewell, I. Pong, N. Martovetsky, and D. C. Larbalestier, Metallographic autopsies of full-scale ITER prototype cable-in-conduit conductors after full testing in SULTAN: 1. The mechanical role of copper strands in a CICC, Supercond. Sci. Technol. 28, 085005 (2015).

    Article  Google Scholar 

  21. D. Yue, X. Zhang, and Y. H. Zhou, Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER Nb3 Sn cable-in-conduit conductors, Acta Mech. Sin. 34, 614 (2018).

    Article  Google Scholar 

  22. J. Tabin, B. Skoczeń, and J. Bielski, Discontinuous plastic flow in superconducting multifilament composites, Int. J. Solids Struct. 202, 12 (2020).

    Article  Google Scholar 

  23. E. Q. Sun, Multi-scale nonlinear stress analysis of Nb3 Sn superconducting accelerator magnets, Supercond. Sci. Technol. 35, 045019 (2022).

    Article  Google Scholar 

  24. W. Prager, A new method of analyzing stresses and strains in work-hardening plastic solids, J. Appl. Mech. 23, 493 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  25. H. Ziegler, A modification of Prager’s hardening rule, Appl. Math. 17, 55 (1959).

    MathSciNet  MATH  Google Scholar 

  26. P. J. Armstrong, and C. O. Frederick, A mathematical representation of the multiaxial Bauschinger effect, Mater. High Temp. 24, 1 (1966).

    Google Scholar 

  27. J. L. Chaboche, Time-independent constitutive theories for cyclic plasticity, Int. J. Plast. 2, 149 (1986).

    Article  MATH  Google Scholar 

  28. F. Yoshida, and T. Uemori, A model of large-strain cyclic plasticity and its application to springback simulation, Int. J. Mech. Sci. 45, 1687 (2003).

    Article  MATH  Google Scholar 

  29. F. Yoshida, and T. Uemori, A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation, Int. J. Plast. 18, 661 (2002).

    Article  MATH  Google Scholar 

  30. M. Lee, D. Kim, C. Kim, M. Wenner, R. Wagoner, and K. Chung, A practical two-surface plasticity model and its application to springback prediction, Int. J. Plast. 23, 1189 (2007).

    Article  MATH  Google Scholar 

  31. J. Y. Lee, M. G. Lee, F. Barlat, and G. Bae, Piecewise linear approximation of nonlinear unloading-reloading behaviors using a multi-surface approach, Int. J. Plast. 93, 112 (2017).

    Article  Google Scholar 

  32. D. C. Pham, Consistent limited kinematic hardening plasticity theory and path-independent shakedown theorems, Int. J. Mech. Sci. 130, 11 (2017).

    Article  Google Scholar 

  33. D. Weichert, and J. Gross-Weege, The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two-surface yield condition, Int. J. Mech. Sci. 30, 757 (1988).

    Article  MATH  Google Scholar 

  34. A. Ghaei, and D. E. Green, Numerical implementation of Yoshida-Uemori two-surface plasticity model using a fully implicit integration scheme, Comput. Mater. Sci. 48, 195 (2010).

    Article  Google Scholar 

  35. A. Ghaei, and A. Taherizadeh, A two-surface hardening plasticity model based on non-associated flow rule for anisotropic metals subjected to cyclic loading, Int. J. Mech. Sci. 92, 24 (2015).

    Article  Google Scholar 

  36. L. J. Jia, Integration algorithm for a modified Yoshida-Uemori model to simulate cyclic plasticity in extremely large plastic strain ranges up to fracture, Comput. Struct. 145, 36 (2014).

    Article  Google Scholar 

  37. H. Hajbarati, and A. Zajkani, A novel analytical model to predict springback of DP780 steel based on modified Yoshida-Uemori two-surface hardening model, Int. J. Mater. Form. 12, 441 (2019).

    Article  Google Scholar 

  38. L. Sun, and R. H. Wagoner, Complex unloading behavior: Nature of the deformation and its consistent constitutive representation, Int. J. Plast. 27, 1126 (2011).

    Article  MATH  Google Scholar 

  39. J. Lee, J. Y. Lee, F. Barlat, R. H. Wagoner, K. Chung, and M. G. Lee, Extension of quasi-plastic-elastic approach to incorporate complex plastic flow behavior—application to springback of advanced high-strength steels, Int. J. Plast. 45, 140 (2013).

    Article  Google Scholar 

  40. E. H. Lee, T. B. Stoughton, and J. W. Yoon, A new strategy to describe nonlinear elastic and asymmetric plastic behaviors with one yield surface, Int. J. Plast. 98, 217 (2017).

    Article  Google Scholar 

  41. H. Hou, G. Zhao, L. Chen, and H. Li, Springback behavior and a new chord modulus model of copper alloy during severe plastic compressive deformation, J. Mater. Process. Tech. 290, 116974 (2021).

    Article  Google Scholar 

  42. N. C. van den Eijnden, A. Nijhuis, Y. Ilyin, W. A. J. Wessel, and H. H. J. ten Kate, Axial tensile stress-strain characterization of ITER model coil type Nb3 Sn strands in TARSIS, Supercond. Sci. Technol. 18, 1523 (2005).

    Article  Google Scholar 

  43. K. Osamura, S. Machiya, Y. Tsuchiya, H. Suzuki, T. Shobu, M. Sato, T. Hemmi, Y. Nunoya, and S. Ochiai, Local strain and its influence on mechanical-electromagnetic properties of twisted and untwisted ITER Nb3 Sn strands, Supercond. Sci. Technol. 25, 054010 (2012).

    Article  Google Scholar 

  44. A. Nijhuis, R. P. Pompe van Meerdervoort, H. J. G. Krooshoop, W. A. J. Wessel, C. Zhou, G. Rolando, C. Sanabria, P. J. Lee, D. C. Larbalestier, A. Devred, A. Vostner, N. Mitchell, Y. Takahashi, Y. Nabara, T. Boutboul, V. Tronza, S. H. Park, and W. Yu, The effect of axial and transverse loading on the transport properties of ITER Nb3 Sn strands, Supercond. Sci. Technol. 26, 084004 (2013).

    Article  Google Scholar 

  45. A. Nijhuis, Mechanical and Electro-Magnetic Performance of Nb3Sn Superconductors for Fusion, Dissertation for Doctoral Degree (University of Twente, Enschede, 2016).

    Google Scholar 

  46. G. Lenoir, P. Manil, F. Nunio, and V. Aubin, Mechanical behavior laws for multiscale numerical model of Nb3 Sn conductors, IEEE Trans. Appl. Supercond. 29, 1 (2019).

    Article  Google Scholar 

  47. H. Bajas, Numerical Simulation of the Mechanical Behavior of the ITER Cable-In-Conduit Conductors, Dissertation for Doctoral Degree (Ecole Centrale de Paris, Paris, 2011).

    Google Scholar 

  48. W. Du, D. Wang, and Y. Zhou, Establishment of 3D multistage models of superconducting cable based on discrete element method, Supercond. Sci. Technol. 34, 085017 (2021).

    Article  Google Scholar 

  49. X. Wang, Y. Li, and Y. Gao, Mechanical behaviors of multi-filament twist superconducting strand under tensile and cyclic loading, Cryogenics 73, 14 (2016).

    Article  Google Scholar 

  50. S. F. Cogan, and R. M. Rose, Fatigue effects in unidirectional composites: Applications to Nb3 Sn superconductors, Appl. Phys. Lett. 35, 884 (1979).

    Article  Google Scholar 

  51. R. Riccioli, Mechanical Modelling of Superconducting Cables for Fusion under Cyclic Electromagnetic and Thermal Loads, Dissertation for Doctoral Degree (University of Bologna, Bologna, 2021).

    Google Scholar 

  52. L. Jiang, X. Su, L. Shen, J. Zhou, and X. Zhang, Damage behavior of Nb3Sn/Cu superconducting strand at room temperature under asymmetric strain cycling, Fusion Eng. Des. 172, 112869 (2021).

    Article  Google Scholar 

  53. A. Vostner, and E. Salpietro, Enhanced critical current densities in Nb3 Sn superconductors for large magnets, Supercond. Sci. Technol. 19, S90 (2006).

    Article  Google Scholar 

  54. C. G. Li, C. J. Xiao, J. Q. Guan, X. G. Sun, J. W. Liu, X. H. Liu, Y. Feng, P. X. Zhang, and J. S. Li, Investigation of superconducting properties of Nb3Sn strands by internal tin process for ITER, IEEE Trans. Appl. Supercond. 20, 1484 (2010).

    Article  Google Scholar 

  55. A. Torkabadi, E. S. Perdahcıoğlu, V. T. Meinders, and A. H. van den Boogaard, On the nonlinear anelastic behavior of AHSS, Int. J. Solids Struct. 151, 2 (2018).

    Article  Google Scholar 

  56. C. S. Grimmer, and C. K. H. Dharan, High-cycle fatigue of hybrid carbon nanotube/glass fiber/polymer composites, J. Mater. Sci. 43, 4487 (2008).

    Article  Google Scholar 

  57. N. Mitchell, Finite element simulations of elasto-plastic processes in Nb3Sn strands, Cryogenics 45, 501 (2005).

    Article  Google Scholar 

  58. J. L. Chaboche, Continuum damage mechanics: Part I—General concepts, J. Appl. Mech. 55, 59 (1988).

    Article  Google Scholar 

  59. J. L. Chaboche, Continuum damage mechanics: Part II—Damage growth, crack initiation, and crack growth, J. Appl. Mech. 55, 65 (1988).

    Article  Google Scholar 

  60. J. Lemaitre, A Course on Damage Mechanics (Springer Science & Business Media, Berlin/Heidelberg, 2012).

    MATH  Google Scholar 

  61. F. Yoshida, T. Uemori, and K. Fujiwara, Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain, Int. J. Plast. 18, 633 (2002).

    Article  MATH  Google Scholar 

  62. M. Safaei, S. Zang, M. G. Lee, and W. De Waele, Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach, Int. J. Mech. Sci. 73, 53 (2013).

    Article  Google Scholar 

  63. D. Systèmes, Abaqus User Subroutines Reference Guide, Version 6.14 (Dassault Systemes Simulia Corp, Providence, 2014).

    Google Scholar 

  64. X. Feng, Y. P. Yao, R. N. Li, Z. Wan, and X. Dai, Loading-unloading judgement for advanced plastic UH model, Acta Mech. Sin. 36, 827 (2020).

    Article  MathSciNet  Google Scholar 

  65. F. Wu, and W. X. Yao, A fatigue damage model of composite materials, Int. J. Fatigue 32, 134 (2010).

    Article  Google Scholar 

  66. J. Lemaitre, and R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures (Springer Science & Business Media, Berlin/Heidelberg, 2005).

    Google Scholar 

  67. V. Kliman, and M. Bílý, Hysteresis energy of cyclic loading, Mater. Sci. Eng. 68, 11 (1984).

    Article  Google Scholar 

  68. Z. Jing, and M. D. Ainslie, Numerical simulation of flux avalanches in type-II superconducting thin films under transient AC magnetic fields, Supercond. Sci. Technol. 33, 084006 (2020).

    Article  Google Scholar 

  69. F. Han, C. Liu, F. Yuan, Y. Zhang, M. Ali, H. Gu, and G. Li, Microscopic characterization on low cycle fatigue behavior at room temperature of Zircaloy-4 alloy with recrystallized microstructure, J. Alloys Compd. 778, 318 (2019).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11872196, 12232005 and U2241267).

Author information

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

    Lang Jiang  (姜浪), Xingyi Zhang  (张兴义) & You-He Zhou  (周又和)

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

    Lang Jiang  (姜浪), Xingyi Zhang  (张兴义) & You-He Zhou  (周又和)

Authors
  1. Lang Jiang  (姜浪)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingyi Zhang  (张兴义)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. You-He Zhou  (周又和)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xingyi Zhang  (张兴义).

Additional information

Author contributions

You-He Zhou and Xingyi Zhang designed the research. Lang Jiang wrote the first draft of the manuscript, set up the experiment set-up and processed the experiment data. Xingyi Zhang helped organize the manuscript, and revised and edited the final version.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, L., Zhang, X. & Zhou, YH. Nonlinear static and dynamic mechanical behaviors of Nb3Sn superconducting composite wire: experiment and analysis. Acta Mech. Sin. 39, 122322 (2023). https://doi.org/10.1007/s10409-022-22322-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-022-22322-x

Search

Navigation