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Damage behavior in Bi-2212 round wire with 3D elastoplastic peridynamic

基于三维弹塑性**场动力学的Bi-2212圆线的损伤行为研究

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Abstract

Bi2Sr2Ca1Cu2O8+x (Bi-2212) wire is the potential material for the design of the high field superconducting magnet. However, compared with excellent current-carrying capacity, low mechanical strength can restrict the wide application of Bi-2212 wire. The superconducting filaments of Bi-2212 wire is sensitive to strain and is prone to fracture, which can lead to the degradation of critical current. Therefore, it is necessary to study the damage behavior of Bi-2212 round wire under external loads. In this paper, the three-dimensional mechanical damage and degradation of critical current in Bi-2212 composite wire under axial tensile load, radial compression load, bending and torsional loads are systematically investigated using ordinary state-based elastoplastic peridynamic (PD). The axial tensile simulations with the process of damage and thermal residual stress are in agreement with the experiment, and the critical current degradation with tensile strain is qualitatively predicted. The effect of plastic deformation of alloy on damage of filament bundles under radial compression load is explored. Finally, the simulations also reveal the damage characteristics of filament bundles in Bi-2212 round wire under torsional and bending loads. The above results are expected to provide a reference for application of Bi-2212 HTS round wire.

摘要

Bi2Sr2Ca1Cu2O8+x (Bi-2212)圆线是高场超导磁体研制中极具潜力的材料. 然而, 与优良的载流能力相比, 其较低的力学**度限制 了Bi-2212圆线的广泛应用. Bi-2212圆线的超导芯丝对应变敏感且容易断裂, 进而导致临界电流发生退化, 因此对Bi-2212圆线在外载荷 作用下的损伤行为进行研究是十分必要的. 本文采用常规态型弹塑性**场动力学(PD)方法, 系统研究了Bi-2212复合线材在轴向拉伸载 荷、径向压缩载荷、弯曲载荷和扭转载荷作用下的力学破坏行为和临界电流退化. 在轴向拉伸的计算中考虑了损伤扩展和热残余应 力, 数值结果与实验结果吻合较好, 并且定性预测了临界电流随拉伸应变的退化, 给出了径向压缩载荷下合金的塑性变形对芯丝束破 坏的影响规律. 最后, 数值模拟结果揭示了Bi-2212圆线在扭转和弯曲载荷作用下的芯丝束的破坏特征, 本文的结果可为Bi-2212高温超 导圆线的应用提供理论基础.

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References

  1. D. C. Larbalestier, J. Jiang, U. P. Trociewitz, F. Kametani, C. Scheuerlein, M. Dalban-Canassy, M. Matras, P. Chen, N. C. Craig, P. J. Lee, and E. E. Hellstrom, Isotropic round-wire multifilament cuprate superconductor for generation of magnetic fields above 30 T, Nat. Mater 13, 375 (2014).

    Article  Google Scholar 

  2. T. Shen, J. Jiang, F. Kametani, U. P. Trociewitz, D. C. Larbalestier, J. Schwartz, and E. E. Hellstrom, Filament to filament bridging and its influence on develo** high critical current density in multi-filamentary Bi2Sr2CaCu2Ox round wires, Supercond. Sci. Technol. 23, 025009 (2009).

    Article  Google Scholar 

  3. J. Jiang, W. L. Starch, M. Hannion, F. Kametani, U. P. Trociewitz, E. E. Hellstrom, and D. C. Larbalestier, Doubled critical current density in Bi-2212 round wires by reduction of the residual bubble density, Supercond. Sci. Technol. 24, 082001 (2011).

    Article  Google Scholar 

  4. D. Liu, H. Yong, and Y. Zhou, Analysis of critical current density in Bi2Sr2CaCu2O8+x round wire with filament fracture, J. Supercond. Nov. Magn. 29, 2299 (2016).

    Article  Google Scholar 

  5. D. Liu, J. **a, H. Yong, and Y. Zhou, Estimation of critical current distribution in Bi2Sr2CaCu2Ox cables and coils using a self-consistent model, Supercond. Sci. Technol. 29, 065020 (2016).

    Article  Google Scholar 

  6. J. M. Rey, A. Allais, J. L. Duchateau, P. Fazilleau, J. M. Gheller, R. L. Bouter, O. Louchard, L. Quettier, and D. Tordera, Critical current measurement in HTS Bi2212 ribbons and round wires, IEEE Trans. Appl. Supercond. 19, 3088 (2009).

    Article  Google Scholar 

  7. X. Su, C. Liu, J. Zhou, X. Zhang, and Y. Zhou, A method to access the electro-mechanical properties of superconducting thin film under uniaxial compression, Acta Mech. Sin. 36, 1046 (2020).

    Article  Google Scholar 

  8. J. K. Shin, S. Ochiai, H. Okuda, Y. Mukai, H. Matsubayashi, S. S. Oh, D. W. Ha, S. C. Kim, and M. Sato, Estimation of Young’s modulus, residual strain and intrinsic fracture strain of Bi2212 filaments in Bi2212/Ag/Ag alloy composite wire, Phys. C-Supercond. 468, 1792 (2008).

    Article  Google Scholar 

  9. C. Dai, B. Liu, J. Qin, F. Liu, Y. Wu, and C. Zhou, The axial tensile stress-strain characterization of Ag-sheathed Bi2212 round wire, IEEE Trans. Appl. Supercond. 25, (2015).

  10. A. Kajbafvala, W. Nachtrab, W. ** Feng Lu, F. Hunte, F. **aotao Liu, N. Cheggour, T. Wong, and J. Schwartz, Dispersion-strengthened silver alumina for sheathing Bi2Sr2CaCu2O8+x multifilamentary wire, IEEE Trans. Appl. Supercond. 22, 8400210 (2012).

    Article  Google Scholar 

  11. X. Peng, H. Yong, and Y. Zhou, Damage analysis of superconducting composite wire with bridging model, Acta Mech. Solid Sin. 31, 19 (2018).

    Article  Google Scholar 

  12. Y. Liu, X. Wang, and Y. Gao, Three-dimensional multifilament finite element models of Bi-2212 high-temperature superconducting round wire under axial load, Compos. Struct. 211, 273 (2019).

    Article  Google Scholar 

  13. Y. Yang, H. Yong, and Y. Zhou, Mechanical behavior in superconducting composite wires, Eur. J. Mech.-A Solids 70, 191 (2018).

    Article  Google Scholar 

  14. K. Katagiri, H. S. Shin, Y. Shoji, N. Ebisawa, K. Watanabe, K. Noto, T. Okada, M. Hiraoka, and S. Yuya, Tensile strain/transverse compressive stress dependence of critical current in Ag-sheathed Bi(2212) 7-core superconducting wires, Cryogenics 36, 491 (1996).

    Article  Google Scholar 

  15. A. Godeke, M. H. C. Hartman, M. G. T. Mentink, J. Jiang, M. Matras, E. E. Hellstrom, and D. C. Larbalestier, Critical current of dense Bi-2212 round wires as a function of axial strain, Supercond. Sci. Technol. 28, 032001 (2015).

    Article  Google Scholar 

  16. N. Cheggour, X. F. Lu, T. G. Holesinger, T. C. Stauffer, J. Jiang, and L. F. Goodrich, Reversible effect of strain on transport critical current in Bi2Sr2CaCu2O8+x superconducting wires: a modified descriptive strain model, Supercond. Sci. Technol. 25, 015001 (2011).

    Article  Google Scholar 

  17. C. Dai, J. Qin, B. Liu, P. Liu, Y. Wu, A. Nijhuis, C. Zhou, C. Li, Q. Hao, and S. Liu, Uniaxial strain induced critical current degradation of Ag-sheathed Bi-2212 round wire, IEEE Trans. Appl. Supercond. 28, 1 (2018).

    Google Scholar 

  18. S. Y. Gao, X. S. Yang, Q. B. Hao, C. S. Li, and Y. Zhao, Critical current degradation behavior in Bi-2212 round wires under cyclic transverse stress, Cryogenics 125, 103511 (2022).

    Article  Google Scholar 

  19. Y. F. Wang, Z. F. Jiang, Z. X. Zhang, and X. F. Gou, Interpretation of compressive strain causing critical current degradation of Bi2212 round wires, IEEE Trans. Appl. Supercond. 32, (2022).

  20. Z. Wang, H. Yong, and Y. Zhou, Degradation of critical current in Bi2212 composite wire under compression load, Appl. Math. Mech.- Engl. Ed. 38, 1773 (2017).

    Article  MathSciNet  Google Scholar 

  21. H. Chen, H. Yong, and Y. Zhou, XFEM analysis of the fracture behavior of bulk superconductor in high magnetic field, J. Appl. Phys. 125, 103901 (2019).

    Article  Google Scholar 

  22. Z. **g, Numerical modelling and simulations on the mechanical failure of bulk superconductors during magnetization: based on the phase-field method, Supercond. Sci. Technol. 33, 075009 (2020).

    Article  Google Scholar 

  23. Z. **g, Coupled multiphysics modeling of the thermal-magnetic-mechanical instability behavior in bulk superconductors during pulsed field magnetization, Supercond. Sci. Technol. 35, 054006 (2022).

    Article  Google Scholar 

  24. Q. F. Liu, W. J. Feng, and J. Y. Liu, Flux-pinning-induced stress behaviors in a long superconducting slab with central cuboid hole, Acta Mech. Sin. 37, 1255 (2021).

    Article  MathSciNet  Google Scholar 

  25. S. A. Silling, M. Epton, O. Weckner, J. Xu, and E. Askari, Peridynamic states and constitutive modeling, J. Elasticity 88, 151 (2007).

    Article  MathSciNet  Google Scholar 

  26. R. B. Lehoucq, and S. A. Silling, Force flux and the peridynamic stress tensor, J. Mech. Phys. Solids 56, 1566 (2008).

    Article  MathSciNet  Google Scholar 

  27. Y. D. Ha, and F. Bobaru, Studies of dynamic crack propagation and crack branching with peridynamics, Int. J. Fract. 162, 229 (2010).

    Article  Google Scholar 

  28. H. Zhang, and P. Qiao, A state-based peridynamic model for quantitative fracture analysis, Int. J. Fract. 211, 217 (2018).

    Article  Google Scholar 

  29. M. N. Rahimi, A. Kefal, M. Yildiz, and E. Oterkus, An ordinary state-based peridynamic model for toughness enhancement of brittle materials through drilling stop-holes, Int. J. Mech. Sci. 182, 105773 (2020).

    Article  Google Scholar 

  30. Y. Zhang, and P. Qiao, Peridynamic simulation of two-dimensional axisymmetric pull-out tests, Int. J. Solids Struct. 168, 41 (2019).

    Article  Google Scholar 

  31. L. Y. Ye, C. Y. Guo, C. Wang, C. H. Wang, and X. Chang, Peridynamic solution for submarine surfacing through ice, Ships Offshore Struct. 15, 535 (2020).

    Article  Google Scholar 

  32. Z. Chen, S. Niazi, and F. Bobaru, A peridynamic model for brittle damage and fracture in porous materials, Int. J. Rock Mech. Min. Sci. 122, 104059 (2019).

    Article  Google Scholar 

  33. S. Yang, X. Gu, Q. Zhang, and X. **a, Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete, Acta Mech. Sin. 37, 1104 (2021).

    Article  MathSciNet  Google Scholar 

  34. H. Shen, Y. Ru, H. Wu, X. Hu, H. Yong, and Y. Zhou, Three-dimensional peridynamic modeling of crack initiation and propagation in bulk superconductor during field cooling magnetization, Supercond. Sci. Technol. 34, 085020 (2021).

    Article  Google Scholar 

  35. Y. Ru, H. Yong, and Y. Zhou, Fracture analysis of bulk superconductors under electromagnetic force, Eng. Fract. Mech. 199, 257 (2018).

    Article  Google Scholar 

  36. Y. Ru, H. Yong, and Y. Zhou, Numerical simulation of dynamic fracture behavior in bulk superconductors with an electromagnetic-thermal model, Supercond. Sci. Technol. 32, 074001 (2019).

    Article  Google Scholar 

  37. Q. V. Le, W. K. Chan, and J. Schwartz, Two-dimensional peridynamic simulation of the effect of defects on the mechanical behavior of Bi2Sr2CaCu2Ox round wires, Supercond. Sci. Technol. 27, 115007 (2014).

    Article  Google Scholar 

  38. J. A. Mitchell, A nonlocal, ordinary, state-based plasticity model for peridynamic, Technical Report (Sandia National Lab. Albuquerque, 2011).

    Google Scholar 

  39. E. Madenci, and S. Oterkus, Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening, J. Mech. Phys. Solids 86, 192 (2016).

    Article  MathSciNet  Google Scholar 

  40. H. Pashazad, and M. Kharazi, A peridynamic plastic model based on von Mises criteria with isotropic, kinematic and mixed hardenings under cyclic loading, Int. J. Mech. Sci. 156, 182 (2019).

    Article  Google Scholar 

  41. M. Asgari, and M. A. Kouchakzadeh, An equivalent von Mises stress and corresponding equivalent plastic strain for elastic-plastic ordinary peridynamics, Meccanica 54, 1001 (2019).

    Article  MathSciNet  Google Scholar 

  42. Z. Liu, Y. Bie, Z. Cui, and X. Cui, Ordinary state-based peridynamics for nonlinear hardening plastic materials’ deformation and its fracture process, Eng. Fract. Mech. 223, 106782 (2020).

    Article  Google Scholar 

  43. F. Mousavi, S. Jafarzadeh, and F. Bobaru, An ordinary state-based peridynamic elastoplastic 2D model consistent with J2 plasticity, Int. J. Solids Struct. 229, 111146 (2021).

    Article  Google Scholar 

  44. S. A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids 48, 175 (2000).

    Article  MathSciNet  Google Scholar 

  45. E. Oterkus, and E. Madenci, Peridynamic analysis of fiber-reinforced composite materials, J. Mech. Mater. Struct. 7, 45 (2012).

    Article  Google Scholar 

  46. S. A. Silling, and E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct. 83, 1526 (2005).

    Article  Google Scholar 

  47. H. Zhang, and P. Qiao, An extended state-based peridynamic model for damage growth prediction of bimaterial structures under thermo-mechanical loading, Eng. Fract. Mech. 189, 81 (2018).

    Article  Google Scholar 

  48. A. Katiyar, J. T. Foster, H. Ouchi, and M. M. Sharma, A peridynamic formulation of pressure driven convective fluid transport in porous media, J. Comput. Phys. 261, 209 (2014).

    Article  MathSciNet  Google Scholar 

  49. M. N. Rahimi, A. Kefal, and M. Yildiz, An improved ordinary-state based peridynamic formulation for modeling FGMs with sharp interface transitions, Int. J. Mech. Sci. 197, 106322 (2021).

    Article  Google Scholar 

  50. Z. F. Jiang, X. F. Gou, and T. G. Wang, Role of the complex interface between Bi2Sr2CaCu2Ox filaments and the Ag matrix in the mechanical and electrical behaviors of composite round wires, IEEE Trans. Appl. Supercond. 30, (2020).

  51. J. K. Shin, S. Ochiai, M. Sugano, H. Okuda, Y. Mukai, M. Sato, S. S. Oh, D. W. Ha, and S. C. Kim, 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, Supercond. Sci. Technol. 21, 075018 (2008).

    Article  Google Scholar 

  52. J. V. J. Congreve, Y. Shi, K. Y. Huang, A. R. Dennis, J. H. Durrell, and D. A. Cardwell, Characterisation of the mechanical failure and fracture mechanisms of single grain Y-Ba-Cu-O bulk superconductors, Supercond. Sci. Technol. 33, 015003 (2019).

    Article  Google Scholar 

  53. A. V. Zlobin, I. Novitski, and E. Barzi, Conceptual design of a HTS dipole insert based on Bi2212 rutherford cable, Instruments 4, 29 (2020).

    Article  Google Scholar 

  54. L. Liu, W. Chen, J. Shi, C. S. Li, Q. Hao, M. Pan, X. Yang, Y. Zhang, and Y. Zhao, Influence of torsional strain on the Bi-2212 tapes and round wires under background field, Fusion Eng. Des. 124, 86 (2017).

    Article  Google Scholar 

  55. N. Mitchell, Analysis of the effect of Nb3Sn strand bending on CICC superconductor performance, Cryogenics 42, 311 (2002).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12172155, U2241267, and 11872195).

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Authors and Affiliations

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

    Yanze **ao  (肖雁泽), Jianbing Wu  (吴建兵), Huiting Shen  (沈慧婷) & Huadong Yong  (雍华东)

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

    Yanze **ao  (肖雁泽), Jianbing Wu  (吴建兵), Huiting Shen  (沈慧婷) & Huadong Yong  (雍华东)

  3. Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, China

    **aokun Hu  (胡晓锟)

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  1. Yanze **ao  (肖雁泽)
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Contributions

Huadong Yong created conceptualization, edited the final version and provided the funding. Yanze **ao carried out numerical simulations, performed the data analysis, and wrote the first draft and Fortran code. Jianbing Wu, **aokun Hu and Huiting Shen performed the data analysis.

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Correspondence to Huadong Yong  (雍华东).

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**ao, Y., Wu, J., Shen, H. et al. Damage behavior in Bi-2212 round wire with 3D elastoplastic peridynamic. Acta Mech. Sin. 39, 422431 (2023). https://doi.org/10.1007/s10409-023-22431-x

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