BIDIRECTIONAL HOMOGENIZATION METHOD FOR ACCURATE ANALYSIS OF MECHANICAL BEHAVIORS OF Nb<sub>3</sub>Sn SUPERCONDUCTING COILS

He An; Li Jianbo; Xue Cun

doi:10.6052/0459-1879-22-033

Volume 54 Issue 5

May 2022

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He An, Li Jianbo, Xue Cun. Bidirectional homogenization method for accurate analysis of mechanical behaviors of Nb3Sn superconducting coils. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1274-1290 doi: 10.6052/0459-1879-22-033

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He An, Li Jianbo, Xue Cun. Bidirectional homogenization method for accurate analysis of mechanical behaviors of Nb₃Sn superconducting coils. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1274-1290 doi: 10.6052/0459-1879-22-033

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BIDIRECTIONAL HOMOGENIZATION METHOD FOR ACCURATE ANALYSIS OF MECHANICAL BEHAVIORS OF Nb₃Sn SUPERCONDUCTING COILS

doi: 10.6052/0459-1879-22-033

He An^*,
Li Jianbo^*,
Xue Cun^{†
,}

*.
College of Science, Chang’an University, Xi’an 710064, China
†.
School of Mechanics, Civil Engineering and Architecture, NorthwesternPolytechnical University, Xi’an 710072, China

Received Date: 2022-01-17
Accepted Date: 2022-03-07

Available Online: 2022-03-08

Publish Date: 2022-05-01

Abstract

Abstract

Nb₃Sn superconducting magnets can produce high magnetic fields during operation, and the Nb₃Sn superconducting coils subjected to strong electromagnetic force can result in great mechanical strain. The strain sensitivity of Nb₃Sn superconducting material will degrade the critical performance of the Nb₃Sn magnet coil, which has a significant impact on the safety and stability of magnets. Therefore, it is of great scientific significance to accurately calculate the mechanical behavior of superconducting magnets under electromagnetic force. Nb₃Sn superconducting magnets are mainly made of superconducting wires wound into coil structure and solidified by epoxy resin. Nb₃Sn superconducting wire is a composite structure mainly made of multiple microfilament embedded in a copper matrix. Therefore, the size from superconducting filaments to superconducting magnets spans several orders of magnitude, which brings challenges for accurate analysis of the mechanical deformation of superconducting coils. Firstly, the representative element (RVE) homogenization method is used to analyze the equivalent mechanical parameters of the whole coil. By comparing the results of the equivalent homogenization model and the actual structure of the coil, it is found that there are significant errors in the equivalent homogenization model. Therefore, we propose a bidirectional homogenization analysis method with high accuracy and low computational cost to study the stress-strain distribution of each component material (Nb₃Sn filament, copper, and epoxy resin) in the superconducting coil. This method does not require large-scale numerical modeling and the results of this method are in good agreement with that of the actual composite coils, which verifies the effectiveness and accuracy of this method. Finally, based on the proposed multi-scale method, we discuss the stress-strain variations of each layer of the Nb₃Sn superconducting coil versus turns and layers under the electromagnetic force in detail.
- superconducting coils,
- bidirectional homogenization method,
- electromagnetic force,
- stress-strain field

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References(39)

References

[1]	王秋良. 高磁场超导磁体科学. 北京: 科学出版社, 2008 Wang Qiuliang. Superconducting Magnet Science with High Magnetic Field. Beijing: China Science Publishing, 2008 (in Chinese)
[2]	Guan MZ, Wang XZ, Ma LZ, et al. Magnetic field and strain measurements of a superconducting solenoid magnet for CADS injector-II during excitation and quench test. Journal of Superconductivity and Novel Magnetism, 2013, 26(7): 2361-2368 doi: 10.1007/s10948-012-1818-4
[3]	岳动华, 张兴义, 周又和. 国际热核聚变实验堆用管内电缆导体力学行为研究进展. 科学通报, 2018, 63(4): 396-414 (Yue Zhenhua, Zhang Xingyi, Zhou Youhe. Research progress on mechanical behavior of in-tube cable conductors for international thermonuclear experimental reactor. Science Bulletin, 2018, 63(4): 396-414 (in Chinese)
[4]	周又和, 王省哲. ITER超导磁体设计与制备中的若干关键力学问题. 中国科学: 物理学力学天文学, 2013, 43(12): 1558-1569 (Zhou Youhe, Wang Xingzhe. Some key mechanical problems in the design and preparation of ITER superconducting magnets. Chinese Science: Physics, Mechanics and Astronomy, 2013, 43(12): 1558-1569 (in Chinese) doi: 10.1360/132013-166
[5]	Ikuta H, Hirota N, Nakayama Y, et al. Giant magnetostriction in Bi₂Sr₂CaCu₂O₈ single crystal in the superconducting state and its mechanism. Physical Review Letters, 1993, 70(14): 2166-2169 doi: 10.1103/PhysRevLett.70.2166
[6]	Johansen TH. Flux-pinning-induced stress and strain in superconductors: case of a long circular cylinder. Physical Review B, 1999, 60(13): 9690-9703 doi: 10.1103/PhysRevB.60.9690
[7]	Johansen TH. Flux-pinning-induced stress and magnetostriction in bulk superconductors. Superconductor Science and Technology, 2000, 13(10): R121-R137 doi: 10.1088/0953-2048/13/10/201
[8]	Chen H, Yong HD, Zhou YH. XFEM analysis of the fracture behavior of bulk superconductor in high magnetic field. Journal of Applied Physics, 2019, 125(10): 103901 doi: 10.1063/1.5063893
[9]	Ru YY, Yong HH, Zhou YH. Numerical simulation of dynamic fracture behavior in bulk superconductors with an electromagnetic-thermal model. Superconductor Science and Technology, 2019, 32(7): 074001 doi: 10.1088/1361-6668/ab0e93
[10]	Xue F, Zhang ZX, Gou XF. Fracture behavior of an inclined crack interacting with a circular inclusion in a high-TC superconductor under an electromagnetic force. AIP Advances, 2015, 5(11): 117141 doi: 10.1063/1.4936422
[11]	Jing Z, Yong HD, Zhou YH. Shear and transverse stress in a thin superconducting layer in simplified coated conductor architecture with a pre-existing detachment. Journal of Applied Physics, 2013, 114(3): 033907 doi: 10.1063/1.4813869
[12]	Xue C, He A, Yong HD, et al. Magneto-elastic behaviour of thin type-II superconducting strip with field-dependent critical current. Journal of Applied Physics, 2013, 113(2): 023901 doi: 10.1063/1.4773483
[13]	Huang CG, Yong HD, Zhou YH. Critical state model for magneto-elastic problem of thin superconducting disks. Journal of Applied Physics, 2013, 114(3): 033913 doi: 10.1063/1.4815951
[14]	Taylor DMJ, Hampshire DP. The scaling law for the strain dependence of the critical current density in Nb₃Sn superconducting wires. Superconductor Science and Technology, 2005, 18(12): S241-S252 doi: 10.1088/0953-2048/18/12/005
[15]	Markiewicz WD. Comparison of strain scaling functions for the strain dependence of composite Nb₃Sn superconductors. Superconductor Science and Technology, 2008, 21(5): 054004 doi: 10.1088/0953-2048/21/5/054004
[16]	Nijhuis A, van Meerdervoort RPP , Krooshoop HJG, et al. The effect of axial and transverse loading on the transport properties of ITER Nb₃Sn strands. Superconductor Science and Technology, 2013, 26(8): 084004 doi: 10.1088/0953-2048/26/8/084004
[17]	杨绪佳, 何宇新, 张鑫等. Nb₃Sn高场复合超导体临界性能力学变形效应的多尺度模拟. 力学学报, 2022, 54(3): 1-13 Yang Xujia, He Yuxin, Zhang Xin, et al. Multiscale simulation of mechanical deformation effect on critical properties of Nb₃Sn high field composite superconductor. Chinese Journal of Theoretical and Applied Mechanics. 2022, 54 (3): 1-13 (in Chinese))
[18]	Vaghar MR, Garmestani H, Markiewicz WD. Elastoplastic stress analysis of Nb₃Sn superconducting magnet. Journal of Applied Physics, 1996, 80(4): 2490-2500 doi: 10.1063/1.363031
[19]	Ilyin Y, Nijhuis A, Wessel WAJ, et al. Axial tensile stress-strain characterization of a 36 Nb₃Sn strands cable. IEEE Transactions on Applied Superconductivity, 2006, 16(2): 1249-1252 doi: 10.1109/TASC.2006.870801
[20]	Bajas H, Durville D, Ciazynski D, et al. Numerical simulation of the mechanical behavior of ITER cable-in-conduit conductors. IEEE Transactions on Applied Superconductivity, 2010, 20(3): 1467-1470 doi: 10.1109/TASC.2010.2042944
[21]	Scheuerlein C, Michiel MD, Buta F, et al. Stress distribution and lattice distortions in Nb₃Sn multifilament wires under uniaxial tensile loading at 4.2 K. Superconductor Science and Technology, 2014, 27(4): 044021 doi: 10.1088/0953-2048/27/4/044021
[22]	van den Eijnden NC, Nijhuis A, Ilyin Y, et al. Axial tensile stress–strain characterization of ITER model coil type Nb₃Sn strands in TARSIS. Superconductor Science and Technology, 2005, 18(11): 1523-1532 doi: 10.1088/0953-2048/18/11/020
[23]	Boso DP. A simple and effective approach for thermo-mechanical modelling of composite superconducting wires. Superconductor Science and Technology, 2013, 26(4): 045006 doi: 10.1088/0953-2048/26/4/045006
[24]	Boso DP, Lefik M, Schrefler BA. A multilevel homogenized model for superconducting strand thermomechanics. Cryogenics, 2005, 45(4): 259-271 doi: 10.1016/j.cryogenics.2004.09.005
[25]	Boso DP, Lefik M, Schrefler BA. Homogenisation methods for the thermo-mechanical analysis of Nb₃Sn strand. Cryogenics, 2006, 46(7-8): 569-580 doi: 10.1016/j.cryogenics.2006.01.005
[26]	Zhu JY, Luo W, Zhou YH, et al. Contact mechanical characteristics of Nb₃Sn strands under transverse electromagnetic loads in the CICC cross-section. Superconductor Science and Technology, 2012, 25(12): 125011 doi: 10.1088/0953-2048/25/12/125011
[27]	Jia SM, Wang DM, Zheng XJ. Multi-contact behaviors among Nb₃Sn strands associated with load cycles in a CS1 cable cross section. Physica C: Superconductivity and its Applications, 2015, 508: 56-61 doi: 10.1016/j.physc.2014.10.019
[28]	Jing Z, Yong HD, Zhou YH. Theoretical modeling for the effect of twisting on the properties of multifilamentary Nb₃Sn superconducting strand. IEEE Transactions on Applied Superconductivity, 2013, 23(1): 6000307 doi: 10.1109/TASC.2012.2232922
[29]	Liu BX, Jing Z, Yong HD, et al. Strain distributions in superconducting strands with twisted filaments. Composite Structures, 2017, 174: 158-165 doi: 10.1016/j.compstruct.2017.04.047
[30]	吴墨, 戴银明. 15 T NbTi/Nb₃Sn超导磁体的设计. 低温与超导, 2021, 49(8): 17-20 (Wu Mo, Dai Yinming. The design of 15 T NbTi/Nb₃Sn superconducting magnet. Cryogenic and superconducting, 2021, 49(8): 17-20 (in Chinese)
[31]	张红洁, 王秋良, 刘宏伟等. 轴对称高场超导磁体电磁应力有限元分析方法. 低温物理学报, 2017, 39(5): 44-50 (Zhang Hongjie, Wang Qiuliang, Liu Hongwei, et al. Finite element analysis method for electromagnetic stress of axisymmetric high field superconducting magnet. Journal of Cryogenic Physics, 2017, 39(5): 44-50 (in Chinese)
[32]	Guan MZ, Wang XZ, Ma LZ, et al. Magneto-mechanical coupling analysis of a superconducting solenoid magnet in self-magnetic field. IEEE Transactions on Applied Superconductivity, 2014, 24(3): 4900904
[33]	Hu Q, Wang XZ, Guan MZ, et al. Magneto-mechanical coupling analysis of a superconducting solenoid using FEM with different approaches. IEEE Transactions on Applied Superconductivity, 2020, 30(4): 4900305
[34]	Wu BM, Wang XZ, Guan MZ, et al. Mechanical responses of a combined support structure for a Nb₃Sn sextupole magnet during assembly and thermal cycle. IEEE Transactions on Applied Superconductivity, 2020, 30(4): 214-217
[35]	Wu BM, Wang XZ, Guan MZ, et al. Mechanical responses of a semi-open split NbTi superconducting magnet reinforced with cantilever structure. IEEE Transactions on Applied Superconductivity, 2020, 30(4): 579-587
[36]	Zhang HJ, Wang QL, Li XQ, et al. Study on the stress of 500 MHz nmr magnet coils with detailed FE model. IEEE Transactions on Applied Superconductivity, 2011, 21(3): 2304-2307 doi: 10.1109/TASC.2010.2092405
[37]	Amin AA, Baig T, Deissler RJ, et al. A multiscale and multiphysics model of strain development in a 1.5 T MRI magnet designed with 36 filament composite MgB₂ superconducting wire. Superconductor Science and Technology, 2016, 29(5): 055008
[38]	Iwasa Y. Case Studies in Superconducting Magnets: Design and Operational Issues. Springer Science & Business Media, 2009: 207-210
[39]	Bobrov ES, Williams JEC, Iwasa Y. Experimental and theoretical investigation of mechanical disturbances in epoxy-impregnated superconducting coils 2 Shear-stress-induced epoxy fracture as the principal source of premature quenches and training theoretical analysis. Cryogenics, 1985, 25(6): 307-316