参考文献
[1] Devred A, Backbier I, Bessette D, et al. Status of ITER conductor development and production [J]. IEEE Trans. Appl. Supercond, 2012, 22(3):4804909.
[2] 王秋良.高磁场超导科学[M].北京：科学出版社，2006.
[3] Ferracin P, Devaux M, Durante M, et al. Development of the EuCARD Nb3Sn dipole magnet FRESCA2 [J]. IEEE Trans. Appl. Supercond, 2013, 23(3):4002005.
[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[J].中国科学：物理学 力学 天文学，2013，43（12）：1558-1569.
[5] C B. Müller and Saur E J. Influence of Mechanical Constraints on the Superconducting Transition of Nb3Sn-Coated Niobium Wires and Ribbons [M]. Springer, 1963.
[6] Buehler E, Levinstein H J. Effect of tensile stress on the transition temperature and current-carrying capacity of Nb3Sn [J]. Appl. Phys, 1965, 36(12):3856-3860.
[7] Ekin J W. Strain scaling law for flux pinning in practical superconductors. Part 1: Basic relationship and application to Nb3Sn conductors [J]. Cryogenics, 1980, 20:611-624.
[8] Nijhuis A, Ilyin Y, Abbas W, et al. Summary of ITER TF Nb3Sn strand testing under axial strain, spatial periodic bending and contact stress [J]. IEEE Trans. Appl. Supercond, 2009, 19(3):1516-1520.
[9] Liu B, Wu Y, Liu F, et al. Axial strain characterization of the Nb3Sn strand used for China's TF conductor [J]. Fusion Eng. Des, 2011, 86(1):1-4.
[10] Zhang P X, Liang M, Tang X D, et al. Strain influence on Jcbehavior of Nb3Sn multifilamentary strands fabricatd by internal tin process for ITER [J]. Physica C, 2008, 46(15-20):1843-1846.
[11] 程军胜，王秋良，戴银明，等.低温超导体Nb3Sn扩散热处理中显微组织的表征与分析[J].稀有金属材料与工程，2008，37（S4）：189-192.
[12] Seeber B, Mondonico G and Senatore C. Toward a standard for critical current versus axial strain measurements of Nb3Sn [J]. Supercond. Sci. Technol, 2012, 25:054002-8.
[13] Oguro H, Awaji S, Watanabe K, et al. Mechanical and superconducting properties of Nb3Sn wires with Nb-rod-processed CuNb reinforcement [J]. Supercond. Sci. Technol, 2013, 26:094002-4.
[14] Ekin J W. Effect of transverse compressive stress on the critical current and upper critical field of Nb3Sn [J]. J. Appl. Phys, 1987, 62:4829-4836.
[15] Ekin J W and Bray S L. Critical current degradation in Nb3Sn composite wires due to locally concentrated transverse stress [J]. Adv. Cryog. Eng, 1992, 38:643.
[16] Mitchell N. Two-way interaction between the strand voltage-current characteristic and the overall conductor behavior in cabled low temperature superconductors [J]. Physica C, 2004, 401:28-39.
[17] Nishijima G, Watanabe K, Araya T, et al. Effect of transverse compressive stress on internal reinforced Nb3Sn superconducting wires and coils [J]. Cryogenics, 2005, 42:653-658.
[18] Chiesa L, Takayasu M, Minervini J V, et al. Experimental studies of transverse stress effects on the critical current of a sub-sized Nb3Sn superconducting cable [J]. IEEE Trans. Appl. Supercond, 2007, 17(2):1386-1389.
[19] Seeber B, Ferreira A, Abacherli V, et al. Critical current of a Nb3Sn bronze route conductor under uniaxial tensile and transverse compressive stress [J]. Supercond. Sci. Technol, 2007, 20: S184-S188.
[20] Nijhuis A, Abbas W, Ilyin Y. Axial and transverse stress-strain characterization of the EU dipole high current density Nb3Sn strand [J]. Supercond. Sci. Technol, 2008, 21:065001-10.
[21] Nijhuis A, Pompe van Meerdervoort R P, Krooshoop H J G, et al. The effect of axial and transverse loading on the transport properties of ITER Nb3Sn strands [J]. Supercond. Sci. Technol, 2013, 26:084004-19.
[22] Mitchell N, Devred A, Larbalestier D C, et al. Reversible and irreversible mechanical effects in real cable-in-conduit conductors [J]. Supercond. Sci. Technol, 2013, 26:114004-19.
[23] Banno N, Uglietti D, Seeber B, et al. Field and strain dependence of critical current in technical Nb3Al superconductors [J]. Supercond. Sci. Technol, 2005, 18: S338-S343.
[24] Osamura K, Machiya S, Tsuchiya Y, et al. Thermal strain exerted on superconductive filaments in practical Nb3Sn and Nb3Al strands [J]. Supercond. Sci. Technol, 2013, 26:094001-8.
[25] Ekin J W. Unified scaling law for flux pinning in practical superconductors: I. Separability postulate, raw scaling data and parameterization at moderate strains [J]. Supercond. Sci. Technol, 2010, 23:083001-30.
[26] Summers L T, Guinan M W, Miller J R, et al. A model for the prediction of Nb3Sn critical current as a function of field, temperature, strain, and radiation damage [J]. IEEE Trans. Magn, 1991, 27(2):2041-2044.
[27] Taylor D M J and Hampshire D P. The scaling law for the strain dependence of the critical current density in Nb3Sn superconducting wires [J]. Supercond. Sci. Technol, 2005, 18: S241-S252.
[28] Ten Haken B, Godeke A. The influence of compressive and tensile axial strain on the critical properties of Nb3Sn conductors [J]. IEEE Trans. Appl. Supercond, 2004, 5(2):1909-1912.
[29] Denis Markiewicz W. Elastic stiffness model for the critical temperature Tcof Nb3Sn including strain dependence [J]. Cryogenics, 2004, 44:767-782.
[30] Denis Markiewicz W. Invariant strain analysis of the critical temperature Tcof Nb3Sn [J]. IEEE Trans. Appl. Supercond, 2005, 15(2):3368-3371.
[31] Denis Markiewicz W. Invariant temperature and field strain functions for Nb3Sn composite superconductors [J]. Cryogenics, 2006, 46:846-863.
[32] Denis Markiewicz W. Comparison of strain scaling functions for the strain dependence of composite Nb3Sn superconductors [J]. Supercond. Sci. Technol, 2008, 21:054004-11.
[33] Oh S, Kim K. A scaling law for the critical current of Nb3Sn strands based on strongcoupling theory of superconductivity [J]. J. Appl. Phys, 2006, 99:033909-8.
[34] Godeke A, ten Haken B, ten Kate H H J, et al. A general scaling relation for the critical current density in Nb3Sn [J]. Supercond. Sci. Technol, 2006, 19: R100-R116.
[35] Godeke A. Performance boundaries in Nb3Sn superconductors [D]. Enschede, The Netherlands: University of Twente, 2005.
[36] Arbelaez D, Godeke A and Prestemon S O. An improved model for the strain dependence of the superconducting properties of Nb3Sn [J]. Supercond. Sci. Technol, 2009, 22:025005-6.
[37] Bordini B, Alknes P, Bottura L, et al. An exponential scaling law for the strain dependence of the Nb3Sn critical current density [J]. Supercond. Sci. Technol, 2013, 26:075014-10.
[38] Valentinis D F, Berthod C, Bordini B, et al. A theory of the strain-dependent critical field in Nb3Sn, based on anharmonic phonon generation [J]. Supercond. Sci. Technol, 2014, 27:025008.
[39] Yong H D, Xue F, Zhou Y H. Effect of strain on depairing current density in deformable superconducting thin films [J]. J. Appl. Phys, 2011, 110:033905-4.
[40] Yong H D, Zhou Y H. Depairing current density in superconducting film with shear deformation [J]. J. Appl. Phys, 2012, 111:053929-5.
[41] Jing Z, Yong H D and Zhou Y H. The effect of strain on the vortex structure and electromagnetic properties of a mesoscopic superconducting cylinder [J]. Supercond. Sci. Technol, 2013, 26:075021-9.
[42] De Marzi G, Corato V, Muzzi L, et al. Reversible stress-induced anomalies in the strain function of Nb3Sn wires [J]. Supercond. Sci. Technol, 2012, 25:025015-7.
[43] Mondonico G, Seeber B, Ferreira A, et al. Effect of quasi-hydrostatical radial pressure on Icof Nb3Sn wires [J]. Supercond. Sci. Technol, 2012, 25:115002-9.
[44] De Marzi G, Morici L, Muzzi L, et al. Strain sensitivity and superconducting properties of Nb3Sn from first principles calculations [J]. J. Phys. : Condens. Matter, 2013, 25(13):135702.
[45] 崔俊芝，曹礼群.基于双尺度渐进分析的有限元算法[J].计算数学，1998，20（1）：89-102.
[46] 杨卫，黄克智.材料的多尺度力学与强韧化设计[C].“力学2000”学术大会论文集，2000：39-47.
[47] 吴世平，唐绍锋，梁军，等.周期性复合材料热力耦合性能的多尺度方法[J].哈尔滨工业大学学报，2006（12）：2049-2053.
[48] 白以龙，汪海英，夏蒙棼，等.固体的统计细观力学——连接多个耦合的时空尺度[J].力学进展，2006，36（2）：286-305.
[49] 范镜泓.材料变形与破坏的多尺度分析[M].北京：科学出版社，2008.
[50] 张洪武.参变量变分原理与材料和结构力学分析[M].北京：科学出版社，2010.
[51] 郑晓霞，郑锡涛，缑林虎.多尺度方法在复合材料力学分析中的研究进展[J].力学进展，2010，40（1）：41-56.
[52] LIorca J, González C, Molina-Aldareguía J M, et al. Multiscale modeling of composite materials: a road map towards virtual testing [J]. Adv. Mater, 2011, 23:5130-5147.
[53] Boso D P, Lefik M, and Schrefler B A. A multilevel homogenized model for superconducting strand thermomechanics [J]. Cryogenics, 2005, 45:259-271.
[54] Boso D P. A simple and effective approach for thermo-mechanical modeling of composite superconducting wires [J]. Supercond. Sci. Technol, 2013, 26:045006-12.
[55] Ravaioli E, Auchmann B, Datskov V I, et al. Advanced quench protection for the Nb3Sn quadrupoles for the high luminosity LHC [J]. IEEE Trans. Appl. Supercond, 2016, 26(3):1-6.
[56] Wipf S. Proceedings of the 1968 summer study on superconducting devices and accelerators. Part I. [EB/OL]. https: //www. osti. gov/biblio/4778086, 2021-3-29.
[57] Bartlett R J, Carlson R V, and Overton Jr W C. Asymmetry of normal zone propagation velocity with respect to current in a multifilamentary composite superconductor [J]. IEEE Trans. Magn, 1979, MAG15(1):343-346.
[58] Clem J R, and Bartlett R J. Theory of current-direction dependence of normal-zone propagation velocity in multifilamentary composite condctors [J]. IEEE Trans. Magn, 1983, MAG19(3):424-427.
[59] Murase S, Murakami T, Seto T, et al. Normal zone propagation and quench characteristics of Nb3Sn wires with jelly-roll and in-situ processed CuNb reinforcements [J]. IEEE Trans. Appl. Supercond, 2001, 11(1):3627-3630.
[60] Ouden A D, Wessel W A J, Krooshoop H J G, Weeren H V, ten Kate H H J, Kirby G A, et al. Conductor related design considerations for a 1 meter 10T Nb3Sn dipole magnet [J]. IEEE Trans. Appl. Supercond, 2003, 13(2):1288-1291.
[61] Ghosh A K, Sperry E A, Cooley L D, et al. Dynamic stability threshold in high-performance internal-tin Nb3Sn superconductors for high field magnets [J]. Supercond. Sci. Technol, 2005, 18: L5-L8.
[62] Caspi S, Bartlett S E, Dietderich D R, et al. Measured strain in Nb3Sn coils during excitation and quench [J]. IEEE Trans. Appl. Supercond, 2005, 15(2):1461-1464.
[63] Yamamoto T, Watanabe K, Murase S, Nishijima G, et al. Thermal stability of reinforced Nb3Sn composite superconductor under crycooled conditions [J]. Cryogenics, 2004, 44:687-693.
[64] Ouden A D, Weeren H V, Wessel W A J, et al. Normal zone propagation in high-current density Nb3Sn conductors for accelerator magnets [J]. IEEE Trans. Appl. Supercond, 2004, 14(2):279-282.
[65] Breschi M, Trevisani L, Bottura L, et al. Comparing thermal stability of NbTi and Nb3Sn wires [J]. Supercond. Sci. Technol, 2009, 22:025019-10.
[66] Rapper, de, Willem Michiel. Thermal stability of Nb3Sn Rutherford cables for accelerator magnets [D]. University of Twente, 2014.
[67] Xu X, Sumption M D, and Collings E W. Influence of heat treatment temperature and Ti doping on low-field flux jumping and stability in (Nb-Ta)3Sn strands [J]. Supercond. Sci. Technol, 2014, 27:095009-10.
[68] Fleiter J, Bordini B, Ballarino A, et al. Quench propogation in Nb3Sn rutherford cables for the Hi-Lumi quadrupole magnets [J]. IEEE Trans. Appl. Supercond, 2015, 25(3):4802504-4.
[69] Salmi, Tiina. Optimization of quench protection heater performance in high-field accelerator magnets through computational and experimental analysis [D]. Tampere: Tampere University of Technology, 2015.
[70] Manfreda G, Bellina F, Bajas H, et al. Analysis of quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part Ⅱ: Model predictions and comparison with experimental results [J]. Cryogenics, 2016, 80:364-373.
[71] Izquierdo Bermudez S, Auchmann B, Bajas H, et al. Quench protection studies of the 11T Nb3Sn dipole for the LHC upgrade [J]. IEEE Trans. Appl. Supercond, 2016, 26(4):4701605-5.
[72] Xu X, Sumption M D, Bhartiya S, et al. Critical current density and microstructures in Rod-in-Tube and Tube Type Nb3Sn strands-Present status and prospects for improvement [J]. Supercond. Sci. Technol, 2013, 26:075015.
[73] Iwasa Y, Kim J B, Ayai N, et al. A niobium-aluminium (Nb3Al) coil: performance, including quench behavior, in the temperature range 4.2-12K [J]. Cryogenics, 1996, 36(9):675-679.
[74] Takeuchi T. Nb3Al conductors for high-field applications [J]. Supercond. Sci. Technol, 2000, 13: R101-R119.
[75] Murase S, Shimoyama M, Nanato N, et al. Quench and normal zone propagation characteristics of RHQT-processed Nb3Al wires under cryocooler-cooling conditions [J]. IEEE Trans. Appl. Supercond, 2009, 19(3):2666-2669.
[76] Wilson M N. Superconducting magnet [M]. New York: Oxford University Press, 1983.
[77] Joshi C H, Iwasa Y. Prediction of current decay terminal voltages in adiabatic superconducting magnets [J]. Cryogenics, 1988, 29(3):157-167.
[78] Chechetkin V R, and Sigov A S. Stability of superconducting magnet systems subject to thermal disturbances [J]. Phys. Rep, 1989, 176:1-81.
[79] Picaud V, Hiebei P, and Kauffmann J M. Superconducting coils quench simulation, the Wilson's method revisited [J]. IEEE Trans. Magn, 2002, 38(2):1253-1256.
[80] Hale J R, and Williams J E C. High-field magnets. 2 The transient stabilization of Nb3Sn composite Ribbon magnets [J]. J. Appl. Phys, 1968, (39):2634-2638.
[81] Ünal A. Operational stability analysis for superconductors under thermal disturbances [D]. Texas, the United States of American: Texas Tech University, 1992.
[82] Shaji A, Freiderg J P. Quench in superconducting magnets. I. Model and numerical implementation [J]. J. Appl. Phys, 1994, 76:3149-3158.
[83] Bottura L. A numerical model for the simulation of quench in the ITER Magnets [J]. Comput. Phys, 1996., 125:26-41.
[84] Koizumi N, Takahashi Y, Tsuji H. Numerical model using an implicit finite difference algorithm for stability simulation of a cable-in-conduit superconductor [J]. Cryogenics, 1996, 36:649-659.
[85] Murakami T, Murase S, Shimamoto S, et al. Two-dimensional quench simulation of composite CuNb/Nb3Sn conductors [J]. Cryogenics, 2000, 40:393-401.
[86] 南和礼.绝热超导磁体失超过渡过程的数值模拟研究[J].低温物理学报，2000（4）：299-305.
[87] Yamada R, Marscin E, Lee A, et al. 2-D/3-D quench simulation using Ansys for epoxy impregnated Nb3Sn high field magnets [J]. IEEE Trans. Appl. Supercond, 2003, 13(2):1696-1699.
[88] Yamada R, Wake M. Three dimensional fem quench simulations of superconducting strands[C]. 19th International Conference on Magnet Technology, Genoa, Italy, 2005.
[89] Pugnat P, and Siemko A. Review of quench performance of LHC main superconducting magnets [J]. IEEE Trans. Appl. Supercond, 2007, 17(2):1091-1096.
[90] Takahashi Y, Yoshida K, Nabara Y, et al. Stability and quench analysis of torodial field coils for ITER [J]. IEEE Trans. Appl. Supercond, 2007, 17(2):2426-2429.
[91] 白质明，吴春俐.超导磁体耐受过电流冲击稳定性的有限元方法研究[J].东北大学学报，2008，29（12）：1799-1802.
[92] Breschi M, Trevisani L, Bottura L, et al. Stability of Nb3Sn superconducting wires: the role of the normal matrix [J]. IEEE Trans. Appl. Supercond, 2008, 18(2):1305-1308.
[93] Breschi M, Trevisani L, Bottura L, et al. Effects of the Nb3Sn wire cross section configuration on the thermal stability performance [J]. IEEE Trans. Appl. Supercond, 2009, 19(3):2432-2436.
[94] Bordini B and Rossi L. Self field instability in high-JcNb3Sn strands with high copper residual resistivity ratio [J]. IEEE Trans. Appl. Supercond, 2009, 19(3):2470-2476.
[95] Salmi T, Ambrosio G, Caspi S, et al. Quench protection challenges in long Nb3Sn accelerator magnets [J]. AIP Conference Proceedings, 2012, 1434:656-663.
[96] Guo X L, Wang L, and Green M A. Coupled transient thermal and electromagnetic finite element analysis of quench in MICE coupling magnet [J]. Cryogenics, 2012, 52:420-427.
[97] Bajas H, Bajko M, Bordini B, et al. Quench analysis of high-current-density Nb3Sn conductors in racetrack coil configuration [J]. IEEE Trans. Appl. Supercond, 2015, 25(3):4004005-5.
[98] Guo X L, Wang L, and Zhang Y. Numerical study on the quench process of superconducting solenoid magnets protected using quench-back [J]. IEEE Trans. Appl. Supercond, 2016, 26(4):4702007-7.
[99] Sorbi M, Ambrosio G, Bajas H, et al. Measurements and analysis of dynamic effects in the LARP model quadrupole HQ02b during rapid discharge [J]. IEEE Trans. Appl. Supercond, 2016, 26(4):4001605.
[100] 燕大鹏.超导线圈失超过程中的热传导数值模拟与分析[D].兰州：兰州大学，2014.
[101] Liu W-B, Yong H-D, Zhou Y-H. Numerical analysis of quench in coated conductors with defects [J]. AIP Adv, 2016, 6:095023-12.
[102] 许少锋，刘旭峰.Nb3Sn超导磁体CICC稳定性分析[J].核聚变与等离子体物理，2012，32（1）：66-69.
[103] Bottura L. A numerical model for the simulation of quench in the ITER magnets [J]. Comput Phys, 1996, 125:26-41.
[104] 武松涛，吴维越，潘引年，等.EAST超导托卡马克装置中的大型超导磁体技术[J].低温物理学报，2005（S1）：1113-1120.
[105] Schoerling D, Zlobin A V. Nb3Sn Accelerator Magnets: Designs, Technologies and Performances [EB/OL]. (2019-11-24)[2021-3-25].
[106] Schwerg N, Auchmann B, and Russenschuck S. Challenges in the thermal modeling of quenches with ROXIE [J]. IEEE Trans. Appl. Supercond, 2009, 19(3):1270-1273.
[107] Verweij A P. CUDI: A model for calculation of electrodynamic and thermal behavior of superconducting Rutherford cables [J]. Cryogenics, 2006, 46:619-626.
[108] Felice H, Todesco E. Quench protection analysis in accelerator magnets, a review of the tools [EB/OL]. (2013-1-15)[2021-3-25].
[109] den Ouden A, van Weeren H, Wessel W A J, et al. Normal zone propagation in highcurrent density Nb3Sn conductors for accelerator magnets [J]. IEEE Trans. Appl. Supercond, 2004, 14(2):279-282.
[110] Salmi T, Chlachidze G, Marchevsky M, et al. Analysis of uncertainties in protection heater delay time measurements and simulations in Nb3Sn high-field accelerator magnets [J]. IEEE Trans. Appl. Supercond, 2015, 25(4):4004212-12.
[111] 苏煜.磁/电智能材料及结构的动态力学问题研究[C].第六届全国强动载效应及防护学术会议暨2014年复杂介质/结构的动态力学行为创新研究群体学术研讨会论文集，2014：15.