含缺陷高温超导带材的磁化和力学特性分析
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摘要
为了分析缺陷对带材磁化及力学性能的影响,基于Bean临界态模型和最小磁能泛函方法,研究了含不同类型缺陷高温超导带材的电磁特性,数值模拟了磁化过程中高温超导带材的应力分布和磁致伸缩行为.研究结果表明:当缺陷偏离带材几何中心时,磁化强度出现水平分量;电磁体力使超导带材发生磁致伸缩;最大应力出现在缺陷附近,当缺陷在带材表面时,最大拉应力出现在外磁场下降阶段;当缺陷位于带材内部时,最大拉应力出现在外磁场最大时刻.根据分析结果可知,垂直磁场中的高温超导带材,其磁化及力学性能受缺陷尺寸和位置影响较大.
To analyze the influence of defect on magnetization and mechanical properties,a study of the electromagnetic properties of various high temperature superconducting strips containing different types of defects based on the Bean critical state model and the minimum magnetic energy variation method was presented. The magnetostrictive behavior and the stress distribution of the high temperature superconducting strip were numerically simulated. Results show that a horizontal component of the magnetization appears as the defect deviates from the centre of the strip. The strip exhibits a magnetostrictive phenomenon and the maximum stress arises nearby the defect on account of the action of electromagnetic body force. The moment of the maximum tensile stress appears in the magnetic field decreasing stage when a strip contains a surface defect. For the case of an interior defect,the tensile stress in a strip reaches its extreme value at the highest magnetic field. The analysis results indicate the magnetization and mechanical properties of a strip in perpendicular magnetic field have distinct dependence on the dimension and location of the defect.
To analyze the influence of defect on magnetization and mechanical properties,a study of the electromagnetic properties of various high temperature superconducting strips containing different types of defects based on the Bean critical state model and the minimum magnetic energy variation method was presented. The magnetostrictive behavior and the stress distribution of the high temperature superconducting strip were numerically simulated. Results show that a horizontal component of the magnetization appears as the defect deviates from the centre of the strip. The strip exhibits a magnetostrictive phenomenon and the maximum stress arises nearby the defect on account of the action of electromagnetic body force. The moment of the maximum tensile stress appears in the magnetic field decreasing stage when a strip contains a surface defect. For the case of an interior defect,the tensile stress in a strip reaches its extreme value at the highest magnetic field. The analysis results indicate the magnetization and mechanical properties of a strip in perpendicular magnetic field have distinct dependence on the dimension and location of the defect.
引文
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[38]YONG H D,ZHOU Y H.Elliptical hole in a bulk superconductor under electromagnetic forces[J].Superconductor Science and Technology,2009,22:025018.
[2]SUNG T H,HAN S C,HAN Y H,et al.Designs and analyses of flywheel energy storage systems using high-Tc superconductor bearings[J].Cryogenics,2002,42(6/7):357-362.
[3]HULL J R.Superconducting bearings[J].Superconductor Science and Technology,2000,13(2):R1-R15.
[4]王秋良.高磁场超导磁体科学[M].北京:科学出版社,2008:16.
[5]YONG H D,YANG Y,ZHOU Y H.Dynamic fracture behavior of a crack in the bulk superconductor under electromagnetic force[J].Engineering Fracture Mechanics,2016,158:167-178.
[6]JOHANSEN T H,WANG C,CHEN Q Y,et al.Enhancement of tensile stress near a hole in superconducting trapped-field magnets[J].Journal of Applied Physics,2000,88(5):2730-2733.
[7]BEAN C P.Magnetization of hard superconductors[J].Physical Review Letters,1962,8(6):250-253.
[8]BEAN C P.Magnetization of high-field superconductors[J].Reviews of Modern Physics,1964,36(1):31-39.
[9]KIM Y B,HEMPSTEAD C F,STRNAD A R.Magnetization and critical super currents[J].Physical Review,1963,129(2):528-535.
[10]FIETZ W A,BEASLEY M R,SILCOX J,et al.Magnetization of superconducting Nb-25%Zr wire[J].Physical Review,1964,136(2A):335-345.
[11]FIETZ W A,WEBB W W.Hysteresis in superconducting alloys—temperature and field dependence of dislocation pinning in niobium alloys[J].Physical Review,1969,178(2):657-667.
[12]IKUTA H,HIROTA N,NAKAYAMA Y,et al.Giant magnetostriction in Bi2Sr2Ca Cu2O8single crystal in the superconducting state and its mechanism[J].Physical Review Letters,1993,70(14):2166-2169.
[13]IKUTA H,KISHIO K,KITAZAWA K.Critical state models for flux-pinning-induced magnetostriction in type-Ⅱsuperconductors[J].Journal of Applied Physics,1994,76(8):4776-4786.
[14]REN Y,WEINSTEIN R,LIU J,et al.Damage caused by magnetic pressure at high trapped field in quasipermanent magnets composed of melt-textured Y-Ba-Cu-O superconductor[J].Physica C,1995,251:15-16.
[15]JOHANSEN T H,BRATSBERG H,LOTHE J.Fluxpinning-induced magnetostriction in cylindrical superconductors[J].Superconductor Science and Technology,1998,11:1186-1189.
[16]JOHANSEN T H.Flux-pinning-induced stress and strain in superconductors:long rectangular slab[J].Physical Review B,1999,59(17):11187-11190.
[17]JOHANSEN T H.Flux-pinning-induced stress and magnetostriction in bulk superconductors[J].Superconductor Science and Technology,2000,13(10):R121-R137.
[18]JOHANSEN T H,LOTHE J,BRATSBERG H.Shape distortion by irreversible flux-pinning-induced magnetostriction[J].Physical Review Letters,1998,80(21):4757-4760.
[19]JOHANSEN T H.Flux-pinning-induced stress and strain in superconductors:case of a long circular cylinder[J].Physical Review B,1999,60(13):9690-9703.
[20]JOHANSEN T H,SHANTSEV D V.Magnetostrictive behaviour of thin superconducting disks[J].Superconductor Science and Technology,2003,16(9):1109-1114.
[21]KOZIOL Z,DUNLAP R.Magnetostriction of a superconductor:results from the critical-state model[J].Journal of Applied Physics,1996,79(8):4662-4664.
[22]YONG H D,Zh OU Y H.Effect of nonsuperconducting particles on the effective magnetostriction of bulk superconductors[J].Journal of Applied Physics,2008,104(4):043907.
[23]YONG H D,ZHOU Y H.Stress distribution in a flat superconducting strip with transport current[J].Journal of Applied Physics,2011,109(7):073902.
[24]BRANDT E H.Superconductor disks and cylinders in an axial magnetic field.I.flux penetration and magnetization curves[J].Physical Review B,1998,58(10):6506-6522.
[25]BRANDT E H.Superconductor disks and cylinders in an axial magnetic field.Ⅱ.nonlinear and linear ac susceptibilities[J].Physical Review B,1998,58(10):6523-6533.
[26]PRIGOZHIN L.Analysis of critical-state problems in type-Ⅱsuperconductivity[J].IEEE Transactions on Applied Superconductivity,1997,7(4):3866-3873.
[27]PRIGOZHIN L.Solution of thin film magnetization problems in type-Ⅱsuperconductivity[J].Journal of Computational Physics,1998,144(1):180-193.
[28]SANCHEZ A,NAVAU C.Influence of demagnetizing effects in superconducting cylinders[J].IEEE Transactions on Applied Superconductivity,1999,9(2):2195-2198.
[29]SANCHEZ A,NAVAU C.Magnetic properties of finite superconducting cylinders.I.uniform applied field[J].Physical Review B,2001,64(21):214506.
[30]NAVAU C,SANCHEZ A,PARDO E,et al.Critical state in finite type-Ⅱsuperconducting rings[J].Physical Review B,2005,71(21):214507.
[31]PARDO E,SANCHEZ A,NAVAU C.Magnetic properties of arrays of superconducting strips in a perpendicular field[J].Physical Review B,2003,67(10):104517.
[32]SANCHEZ A,DEL VALLE N,PARDO E,et al.Magnetic levitation of superconducting bars[J].Journal of Applied Physics,2006,99(11):113904.
[33]HUANG C G,ZHOU Y H.Magnetic and magnetostrictive properties of finite superconducting cylinders containing a cavity[J].Journal of Applied Physics,2014,115(3):033904.
[34]LIU J,HUANG C G,YONG H D,et al.Simulation of magnetization and levitation properties of arrays of ringshaped type-Ⅱsuperconductors[J].Physica C,2017,534:55-60.
[35]黄晨光.复杂高温超导结构的交流损耗和力学特性[D].兰州:兰州大学,2015.HUANG C G.AC losses and mechanical properties of complex high temperature superconducting structures[D].Lanzhou:Lanzhou University,2015.(in Chinese)
[36]HUANG C G,LIU J.Magnetic and mechanical properties of a finite-thickness superconducting strip with a cavity in oblique magnetic fields[J].Journal of Applied Physics,2017,121(1):023905.
[37]MIKITIK G P,BRANDT E H,INDENBOM M.Superconducting strip in an oblique magnetic field[J].Physical Review B,2004,70:014520.
[38]YONG H D,ZHOU Y H.Elliptical hole in a bulk superconductor under electromagnetic forces[J].Superconductor Science and Technology,2009,22:025018.