Numerical simulation of the mechanical behavior of superconducting tape in conductor on round core cable using the cohesive zone model

doi:10.1007/s10483-023-3025-7

Abstract

Abstract: Cables composed of rare-earth barium copper oxide (REBCO) tapes have been extensively used in various superconducting devices. In recent years, conductor on round core (CORC) cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties. The REBCO tapes are wound spirally on the surface of CORC cable. Under extreme loadings, the REBCO tapes with layered composite structures are vulnerable, which can lead to degradation of critical current and even quenching of superconducting devices. In this paper, we simulate the deformation of CORC cable under external loads, and analyze the damage inside the tape with the cohesive zone model (CZM). Firstly, the fabrication and cabling of CORC are simulated, and the stresses and strains generated in the tape are extracted as the initial condition of the next step. Then, the tension and bending loads are applied to CORC cable, and the damage distribution inside the tape is presented. In addition, the effects of some parameters on the damage are discussed during the bending simulations.

Key words: high temperature superconducting (HTS) tape, superconducting cable, finite element simulation, cohesive zone model (CZM), damage

2010 MSC Number:

74E30
74S05

Shengyi TANG, Xubin PENG, Huadong YONG. Numerical simulation of the mechanical behavior of superconducting tape in conductor on round core cable using the cohesive zone model. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1511-1532.

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References

[1] VAN DER LAAN, D. C., WEISS, J. D., and MCRAE, D. M. Status of CORC^® cables and wires for use in high-field magnets and power systems a decade after their introduction. Superconductor Science and Technology, 32(3), 033001(2019)
[2] DEMKO, J. A., SAUERS, I., JAMES, D. R., GOUGE, M. J., LINDSAY, D., RODEN, M., TOLBERT, J., WILLEN, D., TRAEHOLT, C., and NIELSEN, C. T. Triaxial HTS cable for the AEP bixby project. IEEE Transactions on Applied Superconductivity, 17(2), 2047-2050(2007)
[3] WEBER, C. S., LEE, R., RINGO, S., MASUDA, T., YUMURA, H., and MOSCOVIC, J. Testing and demonstration results of the 350 m long HTS cable system installed in Albany, NY. IEEE Transactions on Applied Superconductivity, 17(2), 2038-2042(2007)
[4] GOLDACKER, W., FRANK, A., KUDYMOW, A., HELLER, R., KLING, A., TERZIEVA, S., and SCHMIDT, C. Improvement of superconducting properties in ROEBEL assembled coated conductors (RACC). IEEE Transactions on Applied Superconductivity, 19(3), 3098-3101(2009)
[5] CELENTANO, G., MARZI, G. D., FABBRI, F., MUZZI, L., TOMASSETTI, G., ANEMONA, A., CHIARELLI, S., SERI, M., BRAGAGNI, A., and CORTE, A. D. Design of an industrially feasible twisted-stack HTS cable-in-conduit conductor for fusion application. IEEE Transactions on Applied Superconductivity, 24(3), 4601805(2014)
[6] TAKAYASU, M., CHIESA, L., BROMBERG, L., and MINERVINI, J. V. HTS twisted stacked-tape cable conductor. Superconductor Science and Technology, 25(1), 014011(2011)
[7] VAN DER LAAN, D. C. YBa₂Cu₃O_7δ coated conductor cabling for low ac-loss and high-field magnet applications. Superconductor Science and Technology, 22(6), 065013(2009)
[8] JING, Z. Coupled multiphysics modeling of the thermal-magnetic-mechanical instability behavior in bulk superconductors during pulsed field magnetization. Superconductor Science and Technology, 35(5), 054006(2022)
[9] LIU, Q. F., FENG, W. J., and LIU, J. Y. Flux-pinning-induced stress behaviors in a long superconducting slab with central cuboid hole. Acta Mechanica Sinica, 37(8), 1255-1263(2021)
[10] GAO, S. W., FENG, W. J., and LIU, J. X. Fracture problems of a superconducting slab with a central kinked crack. Journal of Applied Physics, 114(24), 243907(2013)
[11] NIU, M. D., XIA, J., and YONG, H. D. Numerical analysis of the electromechanical behavior of high-field REBCO coils in all-superconducting magnets. Superconductor Science and Technology, 34(11), 115005(2021)
[12] LIU, D. H., WEI, W. B., TANG, Y. K., YONG, H. D., and ZHOU, Y. H. Delamination behaviors of an epoxy-impregnated REBCO pancake coil during a quench. Engineering Fracture Mechanics, 281, 109074(2023)
[13] ANVAR, V. A., ILIN, K., YAGOTINTSEV, K. A., MONACHAN, B., ASHOK, K. B., KORTMAN, B. A., PELLEN, B., HAUGAN, T. J., WEISS, J. D., VAN DER LAAN, D. C., THOMAS, R. J., PRAKASH, M. J., HOSSAIN, M. S. A., and NIJHUIS, A. Bending of CORC^® cables and wires: finite element parametric study and experimental validation. Superconductor Science and Technology, 31(11), 115006(2018)
[14] DAS, I., SAHOO, V., and RAO, V. V. Structural analysis of 2G HTS tapes under different loading conditions for HTS power cable using finite element modeling. Physica C: Superconductivity and its Applications, 7, 1353771(2020)
[15] ASHOK, K. B., THOMAS, R. J., PRAKASH, M. J., and NIJHUIS, A. Performance limits in REBCO tape forvariation in winding parameters of CORC^® cable and wire. Physica C: Superconductivity and its Applications, 582, 1353828(2021)
[16] WANG, K. Y., TA, W. R., and GAO, Y. W. The winding mechanical behavior of conductor on round core cables. Physica C: Superconductivity and its Applications, 553, 65-71(2018)
[17] LI, X. H., XU, Y., REN, L., and TANG, Y. J. Improved mechanical models and I_c estimation for the whole life cycle of high temperature superconducting coated conductors. Composite Structures, 298, 116000(2022)
[18] ASHOK, B., THOMAS, R. M. J., and NIJHUIS, A. Effect of winding on the electrical performance of REBCO based CORC^® superconducting cable/wire. International Conference on Aerospace & Mechanical Engineering (ICAME 21), San Francisco (2022)
[19] WANG, K. Y., GAO, Y. W., LUO, W., ZHOU, Y. H., and NIJHUIS, A. Nonlinear contact behavior of HTS tapes during pancake coiling and CORC cabling. Superconductor Science and Technology, 34, 075003(2021)
[20] VAN DER LAAN, D. C., RADCLIFF, K., ANVAR, V. A., WANG, K. Y., NIJHUIS, A., and WEISS, J. D. High-temperature superconducting CORC^® wires with record-breaking axial tensile strain tolerance present a breakthrough for high-field magnets. Superconductor Science and Technology, 34(10), 10LT01(2021)
[21] VAN DER LAAN, D. C., MCRAE, D. M., and WEISS, J. D. Effect of monotonic and cyclic axial tensile stress on the performance of superconducting CORC^® wires. Superconductor Science and Technology, 32(5), 054004(2019)
[22] WANG, K. Y. and GAO, Y. W. The contact behavior of the CORC wires under stretching process. IEEE Transactions on Applied Superconductivity, 30(4), 6601105(2020)
[23] ANVAR, V. A., WANG, K. Y., WEISS, J. D., RADCLIFF, K., VAN DER LAAN, D. C., HOSSAIN, M. S. A., and NIJHUIS, A. Enhanced critical axial tensile strain limit of CORC^® wires: FEM and analytical modeling. Superconductor Science and Technology, 35(5), 055002(2022)
[24] WANG, K. Y., GAO, Y. W., ANVAR, V. A., RADCLIFF, K., WEISS, J. D., VAN DER LAAN, D. C., ZHOU, Y. H., and NIJHUIS, A. Prediction of strain, inter-layer interaction and critical current in CORC^® wires under axial strain by T-A modeling. Superconductor Science and Technology, 35(10), 105012(2022)
[25] VAN DER LAAN, D. C., LU, X. F., and GOODRICH, L. F. Compact GdBa₂Cu₃O_7-δ coated conductor cables for electric power transmission and magnet applications. Superconductor Science and Technology, 24(4), 042001(2011)
[26] VAN DER LAAN, D. C., WEISS, J. D., TROCIEWITZ, U. P., ABRAIMOV, D., FRANCIS, A., GILLMAN, J., DAVIS, D. S., KIM, Y., GRIFFIN, V., MILLER, G., WEIJERS, H. W., COOLEY, L. D., LARBALESTIER, D. C., and WANG, X. R. A CORC^® cable insert solenoid: the first high-temperature superconducting insert magnet tested at currents exceeding 4 kA in 14 T background magnetic field. Superconductor Science and Technology, 33(5), 05LT03(2020)
[27] VAN DER LAAN, D. C., NOYES, P. D., MILLER, G. E., WEIJERS, H. W., and WILLERING, G. P. Characterization of a high-temperature superconducting conductor on round core cables in magnetic fields up to 20 T. Superconductor Science and Technology, 26(4), 045005(2013)
[28] VAN DER LAAN, D. C., WEISS, J. D., NOYES, P., TROCIEWITZ, U. P., GODEKE, A., ABRAIMOV, D., and LARBALESTIER, D. C. Record current density of 344 Amm^-2 at 4.2 K and 17 T in CORC^® accelerator magnet cables. Superconductor Science and Technology, 29(5), 055009(2016)
[29] WEISS, J. D., MULDER, T., KATE, H. J., and VAN DER LAAN, D. C. Introduction of CORC^® wires: highly flexible, round high-temperature superconducting wires for magnet and power transmission applications. Superconductor Science and Technology, 30(1), 014002(2016)
[30] XIAO, G. J., ZHOU, C., QIN, J. G., JIN, H., GAO, P., LIU, H. J., and LIU, F. Experimental study on critical current of bent ReBCO tapes in CORC type cable. Fusion Engineering and Design, 172, 112675(2021)
[31] XIAO, G. Y., ZHOU, C., QIN, J. G., JIN, H., XU, P., and LIU, H. Experimental study on the critical current of CORC cable under cyclic bending-straightening. IEEE Transactions on Applied Superconductivity, 31(8), 4803904(2021)
[32] LI, M., ZHENG, J. X., SHENG, J., CHENG, Y., HONG, Z. Y., YE, H. S., WANG, X. L., LIU, X. F., and LIU, H. Y. Research on a novel HTS double pancake coil based on CORC: used for kA-level SMES of accelerator. Superconductor Science and Technology, 35(12), 125001(2022)
[33] PIERRO, F., ZHAO, Z. J., OWEN, C. M., COLCORD, C., CHIESA, L., HIGLEY, H. C., WANG, X. R., and PRESTEMON, S. O. Finite-element analysis of the strain distribution due to bending in a REBCO coated conductor for canted cosine theta dipole magnet applications. IEEE Transactions on Applied Superconductivity, 29(5), 4600705(2019)
[34] HU, R., YUAN, Y. C., CHEN, Y. J., LI, W. R., YE, H. S., SHENG, J., ZHAO, Y., and JIN, Z. J. Numerical study on mechanical properties of conductors on round core cables. IEEE Transactions on Applied Superconductivity, 31(5), 4801405(2021)
[35] YE, H. S., ZHOU, X., YUAN, Y. C., HU, R., YANG, J. S., JIN, Z. Q., ZHAO, Y., and SHENG, J. Study on torsion behavior of superconducting conductor on round core cable. IEEE Transactions on Applied Superconductivity, 32, 4801005(2022)
[36] VAN DER LAAN, D. C., MCRAE, D. M., and WEISS, J. D. Effect of transverse compressive monotonic and cyclic loading on the performance of superconducting CORC^® cables and wires. Superconductor Science and Technology, 32(1), 015002(2018)
[37] SHI, Y. Y., DAI, S. T., MA, T., LIU, W. X., JIN, H., and QIN, J. G. Analysis on the transverse compression performance of the CORC cable. Superconductor Science and Technology, 35(12), 125005(2022)
[38] MIYAZAKI, H., IWAI, S., TOSAKA, T., TASAKI, K., and ISHII, Y. Delamination strengths of different types of REBCO-coated conductors and method for reducing radial thermal stresses of impregnated REBCO pancake coils. IEEE Transactions on Applied Superconductivity, 25(3), 6602305(2015)
[39] MBAM, S. O. and GOU, X. F. Interface crack growth rate and fatigue life of multilayer-coated conductor tapes. Engineering Fracture Mechanics, 228, 106910(2020)
[40] WANG, T. G., LI, Z. X., CAO, J. J., and GOU, X. F. Mechanical damage of YBa₂CU₃O₇-coated conducting film caused by its CeO₂ interface with defects. International Journal of Applied Mechanics, 11, 1950038(2019)
[41] JING, Z., YONG, H. D., and ZHOU, Y. H. Shear and transverse stress in a thin superconducting layer in simplified coated conductor architecture with a pre-existing detachment. Journal of Applied Physics, 114, 033907(2013)
[42] SHIN, H. S. and GOROSPE, A. Characterization of transverse tensile stress response of critical current and delamination behaviour in GdBCO coated conductor tapes by anvil test. Superconductor Science and Technology, 27, 025001(2014)
[43] VAN DER LAAN, D. C., EKIN, J., CLICKNER, C., and STAUFFER, T. Delamination strength of YBCO coated conductors under transverse tensile stress. Superconductor Science and Technology, 20, 765-770(2007)
[44] SUN, C., LIU, C., ZHANG, X. Y., and ZHOU, Y. H. Sample capacity and anvil size effects for a standardized method to determine the delamination strength of 2G HTS coated conductors. Physica C: Superconductivity and its Applications, 588, 1353929(2021)
[45] MUTO, S., FUJITA, S., SATO, H., AKASHI, K., IIJIMA, Y., and DAIBO, M. Fatigue behavior of REBCO coated conductors under through-thickness tensile stress. Superconductor Science and Technology, 34(7), 075001(2021)
[46] MAEDA, H. and YANAGISAWA, Y. Recent developments in high-temperature superconducting magnet technology (review). IEEE Transactions on Applied Superconductivity, 24(3), 4602412(2014)
[47] YANG, Z. R., LI, Y., SONG, P., GUAN, M. Z., FENG, F., and QU, T. Effect of edge cracks on critical current degradation in REBCO tapes under tensile stress. Superconductivity, 1, 100007(2022)
[48] LIU, W., ZHANG, X. Y., ZHOU, J., and ZHOU, Y. H. Delamination strength of the soldered joint in YBCO coated conductors and its enhancement. IEEE Transactions on Applied Superconductivity, 25(4), 6606109(2015)
[49] ZHOU, Y. H., LIU, C., SHEN, L., and ZHANG, X. Y. Probing of the internal damage morphology in multilayered high-temperature superconducting wires. Nature Communications, 12(1), 3110(2021)
[50] WANG, J., SUN, C., CONG, L., ZHANG, X. Y., and ZHOU, Y. H. Delamination strength of HTS tape under transverse tensile stress and its enhancement by using different Ag layer depositing temperatures. Theoretical and Applied Mechanics Letters, 9(3), 147-151(2019)
[51] CHEN, H. C., TA, W. R., and ZHOU, Y. H. Stress transfer mechanism and shear strength of multilayer composite superconducting tape. Composite Structures, 286, 115336(2022)
[52] DUGDALE, D. S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 8(2), 100-104(1960)
[53] BARENBLATT, G. I. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, 55-129(1962)
[54] GAO, P. F., CHAN, W. K., WANG, X. Z., and SCHWARTZ, J. Mixed-dimensional modeling of delamination in rare earth-barium-copper-oxide coated conductors composed of laminated high-aspect-ratio thin films. Superconductor Science and Technology, 31(7), 074004(2018)
[55] DUAN, Y. J., TA, W. R., and GAO, Y. W. Numerical models of delamination behavior in 2G HTS tapes under transverse tension and peel. Physica C: Superconductivity and its Applications, 545, 26-37(2018)
[56] ZHANG, H. Y., GAO, P. F., and WANG, X. Z. A combination of failures of interfacial delamination and layer cracking in REBCO multilayered conductors. Engineering Fracture Mechanics, 274, 108785(2022)
[57] MATSUDA, T., OKAMURA, T., HAMADA, M., MATSUMOTO, S., UENO, T., PIAO, R., YANAGISAWA, Y., and MAEDA, H. Degradation of the performance of an epoxy-impregnated REBCO solenoid due to electromagnetic forces. Cryogenics, 90, 47-51(2018)
[58] TAKEMATSU, T., HU, R., TAKAO, T., YANAGISAWA, Y., NAKAGOME, H., UGLIETTI, D., KIYOSHI, T., TAKAHASHI, M., and MAEDA, H. Degradation of the performance of a YBCO-coated conductor double pancake coil due to epoxy impregnation. Physica C: Superconductivity and its Applications, 470(17), 674-677(2010)
[59] BARTH, C., BAGRETS, N., WEISS, K. P., BAYER, C., and BAST, T. Degradation free epoxy impregnation of REBCO coils and cables. Superconductor Science and Technology, 26, 055007(2013)
[60] DUAN, Y. J. and GAO, Y. W. Delamination and current-carrying degradation behavior of epoxy-impregnated superconducting coil winding with 2G HTS tape caused by thermal stress. AIP Advances, 10(2), 025320(2020)
[61] PENG, X. B., YONG, H. D., ZHANG, X. Y., and ZHOU, Y. H. Analysis of delamination and heat conductivity of epoxy impregnated pancake coils using a cohesive zone model. Engineering Fracture Mechanics, 245, 107555(2021)
[62] GAO, P. F. and PAN, Y. Z. Delamination model of an epoxy-impregnated REBCO superconducting pancake winding. Superconductor Science and Technology, 35(6), 065009(2022)
[63] PENG, X. B., YONG, H. D., and ZHOU, Y. H. Finite element modeling of single-lap joint between GdBa₂Cu₃O_7-x-coated conductors using cohesive elements. Physica C: Superconductivity and its Applications, 570, 1353600(2020)
[64] PENG, X. B., YONG, H. D., and ZHOU, Y. H. Three-dimensional simulation of single-lap and bridge joints of coated conductor under tension and bending tests. Composite Structures, 284, 115146(2022)
[65] GAO, P. F., CHAN, W. K., WANG, X. Z., ZHOU, Y. H., and SCHWARTZ, J. Stress, strain and electromechanical analyses of (RE)Ba₂Cu₃O_x conductors using three-dimensional/two-dimensional mixed-dimensional modeling: fabrication, cooling and tensile behavior. Superconductor Science and Technology, 33(4), 044015(2020)
[66] SUNDARAM, A., ZHANG, Y., KNOLL, A. R., ABRAIMOV, D., BROWNSEY, P., KASAHARA, M., CAROTA, G. M., NAKASAKI, R., CAMERON, J. B., SCHWAB, G., HOPE, L. V., SCHMIDT, R. M., KURASEKO, H., FUKUSHIMA, T., and HAZELTON, D. W. 2G HTS wires made on 30μm thick hastelloy substrate. Superconductor Science and Technology, 29(10), 104007(2016)
[67] ZHU, Z. M., YANG, Z. R., XIA, Y., and JIANG, H. A review of debonding behavior of soft material adhesive systems. Mechanics of Soft Materials, 4, 7(2022)
[68] YANG, Z. R., ZHU, Z. M., YAO, C. B., XIA, Y., CHEN, K., and JIANG, H. A rate-dependent cohesive zone model for adhesive damage considering fibrillation. International Journal of Mechanical Sciences, 234, 107697(2022)
[69] LIBNER, M., ALABORT, E., CUI, H., RITO, R., BLACKMAN, B. R. K., and PETRINIC, N. Experimental characterisation and numerical modelling of the influence of bondline thickness, loading rate, and deformation mode on the response of ductile adhesive interfaces. Journal of the Mechanics and Physics of Solids, 130, 349-369(2019)
[70] BLACKMAN, B. R. K., HADAVINIA, H., KINLOCH, A. J., and WILLIAMS, J. G. The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints. International Journal of Fracture, 119, 25-46(2003)
[71] CAMACHO, G. T. and ORTIZ, M. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures, 33(20), 2899-2938(1996)
[72] CAMANHO, P., DÁVILA, C., and DE MOURA, M. Numerical simulation of mixed-mode progressive delamination in composite materials. Journal of Composite Materials, 37, 1415-1438(2003)
[73] BENZEGGAGH, M. L. and KENANE, M. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Science and Technology, 56(4), 439-449(1996)
[74] ZHANG, Y. F. Mechanical and electromechanical properties of IBAD-MOCVD-based REBCO coated conductors. International Workshop on Coated Conductors for Applications (CCA), Jeju (2014)
[75] NIU, M. D., XIA, J., YONG, H. D., and ZHOU, Y. H. Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils. Applied Mathematics and Mechanics (English Edition), 42(2), 235-250(2021) https://doi.org/10.1007/s10483-021-2699-6
[76] WANG, X. R., ARBELAEZ, D., CASPI, S., PRESTEMON, S. O., SABBI, G., and SHEN, T. Strain distribution in REBCO-coated conductors bent with the constant-perimeter geometry. IEEE Transactions on Applied Superconductivity, 27(8), 6604010(2017)
[77] OSAMURA, K., SUGANO, M., MACHIYA, S., ADACHI, H., OCHIAI, S., and SATO, M. Internal residual strain and critical current maximum of a surrounded Cu stabilized YBCO coated conductor. Superconductor Science and Technology, 22(6), 065001(2009)