Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

Sun, Eric Qiuli

doi:10.1088/1361-6668/ac5a11

Multi-scale nonlinear stress analysis of Nb₃Sn superconducting accelerator magnets

Journal Article · Mon Mar 14 00:00:00 EDT 2022 · Superconductor Science and Technology

DOI:https://doi.org/10.1088/1361-6668/ac5a11· OSTI ID:1854148

^[1]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

A multi-scale nonlinear procedure to analyze the stress in Nb₃Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets—the issue of stress management. The study demonstrates that gaskets (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb₃Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb₃Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb₃Sn coil was simulated, in three orthongonal axes, by the combined properties of the gaskets (insulation layers) and Hill materials (resin-impreganted cable). The procedure entailes minimal material assumptions because it incorporated measured stress-strain curves in the analysis. The coil was simulated to a high level of detail consisting of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess the stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb₃Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb₃Sn magnets, this procedure can also be employed in the design of LTS, HTS, and room temperature magnets or in any composite structures.

View Accepted Manuscript (DOE)

Research Organization:: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1854148

Report Number(s):: DOE/OR/23177-5020; JLAB-PHY-20-3234; DE-AC05-06OR23177

Journal Information:: Superconductor Science and Technology, Journal Name: Superconductor Science and Technology Journal Issue: 4 Vol. 35; ISSN 0953-2048

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (60)

3-D finite element analysis of composite beams with parallel fibres, based on homogenization theory Lefik, M.; Schrefler, B. A. Computational Mechanics, Vol. 14, Issue 1 https://doi.org/10.1007/BF00350153	journal	April 1994
Ultrasonic velocity in epoxy resin at temperatures down to 4.2 K Perepechko, I. I.; Danilov, V. A.; Nizhegorodov, V. V. Mechanics of Composite Materials, Vol. 32, Issue 4 https://doi.org/10.1007/BF02254743	journal	July 1996
A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials Terada, K.; Kato, J.; Hirayama, N. Computational Mechanics, Vol. 52, Issue 5 https://doi.org/10.1007/s00466-013-0872-5	journal	May 2013
A composite material characterisation tool: UnitCells Li, S.; Jeanmeure, L. F. C.; Pan, Q. Journal of Engineering Mathematics, Vol. 95, Issue 1 https://doi.org/10.1007/s10665-014-9776-4	journal	March 2015
Multiscale Methods for Composites: A Review Kanouté, P.; Boso, D. P.; Chaboche, J. L. Archives of Computational Methods in Engineering, Vol. 16, Issue 1 https://doi.org/10.1007/s11831-008-9028-8	journal	January 2009
Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Guedes, JoséMiranda; Kikuchi, Noboru Computer Methods in Applied Mechanics and Engineering, Vol. 83, Issue 2 https://doi.org/10.1016/0045-7825(90)90148-F	journal	October 1990
Application of the homogenisation method to the analysis of superconducting coils Lefik, M.; Schrefler, B. A. Fusion Engineering and Design, Vol. 24, Issue 3 https://doi.org/10.1016/0920-3796(94)90024-8	journal	June 1994
Development of a Nb3Sn multifilamentary wire for accelerator magnet applications Durante, M.; Bredy, P.; Devred, A. Physica C: Superconductivity, Vol. 354, Issue 1-4 https://doi.org/10.1016/S0921-4534(01)00117-4	journal	May 2001
Multi-scale computational homogenization: Trends and challenges Geers, M. G. D.; Kouznetsova, V. G.; Brekelmans, W. A. M. Journal of Computational and Applied Mathematics, Vol. 234, Issue 7 https://doi.org/10.1016/j.cam.2009.08.077	journal	August 2010
Boundary conditions for unit cells from periodic microstructures and their implications Li, S. Composites Science and Technology, Vol. 68, Issue 9 https://doi.org/10.1016/j.compscitech.2007.03.035	journal	July 2008
Braided textile composites under compressive loads: Modeling the response, strength and degradation Song, Shunjun; Waas, Anthony M.; Shahwan, Khaled W. Composites Science and Technology, Vol. 67, Issue 15-16 https://doi.org/10.1016/j.compscitech.2007.06.008	journal	December 2007
Finite element prediction of the impact compressive properties of three-dimensional braided composites using multi-scale model Wan, Yumin; Wang, Youjiang; Gu, Bohong Composite Structures, Vol. 128 https://doi.org/10.1016/j.compstruct.2015.03.066	journal	September 2015
A multilevel homogenised model for superconducting strand thermomechanics Boso, D. P.; Lefik, M.; Schrefler, B. A. Cryogenics, Vol. 45, Issue 4 https://doi.org/10.1016/j.cryogenics.2004.09.005	journal	April 2005
Homogenisation methods for the thermo-mechanical analysis of Nb3Sn strand Boso, Daniela P.; Lefik, Marek; Schrefler, Bernhard A. Cryogenics, Vol. 46, Issue 7-8 https://doi.org/10.1016/j.cryogenics.2006.01.005	journal	July 2006
A novel modeling to predict the critical current behavior of Nb3Sn PIT strand under transverse load based on a scaling law and Finite Element Analysis Wang, Tiening; Chiesa, Luisa; Takayasu, Makoto Cryogenics, Vol. 63 https://doi.org/10.1016/j.cryogenics.2014.04.020	journal	September 2014
Design and analysis of gasket sealing of cylinder head under engine operation conditions Lee, Chang-Chun; Chiang, Kuo-Ning; Chen, Wen-King Finite Elements in Analysis and Design, Vol. 41, Issue 11-12 https://doi.org/10.1016/j.finel.2004.12.007	journal	June 2005
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G. Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.10.070	journal	February 2017
Elastoplastic stress analysis of Nb ₃ Sn superconducting magnet Vaghar, Mohammad Reza; Garmestani, Hamid; Markiewicz, W. Denis Journal of Applied Physics, Vol. 80, Issue 4 https://doi.org/10.1063/1.363031	journal	August 1996
An exponential scaling law for the strain dependence of the Nb ₃ Sn critical current density Bordini, B.; Alknes, P.; Bottura, L. Superconductor Science and Technology, Vol. 26, Issue 7 https://doi.org/10.1088/0953-2048/26/7/075014	journal	May 2013
Stress distribution and lattice distortions in Nb ₃ Sn multifilament wires under uniaxial tensile loading at 4.2 K Scheuerlein, C.; Di Michiel, M.; Buta, F. Superconductor Science and Technology, Vol. 27, Issue 4 https://doi.org/10.1088/0953-2048/27/4/044021	journal	March 2014
Conductors for commercial MRI magnets beyond NbTi: requirements and challenges Parizh, Michael; Lvovsky, Yuri; Sumption, Michael Superconductor Science and Technology, Vol. 30, Issue 1 https://doi.org/10.1088/0953-2048/30/1/014007	journal	November 2016
Strain sensitivity and superconducting properties of Nb ₃ Sn from first principles calculations De Marzi, G.; Morici, L.; Muzzi, L. Journal of Physics: Condensed Matter, Vol. 25, Issue 13 https://doi.org/10.1088/0953-8984/25/13/135702	journal	March 2013
A review and prospects for Nb ₃ Sn superconductor development Xu, Xingchen Superconductor Science and Technology, Vol. 30, Issue 9 https://doi.org/10.1088/1361-6668/aa7976	journal	August 2017
Transverse-pressure susceptibility of high-J _c RRP and PIT types of Nb ₃ Sn Rutherford cables for accelerator magnets Gao, P.; Dhallé, M.; Bordini, B. Superconductor Science and Technology, Vol. 33, Issue 12 https://doi.org/10.1088/1361-6668/abb8ec	journal	October 2020
Mechanical properties of epoxy impregnated superconducting solenoids Dixon, I. R.; Walsh, R. P.; Markiewicz, W. D. IEEE Transactions on Magnetics, Vol. 32, Issue 4 https://doi.org/10.1109/20.511486	journal	July 1996
Measurement of thermal contraction properties for NbTi and Nb/sub 3/Sn composites Swenson, C. A.; Dixon, I. R.; Markiewicz, W. D. IEEE Transactions on Appiled Superconductivity, Vol. 7, Issue 2 https://doi.org/10.1109/77.614516	journal	June 1997
Tensile measurements of the modulus of elasticity of Nb/sub 3/Sn at room temperature and 4 K Bray, S. L.; Ekin, J. W.; Sesselmann, R. IEEE Transactions on Appiled Superconductivity, Vol. 7, Issue 2 https://doi.org/10.1109/77.620845	journal	June 1997
Mechanical design and analysis of the Fermilab 11 T Nb/sub 3/Sn dipole model Ambrosio, G.; Andreev, N.; Chichili, D. R. IEEE Transactions on Appiled Superconductivity, Vol. 10, Issue 1 https://doi.org/10.1109/77.828235	journal	March 2000
Niobium-tin magnet technology development at Fermilab Chichili, D. R.; Arkan, T. T.; terechkine, I. Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366) https://doi.org/10.1109/PAC.1999.792263	conference	January 1999
The LHC main dipoles and quadrupoles toward series production Rossi, L. IEEE Transactions on Appiled Superconductivity, Vol. 13, Issue 2 https://doi.org/10.1109/TASC.2003.812639	journal	June 2003
Phase Transformations During the Reaction Heat Treatment of Internal Tin Nb $_{3}$ Sn Strands With High Sn Content Scheuerlein, Christian; Di Michiel, Marco; Arnau Izquierdo, Gonzalo IEEE Transactions on Applied Superconductivity, Vol. 18, Issue 4 https://doi.org/10.1109/TASC.2008.2006912	journal	December 2008
Magnet Design of the 150 mm Aperture Low-$\beta$ Quadrupoles for the High Luminosity LHC Ferracin, P.; Ambrosio, G.; Anerella, M. IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 3 https://doi.org/10.1109/TASC.2013.2284970	journal	June 2014
Critical Current Measurements of High-$J_{c}$ $\hbox{Nb}_{3}\hbox{Sn}$ Rutherford Cables Under Transverse Compression Bordini, B.; Alknes, P.; Ballarino, A. IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 3 https://doi.org/10.1109/TASC.2013.2287309	journal	June 2014
Analysis of Superconducting Dipole Coil of 11 GeV Super High Momentum Spectrometer Sun, Eric; Cheng, Gary; Lassiter, Steve IEEE Transactions on Applied Superconductivity, Vol. 25, Issue 3 https://doi.org/10.1109/TASC.2014.2361477	journal	June 2015
Support Structure Design of the $\hbox{Nb}_{3}\hbox{Sn}$ Quadrupole for the High Luminosity LHC Juchno, M.; Ambrosio, G.; Anerella, M. IEEE Transactions on Applied Superconductivity, Vol. 25, Issue 3 https://doi.org/10.1109/TASC.2014.2366034	journal	June 2015
Elastic Anisotropy in Multifilament $\hbox{Nb}_{3}\hbox{Sn}$ Superconducting Wires Scheuerlein, C.; Fedelich, B.; Alknes, P. IEEE Transactions on Applied Superconductivity, Vol. 25, Issue 3 https://doi.org/10.1109/TASC.2014.2371693	journal	June 2015
Assembly Tests of the First Nb ₃ Sn Low-Beta Quadrupole Short Model for the Hi-Lumi LHC Pan, H.; Felice, H.; Cheng, D. W. IEEE Transactions on Applied Superconductivity, Vol. 26, Issue 4 https://doi.org/10.1109/TASC.2016.2516584	journal	June 2016
Development of a 15 T Nb ₃ Sn Accelerator Dipole Demonstrator at Fermilab Novitski, I.; Andreev, N.; Barzi, E. IEEE Transactions on Applied Superconductivity, Vol. 26, Issue 4 https://doi.org/10.1109/TASC.2016.2517024	journal	June 2016
Multiscale Stress Analysis and 3D Fitting Structure of Superconducting Coils for the Helical Fusion Reactor Tamura, Hitoshi; Yanagi, Nagato; Takahata, Kazuya IEEE Transactions on Applied Superconductivity, Vol. 26, Issue 3 https://doi.org/10.1109/TASC.2016.2531008	journal	April 2016
Mechanical Performance of Short Models for MQXF, the Nb3Sn Low-β Quadrupole for the Hi-Lumi LHC Vallone, Giorgio; Ambrosio, Giorgio; Anderssen, Eric IEEE Transactions on Applied Superconductivity, Vol. 27, Issue 4 https://doi.org/10.1109/TASC.2016.2645133	journal	June 2017
A Numerical Approach for the Mechanical Analysis of Superconducting Rutherford-Type Cables Using Bimetallic Description Manil, Pierre; Nunio, Francois; Othmani, Yamen IEEE Transactions on Applied Superconductivity, Vol. 27, Issue 4 https://doi.org/10.1109/TASC.2017.2664803	journal	June 2017
Mechanical Analysis of the Short Model Magnets for the Nb $_{3}$Sn Low-$\beta$ Quadrupole MQXF Vallone, G.; Ambrosio, G.; Bajas, H. IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 3 https://doi.org/10.1109/TASC.2017.2785388	journal	April 2018
Magnetic and Mechanical Design of a 16 T Common Coil Dipole for an FCC Toral, Fernando; Munilla, Javier; Salmi, Tiina IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 3 https://doi.org/10.1109/TASC.2018.2797909	journal	April 2018
Critical Current Measurements Under Transverse Pressure of a Nb ₃ Sn Rutherford Cable Based on 1 mm RRP Wires Duvauchelle, Jean-Eudes; Bordini, Bernardo; Fleiter, Jerome IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 4 https://doi.org/10.1109/TASC.2018.2805158	journal	June 2018
Update on Mechanical Design of a Cosθ 16-T Bending Dipole for the Future Circular Collider Caiffi, Barbara; Bellomo, Giovanni; Fabbricatore, Pasquale IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 4 https://doi.org/10.1109/TASC.2018.2805918	journal	June 2018
FEA Model and Mechanical Analysis of the Nb ₃ Sn 15-T Dipole Demonstrator Kokkinos, Charilaos; Apostolidis, I.; Carmichael, Justin IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 3 https://doi.org/10.1109/TASC.2018.2806399	journal	April 2018
Multiscale Approach to the Mechanical Behavior of Epoxy Impregnated Nb3Sn Coils for the 11 T Dipole Daly, Michael; Loffler, Christian H.; Smekens, David IEEE Transactions on Applied Superconductivity, Vol. 28, Issue 3 https://doi.org/10.1109/TASC.2018.2807373	journal	April 2018
The HL-LHC Low-β Quadrupole Magnet MQXF: From Short Models to Long Prototypes Ferracin, Paolo; Ambrosio, Giorgio; Anerella, Michael IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2895908	journal	August 2019
Preliminary Design of the Interaction Region Beam Transport Systems for JLEIC Wiseman, Mark; Hutton, Chuck; Lin, Fanglei IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2896378	journal	August 2019
Summary of the Mechanical Performances of the 1.5 m Long Models of the Nb $_{3}$ Sn Low- $\beta$ Quadrupole MQXF Vallone, Giorgio; Ambrosio, Giorgio; Anderssen, Eric C. IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2898327	journal	August 2019
Conceptual Design of the Interaction Region Magnets for Future Electron-Ion Collider at Jefferson Lab Rajput-Ghoshal, Renuka; Fair, Ruben; Ghoshal, Probir K. IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2901590	journal	August 2019
Assembly and Tests of Mechanical Models of the 15-T Nb ₃ Sn Dipole Demonstrator Orozco, Charles; Carmichael, Justin; Novitski, Igor IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2903812	journal	August 2019
3-D Mechanical Finite Element Analysis of Impregnated Rutherford Cable Stacks Nunio, Francois; Manil, Pierre; Lenoir, Gilles IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2903981	journal	August 2019
Mechanical Behavior Laws for Multiscale Numerical Model of Nb ₃ Sn Conductors Lenoir, Gilles; Manil, Pierre; Nunio, Francois IEEE Transactions on Applied Superconductivity, Vol. 29, Issue 5 https://doi.org/10.1109/TASC.2019.2905901	journal	August 2019
Quench-Back Management for Fast Decaying Currents in SHMS Superconducting Magnets at Jefferson Lab Sun, Eric; Ghoshal, Probir K.; Fair, Ruben J. IEEE Transactions on Applied Superconductivity, Vol. 30, Issue 3 https://doi.org/10.1109/TASC.2019.2931978	journal	April 2020
Development and First Test of the 15 T Nb ₃ Sn Dipole Demonstrator MDPCT1 Zlobin, Alexander V.; Novitski, Igor; Barzi, Emanuela IEEE Transactions on Applied Superconductivity, Vol. 30, Issue 4 https://doi.org/10.1109/TASC.2020.2967686	journal	June 2020
Mechanical Performance of the First Two Prototype 4.5 m Long Nb ₃ Sn Low-β Quadrupole Magnets for the Hi-Lumi LHC Upgrade Cheng, Daniel W.; Ambrosio, Giorgio; Anderssen, Eric C. IEEE Transactions on Applied Superconductivity, Vol. 30, Issue 4 https://doi.org/10.1109/TASC.2020.2972210	journal	June 2020
A 3D Finite Element Model of the Reversible Critical Current Reduction Due to Transverse Load in Nb$_3$Sn Wires Cattabiani, A.; Baffari, D.; Bordini, B. IEEE Transactions on Applied Superconductivity, Vol. 30, Issue 4 https://doi.org/10.1109/TASC.2020.2977038	journal	June 2020
HE-LHC: The High-Energy Large Hadron Collider: Future Circular Collider Conceptual Design Report Volume 4 Abada, A.; Abbrescia, M.; AbdusSalam, S. S. The European Physical Journal Special Topics, Vol. 228, Issue 5 https://doi.org/10.1140/epjst/e2019-900088-6	journal	July 2019
An Assessment of U.S.-Based Electron-Ion Collider Science No authors listed https://doi.org/10.17226/25171	book	September 2018

Similar Records

Comparison of Multi-Scale Nonlinear and Conventional Linear Methods for Stress Analysis of Nb₃Sn Superconducting Magnets

Journal Article · Mon Mar 06 19:00:00 EST 2023 · IEEE Transactions on Applied Superconductivity · OSTI ID:1970459

The Role of Azimuthal Prestress in the Longitudinal Degradation of Nb₃Sn Superconducting Magnets

Journal Article · Mon Dec 16 19:00:00 EST 2024 · IEEE Trans.Appl.Supercond. · OSTI ID:2504182

Studies on Nb/sub 3/Sn field coils for superconducting machine

Conference · Tue Sep 01 00:00:00 EDT 1981 · IEEE Trans. Magn.; (United States) · OSTI ID:6243357

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Hill
Nb3Sn
Nonlinear
finite element analysis
gasket
homogenization
multi-scale

Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

Citation Formats

References (60)

Similar Records

Related Subjects

Multi-scale nonlinear stress analysis of Nb₃Sn superconducting accelerator magnets