Mechanical Behavior Laws for Multiscale Numerical Model of Nb<sub>3</sub>Sn Conductors

Lenoir, Gilles; Manil, P.; Nunio, F.; Aubin, Véronique

doi:10.1109/tasc.2019.2905901

Cited by 9 publications

(3 citation statements)

References 19 publications

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“…The isotropic hardening law which was adopted to model the plastic cyclic response of both the conductor and the insulation materials is contrasting with findings of other authors who studied the behavior of single Nb 3 Sn strands using a bi-metallic model [32], and found a kinematic hardening rule was best fitting the experimental response. When in this investigation, a kinematic hardening rule was adopted for the conductor phase in the cable model, numerical results evidenced a too early reversal of yielding and excessive stress softening compared to experimental evidence from all 10-stack specimen tests.…”

Section: Discussionmentioning

confidence: 61%

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

Bertarelli,

Guinchard,

Holko

et al. 2024

IEEE Trans. Appl. Supercond.

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The use of superconducting composite cables based on Nb 3 Sn, an intermetallic compound of Niobium and Tin, is one of the favorite routes to reach magnetic fields higher than 10 T in state-of-the-art accelerator magnets. The brittle and nonlinear nature of the epoxy-impregnated Nb 3 Sn Rutherford cable makes challenging to predict its mechanical limits and, consequently, the overall performance of the magnet. In the case of collared magnet structures, peak stresses in coils are usually reached during the collaring procedure performed at room temperature. Hence, it is essential to extensively study stress distribution within the superconducting coils and at their interfaces with other components during this phase. In this context, a combined experimental/numerical methodology was developed at CERN to investigate the effects of the assembling process and geometrical imperfections on the mechanical response of the collared coil of the 11 T HL-LHC dipole. The results of the experimental tests were benchmarked against 3-D non-linear finite element models, using material constitutive laws that mimicked the non-linear responses of the Nb 3 Sn cable, and embedding geometrical imperfections as measured on the tested components. The proposed methodology, used in the early stages of superconducting magnets development, may help to identify limitations in the mechanical design, and understand the impact of geometrical imperfections and tolerances on stress distribution in the magnet structures.

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Section: Discussionmentioning

confidence: 61%

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

Bertarelli,

Guinchard,

Holko

et al. 2024

IEEE Trans. Appl. Supercond.

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“…Critical current I c (estimated by application of the electrical field criterion E c = 1 µV/cm to the voltage V—current I curve) and n -value (estimated as the index n of the approximated I ∝ I n curve in the electrical field range of E = 0.1~10 µV/cm) are reduced under high electromagnetic and mechanic stresses, as have been reported for the superconducting oxide (such as RE(Y, Sm, Dy, Gd,···)Ba 2 Cu 3 O 7-δ : REBCCO) layer-coated tape [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ], and Bi2223 [ 15 , 16 , 17 , 18 , 19 , 20 ]-, MgB 2 [ 21 , 22 , 23 , 24 , 25 ]- and Nb 3 Sn [ 26 , 27 , 28 , 29 , 30 , 31 ]-filamentary types. In this work, we conduct a fundamental study on the influences of cracks in superconducting layer-coated tape on I c .…”

Section: Introductionmentioning

confidence: 99%

Analysis of Critical Current Dependence on Specimen Length and Crack Size Distribution in Cracked Superconductor

Ochiai,

Okuda

2023

Materials

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In order to describe the dependence of critical current on specimen length and crack size distribution in the superconducting tape with cracks of different sizes, a Monte Carlo simulation and a model analysis were carried out, employing the model specimens of various lengths constituted of multiple short sections with a crack per each. The model analysis was carried out to evaluate the effects of the two factors on the critical current of a specimen. Factor 1 is the size of the largest crack in a specimen, and Factor 2 is the difference in crack size among all sections at the critical voltage of critical current. Factors 1 and 2 were monitored by the smallest ligament parameter among all sections constituting the specimen and by the number of sections equivalent to the section containing the largest crack at the critical voltage of the critical current of the specimen, respectively. The research using the monitoring method revealed quantitatively that the critical current-reducing effect with increasing specimen length is caused by the increase in the size of the largest crack (Factor 1), and also, the critical current-raising effect is caused by the increase in the difference of crack size (Factor 2). As the effect of Factor 1 is larger than that of Factor 2, the critical current decreases with increasing specimen length. With the present approach, the critical current reducing and raising effects under various crack size distributions were evaluated quantitatively as a function of specimen length, and the specimen length-dependence of critical current obtained by the Monte Carlo simulation was described well.

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“…Engineers proposed to use multi-scale homogenization (the 3rd method) to analyze superconducting strands or coils to overcome some of the aforementioned deficiencies of the 1st and 2nd methods. For example, a homogenized bi-metal model was proposed to analyze Nb 3 Sn strands and the stressstrain behavior of 10-stack Nb 3 Sn coil samples [24][25][26][27]. Other examples are that homogenization was used to perform linear stress analysis of a toroidal Nb 3 Sn coil and HTS coil [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Multi-scale nonlinear stress analysis of Nb₃Sn superconducting accelerator magnets

Sun¹

2022

Supercond. Sci. Technol.

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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.

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Mechanical Behavior Laws for Multiscale Numerical Model of Nb₃Sn Conductors

Cited by 9 publications

References 19 publications

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

Analysis of Critical Current Dependence on Specimen Length and Crack Size Distribution in Cracked Superconductor

Multi-scale nonlinear stress analysis of Nb₃Sn superconducting accelerator magnets

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Mechanical Behavior Laws for Multiscale Numerical Model of Nb3Sn Conductors

Cited by 9 publications

References 19 publications

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

A Combined Testing and Modelling Methodology for the Mechanics of High-Field Superconducting Magnets

Analysis of Critical Current Dependence on Specimen Length and Crack Size Distribution in Cracked Superconductor

Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

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Product

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Mechanical Behavior Laws for Multiscale Numerical Model of Nb₃Sn Conductors

Multi-scale nonlinear stress analysis of Nb₃Sn superconducting accelerator magnets