Mechanical and magnetic load effects in Nb3Sn cable-in-conduit conductors

Recent electromagnetic analyses of Nb₃Sn cables have suggested that cyclic longitudinal bending strain due to transverse magnetic loads could explain the observed low ‘n’ values and drop in critical current compared to the strand. The paper uses finite element modelling to simulate the strand strain states in the cable, including friction and plasticity effects (which cause permanent strand bending). These results are used to calculate the expected behaviour of the overall cable and of strands extracted from the cable after experiencing operational loads. Comparisons with experimental results are made.     

Tensile strength and flux pinning force of superconducting Nb3Sn compound as a function of grain size

In order to evaluate the influence of grain size on the strength and flux pinning force of the Nb₃Sn compound, the microstructure, tensile behaviour and flux pinning force of the bronze-processed Nb₃Sn superconducting composite materials were investigated under various heat treatments. It was found that the strength of the Nb₃Sn layer has a strong dependency on the grain size and it can be expressed by the Hall-Petch type relation. The flux pinning force was roughly proportional to the inverse grain size, agreeing with the results of former investigations.     

Definitions of terms for practical superconductors 1. Fundamental states and flux phenomena

The definitions of terms used in describing the phenomenology and measurement practices of practical superconductive materials are proposed. The definitions cover the subject categories of: 1. fundamental states and flux phenomena, 2. critical parameters, 3. fabrication, stabilization, and transient losses, and 4. Josephson phenomena. It is intended that these terms will become the basis for the development of standard measurement practices and responses are invited.     

Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. II. Curved flux lines

From the Ginzburg-Landau equations, the order parameter, local magnetic field, supervelocity, and elastic energy are derived for an arbitrarily distorted lattice of curved or straight flux lines. Exact solutions are given for small strains and for fields close to the upper critical fieldH _c2 . These solutions are generalized to large strains and arbitrary inductions. The general expressions approximately reproduce all previous results. They apply even to isolated and to crossed flux lines and to flux line loops. As a first application of the distorted-lattice solutions the pinning force density exerted by a small inclusion on the flux line elements is calculated. It turns out that the force may be concentrated on a flux line section of length smaller than even the coherence length. The response of the flux line lattice to such localized forces requires treatment by a nonlocal theory of elasticity and is much larger than expected so far.     

Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. I. Parallel flux lines

A program for the rigorous calculation of the volume pinning force exerted by-imperfections on the flux line lattice in type II superconductors is outlined. As one step of this program, the order parameter, local magnetic field, supervelocity, and elastic energy of the distorted lattice of still parallel flux lines are calculated from the Ginzburg-Landau theory. These general solutions provide a transformation of the Ginzburg-Landau free energy functional of an imperfect material into a mere function of the flux line positions, and thus allow a definition of elastic and pinning force densities which for the first time apply also to large inductions. First, exact solutions for small strains and for fields close toH _c2 are derived. Then, approximate solutions are presented applying to larger strains and to arbitrary inductions. The forces on each flux line exerted by a small needle-shaped inclusion parallel to the flux lines are calculated.     

Diffusion in the CuSn binary system: application to Nb3Sn composites

Non-parabolic growth of intermediate phases in CuSn binary diffusion couples has been observed at 220° C. The deviation from parabolic behaviour may be attributed to grain boundary diffusion. Diffusion coefficients for both the∈-(Cu₃Sn) andη-(Cu₆Sn₅) phases are typically of the order of 2×10⁻¹¹ cm² sec⁻¹, and are in general agreement with other published values.     

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

Superconducting Nb₃Sn Powder-In-Tube (PIT) strands could be used for the superconducting magnets of the next generation Large Hadron Collider. The strands are cabled into the typical flat Rutherford cable configuration. During the assembly of a magnet and its operation the strands experience not only longitudinal but also transverse load due to the pre-compression applied during the assembly and the Lorentz load felt when the magnets are energized. To properly design the magnets and guarantee their safe operation, mechanical load effects on the strand superconducting properties are studied extensively; particularly, many scaling laws based on tensile load experiments have been established to predict the critical current dependence on strain. However, the dependence of the superconducting properties on transverse load has not been extensively studied so far. One of the reasons is that transverse loading experiments are difficult to conduct due to the small diameter of the strand (about 1 mm) and the data currently available do not follow a common measurement standard making the comparison between different data sets difficult. Recently at the University of Geneva, a new device has been developed to characterize the critical current of Nb₃Sn strands under transverse loads. In this work we present a new 2D Finite Element Analysis (FEA) to predict the electro-mechanical response of a PIT strand that was tested at the University of Geneva when transverse load is applied. The FEA provides the strain map for the superconducting filaments when the load is applied. Those strain maps are then used to evaluate the critical current behavior of a PIT strand using a recently developed scaling law that correlates the superconducting properties of a wire with the strain invariants due to the load applied on the superconductor. The benefits and limitations of this method are discussed based on the comparison between the critical current simulation results obtained with the filament strain map and the experimental results available for PIT strands.     

Superconductivity in irradiated A-15 compounds at low fluences II. Alpha-particle-irradiated Nb3Sn and Nb3Ge

The T _c behavior of vapor-deposited Nb₃Ge and Nb₃Sn is examined as a function of low-fluence alpha-particle irradiation. It is found that for Nb₃Sn with 15 -cm the T _c is insensitive to low doses of radiation, whereas Nb₃Ge with ₀ 50 -cm has its T _c depressed immediately with irradiation. It is suggested that the T _c behavior of A-15 superconductors in the regime of small dose is strongly influenced by the initial state of the sample. Furthermore, it is argued that the behavior of the T _c with dose can be qualitatively explained by considering a sharp structure in the density of states N(E), the smearing of which by defects leads to a depression in T _c .Work performed under the auspices of the U.S. Energy Research and Development Administration.Also at Materials Science Department, SUNY at Stony Brook.Also at Physics Department, SUNY at Stony Brook.     

Definitions of terms for practical superconductors 3. fabrication,stabilization and transient losses

The definitions of terms used in describing the phenomenology and measurement practices of practical superconductive materials are proposed. The definitions cover the subject categories of: 1, fundamental states and flux phenomena; 2, critical parameters; 3, fabrication, stabilization, and transient losses; and 4, Josephson phenomena. It is intended that these terms will become the basis for the development of standard measurement practices and responses are invited.     

High-temperature-tolerable superconducting Nb-alloy and its application to Pb- and Cd-free superconducting joints between NbTi and Nb3Sn wires

For more than 30 years, Pb–Bi alloy and Wood's metal (50% Bi, 26.7% Pb, 13.3% Sn, and 10% Cd) have been used as representative superconducting solder intermedia to establish superconducting joints between NbTi and Nb₃Sn wires in high-field nuclear magnetic resonance magnet systems. However, the use of Pb and Cd has been severely restricted by environmental regulations, such as the Restriction of Hazardous Substances Directive. Herein, a novel method of forming a superconducting joint between NbTi and Nb₃Sn wires without Pb and Cd has been proposed. This approach is based on metallurgical bonding processes using a superconducting Nb-alloy intermedium, whose fine microstructure is maintained even after exposure to temperatures higher than 650 °C. Further, fine crystal defects become sources of magnetic flux pinning centers. Among transition elements close to Nb, Hf is considered the most suitable additive for realizing high-temperature-tolerable (HTT) superconducting Nb-alloy intermedia. Utilizing the HTT characteristic of Nb–Hf, a superconducting joint between Nb₃Sn filaments and one end of the Nb–Hf alloy core was created by forming a superconducting Nb₃Sn layer at the interface through a chemical reaction. The other end of the Nb–Hf alloy core was cold-pressed with NbTi filaments, to connect their active new surfaces to each other in order to create a superconducting joint. Ultimately, a superconducting joint between NbTi and Nb₃Sn wires was realized with a high critical magnetic field (B_c2) of more than 1 T. The formation of the superconducting joint was confirmed by current decay measurements. This method of forming a superconducting joint is promising for application in environmentally friendly nuclear magnetic resonance magnet systems.

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Analysis of the quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part I: Geometric and thermal models

The paper describes the new lumped thermal model recently implemented in THELMA code for the coupled electromagnetic–thermal analysis of superconducting cables. A new geometrical model is also presented, which describes the Rutherford cables used for the accelerator magnets. A first validation of these models has been given by the analysis of the quench longitudinal propagation velocity in the Nb₃Sn prototype coil SMC3, built and tested in the frame of the EUCARD project for the development of high field magnets for LHC machine. This paper shows in detail the models, while their application to the quench propagation analysis is presented in a companion paper.     

A practical in situ wire: a composite wire with many in situ processed Nb3Sn cores of an internal diffusion type

As a superconducting in situ wire for practical use, we propose a new type of composite wire with fine cores consisting of in situ processed wires of an internal diffusion type. These Nb₃Sn wires have merit in a simple fabrication process and a high stability compared with ordinary multifilamentary Nb₃Sn wires. Expected properties of the new type of Nb₃Sn wires were estimated based on a series of experimental results for a single in situ Nb₃Sn wire used as a fine core. A quantitative reliability of the new design estimation was examined by comparing the theoretical values with observed data on the electromagnetic properties of a test wire.     

Hall probe Cdx Hg1-x Te for use in magnetic investigations of Nb3Sn superconducting layers

The critical temperature of a superconducting Nb₃Sn layer has been measured by repulsion of magnetic flux as a function of temperature, using a Hall probe. Hall probes of an active semiconductor film, Cd_xHg_1-xTe (x = 0.175), have been made by thermal evaporation in a vacuum. The chemical composition of the Cd_xHg_1-xTe thin films have been determined by spectrophotometric analysis. The Hall probes have been characterized by electric measurements over a temperature range of 4.2–18.5 K in a magnetic field. The probes are particulary suitable for magnetic measurements of superconducting Nb₃Sn layers at low temperatures.     

Analysis of the quench propagation along Nb3Sn Rutherford cables with the THELMA code. Part II: Model predictions and comparison with experimental results

To improve the technology of the new generation of accelerator magnets, prototypes are being manufactured and tested in several laboratories. In parallel, many numerical analyses are being carried out to predict the magnets behaviour and interpret the experimental results. This paper focuses on the quench propagation velocity, which is a crucial parameter as regards the energy dissipation along the magnet conductor. The THELMA code, originally developed for cable-in-conduit conductors for fusion magnets, has been used to study such quench propagation. To this purpose, new code modules have been added to describe the Rutherford cable geometry, the material non-linear thermal properties and to describe the thermal conduction problem in transient regime. THELMA can describe the Rutherford cable at the strand level, modelling both the electrical and thermal contact resistances between strands and enabling the analysis of the effects of local hot spots and quench heaters. This paper describes the model application to a sample of Short Model Coil tested at CERN: a comparison is made between the experimental results and the model prediction, showing a good agreement. A comparison is also made with the prediction of the most common analytical models, which give large inaccuracies when dealing with low n-index cables like Nb₃Sn cables.     

Fully superconducting rectifiers and fluxpumps Part 1: Realized methods for pumping flux

The magnetic and electrical properties of superconductors were a challenge for many inventors and designers to use superconducting materials in the construction of fully superconducting voltage and current sources commonly called fluxpumps. In the past twenty years a large variety of mechanically or electrically driven devices have been proposed and successfully operated.In this review the basic principle of operation of each class of devices is shown and specific material problems and limitations are reported. The review will be published in two parts.Part 1 deals with mechanical devices such as flux compressors and dynamos. Although those devices must have been of great importance for technical application, their construction and operation offered great experience with regard to the properties of superconducting materials, their joint techniques switching and mechanical and magnetic stability under ac and dc conditions.In this part also a start is made with the more promising class of electrically driven rectifier fluxpumps. With these rectifiers, current levels over 10 kA can be obtained with high efficiency.In part 2 a theoretical comparison between dynamos and transformer rectifiers will conclude the review.     

Grain size and its relation to tensile strength of Nb3Sn compound in bronze-processed multi-filamentary superconducting materials

The grain size and room-temperature tensile strength of Nb₃Sn compound were studied over wide ranges of annealing temperature and time using thin and thick multi-filamentary superconducting composite materials. The strength of Nb₃Sn compound in thick specimens was lower than that in thin specimens at any heat treatment. This result was accounted for by the existence of extra-coarse grains in thick specimens. It was found that the strength of Nb₃Sn compound is nearly proportional to the inverse square root of the grain size.     

Model for practical prediction of natural carbonation in reinforced concrete: Part 1-formulation

A model is proposed for prediction of natural carbonation in reinforced concrete (RC) structures, and is potentially applicable to existing and new RC structures. The major components of the model comprise mathematical functions applied to predict the influence of concrete composition, and environmental factors on natural carbonation.This paper introduces the model concept and explains its structure including derivation, optimization and calibration. Over 163 data sets taken from a 10-year carbonation study were used in the model development and calibration. Only the experimental data that were based on outdoor natural exposure environment were employed in this research. Also in this study, the proposed model is compared with fib-Model Code 2010 using carbonation predictions generated from 346 data sets involving real world, highway structures. It is shown that the proposed model is comparably accurate and involves mainly basic tests with no major anticipated costs.     

Tensile cracking in concrete and sandstone: Part 1—Basic instruments

In this paper, the behaviour of concrete and sandstone specimens subjected to uniaxial tension is described in detail. The results are a summary of the work completed over the past years and will be presented in two parts. A lattice model has been developed, which is used to explain the behaviour observed in laboratory-scale specimens. The model, which will be outlined in this first paper, adopts a perfectly elastic brittle fracture law at the meso-level (particle level) of the material and is capable of simulating crack face bridging in the softening regime quite realistically. The comparison with crack patterns observed in a series of vacuum impregnation tests is quite favourable. Although the crack patterns compare well, the load-deformation diagrams calculated with the model are still too brittle in comparison with experimentally-measured load-displacement responses. Neglecting the small particles in the material structure and omitting the third dimension in the analyses are two reasons for the overrated brittleness and are worked out in this paper. Because of the localised nature of the fracture process in the softening branch, the specimen size and boundary conditions must have a significant effect on the process. The effect of boundary rotations is analysed in part 2 of this paper.