Self-healing effect in strained multifilamentary Nb3Sn conductors

Multifilamentary Nb₃Sn conductors can be strained much more without damage than bare Nb₃Sn. The reason is a compression of the Nb₃Sn filaments which acts as a mechanical reserve. It is caused by a stronger thermal contraction of the bronze in the composite. By overloading the conductor at low temperature the compression of the Nb₃Sn disappears. Afterwards the conductor is subject to damage upon further loading. Measurements of the critical current under strain showed that at least part of the compressive strain can be regained by warming the conductor to room temperature. Analysis of the measured low temperature stress-strain diagram revealed that plastic deformation of the bronze during warming up is the cause of this self-healing.     

Room-temperature tensile behaviour of bronze-processed multi-filamentary Nb3Sn superconducting materials

Structure and its relation to fracture behaviour of multi-filamentary Nb₃Sn superconducting composite materials prepared by the bronze method were studied by tensile testing at room temperature. There were two types of fracture mode. Type I showed high elongation, accompanied by apparent plastic deformation of composites as a whole and the Nb₃Sn layer exhibited multiple fracture. Type II showed no apparent plastic deformation and the composites fractured in a brittle manner. Type I occurred when the fraction of the Nb₃Sn layer was small and the drop of load-bearing capacity due to fracture of Nb₃Sn layer could be compensated mainly by strain hardening of ductile constituents of Nb, Cu-Sn and Cu. On the other hand, Type II occurred when the fraction of Nb₃Sn layer was large and the fracture of the Nb₃Sn layer caused fracture of composites as a whole. To describe the tensile strength of composites for both types, a model was proposed, which explained well the experimental results. It was found that the strength of the Nb₃Sn layer decreases with increasing diameter of composites and with increasing annealing temperature and time.     

A study of the microscopic deformation behavior of Nb3Sn composite superconducting tape using the acoustic emission technique

Nb₃Sn-based composite superconducting tapes have been widely used because of their excellent properties such as high critical current density, low AC loss and high critical temperature. However, one of the disadvantages of Nb₃Sn-based composite superconducting tape is that the Nb₃Sn compound often exhibits multiple cracking owing to its intrinsic brittleness when subjected to mechanical loading such as bending, winding, and operation. Such cracking eventually causes severe degradation of the critical current density. Therefore, it is very important to understand the microscopic deformation behavior of Nb₃Sn-based composite superconducting tape under mechanical loading.In this study, the microscopic deformation behavior and the fracture mechanism of Nb₃Sn-based composite superconducting tape were investigated using acoustic emission (AE) technique at room temperature. The tensile behavior of Nb₃Sn-based composite superconducting tape was analyzed using the AE parameters including amplitude, duration time, and event count, which are representative of various deformation parameters such as elasticity, yielding, and cracking. The results show that the AE technique is very effective for evaluating the deformation behavior of Nb₃Sn-based composite superconducting tape.     

Simulation of transport properties in Nb3Sn strand under bending

Superconducting performance of a large-scale Nb₃Sn cable-in-conduit conductor (CICC) is degraded by periodic bending of strands subjected to a distributed transverse electromagnetic force during operation. The current transport in a single strand depends mainly on the bending strain and transverse resistivity. In particular, in the case of high-level strain and/or crack occurring among the filaments in the strain-sensitive Nb₃Sn strand, these two parameters are required for better understanding of the critical current I_c degradation of a single strand. We use finite element method to simulate transport properties of a single Nb₃Sn strand under bending. The simulation allows treating a wider range of transverse resistivity of strand, compared with our previous analytical method (Cryogenic, 58, 2013). Also, the present simulation incorporates the change of the area of strand cross section due to filament fracture into the boundary of the current transport, rather than simply imposes the condition of vanishing current on the filament fracture region as in the previous analytical method. We show the current/field profiles in the strand for various bending loads and transverse resistivities, as well as the I_c degradation of several types of strands under bending.     

Tensile strain dependence of critical current of RHQ-Nb3Al wires

Nb₃Al superconducting wires produced by rapid heating and quenching (RHQ) have been developed for high-field accelerator magnets. It is known that critical currents of A15 superconductors (e.g., Nb₃Al and Nb₃Sn) have a dependence on stress/strain. It is thus important to clarify the stress/strain behavior of the RHQ-Nb₃Al wires for the development of high-field accelerator magnets. We recently started experimentally investigating the strain dependence of the critical current of the RHQ-Nb₃Al wires with a Ta interfilament by measuring their critical currents under longitudinal tensile strains. To evaluate the effect of residual strain in Nb₃Al filaments induced by thermal contraction of the materials in the wire, neutron diffraction measurements were performed at room temperature.     

The microstructure and mechanical properties of Nb3Sn filamentary superconducting composites

The deformation processes in filamentary superconducting composites at both room temperature and 4.2 K have been studied using transmission and scanning electron microscopy. In all the composites, the filaments consisted of a central core of unreacted niobium surrounded by a reacted layer of Nb₃Sn. The Nb₃Sn failed in an intergranular manner without any prior dislocation activity and the radial cracks formed in the Nb₃Sn layer during deformation were stopped at the niobium core. The observed variations in ductility, fracture stress and secondary modulus between the different composites were accounted for quantitatively by the presence of the niobium cores.     

Strain effects of cable-in-conduit Nb3Sn conductors

Reduced sized cable-in-conduit Nb₃Sn conductors were fabricated with various void fractions as a parameter, before fabricating full size conductors. The relation between critical current and bending strain was investigated. The Nb₃Sn conductors had a 6 × 3 strand cable in a conduit with 0.61 mm diameter strands. The void fractions were changed from 30% to 50%. The conductor with ∼50% void fraction had a critical bending strain (ε_bc) of ∼0.9%, which was nearly equal to that for the strand, while conductors with void fractions below ∼40% behaved like a monolithic conductor with ε_bc below ∼0.5%.     

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.     

Semi-analytical modeling of the coupled strain and low-temperature dependence of the normal-state resistivity in Nb3Sn

A semi-analytical modeling framework on the microscopic basis is proposed in this paper to predict the low-temperature transport properties of strained Nb₃Sn superconductors. The theoretical predictions agree well with experimental observations, which indicate that the competitions between the strain state-dependent variations in the phonon spectrum and the electron density of states (DOS) are an important consideration in interpreting the coupled low temperature-strain sensitivity of resistivity in superconducting Nb₃Sn. The model is helpful for identifying the scaling law describing the anomalies in the strain dependence of superconducting critical properties of Nb₃Sn conductors.     

Electro-mechanical modeling of Nb3Sn CICC performance degradation due to strand bending and inter-filament current transfer

Performance degradation of Nb₃Sn cable-in-conduit conductors (CICCs) is a critical issue in large-scale magnet design such as the International Thermonuclear Experimental Reactor (ITER) and the series-connected hybrid (SCH) magnets currently under development at the National High Magnetic Field Laboratory (NHMFL). Not only the critical current is significantly lower than expectations but also the voltage-current characteristic is observed to have a much broader transition from a single strand to a CICC cable. The variation of conductor voltage-current characteristic as a result of cable electromagnetic, mechanical and thermal interactions is challenging to model. In this paper, we use a new numerical model, called the Florida electro-mechanical cable model (FEMCAM) benchmarked against 40 different conductor tests, to study the influence of bending strain and current non-uniformity on the critical current and n-value of Nb₃Sn strands and CICC cables. The new model combines thermal bending effects during cool-down, electromagnetic bending effects during magnet operation and current transfer in strands with filament fracture. The n-value of a strand under bending is derived from integration of filament critical current over strand cross-section for full and no current transfer. The cable n-value is obtained from the power law relation of cable electric field and critical current curve. By comparing numerical results with measurements of advanced Nb₃Sn strands and various CICC cables, we demonstrate that FEMCAM is self-consistent in modeling inter-filament current transfer. The new model predicts that I_c degradation of bent strands initially follows closely full current transfer but starts deviating and falls between full and no current transfer with an increasing bending strain. The results agree with recent TARSIS measurements for less than 1% bending strain mostly interested in practice. The strand n-value degradation from FEMCAM with no filament current transfer agrees better with measurements than that from full current transfer. Finally, FEMCAM simulated cable n-values are compared with various CICC measurements. The results imply that FEMCAM is a useful tool for the design of Nb₃Sn-based CICCs and both thermal bending and electromagnetic bending play important roles in CICC performance.     

A review of mechanical behaviour and stress effects in hard superconductors

The mechanical properties of type II superconducting materials are reviewed as well as the effect of stress on the superconducting properties of these materials. The bcc alloys Nb-Ti and Nb-Zr exhibit good strength and extensive ductility at room temperature. Mechanical tests on these alloys at 4.2 K revealed serrated stress-strain curves, non-linear elastic effects, and reduced ductility. The non-linear behaviour is probably due to twinning and de-twinning or a reversible stress-induced martensitic transformation. The brittle A-15 compound superconductors, such as Nb₃Sn and V₃ Ga, exhibit unusual elastic properties and structural instabilities at cryogenic temperatures. p]Multifilamentary composites consisting of superconducting filaments in a normal metal matrix are normally used for superconducting devices. The mechanical properties of alloy and compound composites, tapes, as well as composites of niobium carbonitride chemically vapour deposited on high strength carbon fibres are presented. Hysteretic stress-strain behaviour in the metal matrix composites produces significant heat generation, an effect which may lead to degradation in performance of high field magnets. Measurements of the critical current density, J_c, under stress in a magnetic field are reported. Modest stress-reversible degradation in J_c is observed in Nb-Ti composites while more serious degradation is found in Nb₃Sn sample.The importance of mechanical behaviour on device performance is discussed.     

Nb3Sn material development in Russia

In the USSR and later in Russia, the main activities in technical superconductivity were concentrated in the institutes that belonged to the Ministry of Atomic Energy (Minatom). The development of new technologies shortly transferred to the large-scale industrial production of NbTi and Nb₃Sn superconductors in early 1970s. Two main technologies for multifilamentary Nb₃Sn strands were under investigation during that time – bronze-process and internal tin method. More than 25 ton of Nb₃Sn bronze-processed strands were produced for the fabrication of 90 ton of conductors for application in the magnet system of first in the world fusion facility (tokamak T-15) with magnet system based on the intermetallic compound. The characteristics of these strands and conductors have been briefly described. The requirements for the Nb₃Sn strands constantly increased and the main R&D on the enhancement of critical current density have been reviewed. For bronze-processed strands the increase of the tin content in large ingots was the crucial factor. The artificial doping of niobium filaments by niobium–titanium alloy was invented, which enabled to improve the workability of Nb₃Sn strands, with enhanced critical current density in high fields. For internal tin Nb₃Sn strands the main R&D were concentrated on the optimization of the layouts of the strand and on the multistage heat treatment because of the inevitable liquid phase formation which could result in severe distortion of the geometrical arrangement of the filaments and even in destruction of the whole strand. The main results of these investigations have been presented. The corresponding impact of these R&D on the design of bronze-processed and internal tin strands has been analyzed. The quantitative estimations of the grain size were made for bronze-processed and internal tin strands. It was shown that in bronze-processed and internal tin strands subjected to the standard ITER heat treatment characterized by two stages at 575 °C and 650 °C, the variation of Nb₃Sn grain size in the range of 30–300 nm could be observed. The correlations of microstructure and superconducting properties have been discussed. The ITER connected activities in Russia on the development of Nb₃Sn strands, which met the HP-II specification, have been outlined. The results of the ITER Model Coil Program have shown a degradation of the critical current of large cable-in-conduit conductors (CICC) built with Nb₃Sn strands. For this reason, the investigation on the strain dependence of critical current density in Nb₃Sn strands of different designs is of high interest and priority. The R&D on development of bronze-processed and internal tin Nb₃Sn strands with enhanced, by the nanostructured Cu–Nb material, mechanical strength have been reviewed.     

Strain scaling law for flux pinning in practical superconductors. Part 1: Basic relationship and application to Nb3Sn conductors

Critical current and flux pinning densities have been determined for a series of Nb₃Sn, V₃Ga, Nb₃Ge, and NbTi conductors as a function of uniaxial tensile strain in magnetic fields ranging from 4 to 19 T. An empirical relationship has been found at 4.2 K that describes these data over the entire range of field under both compressive and tensile strain. The pinning force F has been found to obey a scaling law of the form $\text{F = [B}{}_{\mathrm{c2}}\text{1(?)]}{}^{\mathrm{n}}\text{f(b)}$, where B_c2¹ is the strain-dependent upper-critical field determined from high-field critical-current measurements and f(b) is a function only of the reduced magnetic field $\text{b  B/B}{}_{\mathrm{c2}}\text{1}$. The detailed shape of f(b) depends on the super-conducting material and reaction conditions, but n was found to be nearly constant for a given type of superconductor. For Nb₃Sn conductors n = 1 ± 0.3, for multifilamentary V₃Gan?1.3, for CVD-Nb₃Ge tape n?1.6, and for multifilamentary NbTi n?3.3. The importance of this relationship is that, for these conductors at least, it is possible to measure F at one strain and then immediately be able to predict F (and thus the critical current) at other strain levels simply by scaling the results by [B_c21(?)]ⁿ. Part I of this paper presents the basic uniaxial-strain scaling relationship and focuses on its application to Nb₃Sn conductors. The strain scaling law with n = 1 ± 0.3 was found to hold for all Nb-Sn based conductors examined thus far, including commercial-multifilamentary conductors, extremely fine-filament composites, partially-reacted specimens, ‘insitu’ conductors, and Nb-Hf/Cu-Sn-Ga conductors. The detailed dependence of B_c21 on strain was-found to be nearly universal for highly-reacted commercial Nb₃Sn specimens, greatly simplifying the application of the scaling law to this group of practical superconductors. These results are discussed within the context of flux pinning models and a general scaling relation is proposed which unifies the usual temperature-scaling relation with this strain-scaling relation.     

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.     

Strength and elongation of multifilamentary Nb3Sn superconducting composite materials with small amounts of Nb3Sn compound

In order to describe the tensile strength and elongation to failure of multifilamentary Nb₃Sn superconducting composite materials with small amounts of Nb₃Sn showing multiple fracture, approximate calculation methods are proposed. In the proposed calculation method, the concept of shear-lag analysis and the plastic instability approach for metallic composites are employed. The experimental results are fairly well described by the present calculation methods.     

Growth of Nb3Sn in multifilamentary bronze composites

Growth of Nb₃Sn layers in multifilamentary composites has been investigated and their superconducting critical temperatures are measured using both resistive and inductive techniques. The growth parameters are discussed in the light of the analytical models of Reddi et al. Results show that for the composites studied, the rate controlling step for Nb₃Sn growth is diffusion of tin through grain boundaries of Nb₃Sn with the time exponent n determined by both the initial grain size and grain growth. T _c measurements show that for composites with a higher filament number, the width of superconducting transition is broader with no significant change in the onset T _c.     

Status and perspective of the Nb3Al development

Nb₃Al has advantages of better tolerance to strain/stress and a higher critical magnetic field (30 T at 4.2 K) for stoichiometric composition over Nb₃Sn. The rapid-heating, quenching and transformation annealing (RHQT) process enables to form a stoichiometric Nb₃Al with fine grain structures via metastable bcc supersaturated-solid-solution. As a result a large critical current density of Nb₃Al is achieved over the whole range of magnetic fields without trading off the excellent strain tolerance. A long-length of RHQ processing has been established, and a rectangular but Cu stabilized Nb₃Al strand is about be commercially available for NMR uses. Ag or Cu internal stabilization and Cu ion-plating/electroplating techniques have been also developed to enable the stabilized round wire for accelerator and fusion magnets. Successfully energized test coils that were manufactured with a wind-and-react technique have demonstrated that a long piece of Cu stabilized RHQT Nb₃Al wire is really available for practical applications.     

Finite element simulations of elasto-plastic processes in Nb3Sn strands

The manufacturing of Nb₃Sn strands, with drawing and annealing of multifilamentary strands followed by a heat treatment at about 900 K to form the Nb₃Sn by reaction of tin and niobium, has the potential to create a complex internal stress system. The strain sensitivity of the Nb₃Sn superconducting properties makes prediction of the internal stresses a necessary step to understanding the performance of Nb₃Sn conductors under the magnetic load conditions experienced in a coil. An elasto-plastic one dimensional finite element model, including temperature dependent stress-strain curves, annealing and manufacturing process stresses, is used to derive the internal stresses of Nb₃Sn strands. The model is benchmarked against a range of experimental data, including stress-strain tensile tests, superconducting critical current-strain tests, and length changes through heat treatment and through a 4 K thermal cycle. The model can predict all the experimental features and shows a number of unexpected conclusions regarding the origin of the Nb₃Sn stresses.     

Changes ofT c,J c,B c2 and the lattice parameter of the Nb3Sn phase formed at the initial stage of growth in a multifilamentary superconductive wire

Investigations were made of the superconducting transition temperature,T _c, the upper critical flux density,B _c2, and the critical current density,J _c, of Nb₃Sn layers in filamentary wire in a bronze matrix. The lattice parameter,a ₀, andT _c of Nb₃Sn layers in 259-filament wire were determined after removal of the bronze matrix. The microstructure and layer thickness were studied using scanning electron microscopy. The diffusion formation of Nb₃Sn phase at 1023 K was studied until the complete reaction of the niobium filaments. It was found that the Nb₃Sn layer begins to form in the manufacturing process during the intermediate annealing at 793 K, and that there is a considerable degradation of critical parameters due to the non-stoichiometry of the Nb₃Sn phase in layers thinner than 1m.     

Effect of bronze on the compression of Nb3Sn in multifilamentary conductors

Nb₃Sn in multifilamentary conductors is subject to compressive strain as a result of the relatively small thermal contraction of the filaments as compared to bronze. The critical current l_c is consequently degraded. The critical current increases, when an external tensile stress is applied, and passes through a maximum. The ratio of the maximum critical current to the initial critical current increases with the flux density and reaches a value of two at a flux density of 16 T for technical conductors. The strain _m, at which the l_c maximum is reached, lies between 0.4% and 0.7% for the conductors investigated and depends on the material parameters. For a constant ratio of bronze to filament cross section this strain _m is reduced as the Nb₃Sn layer thickness is increased and can be determined approximately by a graphical method from the stress-strain diagram. _m is to a large extent dependent on the metallurgical properties of bronze, which vary to a considerable extent depending upon the heat treatment.