1. Introduction
The YBCO high-temperature superconductor (HTS) tapes have become an attractive material for high-field magnets due to their excellent current carrying capacity at temperatures above 4.2 K and magnetic fields above 15 T [1], [2]. Recently, fabrication technologies of YBCO tapes have undergone rapid advancement and commercialization, primarily due to substantial research investments in the development of their applications [3], [4], [5], [6]. For large-scale magnet applications, the YBCO tapes must be made into multi-stage conductors, allowing them to operate at a high magnetic field with a high current carrying capacity.
To overcome the application limitations imposed by the complex multilayer structure and strain dependence of critical current in YBCO tapes, several conceptual designs have been proposed, such as Twisted Stack Tape Conductor (TSTC) [7], Conductor On Round Core (CORC) [8], Roebel [9] and vacuum pressure impregnated, insulated, partially transposed, extruded, and roll-formed (VIPER)cable [10]. At the same time, efforts have been made to reduce the substrate thickness of the tape [11], [12], i.e. from 50 μm to 25 μm, and even to deposit a YBCO on the tape’s neutral layer [13]. In addition, efforts are being made to reduce the width of YBCO tapes [14]. All of these are intended to improve the bending flexibility and current carrying density of YBCO wires or cables, thereby broadening their high-field applications. Furthermore, the configuration of YBCO wires or cables should have desirable characteristics for application such as easy cooling, excellent mechanical performance, and manufacturability. However, there is no evidence that any of the above-mentioned designs can satisfy all the required characteristics simultaneously.
This paper describes the design, manufacturing, and bending flexibility performance qualification of a new type of YBCO cable named Highly Flexible REBCO Cable (HFRC). It was proposed as a possible solution for the central solenoid (CS) coil of the China Fusion Engineering Test Reactor (CFETR), which is expected to operate at a magnetic field of above 15 T and a current of higher than 45 kA. In this new concept, the YBCO and Cu tapes are spirally wound around a central spiral tube to maintain bending flexibility and easy cooling simultaneously. Furthermore, the longer lengths of this type of cable can be easily manufactured on a large scale. Therefore, it is suitable for future large-scale magnets with complex configurations, multi-stage cabling, and high current carrying requirements.
2. The cable design and manufacturing
2.1. Cable design
Considering the advantages of high isotropic bending properties of a round cable, as demonstrated by the CORC concept developed by Advanced Conductor Technologies (ACT), the HFRC concept also employs this technology of forming a round cable. It is based on the specific CORC cable technology of winding HTS tapes into multiple layers to carry a large current.
The proposed HFRC concept is shown in Fig. 1. It is mainly composed of a spiral tube, pure Cu tapes, and YBCO tapes. The Cu and YBCO tapes are designed to be spirally wound around a spiral tube made of helically wound stainless steel strip. The aim is to provide mechanical support while also forming a central channel to carry the cryogenic coolant. The coolant can flow through the gaps between adjacent pitches of the central spiral tube and between adjacent wound tapes to directly cool the YBCO tapes during operation. It is worth noting that the stainless steel strip has a fish-back configuration formed by rounded edges on its outer surface. Its purpose is to avoid the sharp corner, which can easily damage the tapes during cabling and operation.
Fig. 1. The design concept of the HFRC cable. |
Because of the discontinuous profile of the central spiral tube, the first two or more layers are designed to be wound with Cu tapes. This has two functions: one is to provide a relatively flat surface for the subsequent YBCO tape winding, and the other is to increase the copper-to-superconductor ratio to ensure the thermal stability of the cable. Then, the following layers can be made up of any combination of YBCO and Cu tapes. Depending on the outer diameter and other parameters of the winding tapes, one or more YBCO and/or Cu tapes can be wound synchronously per layer.
2.2. Cable manufacturing
As shown in Fig. 2, the equipment developed by the Institute of Plasma Physics, Chinese Academy of Sciences, was used to wind the HFRC cable. Two or three tapes for each layer can be wound synchronously. The YBCO and Cu tapes must be fixed and adjusted to a fixed tension during the cable winding process. The ends of the tapes are then soldered to the central spiral tube using the PbSn solder. For the first two layers of the Cu tapes, the melting temperature of the selected solder can be higher than that used for fixing the YBCO tapes, which should be kept below 200 ℃. In addition, the traction force for cabling should be controlled to avoid the effects of central spiral tube deformation on the cable. Otherwise, the gap between adjacent tapes will be greater than the designed value, especially for the first two layers of Cu tape winding.
Fig. 2. The HFRC cable winding. |
3. Bending performance evaluation
3.1. Sample description
Specimens based on this HFRC design concept have been prepared to evaluate their bending flexibility. The spiral tube with an outer diameter of 4.95 mm and an inner diameter of 3.95 mm was used. It has a helical pitch of 8.6 mm. At the same time, traditional CORC specimens with identical cabling parameters are also prepared for comparison. Based on the results of finite element models [15], [16], the parameters that affect flexibility performance are considered, such as central core diameter, tape geometrical dimensions, winding layers, and winding angle. Thus, three kinds of HFRC and CORC cable specimens were manufactured. Details of the prepared specimens are listed in Table 1. All YBCO tapes are purchased from Fujikura with a substrate thickness of 50 μm. Their width and thickness are around 4 mm and 0.1 mm, respectively. Furthermore, all tape winding angles are set to 46°.
Table 1. Specifications of prepared HFRC and traditional CORC cable specimens. |
| Former OD | Number of SC Tapes | Location of SC Layers | Number of Cu Tapes | Location of Cu Layers | Total Layers | Cable OD | |
|---|---|---|---|---|---|---|---|
| HFRC-1/2 | 4.95 mm | 3 | 3rd | 12 | 1st 2nd 4rd 5th | 5 | 5.75 mm |
| HFRC-3 | 15 | 3rd-7th | 6 | 1st-2nd | 7 | 6.25 mm | |
| HFRC-4 | 3 | 3rd | 6 | 1st-2nd | 3 | 5.45 mm | |
| CORC-1/2 | 5.25 mm | 3 | 1st | 6 | 2nd-3rd | 3 | 5.75 mm |
| CORC-3 | 15 | 1st-5th | / | / | 5 | 6.25 mm | |
| CORC-4 | 3 | 3rd | 6 | 1st-2nd | 3 | 5.75 mm |
All HFRC and CORC specimens in this study are wounded with the winding machine shown in Fig. 2, and their maximum lengths are around 5 m. First, for all HFRC cable specimens, two layers of Cu tapes with a width of 4 mm and a thickness of around 0.075 mm are wound. The goal is to make the winding diameter of the first layer YBCO tapes of about 5.25 mm, which is the same as the diameter of the copper former used for CORC specimens. Then, three YBCO tapes are wound into one layer, and the outermost two layers are made up of six Cu tapes of the same dimensions as the YBCO tapes. The fabricated conductors are named HFRC-1 and HFRC-2 specimens. The CORC-1 and CORC-2 specimens have the same layout as HFRC-1/2, with the innermost layer of YBCO and two outer layers of Cu. The outer diameters of HFRC-1/2 and CORC-1/2 are approximately 5.9 mm. In addition, both the HFRC-3 and CORC-3 specimens contain fifteen YBCO tapes in five layers, which are designed to test the effects of multi-layer winding. The outer diameters of HFRC-3 and CORC-3 are approximately 6.3 mm. The tape layout of HFRC-4 specimens is derived from HFRC-1 by removing the Cu tapes that are located outside of the YBCO tapes. In addition to the above-mentioned samples, CORC-4 with six Cu tapes in two inner layers and three YBCO tapes in the outermost layer is manufactured using an annealed copper former. The yield point of the annealed copper former used for this CORC-4 cable is around 60 MPa, which is only about 40% of the other CORC specimens.
3.2. Cable bending test results
The prepared cables are cut into several sections, one of which is around 700 mm for carrying out the bending test as shown in Fig. 3. The bending radii of G10 moulds are from 150 mm to 12.5 mm. Before bending tests, critical currents of the cable specimens are measured in a straight form at 77 K and self-field. Afterward, the cables are bent into a semicircle with the help of the prepared G10 moulds with diameters ranging from 300 mm to 30 mm. The critical currents of the cable specimens are measured in each bending condition to determine the reduction of its critical current Ic at 77 K and self-field.
Fig. 3. The cable bending and mounting on G10 mould with a bending radius of 40 mm. |
During testing, approximately 50 mm long Cu tapes of the outermost two layers are removed from each end of HFRC-1/2 and CORC-1/2 specimens. The ends are soldered to connect with the current lead, which is made of stacked Bi2223 tapes. Voltage taps are soldered on the YBCO layer at both ends of each cable for the Ic test. This method is used for specimens containing only three YBCO tapes. However, for the multi-layered HFRC-3 and CORC-3 specimens, the wound tapes at both ends are treated as a staircase with a step length of 10 mm. Then the cable ends are inserted into copper terminals and filled with SnPb solder to reduce contact resistance. Fig. 4(a-c) shows the E-I characteristics of the CORC-1 and HFRC-1 specimens with straight cable and different bending diameters (D) at 77 K and self-field. Fig. 4(b) shows that a linear resistance appears before the main transition, which could be caused by a difference in the current sharing condition between the inner layer of YBCO tapes and the outer two layers of Cu tapes. However, it is not observed in the HFRC-3 specimen (as shown in Fig. 6) with all five outer layers of YBCO tapes. The Ic is determined using a fitting equation [17] and a criterion of 1 μV cm−1. Fig. 5 compares the critical currents of CORC-1 and HFRC-1 specimens at different bending diameters. The critical currents for straight HFRC and CORC cable specimens with three YBCO tapes in one layer are approximately 480 A. However, at the bending radius of 80 mm, the critical current degradations of CORC-1 specimens are about 55%, while the critical current of HFRC-1 specimens remains almost unchanged. The cables are tested in bending conditions. Thus, the variation in current carrying performance includes both reversible and irreversible degradations. For the multi-layer HFRC-3 and CORC-3 specimens, the measured critical currents per layer are similar to the conditions in a straight cable. The total currents of CORC-3 and HFRC-3 are about 2350 A and 2374 A, respectively. It shows that there is no observable degradation in the cable fabrication with multiple YBCO layers. Besides the Ic, the n-values of the specimens are determined at an electric field interval from 0.1 to 1 μV cm−1, which mostly falls within a range of 20 to 45.
Fig. 4. E-I characteristics of (a) CORC-1, (b) HFRC-1 specimens and (c) comparison at different bending diameters. |
Fig. 5. The critical current of CORC-1 and HFRC-1 specimens at different bending diameters. |
Fig. 6. E-I characteristics of the HFRC-3 cable at different bending diameters. |
Fig. 7 shows the relationship between normalized current Ic/Ico and bending diameter of YBCO and HFRC cable specimens, where Ic is the measured carrying current and Ico is the critical current. The critical current Ico is the carrying current of the straight cables. It can be seen that different specimens of the same type have similar bending flexibility performance. When the bending diameter decreases from 300 mm to 44 mm, no significant Ic degradation is observed for all HFRC specimens with different tape layouts. When the bending diameter is reduced to around 40 mm, the Ic starts to decrease. The degradation reaches about 5-10% when the bending diameter is close to 30 mm. For CORC specimens with one layer of YBCO tapes, there is no significant Ic degradation when the bending diameter decreases from 300 mm to 100 mm. The Ic of most CORC specimens starts to decline when the bending diameter reaches about 95 mm. A maximum Ic degradation of around 10% has been observed with a bending diameter of around 80 mm. However, the CORC-4 specimen exhibits better flexibility performance than other CORC specimens. Its critical current decline is much slower. One of the reasons could be the use of an annealed Cu former and two inside layers of wound Cu tapes. Because the central former has lower plasticity, the Cu tapes may reduce friction and sliding between tapes and tapes over the core.
Fig. 7. Ic/Ico as a function of the bending diameter. |
Similar to what has been pointed out in [15], the critical bending radius of multi-layered cables is slightly larger for both the HFRC and CORC specimens. Bending the HFRC-3 specimen to a diameter of 30 mm results in a 12% degradation. The variation of Ic degradation is not linear due to the complex friction between the YBCO tape(s) and the central core. The degradation of properties during bending can also be tracked with the help of their n-values. Fig. 8 shows the calculated n-values for specimens including HFRC-1/3 and CORC-1/3 under different bending conditions. Despite differences in the initial n-values, the variation with decreasing bending diameter is almost consistent with the Ic characteristics.
Fig. 8. The calculated n-values as a function of the bending diameter. |
4. Finite element modeling and analysis
4.1. Finite element model
In the above-mentioned bending tests, the HFRC specimens show a lower critical bending diameter when compared to the same layout of CORC specimens. To explore the underlying cause, finite element models were created using the Finite Element Software ABAQUS to analyze the strain and stress distribution on the YBCO tapes during bending for both the traditional CORC cable and the proposed HFRC cable. The three-dimension models of the CORC and HFRC cables are shown in Fig. 9. In the simulation, the layout and parameters are the same for both cables, and the dimensional parameters of the tapes and central former are consistent with the experiment. Because the cable winding stress/strain in the tape is mainly related to the geometric dimensions and the used tension load, the initial conditions of the YBCO tapes in the two kinds of cables are assumed to be the same. In this case, the built model was simplified by ignoring the cable winding stress/strain and comparing only the stress/strain that occurred during cable bending.
Fig. 9. The finite element simulation models of CORC and HFRC cables. |
The cases of a single layer of two tapes are simulated, where the materials of the tapes are homogenized according to the volume fraction of each component material. Young's modulus Eeq of the tape is given as:
$E_{\text {eq }}=\frac{\left(E_{Y \mathcal{P C O}} \cdot t_{Y \mathcal{P C O}}+E_{\text {coppper }} \cdot t_{\text {coppper }}+E_{\text {substrate }} \cdot t_{\text {subslirate }}\right)}{t}$
where, EYBCO, Ecopper, and Esubstrate refer to the Young's modulus of the YBCO layer, copper layer, and substrate layer, respectively. tYBCO, tcopper, and tsubstrate refer to the thickness of the corresponding layers, while t refers to the total thickness of the YBCO tape. Surface-to-surface contact is used in the simulation model for the contact between tape and former as well as between tapes. All of the friction factors are set to 0.15. The detailed geometric dimensions and equivalent mechanical parameters for both the CORC and HFRC cables are summarized in Table 2.
Table 2. The dimensions and mechanical parameters for the cable specimens. |
| Parameters | Value | |
|---|---|---|
| YBCO tape | Thickness | 0.1 mm |
| Width | 4 mm | |
| Thickness of the YBCO layer | 1 μm | |
| Thickness of the Copper layer | 20 μm | |
| Thickness of the Substrate layer | 50 μm | |
| YBCO | Young's modulus, EYBCO | 157 GPa |
| Poisson ratio | 0.3 | |
| Copper | Young's modulus, Ecopper | 89 GPa |
| Poisson ratio | 0.34 | |
| Substrate | Young's modulus, Esubstrate | 229 GPa |
| Poisson ratio | 0.307 | |
| Copper core | Diameter | 4.95 mm |
| SS spiral tube | Inner diameter | 3.95 mm |
| Outer diameter | 4.95 mm | |
| Spiral pitch | 8.6 mm | |
| Friction factor | 0.15 | |
4.2. Modelling results and discussion
To analyze the bending performance of the two kinds of cables, the bending radius R is set to 80 mm. Similar to the cable bending procedure, a quarter circle is formed by fixing one end of the cable and rotating the other end by 90°. Therefore, the cable length built for the modeling analysis is $\pi \cdot R / 2 \text {. }$.
Fig. 10 shows that during the bending process, the maximum strains are concentrated on the extruded inner and the stretched outer side arcs of the wound tapes in both HFRC and CORC cable specimens, while strains in the neutral layer are relatively low. Although the strain distribution patterns are similar for both cables, the maximum value of HFRC cable is only about 55% of that of CORC cable. The reason for the greatest difference is that the central former of HFRC cable is a spiral spring structure, while the central former of CORC cable is a solid copper structure. Therefore, the stainless steel spiral tube of HFRC has a greater elastic coefficient, and the deformation of HFRC former during bending is mainly reflected in the elongation of the pitch, while the elongation of the material is relatively low. However, because the copper core of CORC cable is solid, the deformation is caused by material elongation. So, the strain on the spiral tube of HFRC is lower than that on the copper core of CORC at the same bending radius. Furthermore, the higher the plasticity of the central former, the higher the contact pressure and tape strain at the same bending radius. The CORC-4 specimen with annealed copper former exhibits better flexibility performance than other CORC specimens because the annealed copper is less plastic than the unannealed copper. Because of the higher elasticity coefficient and lower plasticity of stainless steel tube, the tapes of HFRC cable have lower strain than that of CORC cable. The tapes of HFRC cable are less likely to reach the irreversible strain limit that would cause current degradation, so the critical bending radius of HFRC cable is higher than that of conventional CORC cable. For the operation of high field magnets with high current carrying capacity, HFRC cables with high flexibility properties and mechanical stability can be used for the YBCO multi-stage cables.
Fig. 10. Comparison of logarithmic strain of (a) copper core, (b) stainless steel spiral tube. The red and black blocks correspond to the enlarged diagrams. |
5. Conclusion
To promote the high-field applications of the YBCO tapes, we proposed a new type of Highly Flexible Cable (HFRC), which has higher bending flexibility, current carrying capacity, and better cooling properties. HFRC is constructed by YBCO and copper tapes that are wound around a central spiral stainless steel tube. By experiment and simulation, we compared the critical current characteristics at different bending radii of CORC and HFRC cables of the same dimensions. In the experiment, two types of cable specimens are bent into a semicircle with diameters ranging from 300 mm to 30 mm. The critical currents are measured before and after each bending step at 77 K and self-field. The experiment results show that HFRC has a larger critical bending radius compared to cables with the same layout. Additionally, HFRC demonstrates a higher critical current density at equivalent bending radii, especially since its multi-layered specimen (HFRC-4) can be bent to a diameter of 40 mm without significant performance degradation (less than 5%). Finite element models in ABAQUS were created to investigate the mechanical properties of the traditional CORC cable and the proposed HFRC cable. Since the stainless steel spiral tube of HFRC has a higher elastic coefficient and lower plasticity, the tapes of HFRC cable are less likely to reach the irreversible strain limit, which would cause current degradation at the same bending radius. Therefore, both the simulation and the experimental results reached the same conclusion: the critical bending radius of HFRC cable is greater than that of conventional CORC cable. The HFRC cable is thus a promising candidate for future large-scale magnets with high fields and high operating currents. Further research is being planned to examine the mechanical performance stability of the HFRC cable under the influence of mechanical loads and a strong background magnetic field.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was in part supported by the National Key R&D Program of China No. 2022YFE03150200, the Institute of Energy, Hefei Comprehensive National Science Center (Grant No. 21KZS207), National Natural Science Foundation of China (No. 52077212), the Youth Innovation Promotion Association of CAS (Grant No. 2021444), and Hundred-Talent Program, Chinese Academy of Sciences.
