Strain Dependence Of Critical Current Research Articles

Electromagnetic-mechanical coupling analysis of high-temperature superconducting racetrack coil

The second-generation high-temperature superconducting (HTS) coated conductor has been recognized as one of the most promising materialsfor high field magnets due to its superior electromagnetic and mechanical performances. HTS racetrack coils wound with the coated conductors are an extensively used configuration in engineering applications, such as HTS machines and high-speed maglevs. In this paper, in order to analyze the electromagnetic and mechanical behaviors of HTS racetrack coils, a 3D coupled electromagnetic-mechanical model is used to consider the effect of coil deformation and the strain dependence of critical current. The effectiveness of the coupled model is validated by comparing the numerical results with experimental data in the literature. A numerical simulation of a 3D HTS racetrack coil subjected to an external electromagnetic field is carried out using coupled and uncoupled models. The results indicate that the structure deformation can reduce the penetration depth of the screening current, and the hoop stress and strain are mainly concentrated on the circular part of the racetrack coil. Afterwards, the influences of various parameters on the electromagnetic and mechanical responses of the HTS racetrack coil are also investigated.

Stress, strain and electromechanical analyses of (RE)Ba2Cu3Ox conductors using three-dimensional/two-dimensional mixed-dimensional modeling: fabrication, cooling and tensile behavior

High temperature superconducting (HTS) conductors, represented by Rare Earth-Barium-Copper-Oxide (REBCO) conductors, are promising for high energy and high field superconducting applications. In practical applications, however, the HTS conductors experience different stresses and strains, including residual stresses due to thermal mismatch and tensile stresses due to Lorentz forces, resulting in some circumstances to a reduction in the load-carrying capacity as well as the risk of degradation in conductor critical current. In this study a mixed-dimensional high-aspect-ratio laminated composite finite element model for REBCO conductor is developed for stress and strain analyses in the processes of fabricating and cooling, as well as tensile testing. The model includes all the major constituent layers of a typical REBCO conductor and is experimentally validated. First, the thermal residual stresses and strains accumulated during the fabrication and cooling processes are analyzed by a multi-step modeling method that emulates the manufacturing process. Then, with the residual stresses and strains as initial stresses and strains, the mechanical behavior under a tensile load is studied. Lastly, a phenomenological critical current-strain model based on the Ekin power-law formula and the Weibull distribution function is combined with the mixed-dimensional conductor model to predict the strain dependence behavior of critical current in the reversible and irreversible degradation strain ranges. Simulation results show that the multi-step modeling is an effective method for stress and strain analyses of REBCO conductors during the fabrication and cooling processes and under and tensile loads. Compressive thermal residual stress generated on the REBCO layer during fabrication and cooling strongly affects the subsequent mechanical and current-carrying properties. Stress–strain curves generated by tensile loads are analyzed and experimentally validated at both the conductor and constituent-layer levels. Simulation results for the strain dependence of critical current are in good agreement with experiment data in both the reversible and irreversible degradation stages.

Mechanical and electro-mechanical analysis in differently stabilized GdBCO coated conductor tapes with stainless steel substrate

The understanding of the strain dependence of critical current, <TEX>$I_c$</TEX>, in the reversible region is important for the evaluation of the performance of coated conductor (CC) tapes in practical applications. In this study, the stress/strain tolerance of <TEX>$I_c$</TEX> in GdBCO CC tapes with stainless steel substrate stabilized by additional Cu and brass laminate was analyzed quantitatively through <TEX>$I_c$</TEX>-strain measurement at 77 K under self-field. The variation in irreversible strain limits of CC tapes by the addition of stabilizing layers was analyzed through the consideration of the pre-strain induced on the GdBCO coating film. The results were then compared with the ones previously reported for GdBCO CC tapes with Hastelloy substrate. As a result, GdBCO CC tapes with stainless steel substrate showed much higher strain tolerance of <TEX>$I_c$</TEX> as compared with those adopting Hastelloy substrate.

Effect of Subgrain Structure on the Critical Current Density in HTS Films

We have suggested a model of film–substrate interface and calculated its energy. The calculations have shown that rotational relaxation occurs due to the finite size of clusters and to the non-equilibrium effect of the film growth. We have predicted the real subgrain size and the expected rotation of domains. In some kinds of high temperature superconducting films, such as the mostly used YBCO, domains can be subdivided into twin domains. The twin structure has smaller scale since it is being formed at tetra-ortho transition during cooling and/or oxygen annealing when other defects are already formed in tetra-phase during deposition. Usually, twin boundaries have no strong influence on the critical current because they introduce almost no perturbation in the superconducting order parameter. We have shown that when a strain is applied, a difference between critical temperatures of a- and b-oriented twin domains appears and results in an additional pinning and unusual reversible strain dependence of critical current. The suggested model explains experimental strain dependences of the critical current.

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.

Electromechanical Characterization of Bi-2212 Strands

The uniaxial strain dependence of critical current was measured both in tension and compression in Bi2Sr2CaCu2O8+x (Bi-2212) high-temperature superconducting round wires. Permanent damage to the critical current easily occurred due to strain. To improve the electromechanical properties of Bi-2212 wires, development of stronger sheathing materials is needed. Ideal materials would be not only mechanically strong, but also chemically compatible with Bi-2212 during the final heat treatment. To identify such materials, we measured stress-strain properties of some new Ag alloys and extracted their respective Young's modulus values and yield strength. The database may be useful for development of new Bi-2212 strands for fabricating high-field superconducting magnets above 20 T.

Residual and fracture strains of Bi2223 filaments and their relation to critical current under applied bending and tensile strains in Bi2223∕Ag∕Ag alloy composite superconductor

Mechanical and electromagnetic stresses are exerted on Bi2223∕Ag∕Ag alloy superconducting composite tapes during fabrication∕winding and operation, which cause reduction in critical current when the Bi2223 filaments are damaged. In the damage process, the thermally induced residual strain and fracture strain of the Bi2223 filaments play a dominant role. The aim of the present work was to propose a comprehensive method for estimation of these strain values and a quantitative description method of the relation of critical current to the applied bending∕tensile strain, and to examine the accuracy of the method in comparison with the experimental results. The residual strain of Bi2223 filaments in the composite tape was measured by the x-ray diffraction method. The measured residual strain value was used for analysis of the load-strain curve, from which the intrinsic fracture strain of filaments was estimated. The relation of critical current to applied bending∕tensile strain was predicted by the proposed calculation procedure, in which the estimated strain values were input. The predicted critical current-applied strain relation agreed well with the experimental results, suggesting that the present method is a useful tool for prediction∕description of tensile∕bending applied strain dependence of critical current of multifilamentary-type conductors.

Evaluation of bending strain dependence of critical current of Nb 3Al conductor for coils with react-and-wind method

In order to clarify the limitation of bending strain in conductor to fabricate the toroidal field coils of DEMO reactor by react-and-wind (R&W) method, the effect of bending strain on the critical currents ( I c) of Nb 3Al cable-in-conduit (CIC) conductor was investigated using the newly developed apparatus which can bend cooled sample from outside of cryostat. The Nb 3Al strand manufactured by jelly roll process was 0.74 mm in diameter with the copper/non-copper ratio of 4.0. The CIC conductor sample which consisted of 54 Nb 3Al strands and 27 copper wires inserted into a stainless steel conduit was 12.4 mm in diameter and 2.3 m in length. The CIC conductor was wound into a torsion coil spring shape with 4.5 turns and 150 mm in diameter. The bending strain and external magnetic field ranges for I c measurement were from 0% to 0.6% and from 9.2 T to 11.3 T, respectively. It was clearly shown that the I c decrease of the CIC conductor by bending is considerably low compared with that of strand, indicating the relaxation of intrinsic strain in Nb 3Al filaments in CIC conductor due to the cabling effect. The I c was not decreased up to 0.4% in bending strain and slightly decreased to 96% of initial I c at 0.55% in bending strain. This indicates that the R&W method with bending strain of 0.6% is fully applied to the coil fabrication method. The furnace size for heat-treatment for R&W method becomes half of wind-and-react (W&R) method.

Bending strain characteristics of Ag/Bi(2223) tapes at liquid nitrogen temperature

Bending strain dependence of critical current, I c, of Ag/Bi-2223 57 filament tapes was investigated at 77 K and room temperature, RT, using a device invented by Goldacker. The strain where I c start to degrade steeply at 77 K, 0.48%, was larger than that at RT, 0.36%. This is an indication of an additional pre-compression in filaments to be bent at 77 K compared with that at RT. According to the voltage measurements using multiple taps in the longitudinal direction, the I c degradation behaviors at both temperatures varied depending on the section in the tape, due presumably to the difference in the crack propagation characteristics associated with the non-uniformity of the micro-structure. The onset strain for I c degradation was more precisely determined. The degradation characteristics were shifted to the smaller strain in the present result as compared with that obtained by bending tests using G10 sample holders of different bending radius. The difference can be explained by the different thermal history on setting specimens to the holder and the constraints during cooling. The repeated bending tests at 77 K showed that the discrimination between the gradual and steep degradation stages was clear and the degradation was controlled by both the maximum strain and the strain range.