Critical current degradation in an epoxy-impregnated rare-earth Ba_(2)Cu_(3)O_(7-x)coated conductor caused by damage during a quench

High-temperature superconducting(HTS)rare-earth Ba_(2)Cu_(3)O_(7-x)(REBCO)coated conductors(CCs)have significant potential in high-current and high-field applications.However,owing to the weak interface strength of the laminated composite REBCO CCs,the damage induced by the thermal mismatch stress under a combination of epoxy impregnation,cooling,and quenching can cause premature degradation of the critical current.In this study,a three-dimensional(3D)electromagnetic-thermal-mechanical model based on the H-formulation and cohesive zone model(CZM)is developed to study the critical current degradation characteristics in an epoxy-impregnated REBCO CC caused by the damage during a quench.The temperature variation,critical current degradation of the REBCO CC,and its degradation onset temperature calculated by the numerical model are in agreement with the experimental data taken from the literature.The delamination of the REBCO CC predicted by the numerical model is consistent with the experimental result.The numerical results also indicate that the shear stress is the main contributor to the damage propagation inside the REBCO CC.The premature degradation of the critical current during a quench is closely related to the interface shear strength inside the REBCO CC.Finally,the effects of the coefficient of thermal expansion(CTE)of the epoxy resin,thickness of the substrate,and substrate material on the critical current degradation characteristics of the epoxy-impregnated REBCO CC during a quench are also discussed.These results help us understand the relationship between the current-carrying degradation and damage in the HTS applications.

Numerical simulation of the mechanical behavior of superconducting tape in conductor on round core cable using the cohesive zone model

Cables composed of rare-earth barium copper oxide(REBCO)tapes have been extensively used in various superconducting devices.In recent years,conductor on round core(CORC)cable has drawn the attention of researchers with its outstanding current-carrying capacity and mechanical properties.The REBCO tapes are wound spirally on the surface of CORC cable.Under extreme loadings,the REBCO tapes with layered composite structures are vulnerable,which can lead to degradation of critical current and even quenching of superconducting devices.In this paper,we simulate the deformation of CORC cable under external loads,and analyze the damage inside the tape with the cohesive zone model(CZM).Firstly,the fabrication and cabling of CORC are simulated,and the stresses and strains generated in the tape are extracted as the initial condition of the next step.Then,the tension and bending loads are applied to CORC cable,and the damage distribution inside the tape is presented.In addition,the effects of some parameters on the damage are discussed during the bending simulations.

Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils

Quench and mechanical behaviors are critical issues in high temperature superconducting(HTS)coils.In this paper,the quench characteristics in the rare earth barium copper oxide(REBCO)pancake coil at 4.2K are analyzed,and a two-dimensional(2D)axisymmetric electro-magneto-thermal model is presented.The effects of the constituent materials,background field,and coil size are analyzed.An elastoplastic mechanical model is used to study the corresponding mechanical responses during the quench propagation.The variations of the temperature and strain in superconducting layers are compared.The results indicate that the radial strain evolutions can reflect the transverse quench propagation and the tensile hoop and radial stresses in superconducting layers increase with the quench propagation.The possible damages are discussed with the consideration of the effects of the background field and coil size.It is concluded that the high background field significantly increases the maximum tensile hoop and radial stresses in quenching coils and local damage may be caused.

Degradation of critical current in Bi2212 composite wire under compression load

Since Bi2Sr2Ca1Cu2O8＋x（Bi2212） wires are subject to mechanical loadings, degradation of critical current will occur. The effect of compressive loadings on the critical current of Bi2212 wire is studied by considering micro-buckling of filament. A Bi2212 wire is regarded as a unidirectional filament-reinforced composite in the theoretical analysis. By considering the influence of inclusion, the micro-buckling wavelength can be derived by using a two-dimensional model. Based on the experimental results, the critical current is fitted as a function of buckling wavelength. It is found that the decrease of the critical current is directly proportional to the reciprocal of square of the buckling wavelength. Change of micro-buckling wavelength with material parameters is discussed. A critical strain in the wire with a filament bridge is analyzed using the finite element method.

Contact force and mechanical loss of multistage cable under tension and bending

A theoretical model for calculating the stress and strain states of cabling structures with different loadings has been developed in this paper. We solve the problem for the first- and second-stage cable with tensile or bending strain. The contact and friction forces between the strands are presented by two-dimensional contact model. Several theoretical models have been proposed to verify the results when the triplet subjected to the tensile strain, including contact force, contact stresses, and mechanical loss. It is found that loadings will affect the friction force and the mechanical loss of the triplet. The results show that the contact force and mechanical loss are dependent on the twist pitch. A shorter twist pitch can lead to higher contact force, while the trend of mechanical loss with twist pitch is complicated. The mechanical loss may be reduced by adjusting the twist pitch reasonably. The present model provides a simple analysis method to investigate the mechanical behaviors in multistage-structures under different loads.

Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand

For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand,a two-step homogenization method is adopted.Based on the distribution of filaments,the superconducting strand can be decomposed into a set of concentric cylinder layers.Each layer is a two-phase composite composed of the twisted filaments and copper matrix.In the first step of homogenization,the representative volume element(RVE)based finite element(FE)homogenization method with the periodic boundary condition(PBC)is adopted to evaluate the effective thermal conductivities of each layer.In the second step of homogenization,the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers.The accuracy of the developed model is validated by comparing with the local and full-field FE simulation.Finally,the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied.

Numerical modelling of electromechanical coupling behaviors in HTS coil with implementation of H formulation in FE software

(Re)Ba_(2)Cu_(3)O_(7-x)(REBCO)coated conductors(CCs)have attracted considerable concern because of their outstanding current carrying capacity in magnetic fields of high strengths.A huge electromagnetic force is generated in the superconducting coil when conducting large currents in strong magnetic field.Thus,management of stress and strain has become a key technical challenge for the stability and safety of superconducting coil during operation.To accurately predict the electro-magnetic and mechanical characteristics of superconducting coil in strong magnetic field,an electromechanical model on the basis of the H-formulation and arbitrary Lagrangian-Eulerian(ALE)method is proposed here with FE software.To verify the proposed model,the simulation outcomes of the coil during magnetization are compared with the experimental outcomes.The coupling effect of magnet at high field strengths is dependent on the position of the coil.To reduce the screening current effect,the overshoot method with plateau is found superior to the traditional overshoot method,and an increase in the stabilization time can decrease the maximum value of stress.Finally,the electromechanical behaviors of single winding coil and two-tapes co-winding coil are compared.

Mechanical Response of Conductor on Round Core(CORC)Cables Under Electromagnetic Force

The conductor on round core(CORC)cables are fabricated with multilayer high-temperature superconductor tapes,which are helically wound around a circular central former.The large Lorentz force will be generated by the transport current in CORC cables under high magnetic field,which will affect the stress and strain distributions of tapes in the cables and the performance of superconducting tape.This paper establishes a two-dimensional axisymmetric model to analyze the mechanical response of CORC cables subjected to the Lorentz force and analyzes the influence of air gaps on stress and strain distributions inside the cables.The T-A method is used to calculate the distributions of current density,magnetic field and the Lorentz force in CORC cables.The mechanical response of CORC cables is analyzed by applying the Lorentz force as an external load in the mechanical model.The direction of electromagnetic force is analyzed in CORC cables with and without shielding current,and the results show that the shielding current can lead to the concentration of electromagnetic force.The maximum stress and strain occur on both sides of the superconducting tapes in the cables with shielding current.Reducing the size of air gaps can reduce the stress and strain in the superconducting layers.The analysis of mechanical response of CORC cables can play an important role in optimizing the design of CORC cables and improving transmission performance.

Estimation of critical current density of bulk superconductor with artificial neural network

In the applications of superconducting materials,the critical current density J_(c)(B)is a crucial performance parameter.The conventional method of measuring J_(c)(B)of bulk superconductor is magnetization method.However,there are errors in the estimation of J_(c)(B)in the lower field,and the estimation is not applicable in the region where the magnetic field reverses.In this paper,J_(c)(B)of the bulk superconductor is determined by the hysteresis and magnetostriction loops with artificial neural network(ANN),respectively.Compared with double‐output ANN,the critical current density obtained by single‐output ANN is more accurate.Finally,the prediction results given by the hysteresis and magnetostriction loops are discussed.

Fatigue behaviors and damage mechanisms for Nb_(3)Sn triple-helical structure at liquid nitrogen temperature

Nb_(3)Sn triple‐helical structure is the elementary structure in the superconducting cable of ITER magnets and undergoes prolonged fatigue loading in extreme environments leading to serious damage degradation.In this paper,the fatigue behaviors of the Nb_(3)Sn triple‐helical structure have been investigated by the strain cycling fatigue experiments at liquid nitrogen temperature.The results indicate that Nb_(3)Sn triple‐helical structures with short twist‐pitches possess excellent fatigue damage resistance than that of long twist‐pitches,such as longer fatigue life,slower damage degradation,and smaller energy dissipation.Meanwhile,a theoretical model of damage evolution has been established to reveal the effects of twist‐pitches on fatigue properties for triplehelical structures,which is also validated by the present experimental data.Furthermore,one can see that the Nb_(3)Sn superconducting wires in a triple‐helical structure with the shorter twist‐pitches have a larger elongation of helical structure and less cyclic deformation,which can be considered as the main mechanism of better fatigue damage properties for the triple‐helical structures during the strain cycling processes.These findings provide a better understanding of the fatigue properties and damage mechanisms for Nb_(3)Sn triple‐helical structures in superconducting cables of ITER magnets.

Damage Analysis of Superconducting Composite Wire with Bridging Model

The multi-filamentary Bi2Sr2CaCu2O8＋x （Bi-2212） round wires are made of super- conducting filaments, metal Ag and Ag alloy, which are typical composite structure. Since the filament is brittle, there are various defects and cracks in the Bi-2212 round wire after heat treat- ment. In this paper, we assume that the filaments in the wire are uniformly arranged. Adopting the bridging model which is often used in the fiber-reinforced composite, we calculate the ulti- mate strength of the round wire. The effects of the volume fraction, elastic modulus and interface shear strength are discussed in detail.

Electromagnetic-thermal-mechanical characteristics with active feedback control in a high-temperature superconducting noinsulation magnet

High-temperature superconducting(HTS) magnets consisting of no-insulation(NI) double-pancake coils(DPCs) with high thermal stability have been proposed for use in the preparation of high-field magnets. However, increased ramp time is a known disadvantage of the NI approach. To solve this problem, a proportional and integral(PI) active feedback control has been proposed in the charging experiments of the NI magnet. In this study, the electromagnetic-thermal-mechanical characteristics of an NI magnet with and without PI are analyzed to ensure the safety and reliability of PI control. Due to the increase in the radial current of the magnet, the turn-to-turn loss energy of the magnet with PI is more than twice that without PI. However, the magnetization loss energy of the magnet has a small difference with and without PI. It can be also found that the NI magnet with PI has a large temperature rise, and thus it has a low thermal stability margin. Moreover, in the high field, the hoop stress and hoop strain peaks of a magnet with PI are larger than those without PI. Thus, PI control can induce a relatively high risk of mechanical damage in the applications of NI magnets.

Mechanical Analysis of a No-insulation Pancake Coil with the Overband During a Quench

The no-insulation(NI)winding approach can remarkably improve the thermal stability of high-temperature superconducting coil.However,mechanical issues have gradually become a key factor to block the development of NI magnets in recent years.This paper mainly analyzes the effect of the overband on the mechanical behaviors of an NI coil during a quench.A numerical model including a quench model combined with a three-dimensional homogeneous mechanical model is employed to study the change of stress in the coil without and with the over band during a local quench.The results show that the overband has an obvious effect on the stress distribution as the heater is located at the outer turn of the coil.Meanwhile,the values of stress in the coil are also affected by the overband.Moreover,the effects of the thickness of the overband and the location of the heater on the mechanical behaviors of the coil are also discussed.It is worth noting that the overband can remarkably reduce the hoop and axial tensile stresses of the coil during a quench。

Flux avalanche in thin superconducting film with internal crack

When type-II superconductors are in external magnetic field,the magnetic flux would penetrate the superconductors in the form of flux vortex[1].If the superconductor is subjected to a local thermal disturbance,this may trigger a surge of flux vortices into the superconductor.

EFFECT OF MAGNETIC NANOPARTICLES ON THE MECHANICAL PROPERTIES OF TYPE-II SUPERCONDUCTORS

In this paper, the effect of magnetic nanoparticles on the mechanical properties of a type-II superconductor is investigated both theoretically and numerically. Magnetic part of the pinning force associated with the interaction between a finite-size spheroidal magnetic inclusion and an Abrikosov vortex is calculated in the London approximation. It is found that the size and shape of magnetic nanoparticles result in different enhancements of vortex pinning in large-k type-II superconductors. Meanwhile, the screening current induced by a magnetic spheroid suffer the action of Lorentz force, which will lead to prestress in the superconductor, so further numerical calculations are needed to explore the interaction between the spheroidal magnetic particle and superconductor. The distribution of displacement, stress and strain in the superconductor are finally obtained. It is shown that different sizes and shapes of nanoparticles also can change the distributions of these quantities.

Dynamic analysis and active control of hard-magnetic soft materials

The hard-magnetic soft materials which can sustain high residual magnetic flux density gradually attract the attention of researchers because of potential applications in soft robotics and biomedical fields.In this work,we focus on the dynamic response of hardmagnetic soft materials.The dynamic motion equations are derived by the Euler-Lagrange equation.The effects of the aspect radio on the nonlinear vibration of the hard-magnetic soft cuboid under the force and applied magnetic fields in different directions are investigated.The amplitude-frequency curves demonstrate that the aspect ratio also has an influence on the frequency and amplitude of the primary resonance.Moreover,to eliminate undesired vibration responses,the PID controller is applied to the vibration of the hardmagnetic soft materials,and the desired results can be obtained.

A Theoretical Model for Characterizing the Internal Contact of the CICC Strands under Axial Strain

A theoretical model is proposed to calculate the internal contact distributions and contact forces of a 3×4×4×4 twisted NbSn cable under applied axial strain.The critical current density reduction of the whole cable can be calculated.The thin rod theory is employed to analyze the mechanical behavior of each strand.According to the regular helical structure,the contact distribution of each strand is obtained,and the contact force in the cable is analyzed.At last,a prediction about the critical current density of the twisted cable is made.The results show that decreasing the pitch length can reduce the contact forces between strands.