Huadong Yong

Stress distribution in a flat superconducting strip with transport current

The stress and magnetostriction induced by flux pinning for a flat superconducting strip of a type II superconductor are calculated analytically in the presence of transport current. The plane stress approach is used to find the exact solutions. By assuming that the current density is magnetic field independent, the body force and normal stress distributions for increasing and decreasing transport currents are given. In addition, the pinning induced magnetostriction is calculated. The results show that, during the transport current reduction, tensile stress may occur. It is worth pointing out that, in the flat superconducting strip with transport current, the stresses are mainly negative. The hysteresis loop of the magnetostriction cannot be observed for the full cycle of the transport current.

Critical state model for magneto-elastic problem of thin superconducting disks

The magneto-elastic problem of a thin superconducting disk in a perpendicular magnetic field is analyzed with field-dependent critical current. We calculate numerically the body force distribution and discuss the field dependence of Jc on the magneto-elastic behavior during field ascent and descent for three critical state models: Bean, Kim, and exponential models. The results show that when considering a field dependence of Jc, the flux and remagnetization fronts have a larger moving speed towards the center of a disk relative to the Bean model. Simultaneously, the most dangerous stage of possible cracking for the disk will arrive early in the field decreasing stage. The magnetostriction loops are also presented during a full cycle of the applied field. It is interesting that the calculated magnetostriction loops for the Kim and exponential models are quite similar to the corresponding magnetostriction curves at low and high temperatures measured in the experiment.

Effect of flux creep and viscous flux flow on flux-pinning-induced stress and magnetostriction in a long rectangular slab superconductor

The magnetoelastic problem for a superconductor slab placed in a time-dependent magnetic field is considered. Two major components of the flux (vortex) motion: flux creep and viscous flux flow have been considered, among which the logarithmic dependence of activation energy on the current density is assumed for the creep problem. As one of the two parts of flux motion, viscous effect of flux flow dominates the motion of fluxoids at high flux velocities and enhances the maximum tensile stress and the magnetostriction remarkably after zero-field cooling. However, the effect of flux creep cannot be omitted at low magnetic field sweep rate (Ba) and is helpful to alleviate tensile stresses within the superconductor. Apart from this, the position (x0) where the maximum tensile stress occurs has a similar dependence on the sweep rate (Ba) as the stress value itself. All the results indicate that the sweep rate (Ba) should be considered in the magnetization process in order to avoid cracking within the superco...

Dendritic flux avalanches and the accompanied thermal strain in type-II superconducting films: effect of magnetic field ramp rate

Dendritic flux avalanches and the accompanying thermal stress and strain in type-II superconducting thin films under transverse magnetic fields are numerically simulated in this paper. The influence of the magnetic field ramp rate, edge defects, and the temperature of the surrounding coolant are considered. Maxwells equations and the highly nonlinear E–J power-law characteristics of superconductors, coupled with the heat diffusion equation, are adopted to formulate these phenomena. The fast Fourier transform-based iteration scheme is used to track the evolution of the magnetic flux and the temperature in the superconducting film. The finite element method is used to analyze the thermal stress and strain induced in the superconducting film. It is found that the ramp rate has a significant effect on the flux avalanche process. The avalanches nucleate more easily for a film under a large magnetic field ramp rate than for a film under a small one. In addition, the avalanches always initiate from edge defects or areas that experience larger magnetic fields. The superconducting films experience large thermal strain induced by the large temperature gradient during the avalanche process, which may even lead to the failure of the sample.

The characteristics and stability of a dielectric elastomer spherical shell with a thick wall

When a voltage is applied between the internal and external surface of a dielectric elastomer spherical shell, positive charges appear on one surface and negative charges on the other. This gives rise to Coulomb forces between opposite charges, generating a pressure. Thus, the shell reduces in thickness and stretches in area, and a higher electric field is produced. This positive feedback may make the shell continually thin down, eventually causing electrical instability. In this paper we use the neo-Hookean model and the Arruda–Boyce model to analyze the electromechanical instability of the thick-walled shell respectively. The electric field in the shell is inhomogeneous and varies with the radius of the shell. The instability in spherical shells with different thicknesses and boundary conditions is discussed. When the elastomer obeys the Arruda–Boyce model, the stability is related to the parameter n. The spherical shell will appear with snap-through instability and pull-in instability for different values of the parameter n.

Influences of non-uniformities and anisotropies on the flux avalanche behaviors of type-II superconducting films

In this paper, the anisotropic flux avalanche processes in thin square- shaped type- II superconducting films are numerically investigated by solving the coupled nonlinear Maxwells equations and the thermal diffusion equations. Influences of the non- uniformities and intrinsic critical current density anisotropies originate from the manufacturing process are considered in the simulation. In addition, we also studied the effect of the extrinsic anisotropy induced by the in- plane magnetic field. The results demonstrate that the non- uniformities and anisotropies of the critical current density play significant roles in the flux avalanche process of the thin film superconductors. Slight anisotropy ( either intrinsic or extrinsic) can dramatically change the propagation direction of avalanches in the superconducting film, which is consistent with the experimental results. Simulations on the thin square- shaped isotropic superconducting films show that the threshold magnetic field for the flux avalanches increases with the angle between the applied field and the superconducting film- plane. In addition, the flux avalanche patterns change with the angular variation of the in- plane component of external magnetic field. When the in- plane magnetic field component is along the diagonal lines of the superconducting square, symmetric flux avalanche penetration patterns occur to the film.

Interface crack between superconducting film and substrate

The interface crack problem in the superconducting film-substrate structure under the magnetic field is investigated. A solution of the two-dimensional magnetoelastic problem is found. It is assumed that the plane stress state of deformation prevails in the structure. We take into consideration both cases of interface crack in the film-substrate structure and the superconductor slab. The fracture behaviors are considered for the non-superconducting substrate and superconducting substrate. Based on the simple geometrical and material assumptions, we express the explicit analytical description of the stress intensity factor and energy release rate. An increase of the stress intensity factor and energy release rate with the applied field has been observed. During the field reduction, the variations of the fracture behavior exhibit a complex characteristic. In addition, the effect of the deformation of the substrate is significant. This work may provide a tool for the analysis of the mechanical instability in...

Effect of strain on depairing current density in deformable superconducting thin films

The changes of the superconducting depairing current density with applied strain in superconducting films are studied theoretically in this paper. The thin film is assumed to be isotropic. Using phenomenological theory, we obtain the depairing critical current density in the presence of applied strain. The dependence of deparing current density on coupling parameters is discussed. A qualitative agreement between our theoretical predictions with reported experimental results is observed as the coupling parameters are linear function of the applied strain. The results indicate that the coupling parameters have a significant influence on the critical current density in the superconducting film.

Numerical simulation on the flux avalanche behaviors of microstructured superconducting thin films

Controlling and suppressing the propagation of magnetic flux avalanches is an important issue for the application of type-II superconductors. The effects of engineered pinning centers (antidots) on the guidance of flux avalanche propagation paths in type-II superconducting thin films are numerically investigated by solving the coupled nonlinear Maxwells equations and the thermal diffusion equations. The field dependence of critical current density is considered in the simulation in this paper. Dynamic propagations of the thermomagnetic avalanches within the superconducting films patterned with different arrangements of antidots (like random, periodic square, and conformal mapping arrays) are presented. We reveal that presence of the antidots significantly modifies the propagation paths of the avalanches. The flux avalanche patterns of the superconducting films change with the variation of the arrangements of antidots. The patterned antidots in the form of conformal mapping arrays within the superconducti...

Effect of shear stress on electromagnetic behaviors in superconductor-ferromagnetic bilayer structure

In this paper, the electromagnetic response and shielding behaviour of superconductor-ferromagnetic bilayer structure are studied. The magnetomechanical coupling in ferromagnetic materials is also considered. Based on the linear piezomagnetic coupling model and anti-plane shear deformation, the current density and magnetic field in superconducting strip are obtained firstly. The effect of shear stress on the magnetization of strip is discussed. Then, we consider the magnetic cloak for superconductor-ferromagnetic bilayer structure. The magnetic permeability of ferromagnetic material is obtained for perfect cloaking in uniform magnetic field with magnetomechanical coupling in ferromagnet. The simulation results show that the electromagnetic response in superconductors will change by applying the stress only to the ferromagnetic material. In addition, the performance of invisibility of structure for non-uniform field will be affected by mechanical stress. It may provide a method to achieve tunability of sup...