Theoretical Investigations On Magneto-Elastic Coupling Properties For Type-Ⅱ Superconductors

The crack problem and the Magneto-Elastic coupling properties of the superconductors have become the fundamental subjects in both superconducting applications and theories. This thesis presents a theoretical investigation on the mechanical behaviors and fracture properties for the high temperature superconductors. Besides this, the Magneto-Elastic coupling properties of the ideal type-II superconductors are also investigated in this work.Firstly, the mechanical deformation of the high temperature superconductors induced by the electromagnetic forces in the magnetization process is analyzed. Based on the model proposed by Johansen, which is restricted to the critical state models, we consider the effect of the flux creep and flux flow on the stress and magnetostriction of the superconductors. The Anderson's flux creep model is used to model the logarithmic decrement of the magnetostriction, in which the decrease of the current density with the time is considered in the calculation of the electromagnetic body force. The obtained results are consistent with the experiments of Ikuta. It is noted that our model successfully simulate the non-monotonic decrease of the magnetostriction in the ascent branch of the applied field, the time where the maximum value occurs can also be predicted. When the magnetization field is time-dependent and sawtooth-like, the effect of flux flow should be also considered. Both the effects of flux creep and flux flow on the stress and magnetostriction are discussed in our model.Secondly, the singularity of current distribution around the crack in a long cylindrical superconductor and the decrement of the trapped field are investigated analytically. A general model that a long cylindrical superconductor containing an internal elliptical hole placed in a magnetic field is considered. After a simple conformal mapping is employed to the case that the superconductor is fully penetrated, the current streamlines, the current density and the trapped field around the crack in the superconductor without deformation are obtained. On the basis of the Bean model and the Kim model, the dependence of the current concentration with the shape factor of the elliptical hole is discussed. Also, the singularity of current distribution around the crack is obtained. The current density intensity factor KI is defined and found to be independent on the radius of the superconductor and only determined by the crack length α and the critical current density without the crack J1. Thus, the result can be suitable to the generalized case of a crack tip. We also obtain the trapped magnetic field of the superconductor with a crack, the obvious decrement agrees with the reported experimental results. Finally, the Magneto-Elastic coupling properties of the ideal type-II superconductors are studied theoretically. Based on the revised GL equations, the strain effect on the superconducting properties such as wave functions and coherence length is analyzed. We obtain the analytical solution of the ID problem in which the applied magnetic field is assumed to be very small and the second GL equation can thus be omitted. However, for the2D problem in which the magnetic field cannot be ignored we can only solved by numerical methods. In light of the periodicity of the wave functions, we use the Fourier series expansion and iterative algorithm and obtain the wave functions of the superconductors with prestrains. In addition, we also analyze the surface deformation of the ideal type-II superconductors caused by the Abrikosov vortex lattice. It is known that superconductor undertakes a long-range body force caused by the gradient of the electrostatic potential and a surface force induced by the surface dipole. We use the same numerical methods which are used to solve the coupled nonlinear GL equations and obtain the surface deformation based on the theory of linear elasticity.