Flux-pinning-induced Mechanical Characteristics In Circular Cylinder Superconductors

Superconductor material has some very special properties, with the emergence and development of high temperature superconductor materials, which has wide application prospect in electric power, electronics, medical, transportation, high-energy physics and other fields. In nonideal type II superconductors, the internal defects have pinning effect on the flux lines and an influence on the superconductor performance. Flux pinning refers to the nonideal type Ⅱ superconductor internal defects effect on properties of superconductor, and its influence on the pinning effect of the superconductor flux lines. The magnetic flux trapping, hysteresis and the nonuniform distribution of magnetic flux lines in type Ⅱ superconductor show that, besides the Lorentz force, flux lines but also be affected by the force from bugs exist in a superconductor, which is gone by the name of the pinning force, the defect is called pinning centers. The pinning force originated from the magnetic flux lines in the superconducting phase and different energy in defects, flux lines from pinning centers need external energy. That is to say, defect pinning force originated from the material itself or the magnetic flux can’t exercise caused by reducing vortex that lower by the crystal defects,at this time, the pinning force and Lorenz force is equal.In previous studies,the discussion about the superconductor flux pinning properties is based on the basic of Bean model, it defines the distribution of critical current density distribution as linear, however, the distribution of critical current density in the superconductor often isn’t simple like that,in certain circumstances, its distribution is nonlinear, and more complex,now, based on this idea,under this nonlinear distribution of critical current density,we studied the stress and strain problems caused by flux pinning in a full three-dimensional elasticity elastic body, the plane strain approach was used to find an exact consistent solution for a long circular cylinder with free surfaces placed in a parallel magnetic field,we successfully studied its stress and strain problems, and then through the further study, we get the concrete expression of the stress and strain,for external radial magnetostriction results is the same as the earlier established two-dimensional plane stress treatment results, we also found out several relationship between the characteristics of magnetostriction and stress-strain, got the radial and tangential strain in the arbitrary r.Moreover, in this paper we focuses on the research about the stress and strain of superconductors in this new critical current density condition, respective, we study it in the incressing field,and reduceing field condition.then,numerical results are given and analyzed.and gives the stress-strain expression under corresponding conditions, and the image of the stress-strain distribution curve, in particular, we also analyze the magnetostriction case corresponding to the field, and analyze the stress-strain condition after field cooling, and the distribution of maximum stress value, the numerical results can be used in analyze the general cases of the stress and strain distribution, about the type-Ⅱ superconductor in theory.