Study On The Influence Of Non-uniform Current Density On The Mechanical Properties Of Superconducting Structures

With the continuous development and progress of preparation technology and laboratory conditions,superconducting materials with critical temperatures approaching room temperature are constantly being discovered.These high-temperature superconducting materials are widely used in superconducting wires,superconducting magnetic bearings,flywheel energy storage systems,quasi-permanent magnets,magnetics lag motor and other fields,because it has a critical temperature closer to room temperature and a higher current carrying capacity than traditional metal materials.Due to the defects or other various potential wells in the superconducting materials,it traps magnetic flux in the superconducting structures and induces flux pinning force which has an important influence on the practical application of the hightemperature superconducting materials.Thus the electromagnetic mechanical response of hightemperature superconductors becomes the researching hot.Some papers show that the critical current density is not uniformly distributed inside the superconductor.Combining with the application background of high-temperature superconducting materials,the influence of the non-uniform distribution of critical current density on the physical and mechanical properties of a cylindrical superconductors are studies in this paper.First,the flux pinning induced mechanical response of a cylindrical superconducting structure with transporting current is studied.Considering the inhomogeneous distribution of the critical current density,the induced magnetic field and current distribution are obtained based on the Bean model.Combining with the plane strain method and the magnetic flux expression,the analytical solutions of the body force,stress and magnetostriction are obtained.Finally,the result is compared with the uniform distribution condition.The results show that the non-uniform distribution of critical current density has a significant effect on the electromagnetic field distribution and mechanical properties inside the superconductor.The distribution law of the magnetic field and current inside the superconductor changes with the change of the critical current density.The magnetic flux pinning force is significantly increased,the maximum stress in the superconductor is significantly increased,and a larger deformation is generated inside the superconducting structure.Secondly,the flux pinning induced mechanical response of the cylindrical superconducting structure is studied with an applied magnetic field.Considering the nonuniform distribution of critical current density,the induced magnetic field and current distribution in the structure are calculated based on the exponent critical state model.Combining with the plane strain method and the expression of magnetic flux,the analytical solutions of the force,stress and magnetostriction are obtained.Finally,the influence of the non-uniform critical current density on physics and mechanics of the cylinder is studied.The parameter's effect on the mechanical properties of the structure is also discussed.The results show that in cylindrical superconductors excited by a magnetic field,the non-uniform distribution of critical current density causes a significant increase in local stress in the superconducting structure,and in the field-declining stage,the compressive stress in the superconducting structure will be completely converted into tensile stress and this tensile stress is very easy to cause fracture failure of brittle superconducting materials.At the same time,unlike the Bean model,the magnitude of the stress in the superconducting structure does not increase monotonously with the increase of the applied magnetic field,but there is an extreme value.Finally,both the transport current and the applied magnetic field are considered on the superconducting cylinder.Based on the extended elliptical model and the Bean model,the distribution of the magnetic flux density and current density in the cylindrical superconducting structure are obtained.Combining with the plane strain method,the analytical solutions of the internal stress are obtained.Subsequently,the influence of the distribution of critical current density on its mechanical properties is studied.The results show that the stress distribution in the cylindrical superconductor under the excitation of the carrying current and the external magnetic field is consistent with the single field.In the external field descent phase,large tensile stress appears in the structure,and the degree of magnetostriction of the superconductor is higher than that in the case of uniform distribution,that is,the non-uniform critical current density will cause greater magnetostriction in the superconducting structure.