Calibration Of Magnetic Flux Pinning Force Of Deformed Nb₃Sn Composite Superconductor Composite

Nb₃Sn composite superconductors are mainly used in the field of strong magnetic field superconducting magnets.The degradation of superconductivity induced by mechanical deformation is one of the basic topics involved in the preparation of high field superconducting magnets.Grain boundary is the main effective magnetic flux pinning center in Nb₃Sn superconducting materials.Understanding grain boundary deformation plays an important role in revealing the electromechanical coupling response of Nb₃Sn from the viewpoint of mesoscale.Therefore,this paper studies the mechanical deformation of Nb₃Sn composite superconductor,the strain effect of magnetic flux pinning force and the degradation of critical temperature from the viewpoint of mesoscale.Firstly,based on elastic theory of closely packed fiber-reinforced composites and the polycrystalline finite element method,a scale coupling calculation model of grain and grain boundary deformation in Nb₃Sn composite superconductor is established.The computational model can effectively characterize the Nb₃Sn composite architecture at the mesoscale.The relationship between the mesoscopic structure of the Nb₃Sn composite superconductor and meso-local stress distribution?grain and grain boundary deformation characteristics of the columnar and equiaxed regions in the composite?under the uni-axial tensile and compressive loading modes are comprehensively studied.The elastic deformation distribution along the grain boundary in the Nb₃Sn composite superconductor is carefully studied with the aid of the proposed model.The results show that the Mises equivalent stress of polycrystalline Nb₃Sn composite is sharply non uniform in the two different loading modes.The high stress concentration occurs at the junction of the columnar crystal grains,and the interface region between Nb core and polycrystalline Nb₃Sn.The ratio of the mesoscopic local stress to the applied axis stress ranges from-2.19 to 1.31?in uniaxial tensile and compressive loading modes?.The stress fluctuates along grain boundaries,and the magnitude of the change depends on the grain morphology and the composite structure.The results are helpful to understand the deformation behavior of Nb₃Sn composite at the extremely low temperature and reveal the origin of the strain sensitivity of the Nb₃Sn superconducting properties.Secondly,on the basis of the analysis of the deformation behavior of grain and grain boundary,the uniaxial load induced degradation of the critical temperature is predicted with the aid of the semi-phenomenological mechanical-electromagnetic coupling constitutive relationship.The theoretical predictions qualitatively agrees well with the experimental results,indicating the important role which the grain boundary deformation plays in controlling the strain sensitivity of the Nb₃Sn superconductor.Thirdly,the strain effects on the flux pinning force and its distribution characteristics is studied,it is based on the Labusch Model quantitatively describing the magnetic flux pinning force and the aforementioned strain analysis of grain and grain boundary.A quantitative description of the magnetic flux pinning force of the Nb₃Sn superconductor at the cryogenic temperature of 4.2K and under the environmental magnetic field of 12T is given.Finally,in the process of establishing the scale coupling calculation model of grain and grain boundary deformation in Nb₃Sn composite superconductor,with the aid of a foreign polycrystal modeling software Neper,a new program written by Python is developed to generate Voronoi polycrystals in Abaqus automatically,which provides an effective new method for establishing Voronoi polycrystals in Abaqus.In summary,through the work of this paper,the strain effect of Nb₃Sn superconducting materials and the influence of strain on its flux pinning force and critical temperature degradation are further understood.The relevant research results are helpful to understand and reveal the origin of the superconducting mechanical effects of Nb₃Sn composite superconductors in extremely low temperature environments.At the same time,it provides some theoretical guidance for the design and development of high field superconducting magnets and high strain resistant superconducting materials.