A Multi-Scale Method For The Constitutive Relations Describing Coupled Mechanical-Electromagnetic-Thermal Effects In Nb₃Sn Superconducting Materials

A15 superconducting Nb₃Sn has shown great promise for applications in the International Thermonuclear Experimental Reactor,and high energy physics.In these high field applications,the stress/strain arises from the cool-down and operation process of the superconducting magnet,inducing the performance degradation of the Nb₃Sn cable-in-conduit conductors,which is a critical issue in the superconductivity applications and developments.Due to the complex multi-scale structure of the Nb₃Sn composite,the electromechanical coupling responses at different scales are intrinsically interrelated.On the basis of the micro-meso-macro frame analysis,this paper intends to study the effects of strain induced variations of the characteristic parameters of material microstructure on the superconducting properties of Nb₃Sn and establish the constitutive model which accounts for the multiscale coupling in strained Nb₃Sn.A framework for micro-to-macro transitions for multi-scale analysis of multifilamentary superconducting composites is developed.Using this model,we respectively predict the critical performance degradation of the Nb₃Sn polycrystal under hydrostatic pressure and the Nb₃Sn composite under axial loading,the predicted results are in qualitative agreement with the experimental observations.This study reveals the multiscale coupling mechanism behind the electromechanical coupling behavior of the superconducting Nb₃Sn composite.The curve of the electronic state density at the Fermi surface of Nb₃Sn single crystal under the hydrostatic pressure and the combined tension（compression）-shear loading is subsequently given by the first-principles calculation method.Meanwhile,a model for the evolution of electronic state density at the Fermi surface under different loading conditions is established.Based on this model,we predicted the critical temperature degradation of Nb₃Sn single crystal/polycrystal under the hydrostatic pressure and the critical performance degradationof the Nb₃Sn composite polycrystal under the applied axial strain.The predicted values are qualitatively consistent with the experimental results.With the aid of the study,the multiscale features in the electromechanical coupling behavior in Nb based A15-type compounds are identified.The study will promote the material engineering application process,and the results of which are promising to engineer optimized large-scale superconducting high magnetic field systems.It is helpful to improve the understanding and description of the strain sensitivity of Nb₃Sn,and to provide a solid theoretical support for the manufacture of high-field superconducting magnets.The developed simulation model provides a basis for the detailed description of the strain effects on the superconducting properties of Nb₃Sn.Furthermore,the developed multiscale model lays foundation for understanding the empirical relation given by the experiment and opens the way for the parameterization of the strain effects on the superconducting Nb₃Sn.