Thermal Stress Analysis Of Microstructure Of Nb₃Sn Material During Rapid Temperature Rise

Because of the excellent superconductivity,Nb3 Sn has shown great application prospects in building high-field magnets(>10 T).Mechanical deformation will induce the degradation of superconducting properties in Nb3 Sn.In the extreme working environments,the degradation will induce quench.In the transient quench process,the superconducting magnet equipment will suffer huge thermal shocks,it causes damage to the magnet structure.Studying the quench phenomenon of Nb3 Sn is of great significance for the safe and stable operation of the superconducting magnet equipment.In this paper,based on the elastic theory of closely packed fiber-reinforced composites and the finite element method,the Nb3 Sn composite superconductor calculation model is established.The relationship between the microstructure of the Nb3 Sn composite and the local stress distribution(grain and grain boundary deformation in columnar and equiaxed regions)are comprehensively studied.The trends of the stress ratio along grain boundary path is given.The results show that the stress distribution in the Nb3 Sn composite is non-uniform,and its ratio to the axial load stress can be up to 2.08.The stress concentration mainly occurs in the equiaxed crystal regions,where the possibility of generating cracks is higher.The stress distribution is related to the grain morphology and orientation.In order to understand the causes of stress concentration and discover where the stress concentration occurs,the effects of the grain orientation difference on the stress concentration is carefully studied.The results show that the relatively high stress exists at the grain boundaries,and the grain orientations in the stress concentration areas are randomly distributed.For simplicity,we selected the Nb3 Sn polycrystalline model as a research object.By considering the non-linear relationship between the thermodynamic performance parameters and the temperature,we conduct a preliminary simulation of the quench phenomenon of the Nb3 Sn superconductor.In the simulation,we use the UMAT subroutine in Abaqus finite element software and the thermodynamic coupling calculation module.From the perspectives of the microstructure characteristics(Nb3Sn grain size),the transient quench induced thermal stress and thermal distribution are analyzed.The simulation results reveal the stress changes at the grain boundaries and the stress gradients inside the grains.It lay a foundation for the following studies of the quench evolution in Nb3 Sn magnet.In order to study the variations of the elastic constants of Nb3 Sn single crystal in the quench process,we established a theoretical model.It starts from the Gibbs free energy of the lattice,and accounts for the evolution of the electron density of states at the Fermi surface.The model can reproduce the strong nonlinear patterns of the Nb3 Sn elastic constants changing with temperature.