Thermal Stress Analysis And Fracture Behavior Of Nb₃Sn Composite Superconducting Coils

Nb₃Sn superconducting magnets are the most competitive superconducting materials in the fields of large scientific devices,transportation,medical and energy due to their excellent superconducting properties.Higher critical current density and higher superconducting magnetic field strength have become one of the research hotspots in the field of superconducting magnets.Since Nb₃Sn materials have high strain sensitivity,and Nb₃Sn superconducting wires will inevitably be subjected to thermal stress and electromagnetic force during heat treatment,processing,cooling and operation,the larger strain will have a certain impact on the stability of superconducting magnet structure.Therefore,it is especially important to carry out the study of thermal stress analysis and fracture behavior of Nb₃Sn superconducting coils for the safe and stable operation of superconducting magnet coils.In this paper,a three-dimensional finite element model of the Nb₃Sn superconducting coil is established.Considering the composite structure of the superconducting wires inside the superconducting coil,a two-way homogenization method is used to study the stress-strain variation of each material inside the superconducting wire with the number of layers and turns of the coil in order to avoid a large computational effort.In this paper,we first verify the accuracy of calculating the stress-strain of superconducting coils using the bi-directional homogenization method,and then calculate the equivalent mechanical parameters of superconducting wire cells using the representative cell method in fine mechanics,establish a three-dimensional homogenized coil model,and obtain the displacement field of each layer and turn of superconducting wire cells of Nb₃Sn superconducting coils under thermal stress,and then apply the displacement field of equivalent superconducting wire cells The stress-strain variation of each material in the superconducting wire with the number of layers and turns of the coil is then calculated by applying the displacement field of the equivalent superconducting wire unit on the fine superconducting wire unit structure.The results show that when the Nb₃Sn superconducting coil is subjected to thermal stress only,the stress-strain of each material in the superconducting wire exhibits a strong linear relationship with the number of layers and turns of the coil.Then,by varying the number of Nb₃Sn core wires,core wire size and copper base diameter size in the superconducting wire,the relationship of stress-strain in each material with these factors was analyzed.The strength of the superconducting wire is increased when the number of core filaments is higher,the core filament size is larger,or the diameter of the copper base is smaller,so that a reasonable arrangement of superconducting core filaments can be selected to optimize the design of the superconducting wire structure in terms of mechanical properties.Subsequently,the stress-strain of each material in the superconducting wire is given as a function of the number of layers and turns of the superconducting wire under the combined effect of thermal stress and electromagnetic force,and the stress-strain of each material in the superconducting wire is closely related to the distribution of electromagnetic force.During the production,assembly and operation of Nb₃Sn superconducting wire,tiny cracks are inevitably generated,and the existence of these tiny cracks can make the superconducting wire possible to undergo serious fracture damage.In this paper,the stress intensity factor at the crack tip is solved by establishing a two-dimensional finite element model of the Nb₃Sn superconducting wire using J-integral.The variation of the stress intensity factor under tensile strain with the size of the Nb₃Sn core wire and the diameter of the copper base is given first.Subsequently,the stress state of the crack region on each material in the Nb₃Sn superconducting wire under thermal stress is discussed,and the cracks show different expansion states in different regions.The variation of crack length and crack angle in relation to the stress intensity factor at the crack tip under different temperature fields is discussed.Finally,the relationship between the distance between two cracks and the variation of the stress intensity factor is discussed,and the stress intensity factor of the crack tip increases gradually when the cracks are gradually close to each other.