The Multi-helical Structure And Mechanical Property Analysis Of The Nb₃Sn Strand

Most of the current fusion reactors use the tokamak device as the reaction vessel. When fusion reactor running, the superconducting magnet within the tokamak will create strong magnetic field and the plasma will be confined in the annular combustor, in order to achieve control of the fuel. As a core part of the superconducting magnets, the superconducting properties of the cable-in-conduit conductor （CICC） plays an important role during the operating of the magnet system. In the tokamak device, the longitudinal field and center field coils adopted the superconducting cable which are composited by the NbsSn strands. The superconducting properties of the Nb₃Sn are highly sensitive to strain which determines the overall performance of the superconductor cables when working in low temperature and high magnetic field. Therefore, the study of the mechanical properties of the Nb₃Sn strand and CICC will contribute to the design optimization and performance evaluation of the superconducting magnet in the future.According to the transformation matrix between the vectors in the global and local coordinates, the deformation of the strand can be obtained when the first-stage sub-cable suffer axial tension, then the relationship between the helix angle and axial strain can be get. A theoretical model is proposed based on the thin rod theory to analyze the changing of the equivalent moduli of the sub-cables during axial stretching. After that, the expressions of the center line of the strand in second-stage sub-cable was derived according to the differential geometry theory and the effects of the related parameters to the curvature and torsion of the center line was discussed. Based on this, the distributed forces of the strand when the first-stage sub-cable flexed are derived and calculated. The compressional strain between the strand has also been given. According to the results, the equivalent moduli mainly depends on the initial helical angle of the sub-cable. The axial friction will appear and the radial force increased significantly when the sub-cable flexion.In reality, the internal contact of the sub-cable is complicated, in this paper we study the contact situation in the four-stage sub-cable when the cable subjected to axial tension. Firstly, according to the effective moduli and the structure of the sub-cable, we describe the variation of the contact force within the cable versus the axial strain. By expending the inner sub-cables step by step, the locations of the contact points can be determined. Based on the existing experimental results, we shows the critical current density reduction of two types strand when suffer different contact forces in order to highlight the effect of the contact force on the superconducting properties of the strand. The results show that the contact force between the third-stage sub-cables has the most significant effect on the superconducting properties of strand. The magnitude of the contact force can be decreased by reducing the pitch of the sun-cable.For multi-stage helical strand, it becomes complicated when analyzing the stress-strain state of the strand because of its complicated structure. And, the distribution of the stress on the cross section of the strand is also non-uniform as the Nb₃Sn strand is a typical composite material. In this case, we establish the finite element model of the internal-thin-process strand by using the comsol software and examines the stress and strain of the strand globally and locally. We also discuss the effects of the change of the first-stage pitch length to the mechanical properties of the second-stage helical strands. At last, we establish the equivalent model of the sub-cable at each stage. After simulating, the stress-strain curves of the sub-cables when under axial tension loads can be obtained and contrast with the theoretical results. According to the numerical results, the mechanical properties of the strand change obviously after each twisting. The stress and strain of the second-stage helical strand will increase with the pitch of the first-stage helical. the stress-strain curves of the equivalent model are in good agreement with the theoretical result which proves the reliability of theoretical.