Multistage Modeling Of The Superconducting Strand And Cable And Study Of Their Mechanical-electro-magnetic Behaviors

Nb3Sn is one of the main superconducting materials in the coils of the ITER magnet system since its excellent critical superconducting properties. It has strong strain sensitivity that its superconducting properties will be affected obviously by its strain state, which leads to a degradation of its superconducting properties under Lorentz force and thermal expansion. With so many considerations such as the safety, stability and loss situation, all the superconducting strands and cables taking the Nb3 Sn as the main superconducting material are made with the complex twisting structures. This makes the prediction of the mechanical behaviors and critical superconducting properties of these strands and cables complex and pivotal, being one of the hot topics in the applied superconducting field. Thus, this dissertation focuses on the mechanical and electrical behaviors and magnet distribution of the Nb3 Sn strand and the CICC cable.Firstly, taking the LMI strand and the SMI-PIT strand as examples, based on the complex structure of the strand and the GLS theory developed by Curtin and Zhou, The author studies the mechanical behaviors of the strand under axial and cyclic loads through the finite element method, and build the Multi-filament twist model and homogenized model for the LMI strand and SMI-PIT strand, respectively. From the investigation, the author explains the formation mechanisms of the hysteresis loop and “platform” appearing in the stress-strain curves of the LMI strand and SMI-PIT strand, respectively. Meanwhile, based on the FEM models the author also discusses the influences of the helical structure of the filaments, thermal residual stress producing during the manufacturing process, debonding between the filaments and the matrix, the sliding of the two surfaces of the voids, the damage of the filaments and its evolution and the pitch length of the filaments on the mechanical behaviors of the strands. The results of the FEM model agree well with the experimental data.Secondly, based on the Multi-filament twist model, taking the LMI strand as example, the author studies the mechanical behaviors of the strand under bending deformation. Similar as the tension case, the author discusses the effects of the thermal residual stress producing during the manufacturing process, the damage of the filaments and the pitch length of the filaments on the bending behavior of the strand. In addition, the author also investigates some mechanical behaviors of the strand such as the distribution of the breakage in the filaments and its relation with the pitch length of the filaments and the shift of the neutral axis during the bending process. Taking advantage of the Multi-filament twist model and combining with the scaling law expressed by the invariant, the author calculates the critical current of the strand under bending deformation and study the influence of the damage of the filaments and current transfer length. The calculation results agree well with the experimental data.Thirdly, the author models the first three stage subcables through the FEM. Their deformation under the basic loads such as tension, torsion and bending are simulated. The discussions of the effect of the anisotropy of the strand and pitch lengths of each stage on the mechanical behavior of the subcable are also made through the FEM model. Meanwhile, the author also builds the method for the estimation method of the axial strain of the filaments when the cable is under deformation with the consideration of the influence of the friction. The calculation in this method is simple and fast, and its structure is clear. Based on this method, we discuss this different sliding situation between different strands in the subcable. According to the required of the relevant study and engineering, the author builds another more accurate method to calculate the stress and strain distribution of the strand in the cable. This method has the ability to discribe the distribution of the force and bending moment, the contact stress and frition in the strand when the cable is under loads. Meanwhile, we verify the accuracy of these two methods through FEM.Finally, according to the complex structure of the CICC cable, the author builds a fast direct Biot-Savart(FDBS) method for the calculation of the self-field of the cable. The computing time complexity of this method is one order of magnitude lower than that of the direct Biot-Savart(FDBS) method, and this method is more accurate the the traditional algorithms. The author calculates the self-field map of the “petal” subcable and the full size cable with FDBS, and discuss the influence of the pitch lengths of every stage subcable. We verify the accuracy of this method through the comparsion between the results of FDBS and DBS. Meanwhile, the author also estimates the magnetic field of the cable after compression, and verify the results by the experimental data.