Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

A multi-scale nonlinear procedure to analyze the stress in Nb3Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets-the issue of stress management. The study demonstrates that gasket materials (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb3Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb3Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb3Sn coil was simulated, in three orthongonal axes, using the combined properties of the gasket materials (insulation layers) and Hill materials (resin-impreganted cable). The procedure makes very few assumptions with regard to material properties because it incorporates actual measured stress-strain curves in the analysis. The coil was simulated to the level of detail of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb3Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb3Sn magnets, this versatile procedure can also be employed in the design of LTS, HTS, and room temperature magnets or of any structures ultilizing composite materials; specifically, it can be used to manage the stress and strain of HTS fusion magnets.