A Numerical Approach for the Mechanical Analysis of Superconducting Rutherford-Type Cables Using Bimetallic Description

Low-temperature superconductors are widely used in high-field magnets, mostly within Rutherford-type cables. The run for higher fields leads to greater forces on the conductor, which is pushed closer to its mechanical limit. Managing the higher strain and stress levels on the conductor supposes to perform simulation at the strand level, especially with strain-sensitive superconductors such as Nb
₃
Sn. Three-dimensional models are necessary because inside of a magnet, the conductor is subject to a complex combination of axial and transverse loads. Superconducting cables are anisotropic composite structures that can comprise superconducting strands, insulation materials, stabilizing parts, porosities, etc. They have a multiscale architecture, the performance at the magnet scale being driven by the filament scale. This paper proposes a numerical approach for 3-D finite-element (FE) modeling of Rutherford cables, at the scale of the strand. The 3-D mesh of two reference cables is built with a simplified cable forming model. The accuracy of this geometrical model is assessed by comparing sections of the simulated mesh with tomographic data, using relevant criteria and specific geometry analysis tools. In this approach, the strand is considered as bimetallic, with a copper core, a superconducting bundle ring, and an outer copper ring. After mechanical 3-D FE computation on this bimetallic mesh, the strain/stress state on the local compounds of the strand (including Nb
₃
Sn filaments) is obtained by strain projection. The strain/stress state on the Nb
₃
Sn filaments can be used to estimate the cable current transport capability, thanks to the existing scaling laws.