Modelling of current distribution in Nb₃Sn multifilamentary strands subjected to bending

In Nb3Sn cable-in-conduit conductors (CICCs), strands follow complex trajectories that result in a periodic bending strain acting on the strands upon electromagnetic loading and thermal contraction. Such a periodic bending strain leads to degradation of the overall transport performance of a CICC. Aiming for a better understanding and quantitative correlation between strand degradation and CICC test results, a detailed strand model is essential in combination with accurate intra-strand resistance data, the spatial filament strain distribution, and the associated filament crack distribution. Our novel numerical strand model is a 3D network of resistors including superconducting filaments, normal matrix elements, and an outer stabilizing shell or inner core. Along the strand length, matrix elements have Ohmic resistance, there is a filament-to-matrix contact resistance (Rfm) between filaments and matrix elements, while superconducting filaments have a power-law voltage–current (VI) characteristic with critical current (Ic) and an n-value described by the ITER Nb3Sn strain scaling law based on measured strand data. The model simulates the VI characteristic in a periodic bending experiment and provides the associated spatial potential distribution. The VI characteristics representing the low- and high-resistivity limits (LRL and HRL) are identified for periodic and uniform axial bending. The voltage level for the current transfer regime depends on the strand internal resistivities, i.e. the filament-to-matrix contact and the matrix resistivity, the twist pitch and the bending wavelength. The simulation results show good agreement against Ic degradation, as experimentally measured by the TARSIS facility, versus the assessed peak bending strain. In addition we discuss different methods for determining the applied peak bending strain. The model provides a basis to find a practical relationship between a strand's VI characteristic and the periodic bending strain, as well as a mapping of well-characterized strand performance to that of a full-size CICC