Thermo-mechanics of the hierarchical structure of ITER superconducting cables

Recent experimental tests on the Model Coils have shown that the behavior of Nb₃Sn based cables is not as good as expected on the basis of the characteristics evaluated for the uncabled strands. This degradation of the cable performance seems to be due to various factors, among which the strain state of the filaments due to bending and contact phenomena inside the cable. After these results it was decided that high performance strands will be used for ITER magnets, even if they have never been tested on a full size cable. Therefore the capability of evaluating the coil performance from the strands characteristics becomes a crucial point in the Research and Development (R&D) activity. Recently some extrapolations were attempted, but the mechanical model used is rather simplified and needs some fitting parameters which are not known a priori. In this work we present a thermo-mechanical model suitably developed to evaluate the strain state of a Nb₃Sn strand inside a superconducting (SC) cable. It is based on the Idea of multiscale modeling, starting from a enriched formulation of the beam kinematics to take into account the fibrous nature of a multifilamentary strand. The method consists in performing a successive substitution of discrete models involving many beams with a single equivalent beam model, which behavior is identified from the preceding cabling stage. This recursive substitution allows to perform the analysis within a reasonable computational time. Once the stress and strain fields are obtained at the higher level, a suitable unsmearing technique gives the strain till the first level, on the scale of the SC filament. The method is applied to the real case of the 3 × 3 and 3 × 3 × 5 CICC sub-size samples tested at FZK in Germany.