ITER superconducting cable: from filament strain after cool-down to filament strain due to energisation

A Nb3Sn strand inside a superconducting cable behaves like a beam loaded by Lorentz forces and supported by strand-to-strand contacts. Due to the strand material heterogeneity and the complex cable layout the strain field developed is not easy to be studied. In this work we present a hierarchical beam model to analyse a superconducting cable level by level. The basic idea is to perform a recursive substitution of discrete models involving many beams with a single, continuous beam model, which behaviour can be deduced from the preceding cabling stages. The theory of asymptotic homogenisation is here suitably extended for the analysis of the SC fibrous composite with non-linear, temperature dependent components. We account also for local material yielding at the stage of microanalysis. The transformation strains due to cool down from the reaction temperature to the cable operating conditions are computed, as well as the following distribution of strain due to energisation. To recover the strain inside each single strand and in the filaments, a suitable unsmearing technique is applied. The method is applied to the real case of the 3x3 and 3x3x5 CICC sub-size samples tested at FZK in Germany.