Homogenisation methods for the thermo-mechanical analysis of Nb₃Sn strand

An accurate estimation of the strain state of a strand inside a coil is a crucial point in the prediction of Nb₃Sn conductor performance, since Nb₃Sn based strands show a strain-dependence of their critical parameters. To perform a numerical analysis of a superconducting coil it would be impossible to operate a spatial discretization fine enough to take into consideration each single material. Therefore, we make use of homogenisation methods, so that the strand (or the triplet or higher order bundles) can be schematized as an equivalent homogeneous material. This paper presents a general overview of different ways to approach a study of superconducting strands using homogenisation techniques. We aim to point out that there is not a "unique best approach", but different methods have to be chosen depending upon the microstructure of the strand. Three kinds of strands are taken into consideration to exemplify the various techniques: the strand from European Advanced Superconductors (EAS), from Furukawa (FUR) and from Outu Kumpu (OUK) company. For the three strands the thermal strain due to the cool-down from reaction temperature to the coil operating conditions is calculated, making use of the effective properties obtained via the various approaches.