Modelling Stress and Strain in Filamentary Superconductors with Finite Element Method

Abstract

Electrical properties of superconductors are very sensitive to mechanical loading. As the loading in practical applications is often very large, designers should know the mechanical behaviour of conductors well. With the finite element method (FEM), mechanical models on complex loading situations and conductor geometries can be solved. Such models give local information on stress and strain states, which is needed, for example, in predicting a fracture. The aim of this work is to study mechanical modelling of Nb3Sn and Bi-2223 filamentary superconductors with continuum models that are solved with FEM. The focus is on loading conditions that are typical in a magnet. In other words, models are developed for thermal stress, bending, axial tension and transversal compression loading of a conductor.

Filamentary superconductors contain specific features that are complicated to describe in a mechanical model or increase the need of computational resources in the FEM solution. In this work, an auxiliary model approach was proposed to model conductors with a large filament number and an on-off approach was suggested to describe creep deformation. In addition, the modelling of twisted conductor structures and electromagnetic forces were studied. However, computational tests showed that knowing the material behaviour at high temperatures and the stiffness of Bi-2223 filaments is essential for obtaining precise results. Fortunately, some simple measurements on the studied conductor can help in finding these properties.

Results of the models were compared to available measurement data. Unfortunately, direct measurements on local stress and strain states were not found. The models agreed well with the measurements when the conductor properties were modelled realistically. Comparison of the FEM models to analytical models confirmed the benefits of the FEM models. FEM models allowed to model combined loading and predicted a clear variation of stress and notable non-axial stresses that were absent in analytical models.