A thermo-mechanical model for Nb3Sn filaments and wires: strain field for different strand layouts

In Nb3Sn CIC conductors, the superconducting compound is distributed into fine filaments and embedded in a resistive matrix for electrical and thermal stability. Nb3Sn formation requires a solid state diffusion reaction at high temperature, which causes an Sn gradient inside the filaments. It is well known that the critical parameters vary with composition (Sn content) and strain state. In this work the complete 3D strain field is computed for different wire layouts. First, the relation between the grade of filament reaction and strain is investigated: superconducting wires are studied, taking into consideration non-homogeneous Nb3Sn filaments, i.e. considering an unreacted core of pure Nb. Furthermore, the case when the filaments agglomerate together to give a 'macrofilament' is also taken into consideration (internal tin wires). A finite element discretization fine enough to take into consideration non-homogeneous filaments would result in a very high number of unknowns, which could be beyond the capacity of today's computers. Therefore a thermo-mechanical model is formulated, based on the generalized self-consistent method, suitably developed to deal with the material nonlinearity and the coupling between the thermal and mechanical fields. In this way, equivalent homogeneous properties are obtained and the analysis of the wires becomes feasible. An appropriate unsmearing technique finally gives the strain state in the real, not homogenized, materials.