A simple and effective approach for thermo-mechanical modelling of composite superconducting wires

The ability to compute accurately the strain field in Nb3Sn filaments is a crucial point in cable design, due to the significant strain sensitivity of niobium-tin wires. Due to its heterogeneity, a straightforward numerical simulation of a cable, taking into account all the details of the microstructure, would result in an enormous number of unknowns. As an alternative, multiscale approaches can be used to deal with this kind of problem, to understand the behaviour across the various scales. In this framework, a simple and efficient approach to obtain the homogenized properties of a heterogeneous strand is proposed here. This approach is developed for the non-linear, thermo-mechanical field. It consists of the solutions to some boundary value problems formulated on a suitably chosen statistically representative volume element of the wire. Two bronze-route strands and one internal-tin strand are considered and the equivalent parameters are obtained. Finally, the cool down and the subsequent application of a tensile axial load are simulated taking into account the homogenized wires. Computed results are shown to be in excellent agreement with measured stress-strain curves