A novel modeling to predict the critical current behavior of Nb$_{3}$Sn PIT strand under transverse load based on a scaling law and Finite Element Analysis

Superconducting Nb$_{3}$Sn Powder-In-Tube (PIT) strands could be used for the superconducting magnets of the next generation Large Hadron Collider. The strands are cabled into the typical flat Rutherford cable configuration. During the assembly of a magnet and its operation the strands experience not only longitudinal but also transverse load due to the pre-compression applied during the assembly and the Lorentz load felt when the magnets are energized. To properly design the magnets and guarantee their safe operation, mechanical load effects on the strand superconducting properties are studied extensively; particularly, many scaling laws based on tensile load experiments have been established to predict the critical current dependence on strain. However, the dependence of the superconducting properties on transverse load has not been extensively studied so far. One of the reasons is that transverse loading experiments are difficult to conduct due to the small diameter of the strand (about 1 mm) and the data currently available do not follow a common measurement standard making the comparison between different data sets difficult. Recently at the University of Geneva, a new device has been developed to characterize the critical current of Nb$_{3}$Sn strands under transverse loads. In this work we present a new 20 Finite Element Analysis (FEA) to predict the electro-mechanical response of a PIT strand that was tested at the University of Geneva when transverse load is applied. The FEA provides the strain map for the superconducting filaments when the load is applied. Those strain maps are then used to evaluate the critical current behavior of a PIT strand using a recently developed scaling law that correlates the superconducting properties of a wire with the strain invariants due to the load applied on the superconductor. The benefits and limitations of this method are discussed based on the comparison between the critical current simulation results obtained with the filament strain map and the experimental results available for PIT strands.