A 3D Finite Element Model of the Reversible Critical Current Reduction Due to Transverse Load in Nb$_{3}$Sn Wires

For the next generation of high-field accelerator magnets, CERN relies on Nb $_{3}$ Sn Rutherford cables. This material is extremely brittle and its superconducting properties are strongly dependent on the strain state. In the present 16 T magnet designs, transverse pressures exceeding 150 MPa on Nb $_{3}$ Sn Rutherford cables are expected. For these reasons, it is crucial to estimate transverse load effects on cable critical currents (I $_{c}$ ). Measurements at CERN and Twente University show that Nb $_{3}$ Sn Rutherford cables experience already significant reversible I $_{c}$ reduction at 150 MPa. Experiments at the University of Geneva confirm such results at strand level. This paper presents a 3D Finite Element (FE) model that analyses the reversible critical current reduction of a Nb $_{3}$ Sn strand due to transverse loads. In particular, the simulation analyses the behaviour of a 1-mm-diameter Powder-In-Tube (PIT) wire with 192 sub-elements by addressing the complex geometry of the strand without employing any homogenization. The study is based on the COMSOL Multiphysics® software and on a recently developed scaling law that calculates I $_{c}$ as a function of the strain invariants in the Nb $_{3}$ Sn sub-elements. In the end, results are discussed.