New Methodology to Derive the Mechanical Behavior of Epoxy-Impregnated Nb$_3$Sn Cables

The Nb$_3$Sn technology plays a crucial role in developing high-field superconducting magnets. The new-generation Nb$_3$Sn cable greatly contributes to bring the magnetic field produced by the superconducting dipole magnets to the 16 T level; nevertheless, its mechanical properties are largely variable, making it difficult to predict the mechanical behavior of the magnet structure. For this reason, an extended experimental campaign on specimens made from a stack of ten Nb$_3$Sn cables was launched at CERN. The ten-stack can be considered a representative sample of the magnet coil because it is produced following the same construction process: curing, reaction, and impregnation. The experimental campaign consists of compression tests along the three sample directions at room temperature and multiple loading and unloading cycles were performed as it occurs for real magnet coils. A dedicated test bench was designed to measure the vertical and lateral deformations of the sample. This work presents the stress–strain relationships, focusing on the cable-stack stiffness, which strongly depends on the stress level in each loading direction. Moreover, the transverse–longitudinal strain relationships give further information about the complex behavior of the Nb$_3$Sn cable-stack, because the rearrangement of the conductors occurs during the test. A new analytical methodology is proposed to predict the nonlinear behavior of the Nb$_3$Sn composite cable.