Numerical Analysis of Unreacted Nb$_{\text{3}}$Sn Wires Under Compression

Particle accelerator magnets mainly use Nb-Ti ($T_{C}$= 9 K,$B_{c2}$= 14 T), but future machines like FCC-hh will require fields near 14 T. This drives a shift to higher-performance superconductors, with Nb$_{3}$Sn as the baseline choice. Nb$_{3}$Sn high-field magnets are fabricated by winding Rutherford cables made from wires containing Nb$_{3}$Sn precursor materials. During the cabling process, these wires undergo deformation, which increases the likelihood of degradation of their transport properties after reaction. Understanding how unreacted wires behave during uniaxial rolling is essential to optimize and validate designs of Nb$_{3}$Sn wires and cables. To investigate this, a collaboration between the Genoa branch of INFN and CERN is developing a finite element model to simulate the behavior of these wires. This study will focus on the impact of deformation during cabling on unreacted wires. Two-dimensional models of wire cross-sections, some idealized and symmetrical, and others based on SEM images of commercial RRP wires, will be presented. The study will explore differences between these models and quantitatively compare simulation results for the deformed geometry and stress and strain state with data obtained from image analysis of wire cross-sections.