A trans-scale analysis and computation model for transient local stress in Nb3Sn superconductor under quench-induced thermal shock

Superconducting Nb₃Sn is pivotal for high-field (>10 T) magnets, where extreme operating currents enable substantial energy storage. Thermal energy rapidly accumulates in localized magnet coil regions during resistive transition (quench) initiation. This localized overheating creates intense thermal gradients where heat concentration in such a confined area leads to accelerated temperature rise, ultimately posing catastrophic risks to the integrity of the high-field superconducting magnet system. This study employs multiscale modeling to analyze temperature-dependent nonlinearities in thermodynamic parameters and transient local thermal stresses induced by quench-driven thermal shock. The study reveals a non-monotonic temperature dependence of thermal conductivity in Nb₃Sn, governed by synergistic effects of phonon boundary scattering, Umklapp processes, and multi-mechanism electron scattering. The Debye model accurately predicts the nonlinear temperature dependence of Nb₃Sn’s specific heat capacity, following $T^3$ law at cryogenic temperatures, due to phonon energy variations driven by temperature. The thermal expansion coefficient demonstrates nonlinear temperature dependence, with lattice anharmonicity as the dominant mechanism. Furthermore, the temperature sensitivity of d-electron states governs the abnormal elastic behavior of Nb₃Sn during its superconducting transition. Employing an equiaxed-grain polycrystalline Nb₃Sn model demonstrates that thermal stress intensifies with rising temperature fields during quench, exhibiting irregular distributions arising from variations in grain orientation, morphology, and local temperature. These multiscale simulations provide critical insights for superconducting magnet safety assessments under thermal shock conditions.