Multiscale modeling and simulation on the thermal-curing-induced residual stresses in high temperature superconducting coils based on the anisotropic viscoelastic model

Abstract Thermal-curing process, such as the vacuum pressure impregnation, is often used to support and consolidate superconducting (SC) coils that operating at high currents and magnetic fields. However, residual stresses driven by thermal mismatch and chemical shrinkage are unavoidable in this process, which threatening the mechanical integrity and the current carrying capacity of high-temperature superconducting (HTS) tapes. Yet, a dedicated modeling and simulation framework for evaluating the curing-induced residual stress in SC coils is lacking. This study establishes a multiscale, multi-physics coupling framework that considers an anisotropic viscoelastic constitutive model to effectively and accurately predict the curing-induced residual stresses in HTS coils. The cure kinetics equation and a cure- and temperature-dependent viscoelastic constitutive model for the widely used resin system CTD-101K were first developed based on systematic differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) experiments. Then, a numerical homogenization scheme was proposed to depict the macroscopic chemo–thermo–mechanical coupling behaviors of the HTS coils. After that, the accurate microscopic stress state of the HTS tapes was evaluated by coupling the homogenization simulation with an RVE model which represents the detailed configuration of the coils at local regions that are prone to mechanical failure. The numerical modeling and multiscale simulation scheme were validated against benchmarks and full-scale models. Furthermore, comparative analysis reveals that traditional linear elastic models severely overestimate residual stresses. Our results identify microscopic delamination of the SC layer as the primary failure mode, which is widely observed throughout the pancake coil and specifically concentrated in the semicircular section of the racetrack coil. For pancake coils, increasing the inner diameter is prioritized to mitigate this risk. For racetrack coils, a design strategy of ‘a large inner radius and a long straight section’ will be effective to reduce the residual stresses. This work provides numerical simulation tools and guidance for the curing of high performance HTS coils.