Mechanical failure is one of the most significant challenges for the application of bulk superconductors acting as trapped field magnets. In this paper, a numerical simulation framework based on the coupled H-formulation for electromagnetics of superconductors and the phase-field fracture model for solids is proposed and implemented to simulate the crack nucleation and propagation within bulk superconductors during the magnetization process. The thermal stress due to cool down and the huge Lorentz force during the magnetization process are considered in the simulation. The magnetic field, current density and stress/strain field distribution, and the crack initiation and propagation within the homogeneous and inhomogeneous bulk sample under high magnetic field are numerically simulated, respectively. The trapped magnetic fields for the bulk superconductors under different magnetic fields are obtained numerically. In addition, the influences of microstructures such as voids, pre-existing microcracks on the trapped magnetic field of the bulk superconductor are also investigated and presented, which demonstrate the flexibility of the proposed framework to investigate the mechanical failure of bulk superconductors.

中文翻译：

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大块超导体磁化过程中机械失效的数值建模与仿真：基于相场法

机械故障是大块超导体作为俘获场磁铁的应用所面临的最重大挑战之一。在本文中，提出并实施了基于超导体电磁学耦合 H 公式和固体相场断裂模型的数值模拟框架，以模拟磁化过程中块状超导体内裂纹的成核和扩展。模拟中考虑了冷却引起的热应力和磁化过程中巨大的洛伦兹力。分别数值模拟了磁场、电流密度和应力/应变场分布，以及均匀和非均匀块状样品在强磁场下的裂纹萌生和扩展。数值获得了体超导体在不同磁场下的俘获磁场。此外，还研究并展示了诸如空隙、预先存在的微裂纹等微结构对体超导体的俘获磁场的影响，这证明了所提出的框架在研究体超导体机械故障方面的灵活性。