Thermomagnetic instability and accompanied stress intensity factor jumps in type-II superconducting bulks under various magnetization processes

For type-II superconducting bulks used as trapped-field magnets, the thermomagnetic instability, manifested as flux jumps and temperature spikes, frequently takes place, resulting in a large amount of energy dissipation in a short time and further the crack problem due to electromagnetic and thermal stresses. In this paper, based on the magnetic and heat diffusion equations and fracture theory, we develop a thermal-magnetic-mechanical coupling model to analyze the flux-jump and fracture behaviors in bulk samples of BiSrCaCuO under various magnetization processes. This model has an important advantage that the simulation domain can be restricted to the sample itself, without having to consider the air region around it, and its reliability is verified by the existing experimental and numerical results. The effects of the sample size, the ambient temperature, and the sweep rate, direction, and uniformity of the external magnetic field on the flux jumps, and Mode I and Mode II stress intensity factors are fully analyzed under different cooling conditions. It is found that as ambient temperature or field inclined angle increases or field sweep rate decreases, the first flux-jump field presents a trend of monotonically increasing for zero-field-cooling magnetization but it has an opposite trend for field-cooling magnetization. The flux jump can lead to the jump of temperature, electromagnetic force, and stress intensity factor. In addition, the sensitivity of flux-jump and fracture behaviors to different parameters and the influence of flux jump on the demagnetization behavior under crossed magnetic fields are discussed. We also find the levitation force jumping phenomenon when the bulk sample is magnetized in a nonuniform magnetic field. From the results obtained, we provide some general guidelines on how the system parameters of superconducting bulk magnets could be chosen to improve the thermal-magnetic-mechanical stability.