Numerical modelling and simulations on the mechanical failure of bulk superconductors during magnetization: based on the phase-field method

Abstract

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.