XFEM analysis of the fracture behavior of bulk superconductor in high magnetic field

A bulk superconductor in a high magnetic field is subjected to a large electromagnetic force, which can cause crack propagation and damage the bulk. In this paper, we study the fracture behavior of the GdBCO bulk superconductor under a large electromagnetic force based on the Extended Finite Element Method (XFEM). The critical state Kim model and H-formulations are used to obtain the electromagnetic force of a bulk superconductor in the magnetic field first. Second, the Stress Intensity Factor (SIF) of the bulk superconductor for various cracks under the electromagnetic force is presented. Numerical results show that the SIF depends not only on crack angle and length but also on the width of the bulk. For the inclined crack with a large crack angle, with the crack length increase, the SIFs increase first and decrease, while for a small crack angle, the SIFs decrease with the crack length increase. For the kinked crack, the SIFs decrease with the crack length increase. With the XFEM, the growth of the inclined and kinked cracks in the bulk superconductor during field cooling is presented. The crack propagation paths are dependent on the size of the bulk and different for two crack problems. In the process of crack propagation, the propagation path has a certain degree of deflection angle compared with the initial crack.