Fracture analysis for a square crack in a square cross section columnar superconductor

Highlights: • The 3D crack problem of superconductors under applied magnetic field is studied. • The generalized Irie-Yamafuji critical current densities model is introduced. • A novel and suitable crack affected region for a square crack is presented. • Both ZFC and FC activation processes are considered and discussed. In this paper, a square central crack problem is investigated for an infinitely long square cross section superconducting column under electromagnetic forces. The generalized Irie-Yamafuji critical current densities model and the magnetically impermeable crack surface condition are adopted for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes. The distributions of magnetic field and current density are derived in the superconductor, where the crack affected region is introduced. Based on the finite element method (FEM), the stress intensity factors (SIFs) at the edge of square crack in the process of field descent are numerically calculated. Numerical results show that the SIFs at the corner points of square crack are generally larger than the values of other dots at the four edges of square crack in the process of magnetization. In the meantime, the FC process is usually easier to promote crack propagation than the ZFC activation. In addition, both the crack sizes and the introduced index $\gamma$ in the generalized Irie-Yamafuji critical current density model have important and different effects on the crack growth in the ZFC and FC activation processes. These results should be useful for the application of superconducting materials.