Fracture analysis for a penny-shaped crack problem of a superconducting cylinder in a parallel magnetic field

• A penny-shaped crack problem of a superconducting cylinder is investigated.
• The effects of crack on flux density in the cylinder are taken into account.
• The ERR in both the ZFC and FC processes are obtained and numerical calculated.
• The FC process is easier to enhance crack propagation than the ZFC process. For the FC process, the maximal field has important effects on crack propagation.

In this work, the penny-shaped crack problem is investigated for an infinite long superconducting cylinder under electromagnetic forces. The distributions of magnetic flux density in the superconducting cylinder are obtained analytically for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes, where the magnetically impermeable crack surface condition and the Bean model outside the crack region are adopted. Based on the finite element method (FEM), the stress intensity factor (SIF) and energy release rate (ERR) at the crack tips in the process of field descent are further numerically calculated. Numerical results obtained show that according to the maximal energy release rate criterion, the FC process is generally easier to enhance crack initiation and propagation than the ZFC activation process. On the other hand, for the FC activation process, the larger the maximal applied magnetic field, more likely the crack propagates. Additionally, crack size has important and slightly different effects on the crack extension forces for the ZFC and FC cases. Thus, all of the activation processes, the applied field and the diameter of the penny-shaped crack have significant effects on the intensity analysis and design of superconducting materials.