Interaction Among Multiple Parallel Cracks in REBCO Superconductor Bulks Under Applied Magnetic Fields: A Boundary Element Analysis

Large-grain REBa ₂ Cu ₃ O _7−δ (REBCO, RE = rare Earth) superconductor bulks offer promising magnetic field trapping capabilities due to their high critical current density ${{J}_c}$ , making them ideal for many important applications, such as trapped field magnets. However, their ceramic-like brittleness and numerous microstructural cracks pose significant challenges to their structural integrity. Under applied magnetic fields, the substantial Lorentz force resulting from the high critical current density can lead to rapid crack propagation and, in severe cases, superconductor bulk fracture. Therefore, for practical applications of these superconductor bulks, it has been very important to deeply understand the strength issues closely related to cracks all the time. In this study, we focused on the crack strength of multiple parallel cracks on the $a$ / $b$ -plane of REBCO superconductor bulks under an applied magnetic field. By applying the derived boundary integral equations, we comprehensively analyzed the stress intensity factors (SIFs) for modes I and II at the tips of these parallel cracks, considering their sizes, relative positions, and the intensity of applied magnetic fields. Our calculations reveal that, in most cases, the SIF of mode I predominantly governs the strength of the superconductor bulks. We identified critical values for the SIFs of both modes I and II in relation to the relative vertical displacement $d$ / $c$ for regular parallel cracks and $d$ ₁ / $c$ for random parallel cracks. Furthermore, our findings demonstrate that both SIFs consistently exhibit linear increases with the intensity of applied magnetic fields.