Thickness dependence of fracture behaviour in a superconducting strip

Abstract

When subjected to a magnetic field, a superconducting strip will undergo an electromagnetic body force induced by flux pinning. The magnitude of the body force is dependent on the critical current density. It is well known that the critical current density in the strip will decrease with increasing thickness. In addition, the mechanical behaviour of the strip will also be affected by the thickness of the strip. Thus, the strip thickness has an influence on both the electromagnetic and mechanical behaviours. In this paper, we analyse the fracture behaviour by considering the competition of electromagnetic and mechanical behaviours. In order to study the central crack problem of a superconducting strip with different thicknesses, we replace the electromagnetic body force with the total surface force. Using a Fourier transform method, the boundary value problem is reduced to a singular integral equation. By solving the singular integral equation, we obtain the stress intensity factors for two different crack lengths during field descent. The results show that the stress intensity factor is not a monotonic function of the thickness and that two competing factors dominate in different field regions. It is necessary to obtain the optimized thickness by considering both the superconductivity and mechanical behaviour in the superconducting strip.