Crack problem for a functionally graded thin superconducting film with field dependent critical currents

• Crack problem for functionally graded superconducting film is studied.
• Based on the double exponential model, SIFs are obtained analytically.
• Effects of applied field and model parameters on SIFs are numerically analyzed.
• Increasing the gradient parameter can inhibit crack propagation and growth.
• The mode-II SIFs are mainly caused by the inhomogeneous parameter.

In this study, double exponential model is established to investigate the central crack problem for a functionally graded superconducting film with filed dependent critical current. The stress intensity factors (SIFs) are analytically obtained and numerically calculated. Numerical results show the effects of applied magnetic field, model parameters, and crack length on the SIFs. Among others, in the process of field descent, the crack in the superconducting film easily propagates in the mode-I form. Increasing the graded parameter of shear modulus can inhibit crack propagation. For a fixed reduced field (especially for a larger magnetic field), both the mode-I and mode-II SIFs firstly increase, then decrease with the increasing of introduced non-dimensional exponent parameter. This study should be useful for the application of superconducting devices.