Fracture behaviors of a functionally graded thin superconducting film with transport currents based on the strain energy density theory

• Crack problem for functionally graded superconducting film is studied.
• Based on the Kim and hyperbolic function models, EDFs are obtained analytically.
• Effects of transport current, and model parameter, etc., on EDFs are analyzed.
• Increasing the gradient parameter can inhibit crack propagation and growth.
• In general, crack will propagate into the field of shear modulus decreasing.

In this study, the strain energy density theory is used to investigate a central crack problem for a functionally graded superconducting film with the applied transport currents, where the Kim critical state model is adopted and the shear modulus is assumed to vary along the film’s width in a form of hyperbolic function. The flux and current densities, the stress intensity factors (SIFs) and energy density factors (EDFs) are all analytically obtained. Numerical results show the effects of applied transport currents, model parameters, and crack length on the EDFs and/or SIFs. Among others, in the process of descending transport current, increasing the graded parameter of shear modulus can inhibit crack propagation, and in general, the crack will propagate and grow into the field of shear modulus decreasing. Moreover, the fracture angle is independent of the applied transport currents, and the fracture angle generally increases slightly with either the increasing of material graded parameter or the increasing of crack length. This study should be useful for the application of superconducting devices.