Analytical solution for the fracture problem in superconducting tapes with oblique cracks under the electromagnetic force

• Published in: Applied mathematics and mechanics Vol. 46; no. 3; pp. 485 - 500
• Main Authors: Xie, Jinjian, Zhang, Zhaoxia, Shi, Pengpeng, Gou, Xiaofan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Boundary value problems; Chebyshev approximation; Classical Mechanics; Crack propagation; Cracking (fracturing); Electromagnetic forces; Exact solutions; Failure mechanisms; Fluid- and Aerodynamics; Flux density; Force distribution; Fractures; Magnetic flux; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Maxwell's equations; Partial Differential Equations; Quadratures; Singular integral equations; Stress intensity factors; Superconducting tapes; Superconductivity; superconducting tape; electromagnetic body force; integral equation; oblique crack; 74R10; O346.1; distributed dislocation technique (DDT); stress intensity factor (SIF)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3227-6

The fracture behavior of superconducting tapes with central and edge oblique cracks subject to electromagnetic forces is investigated. Maxwell’s equations and the critical state-Bean model are used to analytically determine the magnetic flux density and electromagnetic force distributions in superconducting tapes containing central and edge oblique cracks. The distributed dislocation technique (DDT) transforms the mixed boundary value problem into a Cauchy singular integral equation, which is then solved by the Gauss-Chebyshev quadrature method to determine the stress intensity factors (SIFs). The model’s accuracy is validated by comparing the calculated electromagnetic force distribution for the edge oblique crack and the SIFs for both crack types with the existing results. The findings indicate that the current and electromagnetic forces are significantly affected by the crack length and oblique angle. Specifically, for central oblique cracks, a smaller oblique angle enhances the risk of crack propagation, and a higher initial magnetization intensity poses greater danger under field cooling (FC) excitation. In contrast, for edge oblique cracks, a larger angle increases the likelihood of tape fractures. This study provides important insights into the fracture behavior and mechanical failure mechanisms of superconducting tapes with oblique cracks.