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

doi:10.1007/s10483-025-3227-6

Abstract

Abstract:

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.

Key words: superconducting tape, electromagnetic body force, integral equation, distributed dislocation technique (DDT), oblique crack, stress intensity factor (SIF)

2010 MSC Number:

O346.1

Jinjian XIE, Zhaoxia ZHANG, Pengpeng SHI, Xiaofan GOU. Analytical solution for the fracture problem in superconducting tapes with oblique cracks under the electromagnetic force. Applied Mathematics and Mechanics (English Edition), 2025, 46(3): 485-500.

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