Fracture problem of a nonhomogeneous high temperature superconductor slab based on real fundamental solutions

• We studied firstly nonhomogeneity fracture in HTS base on real fundamental solutions.
• The SIF of nonhomogeneity HTS decrease with nonhomogeneity parameters increasing.
• The greater the applied field, the higher the SIF value.
• The greater critical current density of the nonhomogeneity HTS is, the smaller values of the SIF.

To analyze the fracture problem of the nonhomogeneous high temperature superconductor (HTS) slab under electromagnetic force, we derive the real fundamental solutions based on eigenvalue and eigenvector analyses. The superconductor E-J constitutive law is characterized by the Bean model where the critical current density is independent of the flux density. Fracture analysis is performed by the methods of singular integral equations which are solved numerically by Lobatto–Chybeshev collocation method. Numerical results of the stress intensity factor (SIF) are obtained. Moreover, the crack opening displacement (COD) can be obtained by numerical integration dislocation density functions. The effects of the thickness ratio, HTS material nonhomogeneous parameters, applied magnetic field and critical current density on SIF and COD are discussed. The present work could theoretically provide quantitative predictions of the fracture mechanism of the nonhomogeneous HTS.