Kim model for flux-pinning-induced stress in a long cylindrical superconductor

In this work, the flux-pinning-induced stress distribution in a circular cylinder of high-temperature superconductors is studied by adopting the Kim critical state model to describe the relationship between the magnetic flux density and induced current. Based on the plane strain approach, the analytic expressions of the radial and hoop stress in the cylinder are derived for the zero-field cooling and field cooling magnetization processes. It is shown that the stress distributions depend on the activation processes and the values of the dimensionless parameter p in the Kim model, and the overall maximums of the stresses appear at or near the center of the cylinder where cracking may be most likely initiated. In addition, the Kim model has wider applicability than the Bean model, and the influence of p on the stress depends on the activation process. Generally speaking, these results may be useful for understanding the magnetoelastic problem in practical application of bulk superconductors.