Flux-pinning-induced stress and strain in superconductors: Case of a long circular cylinder

The irreversible behavior of the flux-pinning-induced stress and strain in a long circular cylindrical superconductor placed in a parallel magnetic field is analyzed. An exact solution of the full three-dimensional (3D) magnetoelastic problem is found. The solution differs from the previous simplified 2D plane stress treatments of the same problem. We derive formulas for all stress and strain components, including: the magnetostriction Delta R/R, in terms of the flux density profile in the cylinder. The results are valid for any critical-state model j(c) = j(c)(B). Based on the Bean model, j(c) const, an extensive analysis is made of the elastic behavior during (1) a complete field cycle after zero-field cooling, and (2) field descent to the remanent state after field cooling. Special emphasis is put on the field-sweep stages generating tensile stresses, which tend to create cracking in the cylinder. A comparison is made between the overall maximum tensile stresses encountered in both processes (1) and (2), which one today uses, e.g., to activate superconducting trapped-field or quasipermanent magnets. [S0163-1829(99)06437-1].