Fracture properties of a cylindrical superconductor with a central cross crack

Abstract

In this work, the central cross crack problem is investigated for a long cylindrical high-temperature superconductor under electromagnetic forces. The distributions of both the current density and the magnetic flux density in the cylinder are obtained analytically in either the Bean or the Kim critical state model for both the zero-field cooling and the field cooling magnetization processes. Based on the finite element method, lots of the stress intensity factors at the crack tips for decreasing magnetic fields are numerically calculated. Numerical results obtained show that the field cooling activation process has more significant influence on the stress intensity factors than the zero-field cooling activation process, and that for every activation process, as the applied field decreases, the superconducting cylinder is most dangerous when the currents in the crack region are just be influenced. The safety of the superconducting cylinder with a cross crack depends on not only the magnetic process but also the crack length. Additionally, the introduced dimensionless parameter p in the Kim model has different effects on the stress intensity factors obtained from the most dangerous field and from the trapped field. The present study should be helpful to the design and application of high-temperature superconductors.

Fracture problems of a superconducting slab with a central kinked crack

“…As discussed for the problem of center cross crack in a superconducting cylinder, 19 in the ZFC activation process, when the applied field is reduced from B m to B a , there are three similar situations denoted, respectively, by Case (i), Case (ii), and Case (iii), which are dependent on B a as well. Also, if set B Ã 1 and B Ã 2 , respectively, denote the external applied fields when the situations change from (i) to (ii) and from (ii) to (iii), B Ã 1 and B Ã 2 can be expressed, respectively, as…”

“…19 At this moment, the correspondingly parameters B Ã 1 and B Ã 2 can be expressed as (For clarity, these figures are enlarged both in the width and length directions corresponding to Fig. 2).…”

“…This phenomenon is similar to the center cross crack problem. 19 In addition, it is remarked that in X …”

“…As known, the SIFs at the crack tips are important quantities to denote the fracture properties of crack problems. For the present crack problem, the SIFs are defined as follows: [17][18][19] …”

“…17,18 Recently, Feng et al further studied the corresponding center cross crack problem. 19 However, all the cracks mentioned above are straight. In fact, in practical applications, other forms of cracks, e.g., curved crack, branched crack, etc., are usually inevitable.…”