Theoretical Investigations On Fracture And Magnetostriction Behaviors Of High-Temperature Superconductors

The behaviors of high critical temperature and high critical current density bring opportunities for the development of high-temperature superconductors (HTS) in engineering applications. However, the tensile strength of HTS is very low. Due to the superconductors with high critical current density subjected to a strong electromagnetic body force when they are applied in a strong magnetic field, these excellent behaviors of HTS also bring grim challenges for the safety and effectiveness of HTS in applications. Therefore, the investigations of the fracture and magnetostriction behaviors of HTS in strong magnetic field are very important for improving their development, and these attract many researchers. Based on the effect of the crack on the induced current of HTS, this dissertation investigates the fracture behaviors of cylindrical superconductor with a central crack, an edge-crack, and two collinear edge-cracks, respectively, and the magnetostriction behaviors of long rectangular cylinder are also investigated.Firstly, the crack problem of cylindrical superconductor with a central crack is analyzed. The model of induced current disturbed by the central crack is established based on the critical state theory. Under this model, the distributions of the trapped field well reflect the multi-peak feature observed by many researches in the cracked samples. For the zero-field-cooling and the field-cooling magnetization processes, respectively, the stress intensity factors at the central crack tip of HTS in the decreasing process of the external magnetic field are analyzed by the finite element method. And the effects of the external magnetic field on the stress intensity factor are discussed. According to the comparisons of the results, the effects of the electromagnetic force in the crack region on the final results are analyzed. In addition, the effects of different magnetization processes and different crack lengths on the safety and application effectiveness of HTS are also discussed, respectively.Secondly, considering the uncertainty of the crack position in HTS, the crack problem of cylindrical superconductor with a single edge-crack is investigated. The model of induced current disturbed by the single edge-crack is established based on the critical state theory. Because the edge-crack affects the induced current of the whole superconductor all the time, the edge-crack problem is more difficult than the central crack problem. For the zero-field-cooling and the field-cooling magnetization processes, respectively, the stress intensity factors at the edge-crack tip of HTS in the decreasing process of the external magnetic field are analyzed by the finite element method. Because it can only take a half model which is unconstraint in the horizontal direction to calculate in the single edge-crack problem, the problem will not be calculated caused by the errors of the equivalent node forces. We adopted a reasonable approach to treat the errors of the equivalent node forces, and then the single edge-crack problem can be solved successfully. Based on the analysis of obtained results, the variations of the stress intensity factor are considered in different magnetization processes, external magnetic fields, and the lengths of the edge-crack, respectively. The results of the single edge-crack problem are compared with the results of the central crack problem, and the effects of the crack position on the safety and the trapped field of HTS are analyzed.Thirdly, in order to describe the multiple crack characteristics of HTS more reasonably, the crack problem of cylindrical superconductor with two collinear edge-cracks is investigated. The model of induced current disturbed by two collinear edge-cracks is established based on the critical state theory, and the stress intensity factors at the tips of the two collinear edge-cracks are analyzed based on the finite element method. When the left and the right crack lengths are equal, the crack problem of this special case can be calculated by a half model and a quarter model, respectively. Then, the effectiveness of the reasonable approach which is used to treat the errors of the equivalent node forces in the half model is verified. The variations of the stress intensity factor are considered in two cases, the left and the right crack lengths are equal and increase at the same time, the left crack length is invariant and the right crack length increase, respectively. In addition, the effect of the two collinear edge-cracks on the trapped field of HTS is analyzed.Finally, the magnetostriction problem of HTS with rectangular cross section in the magnetization process is investigated. Due to the complexity of the electromagnetic body force, the magnetostriction problem of HTS with rectangular cross section can not be worked out by directly solving the differential equations. In order to obtain the analytical results of this problem, T. H. Johansen et al. used a simplified approach to approximately treat the magnetostriction problem of HTS with rectangular cross section. However, the effectiveness of their simplified approach is not verified. Due to the complex electromagnetic body force can be treat effectively by the numerical finite element method, we can adopt the finite element method to calculate the magnetostriction problem of HTS with rectangular cross section. Therefore, the effectiveness of Johansen's simplified approach can be test by the finite element method, and the magnetostriction behavior of HTS with rectangular cross section can also be analyzed. By analyzing the specific procedure of Johansen's simplified approach, and compareing the results obtained from these two different methods, we can find that the results obtained from Johansen's simplified approach are accurate only at the center of the cross section. The errors of the results will increase as the position of the point are far from the center, and the results at the corners of the cross section obtained from Johansen's simplified approach are completely inconsistent with the facts. In addition, based on the results obtained from the finite element method, we can find that a series of complex deformations appear in the rectangular cross section of HTS in different magnetization processes, the boundaries of the cross section even appear distortion sometimes. The deformation figure at the midpoint of the right border in the whole magnetization processes well reflects the irreversible magnetostriction characteristic of HTS.