Crack-Inclusion Problem in a Superconducting Cylinder with Exponential Distribution of Critical Current Density
- PDF / 896,877 Bytes
- 6 Pages / 595.276 x 790.866 pts Page_size
- 27 Downloads / 254 Views
ORIGINAL PAPER
Crack-Inclusion Problem in a Superconducting Cylinder with Exponential Distribution of Critical Current Density Yufeng Zhao 1
&
Pengdong Ji 1
Received: 6 April 2020 / Accepted: 25 May 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, the crack-inclusion interaction considering the exponential distribution of critical current density is carried out for a functionally graded superconducting cylinder during the zero-field cooling (ZFC) process. By determining the stress intensity factors (SIFs) at the crack tips and performing magnetoelastic stress analysis, the result indicates that the increase of the gradient parameter of critical current density could effectively reduce the stress intensity factors based on the effect of the gradient parameter on the elastic constants ratio of inclusion/matrix, sizes of the inclusion and crack, and the distance between them upon electromagnetic force. Keywords Crack-inclusion . Exponential distribution of critical current density . Stress intensity factor . Electromagnetic force
1 Introduction In composite materials, fibers or two-phase particles are usually used as reinforcement phase. When the fracture behavior of these materials is studied, the stress-strain field at the crack tip will be strongly affected by the elastic modulus and geometric size of the inclusions [1–3]. Because the stress intensity factor of the crack tip has an important influence on the fracture behavior of materials, the research on the interaction between crack and inclusion has received extensive attention. Recently, the crack-inclusion problem in high-temperature superconductors (HTSs) has been studied [4–6]. Ceniga et al. [7–9] initially pointed out that in an anisotropic particle-matrix system, a crack forms in the matrix around the particle of a radius greater than a critical value under thermal-induced stresses. In the case that the size of inclusion is larger than the coherent length of the superconductor, the crack problem for an inclusion-matrix system is especially important. Then, Gao et al. [10–12] presented a theoretical model to solve the crack-inclusion problem in a type II superconductor under electromagnetic force with finite element methods (FEM).
* Yufeng Zhao [email protected] 1
School of Science, Lanzhou University of Technology, Lanzhou 730050, China
Based on the Bean model, a flux pinning–induced elastic stress analysis considering the crack-inclusion interaction is carried out by Xue et al. [13–15] for a bulk superconductor in the magnetization process, in which the crack is simulated as a continuous distribution of edge dislocations in the solution procedure. Later, they also proposed a simple model to investigate the interaction problem for a circular nonsuperconducting inclusion embedded in a high-temperature superconducting matrix which contains an inclined crack, oriented at an arbitrary angle from the direction of the critical currents. In our previous work [16, 17], we studied the general problem of a
Data Loading...
