Crack nucleation and propagation of electromagneto-thermo-mechanical fracture in bulk superconductors during magnetization

Abstract

Bulk high-temperature superconductors (HTS) like REBCO (RE: rare earth element or Y) have been widely adopted in a variety of engineering applications. With high magnetic flux applied in a short time of milliseconds, significant tensile stresses are induced during pulsed field magnetization by the Lorentz electromagnetic forces and Joule heating thermal expansions. Consequently, potential damage and fracture may occur in bulk HTS, leading to degradation of the capacity in trapping the magnetic field. In this multi-physical problem, due to the complex stress distribution even in the elastic stage and the intensive redistribution once crack nucleation occurs, the resulting fracture pattern is very complicated. Accordingly, it is a challenging issue to model crack nucleation and propagation of such electromagneto-thermo-mechanical fracture involving both the Lorentz electromagnetic forces and the Joule heating. In this work, the mechanical stresses and multi-physical fracture in bulk HTS during magnetization are studied systematically by the phase-field cohesive zone model (PF-CZM). The governing equations and the involved constitutive relations for the electromagnetic, thermal and cracking-mechanical sub-problems are given together with the numerical implementation. The elastic semi-analytical solutions for the Lorentz forces and thermal expansions induced stresses in an infinitely long cylindrical bulk HTS during magnetization are derived for the determination of crack nucleation. Numerical results are then discussed in details regarding the whole fracture process in bulk HTS under isothermal and non-isothermal cases. It is found that the first crack nucleation occurs at a certain interior position along the circumferential direction after which a couple of cracks nucleate and propagate outwards along the radial direction. The effects of Joule heating and cracking on the electromagnetic performances are quantified, and those of the inhomogeneity in the critical current density are also briefly discussed. Moreover, extension of the proposed PF-CZM to more complex cases is straightforward, making it a promising tool in optimizing the fabrication and practical application of bulk HTS.