There are growing concerns about the stresses created by shielding currents in high field superconducting magnets fabricated from tape conductors leading to reduced performance and lifetime. This paper presents results of stress/strain calculations caused by shielding currents assuming the conductor deformations follow a linear constitutive relation. An anisotropic bulk approximation approach was used to calculate the electromagnetic field distributions in a REBCO high field coil with a stack of pancakes and a large number of turns first, and then the Lorentz force distribution and mechanical response characteristics were studied in the two-dimensional axisymmetric configuration. A new discrete contact mechanical model implemented by the finite element method, which is able to simulate the contact and separation behaviors between adjacent turns during the deformation, was proposed to analyze the distributions of hoop stress, hoop strain, radial stress and radial displacement in the coil. The influences of shielding current on those mechanical responses were obtained by comparing the simulation cases with and without taking shielding current into account. Besides, a continuum bulk mechanical model, which is parallel to the discrete contact mechanical model and treats the pancakes as continuum bulks, was modeled as well in order to understand the influences of different models on the simulation results. Furthermore, we studied the influences of a couple of practical factors (including the -value, ramp rate, and operating mode of the REBCO coil winding) on the shielding current and hoop stress. A couple of novel and important conclusions were found. (1) Neglecting the shielding current behavior would significantly underestimate the maximum local hoop stress in a REBCO high field coil. (2) The continuum bulk mechanical model is not adequate for the stress analysis of dry-wound high field coils, by which unreasonably large tensile radial stresses could be obtained. (3) The highest local hoop stresses at the fully-charged moment and the fully-discharged moment are located in a certain pancake near the end of the coil winding and the end pancake, respectively. (4) Decreasing the -value and the ramp rate of the REBCO coil could be two auxiliary ways to suppress the shielding current and maximum local hoop stress in the coil. (5) For the ramp-and-hold operating mode, the REBCO coil experiences the highest stress level at the moment when it right achieves the goal field. (6) The cycling operation of a REBCO high field coil can cause the tape experiencing alternative positive and negative hoop stresses and this may decrease the fatigue life of the tape and then the life of a magnet.
No-insulation (NI) high-temperature superconducting (HTS) coils exhibit high thermal stability and self-protecting features compared with traditional insulated HTS coils. As NI coils experience heat disturbance, the underlying mechanism of the heat propagation, the changes of the central field and voltage of the coil need to be further explored. Moreover, due to the rapid temperature rise caused by the heat disturbance, the coil typically suffers from large strain and stress. Therefore, the mechanical behavior is also a vital factor in the design and operation of superconducting magnets. This paper proposes a multiphysics quench model to study the thermal stability, composed of an equivalent circuit axisymmetric model combined with a two-dimensional magnetic field model and a one-dimensional (1D) heat transfer model. An additional 1D solid mechanical model is used to analyze the mechanical behavior of the NI coil. The results indicate that when the temperature of the coil exceeds its critical value, the current flows along the radial direction. The heat generated by the radial resistance of the coil is small, so that it is difficult to induce a quench. The thermal expansion and heat propagation velocity also affect the distributions of the hoop and radial stresses in the coil. The change of the hoop stress is larger than that of the radial stress, and the electromagnetic force has a relatively small effect in the self-field. The pulsed energy, inner diameter of the coil and location of the heater are all found to have an observable effect on the thermal stability and mechanical behavior.
Dendritic flux avalanches and the accompanying thermal stress and strain in type-II superconducting thin films under transverse magnetic fields are numerically simulated in this paper. The influence of the magnetic field ramp rate, edge defects, and the temperature of the surrounding coolant are considered. Maxwell's equations and the highly nonlinear E-J powerlaw characteristics of superconductors, coupled with the heat diffusion equation, are adopted to formulate these phenomena. The fast Fourier transform-based iteration scheme is used to track the evolution of the magnetic flux and the temperature in the superconducting film. The finite element method is used to analyze the thermal stress and strain induced in the superconducting film. It is found that the ramp rate has a significant effect on the flux avalanche process. The avalanches nucleate more easily for a film under a large magnetic field ramp rate than for a film under a small one. In addition, the avalanches always initiate from edge defects or areas that experience larger magnetic fields. The superconducting films experience large thermal strain induced by the large temperature gradient during the avalanche process, which may even lead to the failure of the sample.
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