Stress and strain analysis of a REBCO high field coil based on the distribution of shielding current

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 n-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 n-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.