Numerical modelling of mechanical stresses in bulk superconductor magnets with and without mechanical reinforcement

The magnetic field trapping capability of a bulk superconductor is essentially determined by the critical current density, J c (B, T), of the material. With state-of-the-art bulk (RE)BCO (where RE = rare earth or Y) materials it is clear that trapped fields of over 20 T are potentially achievable. However, the large Lorentz forces, F L = J × B , that develop during magnetisation of the sample lead to large mechanical stresses that can result in mechanical failure. The radial forces are tensile and the resulting stresses are not resisted well because of the brittle ceramic nature of (RE)BCO materials. Where fields of more than 17 T have been achieved, the samples were reinforced mechanically using resin impregnation and carbon-fibre wrapping or shrink-fit stainless steel. In this paper, two-dimensional (2D) axisymmetric and three-dimensional (3D) finite-element models based on the H -formulation, implemented in the commercial finite element software package COMSOL Multiphysics, are used to provide a comprehensive picture of the mechanical stresses in bulk superconductor magnets with and without mechanical reinforcement during field-cooled magnetisation. The chosen modelling framework couples together electromagnetic, thermal and structural mechanics models, and is extremely flexible in allowing the inclusion of various magnetisation processes and conditions, as well as detailed and realistic properties of the materials involved. The 2D model - a faster route to parametric optimisation - is firstly used to investigate the influence of the ramp rate of the applied field and any heat generated in the bulk. Finally, the 3D model is used to investigate the influence of inhomogeneous J c (B, T) properties around the ab-plane of the bulk superconductor on the developed mechanical stress.