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

Abstract

The magnetic field trapping capability of a bulk superconductor is essentially determined by the critical current density, Jc(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, FL = 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 Jc(B, T) properties around the ab-plane of the bulk superconductor on the developed mechanical stress.

Composite stacks for reliable > 17 T trapped fields in bulk superconductor magnets

“…To design and assess appropriate reinforcement arrangements, two-dimensional (2D) axisymmetric finite-element models, implemented in the commercial finite element software package COMSOL Multiphysics, were used to study the field-trapping potential and mechanical stability of different bulk superconductor structures during the field-cooled magnetization process. Further details on the modeling arrangement and the implementation of the Jc(B, T) data can be found at [18][19][20]. In summary, the 'Magnetic Field Formulation', 'Heat Transfer in Solids' and 'Solid Mechanics' interfaces were coupled together to allow for a comprehensive study of the thermal stresses 𝜎 𝜃 𝐶𝑂𝑂𝐿 arising from differential thermal contraction and the electromagnetic stresses 𝜎 𝜃 𝐹𝐶𝑀 arising from interaction between the current and the magnetic field.…”

Transport Current Measurement of $I_{c}(T, B,\theta)$ and $n(T, B,\theta)$ for a Bulk REBCO Superconductor

“…4, is that the measured n-value varies markedly with applied field and temperature, and never exceeds an absolute value of ∼16. This differs significantly from values often used for bulk GdBCO-Ag in numerical simulations, which typically assume a constant value of n ≈ 20 regardless of field magnitude [13], [51]- [53].…”

Improved trapped field performance of single grain Y‐Ba‐Cu‐O bulk superconductors containing artificial holes

“…It is important to note the estimates given in Table 1 are derived from the stress states at the end of the magnetization process and not during the magnetization cycle itself. The electromagnetic stresses experienced during magnetization can exceed the final stress states, [26][27][28] which is partly why single grain bulk superconductors tend to fail during magnetization rather than afterward. Therefore, the trapped fields calculated in Table 1 should be viewed as slight overestimates based on the tensile strengths obtained.…”

“…Studies on polycarbosilanederived SiC ceramic 25 and SiC/SiC composite 26,27 have shown that porosity decreases and mechanical properties improve with the increasing number of PIP cycles. Zhu et al 28 show that increasing pyrolysis temperature and the concentration of SiC fillers in polycarbosilane polymer result in improved mechanical properties in two-dimensional Carbon/ SiC (C/SiC) composites fabricated using the PIP process.…”