Optimization of Brittle Superconducting ${\rm Nb}_{3}{\rm Sn}$ Strand Designs

Finite element simulations and experimental measurements of deformed strand cross sections were performed to study their structural behavior during cabling. A variety of strand designs were modeled to identify and optimize design parameters like sub-element shape, number of sub-elements, and their spacing. The model results were correlated to the experimental results. This led to a numerical-experimental approach that is effective in predicting fracture, merging, and deformation of the sub-elements. Strains were calculated as a function of strand deformation for strands with 54, 120, and 210 sub-elements and a local Cu-to-non-Cu ratio of 0.165. Strains as a function of strand deformation were also calculated for 120/127 strands with a local Cu-to-non-Cu ratio of 0.11, 50% increased spacing, and 100% increased spacing between sub-elements. Results showed that increasing the spacing by 100% reduces the maximum strain-x, maximum strain-y, and maximum strain-xy by 14%, 13%, and 29% respectively at a 30% strand deformation level. Also, results revealed that the maximum strain components are always located in the sub-elements close to the center of the strands, which agrees with the experimental findings.