Modeling of the Critical-Current Behavior of Nb$_{3}$Sn Subsized Cables Under Transverse Load Using 2D Finite Element Analysis and a Strain Scaling Law

The mechanisms causing the critical-current degradation of ITER-type Nb$_{3}$Sn Cable-in-Conduit-Conductors have been studied in the past decade. One of the origins of the degradation of the performance is the Lorentz load during magnet operations. The strands within the cable subjected to the transverse loads locally experience larger strains than the ones caused by tensile loads. Results obtained with experiments on full size cables are limited due to their cost and difficulty so, to predict the degradations of a Nb$_{3}$Sn CICC under transverse loads, empirical laws should be established. Strain scaling laws are available but have never been used to determine the behavior of strands under transverse load. We propose a new method, by which the critical-current behavior of a subsized cable under transverse loads is derived from the critical-current behavior under uni-axial strains. This method is based on the strain state of the Nb$_{3}$Sn filaments obtained by finite element analysis (FEA). The FEA strain results are used to find the critical-current using tensile scaling laws available. The critical-current behavior obtained by this method is compared with the available experimental data of triplets. The results of this new methodology, its benefits, and limitations are discussed.