Multiscale approach to the mechanical behavior of epoxy impregnated Nb$_{3}$Sn coils for the 11 T dipole

The superconducting 11 T dipole magnets developed at CERN for the HL-LHC project are equipped with coils manufactured from Nb$_{3}$Sn Rutherford cables and following the wind and react fabrication technique. The brittleness of the multifilamentary structure of the Nb$_{3}$Sn within the cable strands exposes the coils to permanent performance degradation when subjected to excessive strain during assembly and operation. This paper will show the characterisation of cable stacks (10-stack) under compression using representative coil material in order to predict the behavior of the Nb$_{3}$Sn coils. By means of standard mechanical measuring techniques and finite element analysis, the results from the 10-stack measurements are extrapolated to an actual and fully detailed coil cross section using two-dimensional imaging techniques. The stress distribution from the actual coil geometry are used to predict the stresses at the strand level and the filaments within the strand. The model of the strand and filaments is based on a scanning electron microscope image of a strand of interest within the original coil in order to provide a realistic geometry and a better representation of the stresses within the multifilament structure. The results from this multiscale approach have allowed for a better understanding of the stresses that are observed at the strand and filament level by accounting for the global stresses of the realistic coil geometry.