Direct measurement of Nb$_{3}$Sn filament loading strain and stress in accelerator magnet coil segments

We have directly measured, for the first time, the Nb$_{3}$Sn and Cu loading strains and stresses in 11 T dipole coil segments upon compressive loading using neutron diffraction. For this purpose a load frame that enables rotation of the sample load axis with respect to the neutron scattering geometry was installed in the Stress-Spec beamline at the Heinz Maier-Leibnitz FRM II neutron source. The neutron diffraction data suggests that the magnet coil wound of Rutherford type cables can be considered as a fibre reinforced composite material. In the axial load direction the load is mainly carried by the Nb$_{3}$Sn filaments and the composite stiffness can be estimated by the rule of mixtures assuming iso-strain conditions in all composite constituents. Under transverse compression the fully annealed Cu provides an isotropic pressure around the Nb$_{3}$Sn filaments. The transverse load stresses in the Cu and Nb$_{3}$Sn are similar, indicating iso-stress behaviour of the coil constituents under transverse compression. The broadening of the Nb3Sn diffraction peaks above critical stress values indicates reversible and irreversible Nb$_{3}$Sn loading stress effects.