Elastic anisotropy in multifilament Nb$_3$Sn superconducting wires

The elastic anisotropy caused by the texture in the Nb$_{3}$Sn filaments of PIT and RRP wires has been calculated by averaging the estimates of Voigt and Reuss, using published Nb$_{3}$Sn single crystal elastic constants and the Nb$_{3}$Sn grain orientation distribution determined in both wire types by Electron Backscatter Diffraction. At ambient temperature the calculated Nb$_{3}$Sn E-moduli in axial direction in the PIT and the RRP wire are 130 GPa and 140 GPa, respectively. The calculated E-moduli are compared with tensile test results obtained for the corresponding wires and extracted filament bundles