For the optimization of Nb3Sn superconducting accelerator magnet design and assembly parameters the stress-strain behavior of the coils needs to be known. We have measured the stiffness of Nb3Sn Rutherford cable stacks with different epoxy volume fraction. The cable stack stiffness is strongly dependent on the load direction. The highest stiffness of about 95 GPa is measured in axial direction, as predicted by the rule of mixtures. In transverse load direction the stiffness is stress dependent, and about half of the axial stiffness. As expected the stiffness of the cable stacks increases with decreasing epoxy volume fraction. The stiffness of a conductor block extracted from an already cold tested 11 T dipole coil is comparable to that of a ten-stack sample with similar epoxy volume fraction.

Effect of Epoxy Volume Fraction on the Stiffness of Nb 3 Sn Rutherford Cable Stacks

For next-generation accelerator magnets for fields beyond those achievable using Nb–Ti, Nb3Sn is the most viable superconductor. The high luminosity upgrade for the Large Hadron Collider (HL-LHC) marks an important milestone as it will be the first project where Nb3Sn magnets will be installed in an accelerator. Nb3Sn is a brittle intermetallic, so magnet coils are typically wound from composite strands containing ductile precursors before heat treating the wire components to form Nb3Sn. However, some mechanical assembly is still required after the coils have been heat-treated. In this paper, we present direct evidence of cracking of the brittle Nb3Sn filaments in a prototype dipole that resulted in degraded magnet performance. The cracking of the Nb3Sn, in this case, can be attributed to an issue with the collaring process that is required in the assembly of dipole accelerator magnets. Metallographic procedures were developed to visualize cracks present in the cables, along with quantitative image analysis for location-based crack analysis. We show that the stresses experienced in the damaged coil are above the critical damage stress of Nb3Sn conductor, as evidenced by a measured Cu stabilizer hardness of 85 HV0.1, which is higher than the Cu stabilizer hardness in a reference Nb3Sn cable ten-stack that was subjected to a 210 MPa transverse compression. We also show that once the collaring procedure issue was rectified in a subsequent dipole, the Nb3Sn filaments were found to be undamaged, and the Cu stabilizer hardness values were reduced to the expected levels. This paper provides a post-mortem verification pathway to analyze the damage, provides strand level mechanical properties, which could be beneficial for improving model prediction capabilities. This method could be applied beyond Nb3Sn magnets to composite designs involving high work hardening materials.

/pdf/metallographic-analysis-of-11-t-dipole-coils-for-high-862klwy383.pdf

Metallographic analysis of 11 T dipole coils for High Luminosity-Large Hadron Collider (HL-LHC)

We have directly measured, for the first time, the Nb3Sn 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 Nb3Sn 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 Nb3Sn filaments. The transverse load stresses in the Cu and Nb3Sn 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 Nb3Sn loading stress effects.

https://iopscience.iop.org/article/10.1088/1361-6668/aaffa3/pdf

Direct measurement of Nb$_3$Sn filament loading strain and stress in accelerator magnet coil segments

Accelerator magnets that can reach magnetic fields well beyond the Nb-Ti performance limits are presently built and developed using Nb3Sn superconductors. This technology requires a reaction heat treatment of the magnet coils, during which Nb3Sn is formed from its ductile precursor materials (wind and react approach). The Nb3Sn microstructure and microchemistry are strongly influenced by the conductor fabrication route, and by the phase changes during the reaction heat treatment. By combining in situ differential scanning calorimetry, high energy synchrotron X-ray diffraction and micro-tomography experiments, we have acquired a unique data set that describes in great detail the phase and microstructure changes during the processing of Restacked Rod Process (RRP), Powder-in-Tube (PIT) and Internal Tin (IT) Nb3Sn wires. At temperatures below 450 °C the phase evolution in the three wire types is similar, with respectively solid state interdiffusion of Cu and Sn, Cu6Sn5 formation, and Cu6Sn5 peritectic transformation. Strong differences in phase evolutions in the different wires are found when temperatures exceed 450 °C. The volume changes of the conductor during Reaction Heat Treatment (RHT) are a main challenge in the production of Nb3Sn accelerator magnets. We compare the wire diameter changes measured in situ by dilatometry with the phase and void volume evolution of the three different Nb3Sn wire types. Unlike the Nb3Sn wire length changes, the wire diameter evolution is characteristic for each Nb3Sn wire type. The strongest volume increase of about 5% is observed in the RRP wire, where the main diameter increase occurs above 600 °C upon Nb3Sn formation.

/pdf/effect-of-the-fabrication-route-on-the-phase-and-volume-1jhgi6bqa7.pdf

Effect of the fabrication route on the phase and volume changes during the reaction heat treatment of Nb 3 Sn superconducting wires

The knowledge of the temperature-induced changes of the superconductor volume and of the thermomechanical behavior of the different coil and tooling materials is required for predicting the coil geometry and the stress distribution in the coil after the Nb3Sn reaction heat treatment. In this paper, we have measured the Young's and shear moduli of the HL-LHC 11 T Nb3Sn dipole magnet coil and reaction tool constituents during in situ heat cycles with the dynamic resonance method. The thermal expansion behaviors of the coil components and of a free standing Nb3Sn wire were compared based on dilation experiments.

Thermomechanical Behavior of the HL-LHC 11 Tesla Nb3Sn Magnet Coil Constituents During Reaction Heat Treatment

Nb3Sn magnets are presently built for the HL-LHC accelerator upgrade and are developed for the Future Circular Collider study. The knowledge of the Nb3Sn strain state distribution in these magnets is required in order to predict their ultimate performance limit. We have measured the Nb3Sn residual strain distribution in an 11 T dipole accelerator magnet coil. Ambient temperature Nb3Sn strain maps across 11 T dipole coil cross sections were acquired by means of fast high energy synchrotron x-ray diffraction. Using complementary neutron diffraction measurements the Nb3Sn residual strain and stress was measured in the four largest conductor blocks of a massive 11 T dipole coil segment.

/pdf/submitter-residual-strain-in-the-nb-3-sn-11-t-dipole-magnet-58kr7ggo76.pdf

M Lorentzon

Papers

Direct measurement of Nb$_3$Sn filament loading strain and stress in accelerator magnet coil segments

submitter : Residual strain in the Nb$_3$Sn 11 T dipole magnet coils for HL-LHC