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Mechanical properties of Nb 3 Sn coil and magnet materials as input for FE simulations

This article discusses the stress-strain behavior and dependence on load direction in stainless steel examples for FE simulations of Nb3Sn coil and magnet materials. It includes information on standardized test samples, Young's modulus measurements, and the elastic anisotropy of the materials.

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Mechanical properties of Nb 3 Sn coil and magnet materials as input for FE simulations

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  1. Mechanical properties of Nb3Sn coil and magnet materials as input for FE simulations C. Scheuerlein EuroCirColWP5 coordination meeting 2921 November 2017

  2. Stress-strain behaviour dependence on the load direction at the example of stainless steel From: The European Stainless Steel Development Association Euro Inox and The Steel Construction Institute, Design manual for structural stainless steel-Commentary (2nd Edition), 2003

  3. Sample geometries for standardised mechanical testing Standardized test samples for dynamic and static tensile and compression tests. All samples have been extracted from a Ti6Al4V pole wedge. Sample for Poisson’s ratio measurement and extensometers for axial and transverse strain measurements. The sample has been extracted from a DISCUP coil wedge.

  4. Static Young’s modulus measurements • Precise Young’s moduli can be derived from stress-strain measurements of materials that exhibit pronounced linear elastic behaviour (e.g. Ti6Al4V). • Comparatively large uncertainty in the Young’s modulus results of materials that do not exhibit linear behaviour, like stainless steels. Comparison of 316LN and Ti6Al4V stress-strain curves and linear fits for the determination of Young’s modulus [v]. Comparison of the RT engineering stress-strain curves of different coil and magnet materials [iv]. [i] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, C. Meyer, “Thermomechanical behavior of the HL-LHC 11 Tesla Nb3Sn magnet coil constituents during reaction heat treatment”, IEEE Trans. Appl. Supercond., submitted [ii] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, P. Uhlemann, “Mechanical properties of the HL-LHC 11 Tesla Nb3Sn magnet constituent materials”, IEEE Trans. Appl. Supercond., 27(4), (2017), 4003007

  5. Young’s modulus (E), shear modulus (G), Poisson’s ratio (µ) relationship Equation 1 • For isotropic materials: • Equation 1 is confirmed for instance for the 11 T dipole Ti6Al4V pole wedges (ETi6Al4V=116 GPa, GTi6Al4V=44.1 GPa and µTi6Al4V=0.32±0.03 are measured, and µ=0.32 is calculated from the measured E and G values). • The relationship is not valid for the strongly textured DISCUPC30/3 11 T dipole coil wedges (EDISCUP-L=98.7 GPa, GDISCUP-L=53.2 GPa and µDISCUP=0.43±0.02 are measured). • For DISCUP Equation 1 is not valid (it would give a negative µ value). [i] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, C. Meyer, “Thermomechanical behavior of the HL-LHC 11 Tesla Nb3Sn magnet coil constituents during reaction heat treatment”, IEEE Trans. Appl. Supercond., submitted

  6. Summary mechanical properties of Ti6Al4V pole wedge • [i] Ti6Al4V at RT: E=116 GPa G=44.1 GPa µ=0.32±0.03 • [ii] Ti6Al4V at RT: E=113.8 GPa G=44.0 GPaµ=0.342. • [i] Ti6Al4Vat 4.2 K*: E=130 GPa G=50 GPa µ=0.34 • *4.2 K values are extrapolated from temperature dependent measurements in the range 20 °C-700 °C [i]. • Ti6Al4V exhibits linear elastic behaviour up to about 800 MPa (at RT), and mechanical properties are not strongly anisotropic. [i] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, C. Meyer, “Thermomechanical behavior of the HL-LHC 11 Tesla Nb3Sn magnet coil constituents during reaction heat treatment”, IEEE Trans. Appl. Supercond., submitted [ii] http://www.matweb.com/search/DataSheet.aspx?MatGUID=a0655d261898456b958e5f825ae85390

  7. Elastic anisotropy in the 11 T dipole DISCUP coil wedges Voigt • In order to take into account anisotropic materials properties the principal stress directions need to be known. • The angular dependence of the DISCUP Young’s modulus has been calculated from texture data obtained by neutron diffraction and from Cu single crystal elastic constants. • The DISCUP wedges are strongly textured (multiples of random orientation MRD=16), which causes a strong elastic anisotropy of about 30%. • The DISCUP Young’s moduli derived from stress-strain compression tests are 89 GPa in the wedge extrusion direction and 96 GPa perpendicular to the extrusion direction [i]. • These values are substantially lower than the values between 115 to 130 GPa found in literature for ODS Copper. Hill • Angular DISCUP Young’s modulus dependence with respect to the wedge extrusion direction. Calculated assuming equal strains (Voigt) and equal stresses (Reuss) in all grains, respectively. Measurement results from [i] are shown for comparison. Courtesy of W. Gan, Helmholtz-ZentrumGeesthacht.

  8. Summary mechanical properties of DISCUP C30/3 coil wedge • [i] DISCUP C30/3 at RT in longitudinal direction: E=92 GPa G=54 GPaµ=0.43±0.02 • [i] DISCUP C30/3at 4.2 K in longitudinal direction*: E=113 GPa G=62 GPa µ=??? • *4.2 K values are extrapolated from temperature dependent measurements in the range 20 °C-700 °C [i]. • Strong elastic anisotropy, maximum E at an angle of about 50° with respect to wedge extrusion direction. [i] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, C. Meyer, “Thermomechanical behavior of the HL-LHC 11 Tesla Nb3Sn magnet coil constituents during reaction heat treatment”, IEEE Trans. Appl. Supercond., submitted

  9. Magnetil mechanical properties v From: F. Bertinelli, S. Comel, P. Harlet, G. Peiro, A. Russo, A. Taquet, “Production of Low-Carbon Magnetic Steel for the LHC Superconducting Dipole and Quadrupole Magnets”, IEEE Trans. Appl. Supercond. vol. 16, no. 2, 2006, pp 1777-1781

  10. Summary of some 11 T dipole elastic and plastic RT materials properties [ii] C. Scheuerlein, F. Lackner, F. Savary, B. Rehmer, M. Finn, P. Uhlemann, “Mechanical properties of the HL-LHC 11 Tesla Nb3Sn magnet constituent materials”, IEEE Trans. Appl. Supercond., 27(4), (2017), 4003007

  11. Annealed Cu in the Nb3Sn conductor block • Rp0.2 of the annealed Cu in the Nb3Sn conductor block is about 45 MPa. Stress-strain curves of Cu wire cold-drawn and after subsequent 695 °C HT [ii].

  12. Thermal expansion Relative length change of DISCUP C30/3, Ti6Al4V, 316LN and the reacted Nb3Sn wire #7419 during cool down from 650 °C. The thermal expansions of Cu, Nb and Nb3Sn bulk are shown for comparison. Comparison of RRP #7419 Nb3Sn wire axial length change during first heating with that of DISCUP C3/30, Ti6Al4V, and 316LN. The relative length changes of a Cu wire and the Nb thermal expansion [iii] are shown for comparison. [iii] N. Mitchell, “Finite element simulations of elasto-plastic processes in Nb3Sn strands”, Cryogenics 45 (2005) 501-505

  13. Some questions • Materials properties of which coil and magnet materials are needed? Are reacted conductor constituent materials properties needed (Cu, Nb, Nb3Sn) ? • What are the acceptable uncertainties? • What are the principal stress directions (to take into account anisotropic materials properties)? • What is the acceptable plastic deformation (how is “stress limit” defined)? Can we use Rp0.2? • What is the stress limit of Magnetil (Rp0.2 of Magnetil is about 120 MPa)? • What is the meaning of the RT and 4.2 K conductor bock stress limits of 150 MPa and 200 MPa, respectively? Is plastic coil deformation acceptable (Rp0.2of annealed Cu is about 45 MPa)? • How are shear moduli taken into account in the FE models? • Are friction coefficients for the relevant materials combinations taken into account in the FE models?

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