1. Sino-German Workshop on Electromagnetic Processing of Materials, 11.10 – 13.10.2004 Shanghai, PR China Use of magnetic fields during solidification under microgravity conditions J.Dagner, M.Hainke, J.Friedrich, G.Müller Outline: oThe conservation equations utilizing the volume averaging technique oModels for time dependent magnetic fields oInfluence of forced flows on the solidification process Contract no. 50WM0042Contract no. 14347/00/NL/SH

2. Microgravity – Is it necessary? Systematic analysis of the influence of convection on ● the evolution of the mushy zone ● micro- and macro segregation ● morphology of dendrites in binary AlSi, ternary AlSiMg and technical A357 alloys. Schematic of dendrites solidifying under the influence of convection Diffusive and controlled convective conditions are achieved by using microgravity environment and time-dependent magnetic fields, i.e. rotating magnetic fields (RMF). Objectives of MICAST ( The effect of magnetically controlled fluid flow on microstructure evolution in cast technical Al-alloys ): MICAST - MAP Project No. AO-99-031

3. Directional solidification with time dependent magnetic fields applied Modeling of (global) heat transfer and macrosegregation Solidification of binary AlSi7 and ternary AlSi7Mg0.6 cast alloys Influence of rotating and traveling magnetic fields on the solidification process Heat flux Bulk liquid Mushy zone Solid Melt flow AlSi7 z T G=4K/mm V g = 0,1mm/s d=8mm Condition for directional solidification The software package CrysVUn

4. The volume averaging technique 1 For a quantity  in the phase k (k= solid or liquid) the volume average is defined: The fraction of phase k is: The intrinsic volume average: Mixture concentration within the REV: Macrosegregation: solidmushliquid Representative elementary volume (REV)  0 ; T s =T l =T; solid liquid Solidifying alloy sample with one of the REV inside the mushy zone (marked) REV [1] Poirier et al. Met. Trans. B. 22 889-900 (1991)

5. Interdendritic convection is causing macrosegregation z T  MZ z C z ll Axial temperature, liquid concentration and liquid volume fraction during directional solidification. Phase diagram Local solute enrichment due to upwards directed flow. As Pr<<Sc the concentration field is changed at much smaller flow velocities than the temperature field. Convective parameter flow  <0 negative macrosegregation 0<  <1positive macrosegregation  >1 remelting

6. Model 2 for directional alloy solidification Energy conservation Species conservation Phase diagram relation Momentum conservation Mass conservation Convective term causing macrosegregation Lorentz – force vector [2] Poirier et al. Met. Trans. B. 22 889-900 (1991) For ternary systems: Plain liquidus surface for primary solidification with isothermal binary valleys

7. Time dependent magnetic fields Lorentz-force: Taylor number : Lorentz-force: Taylor number : Rotating Magnetic Field [3]: Principal action of the Lorentz-force generated by a magnetic field rotating around the axis of a cylindrical melt volume Secondary flows in meridonal plane occur on bottom and top in a finite cylinder geometry Lorentz-force [3] B. Fischer et al., Proc. EPM 2000, 497-502 (2000) Flow field (r: azimuthal, l: meridonal)

8. Time dependent magnetic fields Traveling Magnetic Field [4]: A single axisymmetric harmonic magnetic wave traveling in z direction Lorentz-force r z BrBr BzBz t t+  t [4] K. Mazuruk, Adv. Space Res. 29,4,541-548 (2002) Lorentz –force: Taylor number: Lorentz –force: Taylor number: r z Flow field with f l pointing downward

9. Directional solidification of AlSi7 applying RMF Symmetry axis Mushy zone Azimuthal flow Streamlines for meridonal flow Mixture concentration Liquid fraction Channel formation Experimental result from DLR, Cologne B 0 =2mT v g =0.1mm/s, G l =4K/mm V max = 3.2x10 -4 m/s C mix =8.28wt.% B 0 =2mT v g =0.1mm/s, G l =4K/mm V max = 3.2x10 -4 m/s C mix =8.28wt.% T e =850K Hainke, Friedrich, Müller; J. Mat. Sci., 2004

10. RMF applied to the solidification of a ternary alloy Comparison between the macrosegregation caused by the forced fluid flow for a binary (AlSi7) and a ternary (AlSi7Mg0.6) Aluminum alloy. Extension of mushy zone AlSi7: 37 K AlSi7Mg0.6: 60 K

11. Comparison of the macrosegregation due to TMF and RMF for AlSi7 Resulting macrosegregation for RMF or TMF applied to the solidification of a binary AlSi7 alloy. Left part: stream function; right part: liquid fraction (d  =0.05). The arrow indicates the direction of the Lorentz-force. Dagner, Hainke, Friedrich, Müller; EPM, 2003

12. Conclusions Depending on field configuration and strength, macrosegregation is observed in calculations and experiment even in small samples for AlSi7 and AlSi7Mg0.6 Alloys The differences in the resulting macrosegregation between AlSi7 and AlSi7Mg0.6 within the used model are negligible. Thus AlSi7Mg0.6 can be treated as a binary mixture The calculations suggested that using TMF will lead to a more pronounced effect than in the case of RMF When TMF is used, the direction of the Lorentz-force represents a additional process parameter influencing macrosegregation

13. Acknowledgements Prof. Dr. L. Ratke and S. Steinbach (Institute for Space Simulation, DLR, Cologne) for the experimental results obtained with the ARTEMIS and the ARTEX facilities. This work was financially supported by the DLR under contract no. 50WM0042 and by ESA under contract no. 14347/00/NL/SH within the framework of the European research project MICAST (ESA MAP AO-99-031). http://www.cgl-erlangen.com