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SCALING LAWS TO ESTIMATE GRAIN SIZE AND COARSENING IN THE STIR ZONE

SCALING LAWS TO ESTIMATE GRAIN SIZE AND COARSENING IN THE STIR ZONE. Karem E. Tello Colorado School of Mines Adrian P. Gerlich Patricio F. Mendez Canadian Centre for Welding and Joining University of Alberta. Canadian Centre for Welding and Joining.

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SCALING LAWS TO ESTIMATE GRAIN SIZE AND COARSENING IN THE STIR ZONE

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  1. SCALING LAWS TO ESTIMATE GRAIN SIZE AND COARSENING IN THE STIR ZONE Karem E. Tello Colorado School of Mines Adrian P. Gerlich Patricio F. Mendez Canadian Centre for Welding and Joining University of Alberta

  2. Canadian Centre for Welding and Joining

  3. Canadian Centre for Welding and Joining

  4. Target Question • Can we predict grain size in the stir zone? • With insight • Quickly • In a general way • Reliably • This involves relating processing to microstructure (and readily to properties) • Test case for scaling laws

  5. V=6 mm/s Tool M5 for all cases

  6. “Boundary layer” approach thin region contains complexity and follows tool geometry “outer region” involves simpler physics sticking boundary condition around the pin, mixed stick and slip under the shoulder Focus on deformation around pin Thin layer surrounding pin (shear layer, “Couette flow”/extrusion) Heat Transfer Deformation Base plate Heat Transfer (preheat from shoulder) Hot deformation behavior ~ZenerHollomon coupled coupled Crawford et al. STWJ 06

  7. “Boundary layer” approach thin region contains complexity and follows tool geometry “outer region” involves simpler physics sticking boundary condition around the pin, mixed stick and slip under the shoulder Focus on deformation around pin Thin layer surrounding pin (shear layer, “Couette flow”/extrusion) Heat Transfer Deformation Base plate Heat Transfer (preheat from shoulder) Hot deformation behavior ~ZenerHollomon coupled coupled

  8. “Boundary layer” approach thin region contains complexity and follows tool geometry “outer region” involves simpler physics sticking boundary condition around the pin, mixed stick and slip under the shoulder Focus on deformation around pin Thin layer surrounding pin (shear layer, “Couette flow”/extrusion) Heat Transfer Deformation Base plate Heat Transfer (preheat from shoulder) Hot deformation behavior ~ZenerHollomon coupled coupled

  9. mechanical energy – stored energy mechanical energy – stored energy – thermal energy into pin

  10. “Slow moving heat source” • isotherms near the pin ≈ circular • “Slow mass input” • deformation around tool has radial symmetry concentric with the tool • “Thin shear layer” • the shear layer sees a flat (not cylindrical) tool • “Heat from shoulder results in small T increase” • The heat of the shoulder is distributed over a wide area Va/a << 1 Va /wad << 1 d/a << 1 Tp-T∞ /Ts-T∞<< 1

  11. constant, right order of magnitude simplification valid simpl. invalid gray zone

  12. Can we use scaling laws instead of experiments to predict grain size?

  13. Calibration of scaling law + C1 C2 Need to calibrate T0 and For region of valid hypotheses C1 = 0.835 C2 = 1.10

  14. Calibration of scaling law

  15. Prediction of grain size

  16. Additional check

  17. V=0.42 mm/s 156 rpm Tool 6.35 mm d=5 mm d=85 mm d=110 mm d=120 mm

  18. Prediction of grain size

  19. Discussion Grain size during stirring vs. coarsening during cooling cycle

  20. Grain size during stirring vs. coarsening during cooling cycle McQuenn 75, 02 During stirring

  21. Grain size during stirring vs. coarsening during cooling cycle

  22. Summary • Simple but accurate expressions for grain size in stir zone • Additional experiment supports calculations • Scaling law for temperature • Very close to experimental measurements • Easy to couple with empirical correlations of grain growth • Scaling law for shear • Close to experimental measurements • Supports Sato’s hypothesis that for 6061/3 alloys final grain growth is mostly due to coarsening

  23. Points outside validity of simplification

  24. Alternative interpretation of coarsening • Coarsening: effect of combined time and temperature • Sato: maximum temperature is dominant • Issues to consider: • Coarsening happens outside the shear layer • Inside the shear layer we have DRX, not static coarsening • Maximum temperature is well inside shear layer

  25. Integrate from here

  26. Goal • Create “textbook” type equations for FSW: Discover Scaling Laws • e.g. Christensen’s and Rosenthal’s solutions • approximate • use only parameters known a priori • good for process design, control, robotics (fast calculations) • good for analysis of outliers and to extrapolate across alloys • good for reverse problem • good for summarizing massive amounts of data • good for meta-models • insightful (explicit variable dependences)

  27. Simplified Model of Shear Layer hot and deformed shear layer shear force from tool ∞ ∞ semi-infinite substrate ∞ Schmidt, Acta Mat. 06 d x

  28. Coupling in Shear Layer thickness of shear layer determined by To: “minimum temperature for significant shearing” heat is dissipated away in the substrate Decay in velocity is in a distance of the order of the heat penetration. Shear thinning models: decay in velocity is in smaller distance than heat penetration heat is generated by plastic deformation in the shear layer

  29. Scaling Analysis • 4 equations, 4 unknowns • Equations • shear layer, heat conduction • shear layer, heat generation • constitutive law • base plate, heat conduction • Unknowns • shear layer thickness • temperature jump inside shear layer • frictional heat generated • flow shear stress

  30. Heat Transfer in Shear Layer 1D conservation of energy, steady state conduction heat transfer volumetric heat generation little heat lost to tool T0 : matching parameter

  31. Heat Transfer in Shear Layer normalization of variables normalization of energy equation charact value OM(1) scaling equation 1 equation 3 unknowns 1

  32. Heat Generation in Shear Layer substrate shear layer force equilibrium (near pin) inertial forces are small relative to flow stress t t heat generation t t

  33. Heat Generation in Shear Layer a w • no slip condition at pin / substrate interface • (potential slip at shoulder!) • Schmidt, Modelling Simul. Mater. Sci. Eng. 2004 • when tool comes out has aluminum stuck on it • threads and texture help move the metal around • most wear happens during plunging normalization of heat generation scaling equation 2 equations 4 unknowns velocity decreases with temperature 2 d x shear layer

  34. Constitutive Law in Shear Layer extrapolated values limit of empirical data Al 6061

  35. Constitutive Law in Shear Layer 3 equations 4 unknowns not a power law

  36. Constitutive Law in Shear Layer “no shearing” shearing two regimes for Arrhenius-type function linearized constitutive law B 3 3 equations 4 unknowns

  37. Heat Transfer in Base Plate • Line heat source on a plate • Low Pe: isotherms ≈ circular • Could be many other temperature distributions 4 equations! 4 unknowns 4

  38. System of 4 equations with 4 unknowns d, t, DTs, qc Equations 1 3 = 2 4

  39. Solutions • Have the form of power-laws • Use only tabulated parameters • no need to measure torque or temperatures • involve no empirical factors

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