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Solidification Processing

Solidification Processing. Ingot Casting. Continuous Casting. Shaped Casting. Directional Casting. Welding & Laser Remelting. Dendritic Array Growth. Temperature Gradient, G . R – Tip Radius. l 2 – Secondary Arm Spacing. Growth Velocity, V . Diffusion + Convection exist in the Melt.

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Solidification Processing

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  1. Solidification Processing IngotCasting Continuous Casting ShapedCasting DirectionalCasting Welding & Laser Remelting

  2. Dendritic Array Growth • Temperature Gradient, G  • R – Tip Radius • l2 – Secondary Arm Spacing • Growth Velocity, V  • Diffusion + Convection exist in the Melt • l1 – Primary Arm Spacing

  3. Modeling Dendritic Array Growth • Experimental modeling: TGS + Transparent Materials Controlled G and V Minimum Convection G/V  Dendrites G/V  Cells • Numerical modeling: Self-consistent model • Single Cell/Dendrite • Cellular/Dendritic Array

  4. Basic Parameters Given : § G s D Materials Properties: C , m , k , D , ( / S), E , 0 L L 4 Solidification Condition: G and V Unknown: § l D R, , T (T ) 1 i Numerical Modeling of Cellular/Dendritic Array Growth(Diffusion Controlled Growth + No Convection concerned)

  5. Numerical Modeling of Cellular/Dendritic Array Growth(Diffusion Controlled Growth + No Convection concerned)

  6. Numerical Method Solute Flow: i+1Ci+1 - iCi = AN(VNC + DdC/dr)Ndt – AS(VSC + DdC/dr)Sdt + AE(VEC + DdC/dx)Edt – Aw(VWC + DdC/dx)wdt :

  7. Spacing Adjustment of Array Growth Mechanism of Spacing Adjustment Lower Limit Upper Limit V Spacing, l1 as Velocity, V

  8. Solute Solute Array Stability Criterion Unstable Stable

  9. Result I: Shapes of Single Cell/Dendrite

  10. Result I: Single Cell Growth in fine capillary tubes 200 mm Stable Cell Perturbed Cell

  11. Result II: Primary Spacing

  12. Result II: Primary Spacing – SCN – 5.6 wt.% H2O System

  13. Result II: Primary Spacing – NH4Cl - 70 wt.% H2O System

  14. 20 mm Result III: Tip Radius The relation, R2V = Constant, is confirmed for all the cases examined in both experimental modeling and numerical modeling.

  15. DT Result IV: Growth Undercooling TL Ti

  16. Result V: The Effect of Temperature Gradient

  17. Modeling Rapid Solidification • Diffusion Coefficient – Temperature Dependent: D as T  • D = D0exp[-Q/(RT)] • Distribution Coefficient – Velocity Dependent: k as V , Aziz (1988) Laser Remelting where • Non-equilibrium vs. Equilibrium: Boettinger etc. (1986) G , V  , DT  

  18. Result VI: Rapid Solidification

  19. Result VII: Global Structure PlanarCellularDendriticCellularPlanar V

  20. Development of Semi-analytical Expressions (Hunt/Lu Model) • Variables: Composition, C0, Liquidus Slop, m, Distribution Coefficient, k, Diffusion Coefficient, D, Gibbs-Thompson Coefficient, G, Surface Energy Anisotropy Coefficient, E4, Growth Velocity, V, Temperature Gradient, G, Primary Spacing, l, and Tip Undercooling, DT. • Dimensionless Parameters: • Temperature Gradient: G’ = GGk/DT02 • Growth Velocity: V’ = VGk/(DDT0) • Primary Spacing: l’ = lDT0/(kG) • Tip Undercooling: DT’ = DT/DT0 where DT0 = mC0(1-1/k) • Properties of the Non-dimensionalization: • G’ = V’: Constitutional Undercooling Limit --- V = GD/DT0 • V’ = 1: Absolute Stability Limit --- V = DT0D/(kG) • DT’ = 1: The undercooling with a planar front growth --- DT = DT0 = mC0(1-1/k)

  21. Result VIII: Semi-analytical Expressions (Hunt/Lu Model) • Cellular Growth (Derived from the Array Stability Criterion): • Undercooling: DT’ = DT’s + DT’r DT’s= G’/V’ + a +(1-a)V’0.45 – G’/V’[a + (1-a)V’0.45] where a = 5.273 x10-3 + 0.5519k – 0.1865k2 DTr’ = b(V’ – G’)0.55(1-V’)1.5 where b = 0.5582 – 0.2267log(k) + 0.2034{log(k)]2 • Cell Spacing: l’1 = 8.18k-0.485V’-0.29(V’ – G’)-0.3DT’s-0.3(1-V’)-1.4 • Dendritic Growth: • Undercooling: DT’ = DT’s + DT’r DT’s = G’/V’ + V’1/3 DT’r = 0.41(V’ – G’)0.51 • Primary Dendrite Spacing (Derived from the Array Stability Criterion): l’1 = 0.156V’(c-0.75)(V’ – G’)0.75G’–0.6028 where c = -1.131 – 0.1555log(G’) – 0.7598 x 10-2[log(G’)]2 * Expressions are developed with the Array Stability Criterion

  22. Experimental Modeling of Grain Formation in Casting

  23. Experimental Modeling: Effect of Deceleration on the Dendritic Array Growth (SCN - 5.5 wt.% H2O System) R Tip Radius, R , Spacing, l1 as Velocity, V l1 Deceleration • Tip Radius, R: Rapid response to velocity change. Every individual dendrite follows the Marginal Stability criterion approximately during deceleration. • Primary Spacing, l1: Slow response to velocity change.The array is unstable and is in transient condition during deceleration.

  24. High Velocity Low Velocity Continuous Deceleration, a = -1.0 mms-2 Experimental Modeling: Effect of Deceleration on the Dendritic Array Growth – Fragmentation (SCN - 5.5 wt.% H2O System) • Secondary Arm, l2, Detached due to deceleration – Accelerated ripening process. The fragmentation rate is proportional to the deceleration.

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