Abstract
In the present work, we developed an analytical model to describe the effect of pouring temperature on the crystallite density, remelting, growth kinetics, and the resultant final grain size for aluminum (Al)-based alloys synthesized using gravity casting. The model predicts that there are three regimes of pouring temperature/grain size-related behavior: (i) at low superheats, grain size is small and relatively constant; (ii) at intermediate levels of superheat, there appears to be a transitional behavior where grain size increases in a rapid, non-linear fashion; and (iii) at high superheats, grain size increases linearly with increasing temperature. This general pattern is expected to be shifted upward as distance from the bottom of the casting increases, which is likely a result of the slower cooling rates and/or longer solidification times with increasing distance from the bottom of the casting. To validate the model, a set of experiments has been conducted using Al-Cu and Al-Si alloys (i.e., Al-3.0 wt pct Cu, Al-4.5 wt pct Cu, and Al-A356.2 alloys), and the experimental measurements showed consistent results with theoretical predictions.
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Abbreviations
- \( a \) :
-
rate of change of dendrite arm spacing with square root of time
- \( A_{\text{sf}} \) :
-
instantaneous area of solidification front
- \( \bar{A}_{\text{sf}} \) :
-
time averaged area of the solidification front
- \( C \) :
-
proportionality constant in Gaussian distribution
- \( d \) :
-
dendrite arm spacing
- \( D \) :
-
grain or crystallite Diameter
- \( \left( {\Delta D/\Delta t} \right)_{\text{average}} \) :
-
average crystallite growth rate
- \( \left( {\Delta D/\Delta T_{\text{super}} } \right)_{\text{average}} \) :
-
average crystallite growth rate due to superheat
- \( D\left( h \right) \) :
-
grain diameter at height \( h \)
- \( D_{H} \left( h \right) \) :
-
maximum grain diameter that can be achieved at height \( h \) by crystallite remelting
- \( D_{{{\text{liq}}_{L} }} \left( h \right) \) :
-
grain diameter at height h for casting where \( T_{\text{pour}} \) = \( T_{\text{liq}} \)
- \( D_{\text{remelt}} \left( h \right) \) :
-
grain diameter at height h that results from remelting of small crystallites, but excludes any crystallite growth
- \( f_{\text{free}} \) :
-
instantaneous frequency at which free dendrites are generated
- \( \bar{f}_{\text{free}} \) :
-
average frequency at which free dendrites are generated
- h :
-
height from bottom of cylindrical casting
- K :
-
proportionality constant
- m(h):
-
change in grain size with change in superheat at height h in the high superheat regime
- \( n_{{ \ne_{\text{free}} }} \) :
-
total no. of free dendrites generated
- \( \Delta n_{{ \ne_{\text{free}} }} \) :
-
change in the total no. of free dendrites
- \( n_{ \ne } \left( S \right) \) :
-
number of free dendrites of size S
- \( n_{ \ne } \left( {S_{ \hbox{max} } } \right) \) :
-
number of free dendrites of size \( S_{ \hbox{max} } \)
- \( n_{{ \ne {\text{free}}_{\text{total}} }} \) :
-
total no. of free dendrites generated
- S :
-
size of free dendrite
- \( \bar{S} \) :
-
average size of free dendrites
- \( S_{ \hbox{max} } \) :
-
maximum size of a free dendrite that can melt at a given superheat (i.e., all larger sizes are stable)
- \( S_{\text{w}} \) :
-
size width parameter (governs the range of sizes over which transition occurs)
- \( t_{\text{columnar}} \) :
-
time at which solidification of the columnar region of the casting is complete
- \( t_{\text{growth}} \left( h \right) \) :
-
time available for growth of free dendrites into grains at height h
- \( t_{\text{solidification}} \) :
-
solidification time
- \( \Delta t \) :
-
elapsed time
- \( \Delta T \) :
-
change of temperature
- \( \left( {\Delta T/\Delta t} \right)_{\text{average}} \) :
-
average cooling rate
- \( T_{\text{liq}} \) :
-
liquidus temperature of the alloy
- \( T_{\text{pour}} \) :
-
pouring temperature of the casting
- \( T_{\text{solidus}} \) :
-
solidus temperature of the alloy
- \( T_{\text{super}} \) :
-
superheat, (\( T_{\text{pour}} \) − \( T_{\text{liq}} \))
- \( T_{\text{super}}^{*} \left( h \right) \) :
-
critical superheat at height h
- \( T_{\text{w}} \) :
-
temperature width parameter (governs the range of superheats over which transition occurs)
- \( V_{\text{columnar}} \) :
-
volume of the solidified casting occupied by columnar-shaped grains
- \( V_{\text{equiaxed}} \) :
-
volume of the solidified casting occupied by equiaxed grains
- \( V_{\text{liquid}} \) :
-
volume of liquid and free dendrites in the casting
- \( V_{\text{total}} \) :
-
total volume of the casting
- \( \rho /\rho_{\text{o}} \) :
-
ratio of crystallite density at a given superheat to the crystallite density without superheat
- \( \rho_{{A_{ \ne } }} \) :
-
areal density of dendrites
- \( \rho_{{ \ne_{\text{free}} }} \) :
-
density of free dendrites in the liquid portion of casting during solidification
- \( \rho_{{ \ne_{\text{free}} { \hbox{max} }}} \) :
-
maximum density of free dendrites in the liquid portion of casting during solidification
- \( \rho_{{ \ne_{\text{free}} {\text{remelt}}}} \) :
-
density of free dendrites in the liquid portion of casting during solidification that will remelt
- \( \rho_{{ \ne_{\text{free}} {\text{stable}}}} \) :
-
density of stable (i.e., immune to remelting) free dendrites in the liquid portion of casting during solidification
- \( \rho_{{ \ne_{\text{free}} {\text{total}}}} \) :
-
density of all free dendrites ever generated in the liquid portion of casting during solidification
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Acknowledgments
This material is based upon work supported by the U.S. Army Research Laboratory under Cooperative Agreement No. W911NF-08-2-0014. The views, opinions, and conclusions made in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
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Manuscript submitted October 29, 2013.
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Ferguson, J.B., Tabandeh-Khorshid, M., Mantas, J.C. et al. Predicting the Effect of Pouring Temperature on the Crystallite Density, Remelting, and Crystal Growth Kinetics in the Solidification of Aluminum Alloys. Metall Mater Trans B 45, 1407–1417 (2014). https://doi.org/10.1007/s11663-014-0044-9
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DOI: https://doi.org/10.1007/s11663-014-0044-9