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Four-Phase Dendritic Model for the Prediction of Macrosegregation, Shrinkage Cavity, and Porosity in a 55-Ton Ingot

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Abstract

A four-phase dendritic model was developed to predict the macrosegregation, shrinkage cavity, and porosity during solidification. In this four-phase dendritic model, some important factors, including dendritic structure for equiaxed crystals, melt convection, crystals sedimentation, nucleation, growth, and shrinkage of solidified phases, were taken into consideration. Furthermore, in this four-phase dendritic model, a modified shrinkage criterion was established to predict shrinkage porosity (microporosity) of a 55-ton industrial Fe-3.3 wt pct C ingot. The predicted macrosegregation pattern and shrinkage cavity shape are in a good agreement with experimental results. The shrinkage cavity has a significant effect on the formation of positive segregation in hot top region, which generally forms during the last stage of ingot casting. The dendritic equiaxed grains also play an important role on the formation of A-segregation. A three-dimensional laminar structure of A-segregation in industrial ingot was, for the first time, predicted by using a 3D case simulation.

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Abbreviations

c 0 :

Initial concentration (wt pct)

c ref :

Reference concentration (wt pct)

C ls, C lc :

Species exchange (kg m−3 s−1)

D l :

Diffusion coefficient (m2 s−1)

f l, f s, f env, f c, f a :

Volume fraction (1)

\( \overrightarrow {{g_{\text{l}} }} , \overrightarrow {{g_{\text{s}} }} , \overrightarrow {{g_{\text{a}} }} \) :

Reduced gravity (m s−2)

H* :

Volume heat transfer coeff. (W m−3 °C−1)

Δh f :

Latent heat (J kg−1)

k l, k s, k c, k a :

Thermal conductivity (W m−1 °C−1)

m :

Slope of the liquidus in phase diagram (°C)

n :

Grain number density (m−3)

Q ls, Q lc, Q la, Q cs, Q ca, Q sa :

Energy transfer (J m−3 s−1)

S env :

Surface area concentration of envelope (m−1)

\( \dot{T} \) :

Cooling rate ( C s−1)

\( \overrightarrow {{u_{\text{l}} }} , \overrightarrow {{u_{\text{s}} }} , \overrightarrow {{u_{\text{a}} }} \) :

Velocity (m s−1)

v Rc :

Columnar growth speed in radius direction (m s−1)

v tip :

Dendrite tip velocity (m s−1)

\( \Upgamma_{\text{env}} \) :

Envelope transfer rate (kg m−3 s−1)

ρ l, ρ s, ρ c, ρ a :

Density (kg m−3)

c l, c s, c c :

Species concentration (wt pct)

c mix :

Mix concentration (wt pct)

c p, c p_a :

Specific heat (J kg−1 °C−1)

d s, d env :

Diameter of solid and envelop (m)

G :

Temperature gradient (°C m−1)

H :

Heat transfer coefficient (W m−2 °C−1)

h l, h s, h c, h a :

Enthalpy (J kg−1)

k :

Solute partitioning coeff. (l)

M ls, M lc :

Net mass transfer rate (kg m−3 s−1)

N e :

Grain production rate by nucleation (m−3 s−1)

p :

Pressure (N m−2)

S s :

Surface area concentration of solid phase (m−1)

T :

Temperature (°C)

t :

Time (s)

U ls, U lc, U la, U cs, U ca, U sa :

Momentum exchange rate (kg m−2 s−2)

v Rs :

Solid phase growth speed (m s−1)

β :

Solidification shrinkage (l)

λ 1 :

Columnar grain space (m)

μ l :

Viscosity (kg m−1 s−1)

l:

Liquid phase (melt)

env:

Grain envelope

a:

Air phase

s:

Solid phase (solid skeleton)

c:

Columnar phase

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Acknowledgments

This work is sponsored by the National Key Research and Development Plan (No. 2016YFB0701204), National Natural Science Foundation of China (Grant Nos. 51404152, 51171115, 51305216), Shanghai Pujiang Program (Grant No. 14PJ1404800), Shanghai International Cooperation Project (Grant No. 14140711000), and National Basic Research Program of China under contract No. 2011CB012900, Joint Funds of the National Natural Science Foundation of China (No. U1660203). The authors H. Ge and J. Li would like to thank Dr. Jiehua Li from the University of Leoben, Leoben, Austria for discussion on the current manuscript.

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Authors and Affiliations

  1. School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China

    Honghao Ge, Fengli Ren, Jun Li, Xiujun Han, Mingxu Xia & Jianguo Li

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  1. Honghao Ge
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Correspondence to Jun Li.

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Manuscript submitted May 24, 2016.

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Ge, H., Ren, F., Li, J. et al. Four-Phase Dendritic Model for the Prediction of Macrosegregation, Shrinkage Cavity, and Porosity in a 55-Ton Ingot. Metall Mater Trans A 48, 1139–1150 (2017). https://doi.org/10.1007/s11661-016-3910-z

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