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Simulation of Macrosegregation and Shrinkage Cavity in an Al-4.5 Wt Pct Cu Ingot Using a Four-Phase Model

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Abstract

A four-phase dendritic solidification model is employed to calculate the formation of macrosegregation, as-cast structure, and shrinkage cavity of Al-4.5 wt pct Cu ingot. This model couples phenomena of thermal–solutal buoyancy, crystals sedimentation, shrinkage formation, heat transfer, nucleation and growth of equiaxed grains, and columnar-to-equiaxed transition. An additional air phase is introduced to feed the shrinkage cavity during the solidification. A laboratory scale ingot with Al-4.5 wt pct Cu is fabricated for the verification of the numerical simulation results. The predicted macrosegregation, characteristics of shrinkage cavity, and as-cast structure have a good agreement with the corresponding experimental results. Furthermore, various initial mold temperatures are investigated using this numerical model. It indicates that the initial mold temperature plays an important role in the macrosegregation formation by changing the solidification sequence. The higher the initial mold temperature is, the severer the macrosegregation that will occur. Meanwhile, the higher initial mold temperature is beneficial for the growth of equiaxed grains, which results in the final as-cast structures and an increased depth of shrinkage cavity.

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Abbreviations

c 0 :

Initial concentration (wt pct)

ρ l, ρ s, ρ c, ρ a :

Density (kg m−3)

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)

\( \overrightarrow {{{{g}}_{{{l}}} }} ,\;\overrightarrow {{{{g}}_{{{s}}} }} ,\;\overrightarrow {{{{g}}_{{{a}}} }} \) :

Reduced gravity (m s−2)

H*, \( H_{\text{la}}^{*} ,\;H_{\text{sa}}^{*} ,\;H_{\text{ca}}^{*} \) :

Volume heat-transfer coefficient (W m−3 K−1)

Δh f :

Latent heat (J kg−1)

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

Thermal conductivity (W m−1 K−1)

m :

Slope of the liquidus in phase diagram (K)

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 (k s−1)

\( \overrightarrow {{{{u}}_{{{l}}} }} ,\;\overrightarrow {{{{u}}_{{{s}}} }} ,\;\overrightarrow {{{{u}}_{{{a}}} }} \) :

Velocity (m s−1)

v Rc :

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

v tip :

Dendrite tip velocity (m s−1)

Γenv :

Envelope transfer rate (kg m−3 s−1)

β T :

Thermal expansion coefficient (k−1)

β c :

Solutal expansion coefficient (wt pct−1)

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 K−1)

d s, d env :

Diameter of solid and envelope (m)

G :

Temperature gradient (K m−1)

H :

Heat-transfer coefficient (W m−2 K−1)

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

Enthalpy (J kg−1)

k :

Solute partitioning coefficient (1)

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 (K)

μ l :

Viscosity (kg m−1 s−1)

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 (1)

λ 1 :

Primary dendrite arm spacing (m)

λ 2 :

Secondary dendrite arm spacing (m)

n max :

Maximum equiaxed grain density (m−3)

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 R&D Program of China (Grant No. 2017YFB0305301), the Joint Funds of the National Natural Science Foundation of China (Grant No. U1660203), the National Natural Science Foundation of China (Grant Nos. 51404152 and 51774201), and the Shanghai Pujiang Program (Grant No. 14PJ1404800).

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Authors and Affiliations

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

    Fengli Ren, Duanxing Cai, Jun Li, Qiaodan Hu, Mingxu Xia & Jianguo Li

  2. Institute of Laser Advanced Manufacturing, Zhejiang University of Technology, Hangzhou, 310014, China

    Honghao Ge

  3. Department of Engineering, University of Leicester, Leicester, LE1 7RH, UK

    Jun Li

  4. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jianguo Li

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  1. Fengli Ren
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  2. Honghao Ge
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Correspondence to Jun Li.

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Manuscript submitted January 15, 2018.

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Ren, F., Ge, H., Cai, D. et al. Simulation of Macrosegregation and Shrinkage Cavity in an Al-4.5 Wt Pct Cu Ingot Using a Four-Phase Model. Metall Mater Trans A 49, 6243–6254 (2018). https://doi.org/10.1007/s11661-018-4892-9

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  • DOI: https://doi.org/10.1007/s11661-018-4892-9

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