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Numerical Simulation of Solidification and Prediction of Mechanical Properties in Magnesium Alloy Casting

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Abstract

In this paper, a volume-averaged numerical formulation combined with experimentally derived correlations is used to predict the local cooling rate, grain size (GS), and yield strength of a wedge-shaped magnesium casting. The predicted cooling rates and experimental correlations are used to predict the local GS. To predict the average yield strength, the GS and thickness of the skin and core regions are taken into account. Results are shown to be in good accordance with previously reported experimental data.

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Abbreviations

a :

Active coefficient in discretized equation

A :

Area, m2

b :

Body force

\( C_{{{\text{p}}_{k} }} \) :

Specific heat of constituent k, J/Kg k

d :

Grain size in Hall–Petch equation

f k :

Volume fraction of constituent k

\( \vec{g} \) :

Gravity vector

h k :

Sensible enthalpy of constituent k

k :

Hall–Petch slope on a plot of true stress, σ, vs d 1/2

k k :

Thermal conductivity of constituent k, W/m K

k P :

Partition coefficient

L ls :

Latent heat of fusion, kJ/kg

m :

Iteration number

\( \dot{m} \) :

Mass flux, kg/s

\( \hat{n} \) :

Unit normal vector

P k :

Pressure

R :

Cooling rate

t :

Time, s

t s :

Local solidification time, s

T ref :

Reference temperature, K (°C)

T k :

Temperature of constituent, K (°C)

T mlt :

Melting temperature of alloy, K (°C)

T sol :

Solidus temperature of alloy, K (°C)

T Eut :

Eutectic temperature of alloy, K (°C)

T liq :

Liquidus temperature of alloy, K (°C)

\( \hat{\vec{v}} \) :

Advecting velocity, m/s

V k :

Volume of constituent in REV

V :

Volume of REV

\( \vec{x} \) :

Position vector

〈〉:

Denotes extrinsic volume average

〈〉k :

Denotes intrinsic volume average with respect to constituent k

β :

Volumetric thermal expansion, k−1

μ :

Dynamic viscosity, kg/ms

∂ Ω P :

Denotes a surface bounding a control volume

Ω P :

Denotes the dimension of a control volume

δ t :

Skin thickness fraction

φ k :

Generic field variable for constituent k

σ :

Yield or flow strength

ρ k :

Density of constituent, kg/m3

σ 0 :

Intercept stress

κ :

Morphology factor

k :

K ∈ {l(liquid), s(solid), m(mixture)}

P :

Quantity evaluated at or associated with a particular control volume

ip:

Quantity evaluated at or associated with an integration point

nb:

Quantity evaluated at or associated with a neighboring control volume

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Acknowledgments

The authors would like to thank Meridian Lightweight Technologies Inc. and the AUTO21 Network of Centres of Excellence for funding this project and SHARCNET for facilitating their computational resources.

Author information

Authors and Affiliations

  1. Department of Product Development and Analysis, Wescast Industries Inc., Brantford, ON, N3V 1E7, Canada

    Mehdi Farrokhnejad (CAE Analyst)

  2. Department of Mechanical and Materials Engineering, Western University Canada, London, ON, N6A 5B8, Canada

    Anthony G. Straatman (Professor) & Jeffrey T. Wood (Associate Professor)

Authors
  1. Mehdi Farrokhnejad
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  2. Anthony G. Straatman
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  3. Jeffrey T. Wood
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Corresponding author

Correspondence to Mehdi Farrokhnejad.

Additional information

Manuscript submitted July 25, 2013.

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Farrokhnejad, M., Straatman, A.G. & Wood, J.T. Numerical Simulation of Solidification and Prediction of Mechanical Properties in Magnesium Alloy Casting. Metall Mater Trans B 45, 2357–2369 (2014). https://doi.org/10.1007/s11663-014-0131-y

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