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Mathematical modeling of microstructural development in hypoeutectic cast iron

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Abstract

A mathematical heat-transfer/microstructural model has been developed to predict the evolution of proeutectic austenite, white iron eutectic, and gray iron eutectic during solidification of hypoeutectic cast iron, based on the commercial finite-element code ABAQUS. Specialized routines which employ relationships describing nucleation and growth of equiaxed primary austenite, gray iron eutectic, and white iron eutectic have been formulated and incorporated into ABAQUS through user-specified subroutines. The relationships used in the model to describe microstructural evolution have been adapted from relationships describing equiaxed growth in the literature. The model has been validated/fine tuned against temperature data collected from a QuiK-Cup sample, which contained a thermocouple embedded approximately in the center of the casting. The phase distribution predicted with the model has been compared to the measured phase distribution inferred from the variation in hardness within the QuiK-Cup sample and from image analysis of photomicrographs of the polished and etched microstructure. Overall, the model results were found to agree well with the measured distribution of the microstructure.

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Abbreviations

A :

nucleation coefficient (m−3 K−2)

pct C, Si, and P:

concentration carbon, silicon, and phosphorus in liquid (wt pct)

C L :

liquid composition (wt pct)

C 0 :

initial liquid composition (wt pct)

C p :

specific heat (J kg−1 K−1)

f cond :

fraction of gap heat transfer via conduction

f lim :

fraction limit of gap heat transfer via conduction

f s :

volume fraction transformed

f s :

rate of solidification (s−1)

h conv :

film coefficient for free convection (W m−2 K−1)

h eff :

effective heat-transfer coefficient (W m−2 K−1)

h cond :

conductive component of h eff (W m−2 K−1)

h rad :

radiative component of h eff (W m−2 K−1)

k :

segregation coefficient, or conductivity (W m−1 K−1)

L :

volumetric latent heat (J m−3)

N :

number of grains per unit volume (m−3)

Q :

volumetric heat-source term (W m−3)

q″:

heat flux (W m−2)

R :

grain radius (m)

T :

temperature (°C)

T L :

liquidus temperature (°C)

T eut :

graphite eutectic temperature (°C)

T carb :

iron carbide eutectic temperature (°C)

T cast :

temperature of the casting surface (°C)

T mold :

temperature of the mold surface (°C)

T surf and T ∞ :

surface and ambient temperature (°C)

ΔT :

liquid undercooling (K)

t :

time (S)

t cast :

casting time (S)

V :

growth velocity (m s−1)

ε eff :

effective radiation emissivity

ε cast and ε mold :

emissivity of cast and mold

ø e :

total extended volume fraction

ø e,j :

extended volume fraction of phase j

μ :

growth coefficient

ρ :

density (Kg m−3)

σ :

Stefan-Boltzmann constant (5.6696(10)−8) (W m−2 K−4)

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Authors and Affiliations

  1. the Department of Metals and Materials Engineering, University of British Columbia, V6T 1Z4, Vancouver, BC, Canada

    D. Maijer (Research Associate) & S. L. Cockcroft (Associate Professor)

  2. Walzen Irle GmbH, D-57244, Netphen-Deuz, Germany

    W. Patt (Managing Director)

Authors
  1. D. Maijer
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  2. S. L. Cockcroft
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  3. W. Patt
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Maijer, D., Cockcroft, S.L. & Patt, W. Mathematical modeling of microstructural development in hypoeutectic cast iron. Metall Mater Trans A 30, 2147–2158 (1999). https://doi.org/10.1007/s11661-999-0026-8

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  • DOI: https://doi.org/10.1007/s11661-999-0026-8

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