Metallurgical and Materials Transactions A

, Volume 30, Issue 8, pp 2147–2158 | Cite as

Mathematical modeling of microstructural development in hypoeutectic cast iron

  • D. Maijer
  • S. L. Cockcroft
  • W. Patt
Article
Received:

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.

Keywords

Austenite Material Transaction Cast Iron Gray Iron White Iron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Table of Symbols

A

nucleation coefficient (m−3 K−2)

pct C, Si, and P

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

CL

liquid composition (wt pct)

C0

initial liquid composition (wt pct)

Cp

specific heat (J kg−1 K−1)

fcond

fraction of gap heat transfer via conduction

flim

fraction limit of gap heat transfer via conduction

fs

volume fraction transformed

fs

rate of solidification (s−1)

hconv

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

heff

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

hcond

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

hrad

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)

TL

liquidus temperature (°C)

Teut

graphite eutectic temperature (°C)

Tcarb

iron carbide eutectic temperature (°C)

Tcast

temperature of the casting surface (°C)

Tmold

temperature of the mold surface (°C)

Tsurf and T∞

surface and ambient temperature (°C)

ΔT

liquid undercooling (K)

t

time (S)

tcast

casting time (S)

V

growth velocity (m s−1)

Greek Symbols

εeff

effective radiation emissivity

εcast and εmold

emissivity of cast and mold

øe

total extended volume fraction

øe,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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Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 1999

Authors and Affiliations

  • D. Maijer
    • 1
  • S. L. Cockcroft
    • 1
  • W. Patt
    • 2
  1. 1.the Department of Metals and Materials EngineeringUniversity of British ColumbiaVancouverCanada
  2. 2.Walzen Irle GmbHNetphen-DeuzGermany

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