Metallurgical and Materials Transactions A

, Volume 40, Issue 3, pp 662–672

A Comparison of Columnar-to-Equiaxed Transition Prediction Methods Using Simulation of the Growing Columnar Front

Article

DOI: 10.1007/s11661-008-9708-x

Cite this article as:
McFadden, S., Browne, D. & Gandin, C. Metall and Mat Trans A (2009) 40: 662. doi:10.1007/s11661-008-9708-x

Abstract

In this article, the columnar-to-equiaxed transition (CET) in directionally solidified castings is investigated. Three CET prediction methods from the literature that use a simulation of the growing columnar front are compared to the experimental results, for a range of Al-Si alloys: Al-3 wt pct Si, Al-7 wt pct Si, and Al-11 wt pct Si. The three CET prediction methods are the constrained-to-unconstrained criterion, the critical cooling rate criterion, and the equiaxed index criterion. These methods are termed indirect methods, because no information is required for modeling the equiaxed nucleation and growth; only the columnar solidification is modeled. A two-dimensional (2-D) front-tracking model of columnar growth is used to compare each criterion applied to each alloy. The constrained-to-unconstrained criterion and a peak equiaxed index criterion agree well with each other and some agreement is found with the experimental findings. For the critical cooling rate criterion, a minimum value for the cooling rate (between 0.07 and 0.11 K/s) is found to occur close to the CET position. However, this range of values differs from those cited in the literature (0.15 to 0.16 K/s), leading to a considerable difference in the prediction of the CET positions. A reason for this discrepancy is suggested, based on the fundamental differences in the modeling approaches.

Nomenclature

A

dendrite growth coefficient

a0

polynomial coefficient

a1

polynomial coefficient

a2

polynomial coefficient

CCV

specific heat for a control volume

CL

specific heat for liquid

CS

specific heat for solid

cp

specific-heat capacity

D

diameter of ingot

d

volume fraction of a control volume

e

error

gs

solid fraction

H

height of the ingot

I

equiaxed index

i

grid coordinate

j

grid coordinate

K

thermal conductivity

KCV

thermal conductivity of a control volume

KD

derivative gain

KI

integral gain

KL

thermal conductivity of liquid

KP

proportional gain

KS

thermal conductivity of solid

L

latent heat

n

dendrite growth law exponent

ncols

number of columns in a grid

nrows

number of rows in a grid

P

general polynomial value

Q

growth restriction

q

heat flux at the chill surface

qloss

heat flux at the free liquid surface

s

Laplace coordinate

T

temperature

TE

eutectic temperature

Tinit

initial temperature

TL

liquidus temperature

TM

melting temperature of solvent material

t

time coordinate

tq

cutoff time for heat loss

Ub

undercooled bulk liquid

VCV

control volume size

Vm

volume of mush in a control volume

vt

dendrite growth velocity

ΔT

undercooling

ΔTn

nucleation undercooling

Δt

time-step

Δx

grid spacing

Δy

grid spacing

ρ

density

τ

first-order lag constant

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2009

Authors and Affiliations

  1. 1.School of Electrical, Electronic, and Mechanical EngineeringUniversity College DublinDublin 4Ireland
  2. 2.CEMEF - UMR CNRS 7635MINES ParisTechSophia AntipolisFrance