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



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.



dendrite growth coefficient


polynomial coefficient


polynomial coefficient


polynomial coefficient


specific heat for a control volume


specific heat for liquid


specific heat for solid


specific-heat capacity


diameter of ingot


volume fraction of a control volume




solid fraction


height of the ingot


equiaxed index


grid coordinate


grid coordinate


thermal conductivity


thermal conductivity of a control volume


derivative gain


integral gain


thermal conductivity of liquid


proportional gain


thermal conductivity of solid


latent heat


dendrite growth law exponent


number of columns in a grid


number of rows in a grid


general polynomial value


growth restriction


heat flux at the chill surface


heat flux at the free liquid surface


Laplace coordinate




eutectic temperature


initial temperature


liquidus temperature


melting temperature of solvent material


time coordinate


cutoff time for heat loss


undercooled bulk liquid


control volume size


volume of mush in a control volume


dendrite growth velocity




nucleation undercooling




grid spacing


grid spacing




first-order lag constant


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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

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