A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification

Abstract

A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during solidification of binary alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar frontas opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity (V T ) vs temperature gradient (G) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional solidification experiments involving Al-Si alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites.

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

“…[105][106][107] Martorano et al examined the viability of a CET criterion based on the arrest of columnar solidification by the solute field of growing equiaxed grains ahead (so-called 'soft-blocking'). 108) This was compared to the classical mechanical blocking criterion, in which equiaxed grains ahead of a columnar front physically impede its progress.…”

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

“…Moreover, this is not simply an academic problem. As pointed out be Rebow & Browne [25], the stability constant is an intrinsic part of many alloy solidification models, including cellular automaton [26,27], front-tracking [28] and one-domain multiphase models of both the volume [29,30] and ensemble [31] averaging types. In general such models have tended to use (either explicitly or implicitly) the analytical value of σ * as given by marginal stability theory, although in principal other values, either calculated or experimentally estimated [25], could also be used.…”

Transient growth and interaction of equiaxed dendrites

“…An attempt has been made to model the interactions between dendrites in an average sense, by basing the supercooling that drives dendritic growth on the time-varying average temperature (or solute concentration) in the ''extradendritic'' liquid between the grains [12]. This and similar approaches in modeling of the interactions between dendrites have resulted in many interesting predictions of the grain structure in castings [12][13][14]. However, averaged models are not well validated and many open questions remain regarding transient growth of multiple dendrites, including the nature of the thermal field between the dendrites and the tip operating state selection for a non-constant tip velocity.…”