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The growth restriction factor is a parameter derived from binary phase diagrams and is a useful predictor for the grain refining response when a solute is added to a base alloy. This work investigates the relevance of growth restriction theory to titanium alloys where solidification rates are an order of magnitude faster than previous studies in aluminumand magnesium-based systems. In particular, the segregation of Fe and Cr in titanium is investigated and the effects on grain size studied. It was found that the Scheil equation reasonably modeled solidification of titanium where cooling rates approach 120
C/s, and the growth restriction factors for Fe and Cr were useful in predicting prior-b grain refinement. However, it was found that caution must be used when calculating growth restriction factors from binary phase diagrams.

I. INTRODUCTION

The multiple phase transformations that occur in titanium alloys provide opportunities for designing the microstructure to suit particular applications. It is common to create desirable microstructures by combining heat treatments and mechanical processing at temperatures in the vicinity of the beta transus while the alloy is fully solid.1–5 In contrast, there is relatively little knowledge on manipulating the liquid–solid transformation in titanium alloys to achieve a refined primary grain structure. However, primary grain refinement will improve the homogeneity of the as-cast structure along with a variety of mechanical and in-service properties. Literature on primary grain refinement specific to titanium alloys is scarce. A few early works identified elements that were associated with grain refinement6–8; however, they proposed little in the way of mechanisms, or a theoretical rationale with which to understand or further develop the grain refining process. It is well known that the mechanism of grain refinement requires two components; nuclei and solute.9–12 Potent nuclei activate nucleation at low undercoolings while the solute provides constitutional undercooling allowing activation of adjacent nuclei. The faster a constitutionally undercooled zone develops the sooner further nucleation will occur ahead of an advancing solid–liquid interface and the smaller the resulting grain size. Recently, the following expression was developed to account for the effects of nuclei and solute10,13:

a)

Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0173 J. Mater. Res., Vol. 24, No. 4, Apr 2009

http://journals.cambridge.org

Downloaded: 19 Mar 2015

1 b1 DTn ffiffiffiffiffiffi þ d¼p 3 Q r:f

;

ð1Þ

where d is grain size, r is the volume density of nucleant particles, f is the faction of these particles that are activated, b1 is a constant, DTn is the undercooling necessary to activate nucleation, and Q is the growth restriction factor; defined by mlco(k–1) where ml is the slope of the liquidus, co is the nominal solute composition (wt%) in a binary alloy, and k is the partition coefficient. The first term of Eq. (1) refers to the availability