Modeling of grain refinement: Part I. Effect of the solute titanium for aluminum
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S.D. McDonald and A.K. Dahle CRC Centre for Metals Manufacturing (CAST) Cooperative Research Centre, University of Queensland, Brisbane, 4072 QLD, Australia
C.J. Davidson Commonwealth Scientific and Industrial Research Organization (CSIRO)—Manufacturing & Infrastructure Technology, Kenmore, 4069 QLD, Australia
D.H. StJohn CRC Centre for Metals Manufacturing (CAST) Cooperative Research Centre, University of Queensland, Brisbane, 4072 QLD, Australia (Received 22 November 2007; accepted 10 January 2008)
Over the past few decades, the grain refinement of Al alloys has been extensively investigated theoretically and experimentally. However, the relative importance of the parameters that contribute to grain refinement still remains unclear and is likely to be dependent on specific solidification conditions. This paper aims to investigate the mechanisms by which Ti, a common grain-refining addition in commercial-purity aluminum (CP), contributes to grain refinement using a cellular automaton—finite control volume method (CAFVM). CAFVM is used to model the grain formation and microstructure morphology under different conditions, e.g., with and without refiners, for Al alloys. In this Part I, the effect of adding solute of Ti on grain formation through its effect on growth restriction, constitutional undercooling, and the formation of extra-potential particles are taken into account in the calculations. It is shown that the calculated results are in reasonable agreement with the experimental data. I. INTRODUCTION
Grain refinement of aluminum alloys has been extensively practiced in industry to improve the mechanical properties and castability of aluminum alloys.1 The additions of grain refiners, usually master alloys containing potential nucleant particles, promote the formation of a fine equiaxed structure by suppressing the growth of columnar grains. The fine equiaxed structure of castings reduces the size of defects such as microporosity and second-phase particles2 and improves feeding and the resistance to hot tearing.3 There is great interest in the quantitative prediction of solidification microstructure in general and grain size in particular, and numerous models have been developed. Maxwell and Hellawell4 developed an empirical model to consider the growth of spherical crystal restricted by the partitioning of a single solute and presented the concept of a growth-restriction factor (GRF). To a good approximation, the growth rate for a given undercooling a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0153 1282 J. Mater. Res., Vol. 23, No. 5, May 2008 http://journals.cambridge.org Downloaded: 18 Mar 2015
is inversely proportional to the growth-restriction factor. This model has been shown to be valid for specific conditions and has formed the basis of subsequent work. It is limited by its neglect of important variables such as nucleant characteristics and its inability to deal with the presence of multiple solute elements. Desnain et al.5 extended the Maxwell–Hellawel
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