Equiaxed Grain Count in Aluminum Alloy Castings: Theoretical Background and Experimental Verification
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INTRODUCTION
A large number of structural alloys used in practice, such as steel, aluminum-silicon, aluminum-copper, nickel, and copper base alloys, exhibit as the final product of solidification a fully dendritic morphology. Figure 1 shows computer simulations of dendritic structures for the solidification process in single-phase alloys. In the solidified structure, grain size in single-phase alloys is one of the most important factors in determining the quality of the cast alloy. In general, a small equiaxed grain structure is preferred as it promotes increasing resistance to hot tearing and mass feeding. In addition it improves both alloy strength and ductility. Another contributing factor of vital importance is the overall increase in the homogeneity of an equiaxed grain structure. As a result, these castings exhibit reduced segregation combined with a highly uniform distribution of any casting defect such as porosity as well as an improved response to heat treating. Grain refinement of aluminum and Al alloys is common practice in the industry. This field has been extensively investigated by numerous workers for over 50 years, not only to develop efficient grain refiners but also to achieve a clear understanding of the grain refinement mechanisms.[1] In a previous work,[2,3] an analytical model was satisfactorily used for predictions of volumetric densities of eutectic cells in flake or nodular graphite iron. Accordingly, in this work, the proposed model is extended to consider single-phase Al alloys. EDWARD FRAS´ and K. WIENCEK, Professors, M. GO´RNY, Associate Professor, and E. OLEJNIK, Lecturer, are with the Foundry Institute, AGH University of Science and Technology, Mickiewicza 30, Krakow, Poland. HUGO F. LO´PEZ, Professor, is with the Department of Materials Science and Engineering, University of Wisconsin-Milwaukee, P.O. Box 784, Milwaukee, WI 53201. Contact e-mail: [email protected] Manuscript submitted April 15, 2013. Article published online August 22, 2013 5788—VOLUME 44A, DECEMBER 2013
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ANALYTICAL MODEL
The volumetric grain density can be directly related to the nucleation process and there are considerable works published on the role of heterogeneous nucleation sites. From the classical nucleation theory,[3–5] the frequency (Hz/m3) for steady-state nucleation can be established, but not the density of grain nuclei. Thus, quantitative determinations using the classical theory are difficult to make as the nucleation frequency is highly sensitive to the solid–liquid interfacial energy, r, and to the wetting angle, h. In general, highly accurate r values are needed, while h values are usually unknown. It has been long known that the nucleation of a spherical semi-cap model fails at h < 10 deg as the nucleus is less than a monolayer thick. In gray and nodular irons, the density of eutectic cells or graphite nodules is often related to the maximum melt undercooling DTm by empirical expressions of the type.[6–8] N ¼ wðDTm Þk
N¼
3 X
ai ðDTm Þi
½1
½2
i¼0
where W; ai ; k; i ¼ 0; 1; 2; 3; are experimentally
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