Mechanical Blocking Mechanism for the Columnar to Equiaxed Transition
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I.
INTRODUCTION
IN the as-cast macrostructure of a casting, the transition from columnar to equiaxed grains is called the columnar to equiaxed transition (CET). The CET position determines the amount of columnar and equiaxed grains, which strongly affects the properties of castings. Different mechanisms have been proposed to explain the CET during solidification, but it is generally accepted that it occurs when equiaxed grains block the growth of columnar grains.[1–3] Therefore, mathematical models to predict the position of the CET have usually considered the growth of both columnar and equiaxed grains. One of the first mathematical models to predict the CET was proposed by Hunt,[4] who assumed unidirectional steady-state solidification. In this model, equiaxed grains nucleate at a prescribed nucleation temperature and grow in the constitutionally undercooled zone ahead of the growing columnar front. To determine the CET, Hunt[4] considered that the moving columnar front would be blocked when the volume fraction of equiaxed grains growing ahead was larger than 0.49. This criterion, which was later called the mechanicalblocking criterion,[5] hinges upon the concept that columnar grains would be blocked if they were unable to grow along a distance larger than the equiaxed-grain diameter.[4] Although the 0.49 fraction has never been questioned, it has been adopted in numerous deterministic models to predict the CET.[6–10]
V.B. BISCUOLA, Graduate Student, and M.A. MARTORANO, Professor, are with the Department of Metallurgical and Materials Engineering, University of Sa˜o Paulo, Av. Prof. Mello Moraes, 2463 Sa˜o Paulo-SP, 05508-900, Brazil. Contact email: [email protected] Manuscript submitted on February 26, 2008. Article published online September 11, 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
In the extension of the model of Wang and Beckermann,[8] proposed by Martorano et al.,[5] no criterion was necessary to predict the columnar-front blocking and the CET. In this model, the columnar front was automatically blocked (causing the CET) when the solute rejected by the equiaxed grains growing ahead of the front decreased the undercooling available for dendritic growth. Nguyen-Thi et al.[3] have presented some in-situ X-ray radiographic images of dendritic solidification in an Al-3.5 pct Ni alloy that confirm this effect, referred to as solutal blocking. Nevertheless, these images were obtained for solidification in a thin container (150 to 200 lm in thickness), whose walls might have affected the columnar-front blocking, as shown by Mathiesen and Arnberg[11] and Mathiesen et al.[12] Ludwig and Wu[13] and Ciobanas et al.[14] considered both mechanical and solutal blockings in their models, suggesting that the two blocking mechanisms should play an important role in causing the CET. Browne[15] proposed an equiaxed index based on the time evolution of the liquid undercooling ahead of the columnar front. When this index reached its maximum value, Browne[15] assumed that the CET would occur. Banaszek et al.[16] observed that, in
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