Application of the phase-field method to the solidification of hot-dipped galvanized coatings
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I. INTRODUCTION
SOLIDIFICATION of thin films of zinc deposited on steel sheets by the hot-dipping process has been studied for more than 30 years,[2] but the models proposed so far to describe the solidification process and the final microstructure are still sketchy.[1,3,4] The zinc used to galvanize steel sheets typically contains 0.5 at. pct Al and 0.06 at. pct of Pb or more, plus some other impurities. Aluminum prohibits the growth of intermetallic compounds at the steel-zinc interface, while lead is known to increase the size of the zinc grains—also called spangles—to typically 1 cm in diameter. Within a single spangle, different regions can be distinguished simply by visual inspection (Figure 1). Using the terminology of Strutzenberger and Faderl,[1] the “shiny region” of the grain on the right-hand side of Figure 1 corresponds to long primary dendrite arms with visible secondary and tertiary arms, while only an array of dots is visible in the “dimpled region” of the same grain. Strutzenberger and Faderl have shown that these different aspects are related to the crystallographic orientation of the spangle. Moreover, they found that the concentrations of lead and aluminum on the shiny surface were much lower than those measured on the dimpled surface (Figure 9 of Reference 1). Fasoyinu and Weinberg[5] measured the surface roughness of spangles: they showed that the dimpled (called “frosty,” in their article) regions are rough, while the shiny ones are smooth. The large size of spangles has long fascinated scientists, but has still not been explained satisfactorily. Among other hypotheses, Fasoyinu and Weinberg[3] have proposed that wetting effects on the boundaries increase the growth velocity of the dendrites. The wetting phenomena considered here ´ A. SEMOROZ, Doctoral Student, and M. RAPPAZ, Professor, are with ´ ´ ´ the Laboratoire de Metallurgie Physique, Department des Materiaux, Ecole ´ ´ Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland. S. ´ HENRY, formerly Doctoral Student, Laboratoire de Metallurgie Physique, ´ ´ ´ ´ Departement des Materiaux, Ecole Polytechnique Federale de Lausanne, is Research Engineer, Pechiney Centre de Recherches de Voreppe, F-38341 Voreppe, Cedex, France. Manuscript submitted January 19, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
and throughout this article occur at the triple points, the junctions of the solid dendrite, the liquid melt, and the boundary (either the steel substrate covered by an intermetallic layer or the oxide layer at the free surface). Wetting of a growing solid phase on a boundary has already been observed in directional solidification of transparent substances such as succinonitrile[6] (Figure 2): a dendrite growing along a good wetting boundary has a triangular tip characterized by a small wetting angle, while a nonwetting boundary keeps the dendrite tip away (large wetting angle).* *In the case of a triple point between the substrate, liquid film, and air, it has been reported that dynamic wetting is not fully described by the wet
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