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ODUCTION

IN recent

years, the continuous casting process has been widely adopted in the steel and nonferrous metalproducing industry. The quality and properties of cast products strongly depends on the microstructure developed during solidification.[1,2] Therefore, it is of great interest to analyze the interdependence of the cast microstructure and process parameters for improved product quality and development of superior methods for quality castings. Nearly all of the solidification microstructures that can be exhibited by a pure metal or an alloy can be divided into two groups: single-phase primary crystals and polyphase structures.[3] The most important growth form is the treelike primary crystal, i.e., the dendrite (from the Greek, dendron = tree). Under industrial conditions, metallic alloys usually solidify in dendritic interfaces. The microstructural scale of dendrites, such as primary dendrite arm spacings (PDASs, k1) and secondary dendrite arm spacings (SDASs, k2), controls the segregation profiles and determines the properties of cast structures.[4] There have been some studies reported in the literature[5–9] describing the relationship between cast microstructure and solidification parameters such as growth rate and thermal gradient. The theoretical models available in literature[10–12] for determination of interdendritic spacings are indicated subsequently: 1

1

1

k1 ½10
¼ 2:83½CmL Co ð1  ko ÞD
4 G 2 R 4

½1


SUVANKAR GANGULY and S.K. CHOUDHARY, Researchers, are with R & D Division, Tata Steel, Jamshedpur 831007, India. Contact e-mail: [email protected] Manuscript submitted July 18, 2008. Article published online April 21, 2009. METALLURGICAL AND MATERIALS TRANSACTIONS B

k1

½11



1 CDTD 4 1 1 ¼ 4:3 G2R4 ko 1

½2
1

1

k1 ½12
¼ 2:83½CLmL Co ð1  ko ÞD
4 G 2 R 4

½3


where C is the Gibbs–Thomson coefficient, mL is the liquidus line slope, ko is the solute partition coefficient, Co is the alloy composition, D is the liquid solute diffusivity, DT is the difference between the liquidus and solidus equilibrium temperature, R is the dendrite tip growth rate, and G is the temperature gradient in front of the liquidus isotherm. From the preceding equations, it is clear that, in all these models, k1 is related to the solidification rate R and thermal gradient G in the solidifying domain and can be expressed in a general form according to the following equation: k1 ¼ C1 Rm Gn

½4


Equation [4] represents a generic form of the theoretical model characterizing the columnar growth and depicts the relationship between PDASs and thermal and physical parameters. It may be mentioned here that most of the models[8–12] agree in the magnitude of the exponents m and n; however, the constant C1 varies in its form and value, giving rise to discrepancies between different authors on the predicted value of k1. With regard to secondary dendrites, a ripening process causes the dendrite arms to change with time into coarser less branched dendrites growing perpendicularly to the primary trunk.[3] Several studies in th