• Journal of Welding and Joining
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• v.17 no.4
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• pp.60-68
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• 1999

The previously developed two dimensional model was modified in order to predict more accurately the degree of microsegregation and eutectic fraction on in weld metal whose solidification rate is very fast. The model employed the same assumptions with previous model but considered of a tip undercooling. The previously predicted microsegregation and eutectic fraction has the discrepancies between simulated and examined results in the weld metal solidification. The experiments for the weld metal solidification of 2024 A1 and Fe-Ni alloy were carried out in order to examine the reasonability and feasibility of this modified model. The concentration profile of the solute and eutectic fraction predicted by the simulation agreed well with those found from experimental works. According to the results, it was believed that the dendrite tip undercooling considered in the modified model be reasonable for predicting the degree of microsegregation more accurately in weld metla solidification. In the GTA welds, degree of dendrite-tip undercooling increases with increasing solidification rage(welding speed). This serves to increase the concentration of dendrite core and thus result in reducing the degree of segregation. And solid state diffusion(back diffusion) during solidification is very low in the weld metal solidification so that little additional homogenization of solute occurs during solidification. With consideration of tip undercooling this modified model can predict exactly degree of microsegregation and eutectic fraction from slow solidification(casting) to fast solidification(welding).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2367-2374
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• 1996

A generalized Scheil equation for the solute redistribution in the absence of the back diffusion during the dendritic solidification of binary alloys is derived, in which coarsening of the secondary dendrite arms is taken into account. The obtained equation essentially includes the original Scheil equation as a subset. Calculated results for typical cases show that the coarsening affects the microsegregation significantly. The eutectic fraction predicted for coarsening is considerably smaller than that for fixed arm spacing. The most important feature of the present equation in comparison with the Scheil equation lies in the fact that there exists a lower limit of the initial composition below which the eutectic is not formed. Based on the generalized Scheil equation and the lever rule, a new regime map of the eutectic formation on the initial composition-equilibrium partition coefficient plane is proposed. The map consists of three regimes: the eutectic not formed, conditionally formed and unconditionally formed, bounded by the solubility and diffusion controlled limit lines.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.3
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• pp.426-434
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• 2000

This paper deals with a generalized similarity solution for the one-dimensional solidification of ternary or higher-order multicomponent alloys. The present approach not only retains the existing features of binary systems such as temperature- solute coupling, shrinkage-induced flow, solid-liquid property differences, and finite back diffusion, but also is capable of handling a multicomponent alloy without restrictions on the partition coefficient and microsegregation parameter. For an alloy of N-solute species, governing equations in the mushy region reduce to (N+2) nonlinear ordinary differential equations via similarity transformation, which are to be solved along with the closed-form solutions for the solid and liquid regions. A linearized correction scheme adopted in the solution procedure facilitates to determine the solidus and liquidus positions stably. The result for a sample ternary alloy agrees excellently with the numerical prediction as well as the reported similarity solution. Additional calculations are also presented to show the utility of this study. Finally, it is concluded that the present analysis includes the previous analytical approaches as subsets.