Numerical modeling of diffusion-controlled phase transformations in ternary systems and application to the ferrite/auste
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INTRODUCTION
ANALYTICAL solutions for the diffusion behavior in infinite and semi-infinite binary systems are readily available. tl,2j For ternary alloys, analytical solutions for diffusion-controlled transformations in infinite and semi-infinite systems are also available, although they are somewhat more complicated.[ 1,21However, for realistic systems of finite length and particularly where the second phase is more than a minor constituent, an analytical solution can only be used as long as the system can be considered infinite in size and the diffusion fields from neighboring areas do not overlap. This restriction can be avoided with the use of numerical solutions. Numerical modeling also has the added advantage that in principle, there are no restrictions with regard to the analysis of nonisothermal aging. The numerical approach has been used to study precipitation behavior in ternary and higher order steel alloy systems.[3~] The study of the ferrite-to-austenite transformation in cast or welded stainless steels is also ideally suited for numerical evaluation. In these steels, ferrite that forms during solidification transforms to austenite during cooling. Typically, this reaction does not proceed to completion, and the extent of this diffusion-controlled transformation will affect
J.M. VITEK, Senior Research Staff Member, and S.A. DAVID Group Leader, are with Oak Ridge National Laboratory, Oak Ridge, TN 37831. S.A. VITEK, formerly at Oak Ridge National Laboratory, is now a student at Massachusetts Institute of Technology, Cambridge, MA. Manuscript submitted July 19, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
the final properties of the weld. Also, during subsequent elevated-temperature exposure, either in multipass welding procedures or during service, the transformation may proceed still further, thereby altering the microstructure and properties. Finally, the reverse transformation (namely the austenite-to-ferrite transformation) in the heat-affected zone (HAZ) of welds may be important in determining the solidification behavior in the fusion zone. Since weld solidification occurs primarily by an epitaxial process, the weld microstructure in the HAZ immediately adjacent to the molten pool may play a role in determining the solidification behavior and microstructure. At extremely high temperatures near the solidus, the austenite is less stable and is likely to transform to ferrite. Therefore, the elevated-temperature microstructure may be quite different from that in the base material prior to welding, and it may play a role in the solidification process that is unexpected, based on the room-temperature microstructure. In all these cases, it is desirable to evaluate the transformation reaction and its kinetics in order to determine the extent of the phase changes that take place during elevated-temperature exposure. Experimental evaluation of the transformation behavior is difficult. In particular, experimental studies are hindered by the inability to effectively quench the elevated-temperature m
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