Mushy zone modeling with microstructural coarsening kinetics
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INTRODUCTION
P H A S E coarsening, or Ostwald ripening, is a microscale process occurring in all finely divided two-phase mixtures. The driving force for coarsening is the-reduction of the free energy stored in the interfaces separating the phases. The net result of phase coarsening is an increase in the average microstructural lengthscale and a concomitant decrease in the amount of interfacial area per unit volume of microstructure. Coarsening can occur with or without net phase transformation, because both species and enthalpy are conserved among the participating phases. Thus, the coarsening process induces microscopic transport fields that communicate solutal and thermal fluxes over active regions of the interface. In the case of solid-liquid systems, which will be specifically treated in this article, the microscale transport fields (1 to 100/xm) are virtually independent of the long-range macrotransport fields (0.01 to 1 m) responsible for net solidification. A challenge facing current heat-transfer modeling of solidification is to bridge the gap in the lengthscales between the microscopic and the macroscopic. Coarsening effects may be observed easily in casting and welding processes, alloy heat treatment, liquid-phase sintering, powder atomization, as well as in many other material processes which involve more than one phase. Inasmuch as coarsening determines the distribution of microstructural lengthscales and their local chemical composition, it has a profound effect on the physical and mechanical properties of the resultant material. A quanMARTIN E. GLICKSMAN, John Tod Horton Professor of Materials and Chemical Engineering, and RICHARD N. SMITH, Associate Professor of Mechanical Engineering, are with the Rensselaer Polytechnic Institute, Troy, NY 12180-3590. STEVEN P. MARSH, Resident Postdoctoral Research Associate, is with the Physical Metallurgy Branch, Naval Research Laboratory, Washington, DC 20375-5000. ROBERT KUKLINSKI, Technical Staff Member, is with the Naval Underwater Systems Center, Newport, RI 02841-5047. Manuscript submitted June 5, 1991. METALLURGICAL TRANSACTIONS A
titative understanding of the kinetics of phase coarsening is essential for designing and optimizing most processes for which prediction and control of the final structure are important. The modeling of mushy zones, as discussed in this article, comprises both the prediction of the evolution of microstructural lengthscales under adiabatic conditions and the adaptation of that theory to macroscopic transport processes occurring in net solidification. Bridging between microscopic and macroscopic scales has only been attempted heretofore under limited conditions, and so we shall also use a rather rudimentary description of heat transfer in one-dimensional freezing to accomplish the micro/macro modeling. The second half of this article is devoted to applying the fundamental microscopic theory to the specific problem of freezing a quiescent binary alloy melt subject to a constant mold wall temperature. Interpretation of these re
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