Numerical treatment of rapid solidification
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I.
INTRODUCTION
THE development
of metastable structures by Rapid Solidification Processing (RSP) has received an enormous amount of study in recent years ~-5 and continues to be the subject of intensive research. One of the most interesting and important aspects of this topic is that relating the heat flow characteristics to the solidification behavior and resultant microstructure. Features of the heat flow constrain the combinations of system dimensions, cooling rate, and growth velocity that may in practice be achieved. Several conventional solidification heat flow analyses have been extended to encompass RSP conditions, 6-~3 allowing characterization of some of the limitations expected. However, although a rapidly-solidifying system is normally under heat flow control, process analysis is complicated by the degree to which kinetic factors can be responsible for departure from thermodynamic equilibrium. ~4:5't6 For example, in many cases the nucleation and growth characteristics are such that the temperature at the solidification front is variable and may differ markedly from the value dictated by the phase diagram. The phenomena associated with this effect range from reduced partition ("solute trapping") and morphological stabilization to rapid heat evolution from a moving source, tending to generate recalescence and temperature inversion. From the modeling viewpoint the removal of a boundary condition specifying T: (orf~(T) for a mushy zone) at the growth front introduces an extra degree of freedom. In order to handle this, a relationship is needed between growth velocity and interfacial undercooling: Levi and Mehrabian ~7,m,mhave recently employed such expressions in modeling of atomization. In the present paper, a review is presented describing the incorporation of various thermodynamic and kinetic factors into a numerical heat flow model, and attention is drawn to certain important features of RSP with the help of illustrative computed data. T.W. CLYNE is a Lecturer, Department of Materials Science and Engineering, Universityof Surrey, Guildford,Surrey,GU2 5XH, United Kingdom. ManuscriptsubmittedJanuary20, 1983. METALLURGICALTRANSACTIONSB
II.
GEOMETRY
While much of the effort in numerical modeling of conventional solidification processes is often devoted to representing geometrically complex shapes, the requirement for heat flow optimization has tended to limit RSP configurations to simple geometries. The majority of processes fall into one of the categories illustrated in Figure 1, exhibiting planar, radial, or spherical symmetry (although rather more complex geometries can arise with the moving source "self-substrate" cases such as laser glazing). In practice the batch processes of primary interest are atomization
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$ Spheroidal
Discoidal BATCH
Cglindrical
Planar CONTINUOUS
Fig. 1--Schematic illustrationof the heat flow geometriesfor the main classes of rapid solidificationprocesses. VOLUME15B,JUNE1984--369
and splat quenching (including flake atomization and controlled spray
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