Heat transfer-solidification kinetics modeling of solidification of castings
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I.
INTRODUCTION
IT is now widely accepted that a complete model for the simulation of solidification of castings should include the following: (1) macromodeling of heat transfer (HT modeling), of fluid flow during mold filling, and of stress distribution and (2) micromodeling of solidification kinetics (SK modeling) and of fluid flow in the mushy zone. Solidification kinetics modeling should then be extended to commonly occurring solid-state transformations, like pearlitic, martensitic, or bainitic transformations for Fe-C alloys. Finally, the data base for structureproperties correlation should be included in the model. Such a model will allow not only for accurate prediction of shrinkage but also of hot and cold cracking due to thermal stress, as well as of microstructural features, including microporosity, and of mechanical properties. At the present time, the task of including all of these models in a comprehensive solidification package is far from being complete, although significant progress has been achieved in each field. This paper will mainly address one aspect of solidification modeling, that is, solidification kinetics (SK). Nevertheless, it is obvious that in order to validate any type of solidification kinetics model, it is important to couple such a model with a HT model. A variety of computer programs (FDM or FEM) are available for HT modeling, and any of them can be used to this effect. As will be explained in this paper, the main problem in coupling SK and HT consists in DORU M. STEFANESCU, University Research Professor and Director of the Solidification Laboratory, G. UPADHYA, Graduate Research Assistant, and D. BANDYOPADHYAY, Graduate Council Research Fellow, are with the Department of Metallurgical and Materials Engineering, The University of Alabama, Tuscaloosa, AL 35487. Manuscript submitted May 22, 1989. METALLURGICAL TRANSACTIONS A
incorporating the latent heat evolved during solidification, which is calculated by the SK model, in the HT model, which calculates the overall cooling of the casting. To calculate latent heat evolution, it is necessary to calculate the evolution of fraction of solid. The different avenues presently available for the calculation of fraction of solid, based on experimental data, will be discussed in this paper.
II.
FORMULATION
As discussed in previous papers, 0,2,3] HT modeling for a given casting-mold combination requires solving the energy conservation equation for heat conduction (refer to List of Symbols for notations):
OT(x, t)
V" [K(T) V r ( x , t)] + Q = pCp(T) - -
Ot
[1]
Here, p, Cp, and K assume the value of the particular phase or mixture of phases prevailing at a given temperature and location in casting. The source term, Q, describes the rate of latent heat evolution during any liquid-solid transformation and may be written as
Ofs(x, t) Q = L- Ot
[2]
where L is the constant volumetric latent heat of fusion during the phase transformation. In conventional HT modeling, the fraction of solid, fs, cannot be calculated from first principles f
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