A unified microscale-parameter approach to solidification-transport phenomena-based macrosegregation modeling for dendri
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tural applications will undergo a dendritic solidification process, no matter whether these materials are in the final-part forms, as various castings, or in middle-stage forms as various ingots for the subsequent mechanical processing. The dendritic solidification behaviors are critical in determining the properties of the formed parts/materials. One of the important solidification process–related aspects is the formation of compositional inhomogeneities in the resulting materials, i.e., micro/macrosegregation. The segregation defects cause the inhomogeneities in the electrochemical and mechanical properties of the solidified materials, lowering their melting-start temperatures and, therefore, deteriorating the performances of the as-cast/wrought products at room and high working temperatures. Therefore, it has become a major task for materials-processing researchers to work on segregation modeling for dendrite solidification, to provide a useful theoretical tool for the optimum controls of various metallic alloy solidification processes. Due to the nature of various segregation formations in dendrite solidifying castings/ingots, macrosegregation modeling has to account for the microscale solute redistribution behaviors that usually result in microsegregation in the final DAMING XU, Professor, is with the School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China. Manuscript submitted September 8, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS B
solidified materials. This can be seen from the early macrosegregation modeling[1,2] to the recent solidification-transport phenomena (STP)–based numerical simulations.[3–7] In a continuum/mixture-averaging[3] or one-phase[5] STP-based macrosegregation model, linkage with the microscale solute redistribution behavior is simply embodied through the timedifferential term for the mixture-averaged composition, i.e., the ⭸( C )m/⭸t (equal to ⭸( fS 具SCS典S ⫹ fL 具LCL典L)/⭸t) term, along with the thermodynamic relationships for the involved phases of the alloy. To simplify the dendritic alloy solidification modeling, it is common to assume either a level-rule– type (i.e., let DS → ⬁, e.g., in the models of References 3 through 5) or Scheil-type (DS ⫽ 0, as in References 2 and 5 through 7) microscale solidification model, depending on the solute diffusivity in the solidifying phases. For these two limiting cases, the time-differential mixture-averaged composition (TDMAC) term can be written as ⭸( C )m /⭸t ⫽ (SCS)⭸fS /⭸t ⫹ fS⭸(SCS)/⭸t ⫹ (LCL)⭸fL /⭸t ⫹ fL⭸(LCL)/⭸t
[1]
and ⭸( C )m /⭸t ⫽ (SCS)*⭸fS /⭸t ⫹ (LCL)⭸fL /⭸t ⫹ fL⭸(LCL)/⭸t
[2]
respectively. It can be seen from Eqs. [1] and [2] that, if either of the limiting solute-redistribution models is applicable, no specific treatment for the geometrical details of growing dendrites is required in the modeling. This is because, for VOLUME 32B, DECEMBER 2001—1129
both the limiting solidification cases, there is no need to quantify the microscale solutal-mass fluxes th
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