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Fig. 1—Schematic diagram of pseudobinary phase diagram of a Ni-base superalloys
and k⫽
TNi ⫺ TL TNi ⫺ TS
[7]
For the superalloy used, one obtains m ⫽ ⫺3.306 ⬚C/wt pct and k ⫽ 0.506. Using this method to evaluate pseudobinary phase diagram data, the calculated TL is by definition identical with the experimentally measured liquidus temperature. This ensures an accurate determination of the grain nucleation temperature (TL minus nucleation undercooling) and the growth front temperature (TL minus tip undercooling) and, hence, provides a reasonable CAFE simulation of grain structure formation. REFERENCES 1. A. Kermanpur, N. Varahram, P. Davami, and M. Rappaz: Metall. Mater. Trans. B, 2000, vol. 31B, pp. 1293-1304. 2. C.-A. Gandin and M. Rappaz: Acta Metall. Mater., 1997, vol. 45, pp. 2187-95. 3. E. Scheil: Z. Metallkd., 1942, vol. 34, pp. 70-72. 4. W. Kurz, B. Giovanola, and R. Trivedi: Acta Metall., 1986, vol. 34, pp. 823-30. 5. M.A. Taha and W. Kurz: Z. Metallkd., 1981, vol. 72, pp. 546-49. 6. J.L. Murray, L.H. Bennet, and H. Baker: Binary Alloys Phase Diagrams, ASM, Metals Park, OH, 1986, vols. 1–2.
Authors’ Reply A. KERMANPUR, N. VARAHRAM, P. DAVAMI, and M. RAPPAZ We agree with most of the comments of Dr. Ma. However, in order to obtain quantitative values on the growth kinetics of Ni-base superalloys, and thus on nucleation undercoolings, many more aspects should be considered besides a few specific values of partition coefficients and/or liquidus slopes. Among these are cross-diffusion of solute elements, which is very important in these alloys; anisotropy of the interfacial solid-liquid energy, which is influenced also by the alloy composition; multicomponent phase diagram data and diffusion coefficients in the liquid, which are not well known. The intent of the CAFE calculations presented in this article was to clearly illustrate the effect of cooling METALLURGICAL AND MATERIALS TRANSACTIONS B
W Co m k
mi (Old, Incorrect)
mi (New, Correct)
⫺2.4 ⫺0.4 ⫺2.556 0.656
2.4 0.4 ⫺1.995 0.56
Finally, it has been concluded that solidification defects of the blade have occurred as a result of the curved shape of the liquidus surface. But again, the difference between the liquidus measured by differential thermal analysis (1332 ⬚C) and the value calculated with the equivalent binary alloy (1342 ⬚C) will not change the conclusions.
The Sensitivity of the Interface HeatTransfer Coefficient to Pressure and Fluid Flow J.A. SEKHAR A small grain size distribution is a critical feature that controls the quality (reliability, fatigue strength, and hot cracking tendency) of net-shaped castings and cast sheets of aluminum, nickel, or ferrous alloys.[1,2,3] In this respect, fluid flow often plays a large part in controlling the grain size either directly (momentum transfer to a weak evolving solidifying structure) or by directly influencing the composition and thermal gradients in the solidifying casting.[2,4,5] Fluid flow has also been noted to influence the interface heat-transfer coefficient[3] between the casting and it
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