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Averaged Voronoi polyhedron in the peritectic transformation modelling

  Peritectic solidification of the alloys is in the centre of attention of researchers. This is a mechanism of the structure formation for many technical alloys. Peritectic solidification is believed to be the major cause of crack formation during the solidification of many steels [1]. During the peritectic solidification primary solid phase vanishes simultaneously along with liquid phase and new secondary (peritectic) phase grows as a solidification product. In the carbon steel γ-phase (austenite) appears, replacing δ-phase (ferrite) and liquid. Two separate mechanisms of peritectic solidification are known as: - peritectic reaction: when dissolution of primary phase, directly in liquid phase, is possible independently from the secondary one [2], - peritectic transformation: when primary phase is completely separated from liquid by the layer of secondary phase [3]. An analytical model of the kinetics of peritectic transformation, based on the linearized concentration gradient of the solute, has been presented by Das et al. [4]. The results shown in this paper exhibit a good agreement with the experimental results, but the difference between rates obtained by the computer modelling and relevant experimental data increase at the later stages of transformation. According to authors of [4] one of the reasons of this disagreement is the deviation from the idealized geometry. The idealized geometry of the elementary peritectic cell is usually used in the known numerical models. Furthermore, the idealized initial concentration profile of the solute in the preperitectic phase is assumed. Spherically symmetrical cell of radius (3/4n)1/3 was applied in [5], where n is the number of peritectic cells per unit volume. In the Ref. [6] only a plane spatial segment of the melt pool was used as the simulation domain. According to the analysis of diffusion transformations presented in [7], a single common mathematical model allows fo[...]

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