By Doru Stefanescu
ISBN-10: 0387746099
ISBN-13: 9780387746098
Stefanescu right here makes an attempt to explain solidification idea during the advanced mathematical equipment required for a primary remedy of the matter. the math is in spite of the fact that constrained to the weather necessary to reach a operating wisdom within the box. this is often in accordance with the most target of the publication, that's to teach the reader within the fast paced sector of computational modeling of solidification of castings. a unique attempt has been made to introduce the reader to the newest advancements in solidification concept together with, during this moment version, a brand new bankruptcy on semi-solid casting.
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Extra info for Science and Engineering of Casting Solidification, Second Edition
Example text
The liquid and solid phase compositions are equal along the To curve. 14. They can be used to evaluate the possibility of extension of solubility by rapid melt quenching. 14a) single phase α or β crystals with compositions beyond their respective To cannot form from the melt. The solidification temperature in the vicinity of the eutectic composition can be depressed to the point where an increased liquid viscosity stops crystallization (glass temperature transition, Tg). 14b), for composition below both To curves, a mixture of α and β crystals could form, each phase having the same composition as the liquid.
Schematic representation of the computational domain and physical quantities for two-phase models. and Beckermann 1996, Wu and Ludwig 2006). However, the lack of information regarding the microscopic configuration at interface boundaries is a serious complication. While these models will be discussed in more details in Chapter 13, because of space restrictions, in this text we will develop only the mixture-theory model. The typical mixture theory relationships used in the continuum mixture-theory model are derived based on the spatial average: φ = 1 φ dv v ∫v where φ is the averaged value of φ over both the solid and liquid phases, and v is the volume.
The composition of the liquid at the interface is CL* = Co /k and then decreases according to Eq. 5), and reaches Co after a distance of approximately 2DL/V. Steady state exists as long as there is enough liquid ahead of the interface for the forward diffusion of the solute to occur, and as long as solidification velocity remains constant. 7). This is the final transient. The length of the final transient is that of the solute boundary layer, DL/V. As shown by Smith et al. (1955), the solid composition in the final transient can be calculated with: CS (1 − k )(2 − k )exp⎛ − 6V x ⎞ + 1− k ⎛ 2V x ⎞ =1+ 3 exp⎜ − ⎟+5 ⎜ ⎟ (1 + k )(2 + k ) ⎝ D ⎠ Co 1+ k ⎝ D ⎠ + ...
Science and Engineering of Casting Solidification, Second Edition by Doru Stefanescu
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