ON THE SOLIDIFICATION OF DENDRITIC ARRAYS - AN ASYMPTOTIC THEORY FOR THE DIRECTIONAL SOLIDIFICATION OF SLENDER NEEDLE CRYSTALS

Citation
Bj. Spencer et He. Huppert, ON THE SOLIDIFICATION OF DENDRITIC ARRAYS - AN ASYMPTOTIC THEORY FOR THE DIRECTIONAL SOLIDIFICATION OF SLENDER NEEDLE CRYSTALS, Acta materialia, 45(4), 1997, pp. 1535-1549
Citations number
18
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Material Science","Metallurgy & Metallurigical Engineering
Journal title
ISSN journal
1359-6454
Volume
45
Issue
4
Year of publication
1997
Pages
1535 - 1549
Database
ISI
SICI code
1359-6454(1997)45:4<1535:OTSODA>2.0.ZU;2-F
Abstract
We consider a mathematical model for directional solidification of a b inary alloy as a periodic array of three-dimensional needle crystals. Arguing from an analysis of published experimental data for dendritic growth, we identify a natural separation of characteristic length scal es;br dendrites. We use these observed disparities in length scales to define a small parameter for dendritic growth and identify scalings f or all the process parameters in terms of this small parameter. We the n solve the resulting free boundary problem using matched asymptotic e xpansions. Our analysis results in an Integral equation for the shape of the needle crystal. We suggest that the integral equation contains a mechanism for the unique selection of the tip radius of the needle c rystal independent of surface energy. This is in sharp contrast to pre vious studies regarding determination of the tip radius of an isolated , single-component, isothermal dendrite. Our results suggest that sele ction of the tip radius is linked to the spacing of the array. (C) 199 7 Acta Metallurgica Inc.