Modeling of base metal dissolution behavior during transient liquid-phase brazing
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I.
INTRODUCTION
TRANSIENTliquid-phase (TLP) brazing involves a series of steps, namely, melting of the filler metal (at temperature Tm), heating to the final brazing temperature (Tb), base metal dissolution, isothermal solidification, and homogenization, tl] This paper models the TLP brazing process by treating base metal dissolution, isothermal solidification, and homogenization as one sequential process. Base metal dissolution is examined assuming that the heating rates from T,~ to Tb range from 0.05 K / s to infinity. In this work, two brazing situations are considered, namely, constant liquid width (where liquid is continuously expelled throughout the brazing process) and variable liquid width (where the solid-liquid interface is able to move in an unrestricted manner throughout base metal dissolution). II.
BACKGROUND
The Nernst-Brunner theory of solid dissolution into liquid was derived based on the key assumptions that the liquid zone can be considered as a constant volume bulk H. NAKAGAWA, formerly Visiting Research Scientist, Department of Metallurgy and Materials Science, University of Toronto, is Research Instructor, Japan Welding Research Institute, Osaka University, Osaka, Japan. C.H. LEE, formerly Postdoctoral Fellow, Department of Metallurgy and Materials Science, University of Toronto, is Research Engineer, Research Institute of Industrial Science and Technology (RIST), Pohan, South Korea. T.H. NORTH, WIC/NSERC Professor, is with the Department of Metallurgy and Materials Science, University of Toronto, Toronto, M5S 1A4, ON, Canada. Manuscript submitted September 28, 1989. METALLURGICALTRANSACTIONSA
layer with a thin, constant thickness boundary film at the solid-liquid interface. Dissolution is determined by either the interface reaction or by the transport of material from the solid-liquid interface into the bulk liquid, t21 Most experimental results support the idea that dissolution depends on transport processes, and that the interface reaction is not rote-controlling, except when high dissolution rates are promoted by forced stirring of the liquid. Lowell and C h a l m e r s [31 theoretically examined the dissolution of solid in liquid and indicated, that in an unstirred liquid system, movement of the solid-liquid interface was dependent on the square root of the holding time and that the boundary layer thickness also increased in a similar manner. In TLP brazing, the liquid can be considered to be unstirred because it is an extremely thin region. Dissolution during TLP brazing has been examined in detail by Nakao et al. [41 and by Tuah-Poku et al. tsl Nakao et al. taj developed a dissolution parameter based on the Nernst-Brunner theory; i.e., the dissolution rate of solid into liquid is given by the relation C = Csadl - exp ( - K ( A / V ) t ] where C Cat K V A t
= = = = = =
[1]
solute concentration in the liquid; solute concentration at saturation; the dissolution rate; volume of liquid; area of solid-liquid interface; and time.
Differentiating Eq. [ 1] gives d c / d t = K ( A / V ) (
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