The effects of interface attachment kinetics on solidification interface morphologies
- PDF / 2,344,172 Bytes
- 15 Pages / 597.6 x 774 pts Page_size
- 49 Downloads / 205 Views
I.
INTRODUCTION
DENDRITIC structures are commonly observed during the solidification processing of alloys. These highly complex branched structures give rise to microsegregation of solute, and they often are associated with many defects that occur in casting and welding. Thus, in order to understand the principles which dictate the dendritic microstructural characteristics, several theoretical and experimental studies have been reported in the literature. [1-12J For an isolated dendrite, such as the one that can be formed under controlled conditions in an undercooled melt, the key aspect is to correlate undercooling with the dendrite tip velocity, tip radius, and the secondary arm spacings. For a constrained growth, experimental studies are generally carried out to correlate the imposed velocity with the dendrite tip radius, tip temperature, primary dendrite spacing, and the secondary arm spacings. Understanding of dendritic microstructural scales has largely come from critical experiments in model transparent systems. The first detailed and classical study, carried out by Glicksman et al.[6] in pure undercooled succinonitrile, provided several critical scaling laws of a dendritic structure: the correlation between the velocity and the dendrite tip radius with undercooling and the proportionality between the initial secondary arm spacing near the tip with the dendrite tip radius. These crit-
R. TRIVEDI, Senior Scientist and Professor, and J.T. MASON. Associate Metallurgist, are with Ames Laboratory, United States Department of Energy and the Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011. Manuscript submitted JuJy 10, 1989. METALLURGICAL TRANSACTIONS A
ical experiments clearly showed the invalidity of the maximum growth rate criterion which was then widely used in the literature. These experimental results also led to the theoretical development by Langer and MullerKrumbhaar, [7J who examined the selection criterion for the dendrite tip radius. They examined the stability of a parabolic dendrite tip front and concluded that the dendrite tip assumes the radius value which is just stable with respect to the tip-splitting instability. A more recent development, called the solvability condition, predicts that a unique dendrite tip selection occurs due to the presence of anisotropy in the interfacial energy. [13-17J It is important to note that the marginal stability and the solvability condition both give rise to precisely the same relationship, the only difference being in the value of the operating parameter, (T*. The value of (T* is predicted by the marginal stability criterion to be a constant equal to 0.025, which is close to the value of 0.02 observed experimentally by Huang and Glicksman[9,1O] in undercooled pure succinonitrile. The solvability condition, on the other hand, predicts (T* to be a function of the interface energy anisotropy parameter, E, so that it has a specific constant value for a given system only. The parameter E is defined by the relationship which
Data Loading...