Theoretical - Experimental Analysis of Cellular and Primary Dendritic Spacings during Unidirectional Solidification of Sn-Pb Alloys

Abstract

Structural parameters as grain size, dendritic and cellular spacings, segregated products, porosity and other phases are strongly influenced by the thermal behavior of the metal/mold system during solidification, imposing a close correlation between this and the resulting microstructure. Several unidirectional solidification studies with the objective of characterizing cellular and dendritic spacings have been developed in large scale involving solidification in steady-state heat flow. The main objective of this work is to determine the thermal solidification parameters during the cellular/dendritic transition as well as to compare theoretical models that predict cellular and primary dendritic spacings with experimental results for solidification situations in unsteady-state heat flow. Experiments were carried out in a water cooled unidirectional solidification apparatus and dilute alloys of the Sn-Pb system were used (Sn 1.5wt%Pb, Sn 2.5wt%Pb and Sn 5wt%Pb). The upper limit of the Hunt-Lu cellular growth model closely matched the experimental spacings. The lower limit calculated with the Hunt-Lu dendritic model best generated the experimental results. The cellular/dendritic transition was observed to occur for the Sn 2.5wt%Pb alloy over a range of analytical cooling rates from 0.28 K/s to 1.8 K/s.

The role of eutectic colonies in the tensile properties of a Sn–Zn eutectic solder alloy

“…Previous studies focusing on the growth of monophasic cells demonstrated that 0.55 and 1.1 exponents are effective in representing the variation of cell spacing against solidification cooling rate and solidification velocity, respectively [36,37]. The exponents derived based on the present results are quite similar to those reported in the literature.…”

The influence of melt convection on dendritic spacing of downward unsteady-state directionally solidified Sn-Pb alloys

“…It can be seen that, for the downward solidification, the same power law represents the variation of primary spacings with tip cooling rate for the 5 and 15wt.%Pb alloys. Figure 2a shows also a comparison with the experimental laws obtained from the vertical upward directional solidification of these two alloys 11 . As can be seen, for a same cooling rate, the primary spacing is reduced (about 2 to 3 times) for conditions of downward vertical solidification.…”

“…The experiments were performed with Sn-Pb alloys (5, 15 and 20wt.%Pb) with melt superheats of 7 °C above the liquidus temperature, and under a thermal contact condition at the metal/mold interface corresponding to the heat-extracting surface being polished. The employed thermophysical properties of these alloys are those reported in a previous article 11 .…”

“…Although convection effects strongly influence on the development of solidification microstructure, the main theoretical dendritic models from the literature are based on purely diffusive transport mechanisms. In addition, recent articles on cellular 9,10 and primary dendritic 11 growth under unsteady-state solidification conditions have shown that the predictive theoretical models existing in the literature did not generate the experimental observations.…”

Modelagem numérica e análise experimental de parâmetros térmicos e microestruturais na solidificação radial de ligas binárias

“…Vários pesquisadores têm proposto correlações entre microestrutura de solidificação e parâmetros térmicos para ligas de vários sistemas binários Rocha, 2002;Bouchard-Kirkaldy, 1997;Çardili e Gündüz, 2000;Cruz, 2008;Santos, 2001] utilizando-se da determinação experimental dos espaçamentos celulares ou dendríticos e dos parâmetros térmicos de solidificação. Esses parâmetros são velocidades da isoterma liquidus, gradientes de temperatura e taxas de resfriamento.…”