Heat flow parameters affecting dendrite spacings during unsteady-state solidification of Sn-Pb and Al-Cu alloys

Abstract

Solidification thermal parameters and dendrite arm spacings have been measured in hypoeutectic SnPb and Al-Cu alloys solidified under unsteady-state heat flow conditions. It was observed that both primary and secondary spacings decreased with increased solute content for Sn-Pb alloys. For Al-Cu alloys, the primary spacing was found to be independent of composition, and secondary spacings decrease as the solute content is increased. The predictive theoretical models for primary spacings existing in the literature did not generate the experimental observations concerning the Sn-Pb and AlCu alloys examined in the present study. The theoretical Bouchard-Kirkaldy's (BK's) equation relating secondary spacings with tip growth rate has generated adequately the experimental results for both metallic systems. The insertion of analytical expressions for tip growth rate and cooling rate into the predictive model, or into the resulting experimental equations in order to establish empirical formulas permitting primary and secondary dendritic spacings to be determined as functions of unsteadystate solidification parameters such as melt superheat, type of mold, and transient metal/mold heattransfer coefficient is proposed.for instance, the solidification conditions of a body of irregular shape, these variables are interdependent, cannot be controlled, and vary freely with time. The analysis of dendritic structures in the unsteady-state regime is very important, since it encompasses the majority of industrial solidification processes.The measurements of primary and secondary dendrite arm spacings involve looking at the microstructure after complete solidification. Primary spacings do not coarsen with time and can be accurately measured from the microstructure and compared with growth models. On the other hand, secondary spacings are seen to rapidly coarsen during solidification, and the effect of coarsening has to be taken into account by the predictive growth models. [29] Most of the results in the literature, concerning steady and unsteady regimes, pertaining to l 2 in hypoeutectic alloys, indicate a decrease in spacing with increasing cooling rate for a given alloy composition and with increasing solute content for a given cooling rate. [28,29,38,39] The reports in the literature also indicate that for steady or unsteady growth conditions, the primary arm spacings decrease as G L or V L increases. On the other hand, there has been some disagreement in the literature regarding the influence of the initial alloy composition on primary spacings. It has been reported in the majority of cases that l 1 increases as C 0 (for hypoeutetic alloys) increases for both steady and unsteady growth conditions. [28,29] However, Sharp and Hellawell [44] found that C 0 has little effect on primary spacings and Spittle and Lloyd [46] reported that for steady-state growth with low G L , l 1 decreased as C 0 increased and was independent of C 0 for high G L , and for unsteady solidification l 1 decreased as C 0 increased.The present article focuse...

Influence of upward and horizontal growth direction on microstructure and microhardness of an unsteady-state directionally solidified Al-Cu-Si alloy

“…In order to determine more accurate values of these parameters, the results of experimental thermal analysis, shown in Figure 4a have been used to generate a plot of position from the metal/ mold interface as a function of time corresponding to the liquidus front passing by each thermocouple. This methodology has been detailed in our recently published articles [7][8][9][10][11][12][13][14]. A curve fitting technique on such experimental points has generated a power function of position as a function of time (see Figure 4b).…”

“…The derivative of this function with respect to time has yielded values for VL, shown in Figure 5a. Figure 5b shows the TR profile, which was calculated by considering the thermal data recorded immediately after the passing of the liquidus front by each thermocouple [7][8][9][10][11][12][13][14]. It can be seen in Figures 5a and 5b that the use of a water cooled mold imposes higher values of VL and TR near the metal/mold interface and a decreasing profile along the casting due to the increasing thermal resistance of the solidified layer with distance from the heat-extracting surface.…”

“…Image processing system Olympus BX51 and Image Tool (IT) software were used to measure primary arm spacing (about 20 independent readings for each selected position, with the average taken to be the local spacing) and their distribution range. The method used for measuring the primary arm spacing on the transverse section was the triangle method [10]. Measurement of the primary dendritite arm spacings on the transverse section was carried out using the triangle method [25,28].…”

“…Nowadays these alloys are supplied in a wide range of chemical compositions [1][2][3][4][5][6][7][8][9][10][11][12]. We highlight the Al-Cu-Si ternary system because of particular outstanding properties such as high mechanical strength, low weight and very good fluidity [3][4][5][6][7][8][9][10][11][12].…”

“…This is known that the values of 1, 2 and 3 are strongly influenced by solidification thermal parameters such as growth rate (VL) and cooling rate (TR) [1,2,3,[7][8][9][10][11][12]. Several directional solidification studies have been reported in the literature to characterize and quantify these parameters as a function of solute concentration C0, VL and TR.…”