METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 34A, APRIL 2003—995 Heat Flow Parameters Affecting Dendrite Spacings during Unsteady-State Solidification of Sn-Pb and Al-Cu Alloys OTÁVIO L. ROCHA, CLÁUDIO A. SIQUEIRA, and AMAURI GARCIA Solidification thermal parameters and dendrite arm spacings have been measured in hypoeutectic Sn- Pb 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 de- crease as the solute content is increased. The predictive theoretical models for primary spacings ex- isting in the literature did not generate the experimental observations concerning the Sn-Pb and Al- Cu 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 formu- las permitting primary and secondary dendritic spacings to be determined as functions of unsteady- state solidification parameters such as melt superheat, type of mold, and transient metal/mold heat- transfer 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 com- plete solidification. Primary spacings do not coarsen with time and can be accurately measured from the microstruc- ture 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. [1–54] On the other hand, there has been some disagreement in the literature regarding the influence of the initial alloy com- position 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 con- ditions. [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 focuses on the dependence of den- drite arm spacings on solidification thermal parameters, i.e., dendrite tip growth rate, temperature gradient in front of the liquidus isotherm, and tip cooling rate, and on the alloy solute content under unsteady-state solidification con- ditions. The experimental data concerning the solidification I. INTRODUCTION DURING solidification of alloys, the observed mi- crostructures are diverse, but in general can be classified into two basic groups: cells/dendrites and eutectic mor- phologies. Dendrite growth is the common mechanism of crystallization from metallic melts, and the morphology, which is formed, consists of an array of dendrites with a sidebranch configuration. The solute, which is redistributed due to the solubility difference between the solid and liq- uid phases, provokes an important consequence of such a structure, i.e., the occurrence of microsegregation between the dendrites branches. The dendritic array characterized by primary and secondary spacings and the segregated prod- ucts greatly affect the mechanical properties and homoge- nization kinetics of solidified alloys. [1,2] Therefore, in order to control the properties of casting materials, it is important to understand the solidification parameters that affect the growth of dendritic spacings during solidification. Numerous directional solidification studies have been re- ported with a view to characterizing primary (l 1 ) and sec- ondary (l 2 ) dendrite arm spacings as a function of alloy solute concentration (C 0 ), tip growth rate (V L ), and tempera- ture gradient ahead of the macroscopic solidification front (G L ). [1–54] A recent article by Bouchard and Kirkaldy [29] has summarized these studies grouped into two categories: those involving solidification in steady-state heat flow and those in unsteady-state regime. In the former category, solidifica- tion is controlled and the significant controllable variables, G L and V L , are maintained constant and are practically in- dependent of each other. In the latter, which characterizes, OTÁVIO L. ROCHA and CLÁUDIO A. SIQUEIRA, Doctorate Stu- dents and Research Assistants, and AMAURI GARCIA, Professor, are with the Department of Materials Engineering, State University of Campinas— Unicamp, 13083-970 Campinas-SP, Brazil. Contact e-mail: amaurig @fem.unicamp.br Manuscript submitted July 12, 2002.