Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.     

Measurements and modeling of the microstructural morphology during equiaxed solidification of Al-Cu alloys

The morphology predicted by an equiaxed growth model recently presented elsewhere has been compared with quantitative experimental morphology measurements on a range of Al-Cu alloys. In the experiments, the samples have been solidified with a uniform temperature and quenched from the mushy state at the instant when the eutectic temperature was reached. The copper content and the amount of grain-refiner additions have been varied, resulting in both “clover-leaf” and dendritic equiaxed morphologies. Morphology characterization on both the intragranular and extragranular length scales has been performed on the quenched samples. Average heat-extraction rates, grain densities, and alloy compositions from the experiments have been used as input to the equiaxed grain-growth model, and the resulting morphology predictions have been compared with the morphology measurements. For the morphologies observed in the present study, the equiaxed growth model predicts higher values of the internal solid fraction than observed experimentally. This has been indicated to be due to the failure of commonly made modeling assumptions during the later stages of the solidification.     

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

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 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 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 formulas 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 heattransfer coefficient is proposed.     

Correlation between unsteady-state solidification conditions, dendrite spacings, and mechanical properties of Al-Cu alloys

The wide range of operational conditions existing in foundry and casting processes generates as a direct consequence a diversity of solidification microstructures. Structural parameters such as grain size and interdendritic spacings are strongly influenced by the thermal behavior of the metal/mold system during solidification, imposing, as a consequence, a close correlation between this system and the resulting microstructure. Mechanical properties depend on the microstructural arrangement defined during solidification. Expressions correlating the mechanical behavior with microstructure parameters should be useful for future planning of solidification conditions in terms of a determined level of mechanical strength, which is intended to be attained. In the present work, analytical expressions have been developed describing thermal gradients and tip growth rate during one-dimensional unsteady-state solidification of alloys. Experimental results concerning the solidification of Al-4.5 wt pct Cu and Al-15 wt pct Cu alloys and dendritic growth models have permitted the establishment of general expressions correlating microstructure dendrite spacings with solidification processing variables. The correlation of these expressions with experimental equations relating mechanical properties and dendrite spacings provides an insight into the preprogramming of solidification in terms of casting mechanical properties.     

Quantification of microsegregation during rapid solidification of Al-Cu powders

A new technique is introduced to quantify microsegregation during rapid solidification. The quantification involves calculation of the average solute solubility in the primary phase during solidification of an Al-Cu binary alloy. The calculation is based on using volume percent eutectic and weight percent of second phase (in the eutectic), which were obtained experimentally. Neutron diffraction experiments and stereology calculation on scanning electron microscope images were done on impulse atomized Al-Cu alloys of three compositions (nominal), 5 wt pct Cu, 10 wt pct Cu, and 17 wt pct Cu, atomized under N₂ and He gas. Neutron diffraction experiments yielded weight percent CuAl₂ data and stereology yielded volume percent eutectic data. These two data were first used to determine the weight percent eutectic. Using the weight percent eutectic and weight percent CuAl₂ in mass and volume balance equations, the average solute solubility in the primary phase could be calculated. The experimental results of the amount of eutectic, tomography results from previous work, and results from the calculations suggest that the atomized droplets are in metastable state during the nucleation undercooling of the primary phase, and the effect of metastability propagates through to the eutectic formation stage. The metastable effect is more pronounced in alloys with higher solute composition.     

Densities of Pb-Sn alloys during solidification

Data for the densities and expansion coefficients of solid and liquid alloys of the Pb-Sn system are consolidated in this paper. More importantly, the data are analyzed with the purpose of expressing either the density of the solid or of the liquid as a function of its composition and temperature. In particular, the densities of the solid, Eqs. [15] and [16], and of the liquid, Eqs. [24] and [25], during dendritic solidification are derived. Finally, the solutal and thermal coefficients of volume expansion for the liquid are given as functions of temperature and composition (Figure 9).     

A numerical and experimental study of the solidification rate in a twin-belt caster

A numerical and experimental study was carried out to investigate the solidification process in a twin-belt (Hazelett) caster. The numerical model considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the cast. Ak-ε turbulence model is used to calculate the turbulent viscosity in the melt pool. The process variables considered are the belt speed, strip thickness, nozzle width, and heat removal rates at the belt-cast interface. From the computed flow and temperature fields, the local cooling rates in the cast and trajectories of inclusions were computed. The cooling rate calculations were used to predict the dendrite arm spacing in the cast. The inclusion trajectories agree with earlier findings on the distribution of inclusion particles for near horizontally cast surfaces. This article also reports the results of an experimental study of the measurement of heat flux values at the belt-cast interface during the solidification of steel and aluminum on a water-cooled surface. High heat fluxes encountered during the solidification process warranted the use of a custom-made heat flux gage. The heat flux data for the belt surface were used as a boundary condition for the numerical model. Objectives of the measurements also included obtaining an estimate of the heat-transfer coefficient distribution at the water-cooled side of the caster belt. Y.G. KIM, formerly Graduate Student, Materials Engineering Department, Drexel University.     

Numerical modeling of solidification and subsequent transformation of Fe-Cr-Ni alloys

A computational method for the analysis of phase transformation involving solidification was developed with the assumption of thermodynamic equilibria at interfaces. The region of interest was divided into finite segments, and solute diffusion across the segments was computed by the use of the direct finite difference method (FDM). Simultaneously, thermodynamic equilibrium at each interface was updated at every step of the diffusion analysis to determine the location of the interfaces. The temperature decrease and the increment of fraction solid were calculated based on thermal balance, including a heat extraction condition. Solid state transformation from δ to γ phase within each FDM segment was modeled by the use of a Clyne-Kurz (C-K) type analysis with assumptions of complete mixing of solutes in theδ phase and limited back diffusion in theγ phase. The calculation results were compared with welding solidification experiments in the iron-chromium-nickel ternary system. Good agreement was obtained with respect to solute distribution and residual fraction ofδ phase over different compositions and solidification modes of the alloys used.     

Contraction of aluminum alloys during and after solidification

A technique for measuring the linear contraction during and after solidification of aluminum alloys was improved and used for examination of binary and commercial alloys. The effect of experimental parameters, e.g., the length of the mold and the melt level, on the contraction was studied. The correlation between the compositional dependences of the linear contraction in the solidification range and the hot tearing susceptibility was shown for binary Al-Cu and Al-Mg alloys and used for the estimation of hot tearing susceptibility of 6XXX series alloys with copper. The linear thermal contraction coefficients for binary and commercial alloys showed complex behavior at subsolidus temperatures. The technique allows estimation of the contraction coefficient of commercial alloys in a wide range of temperatures and could be helpful for computer simulations of geometrical distortions during directchill (DC) casting.     

Macrosegregation during directional solidification of Pb-Sb alloys

Macrosegregation of Sb was investigated during directional solidification of binary Pb-Sb alloys containing 2.2 and 5.8 wt% Sb over growth rates varying from 0.8 to 30 μm s^?1. The cellular to dendritic transition was observed at a growth rate of 3.0 μm s^?1 in Pb-2.2 Sb alloy in contrast to a growth rate of 1.5 μm s^?1 in Pb-5.8 Sb alloy. The chemical analysis data revealed considerable macrosegregation of Sb along the longitudinal section of alloys. The degree of macrosegregation increased with a decrease in the growth rate. This behavior is discussed in light of thermo-solutal convection in the mushy zone as well as that in the melt ahead of the solid-liquid interface.     

Rheological behavior of Al-Mg-Si-Cu alloys in the mushy state obtained by partial remelting and partial solidification at high cooling rate

This work investigates the mechanical behavior of two aluminum alloys in the mushy state, the alloy AA6056 and an alloy based on mixing AA6056 and AA4047. These alloys have been studied to give insight into the susceptibility to hot tearing, which occurs during laser welding of AA6056 with 4047 filler wire. Two types of isothermal tensile tests have been conducted: (1) tests during partial remelting and (2) tests after partial solidification at a high cooling rate. Results show that the maximum tensile stress increases with increasing solid volume fraction. Both materials exhibit visco-plastic behavior for solid fractions in the range 0.9 to 0.99, except for a critical solid fraction of 0.97, where the semisolid material also shows minimum ductility. The stress levels observed for the remelting experiments are larger than those found for partial solidification experiments at the same solid fraction due to the influence of the microstructure. The influence of temperature and strain rate on the maximum stress is described by using a constitutive law that takes into account the fraction of grain boundaries wetted by the liquid.     

Equilibrium phase relationships during solidification of Fe-O-C-X alloys

Abstract

Analysis of the solidification process of alloys requires that the phase relationships at equilibrium be known. The problem is complex and difficult for commercial ferrous alloys because of the presence of iron, carbon, oxygen, a deoxidizer, manganese, sulphur, etc. This study develops the phase relationships in the iron-rich corner of four component systems and covers the Fe-O-C-Si and Fe-O-C-Al systems specifically. The equilibrium state is treated at 1 atm pressure. The effects of suppression of formation of CO and of segregation of elements between liquid and solid iron are then analyzed.

Résumé

L'analyse du procédé de solidification des alliages requiert que la relation des phases à l'equilibre soit connue. Le problème est complexe et difficile pour les alliages ferreux commerciaux à cause de la présence de fer, de carbone, d'oxygene, d'un désoxydant, de manganèse, de soufre, etc. L'étude présente développe la relation des phases dans la région riche en fer d'un système à quatre composants, en particulier les systèmes Fe-O-C-Si et Fe-O-C-Al. L'équilibre est traité à 1 atm. de pression. Les effets de la suppression de formation de CO et de ségrégation d'éléments entre le fer liquide et solide sont ensuite analysés.     

Microstructural development during solidification of stainless steel alloys

The microstructures that develop during the solidification of stainless steel alloys are related to the solidification conditions and the specific alloy composition. The solidification conditions are determined by the processing method,i.e., casting, welding, or rapid solidification, and by parametric variations within each of these techniques. One variable that has been used to characterize the effects of different processing conditions is the cooling rate. This factor and the chemical composition of the alloy both influence (1) the primary mode of solidification, (2) solute redistribution and second-phase formation during solidification, and (3) the nucleation and growth behavior of the ferrite-to-austenite phase transformation during cooling. Consequently, the residual ferrite content and the microstructural morphology depend on the cooling rate and are governed by the solidification process. This paper investigates the influence of cooling rate on the microstructure of stainless steel alloys and describes the conditions that lead to the many microstructural morphologies that develop during solidification. Experiments were performed on a series of seven high-purity Fe-Ni-Cr alloys that spanned the line of twofold saturation along the 59 wt pct Fe isopleth of the ternary alloy system. High-speed electron-beam surface-glazing was used to melt and resolidify these alloys at scan speeds up to 5 m/s. The resulting cooling rates were shown to vary from 7°C/s to 7.5×10⁶°C/s, and the resolidified melts were analyzed by optical metallographic methods. Five primary modes of solidification and 12 microstructural morphologies were characterized in the resolidified alloys, and these features appear to be a complete “set” of the possible microstructures for 300-series stainless steel alloys. The results of this study were used to create electron-beam scan speedvs composition diagrams, which can be used to predict the primary mode of solidification and the microstructural morphology for different processing conditions. Furthermore, changes in the primary solidification mode were observed in alloys that lie on the chromium-rich side of the line of twofold saturation when they are cooled at high rates. These changes were explained by the presence of metastable austenite, which grows epitaxially and can dominate the solidification microstructure throughout the resolidified zone at high cooling rates. J. W. ELMER, formerly Graduate Student at the Massachusetts Institute of Technology     

Phase selection during directional solidification of peritectic alloys

Directional solidification studies have been conducted using Pb-Bi peritectic alloys over a wide range of compositions, temperature gradients, and growth velocities to characterize the primary α- to primary β-phase transitions, which have been observed at both very low and very high velocities. The critical conditions for these transitions correspond to the simultaneous growth of the α and β phases at or close to a single isotherm. The low velocity transition occurs under very specific conditions of composition, temperature gradient, and growth velocity. Since the transition conditions are composition dependent, they change continuously under terrestrial conditions where rejected solute is convectively mixed into the liquid. Detailed experimental studies have been carried out to examine the phase selection in the immediate vicinity of the critical velocity for the α to β transition, and the effect of convection on this transition is examined experimentally in the Pb-Bi system. The dynamic condition, at which both phases are present at the same isotherm, was shown to depend not only on velocities, temperature gradients, and bulk (nominal) alloy compositions, but also on the volume fractions of solid. A quantitative expression for the α- to β-phase transition condition was obtained by using the boundary layer model of fluid flow, which showed good agreement with the experimental results. It is shown that the transition occurs at the volume fraction where the bulk composition reaches the critical composition value predicted by the diffusive model. The modification in the microstructure map for the trailing planar or nonplanar β phase is discussed.     

Predicted volume change behavior accompanying the solidification of binary alloys

For the volume changes accompanying solidification, distinctions are made between the volume changeβ _Mfor the whole freezing process, the volume changeβ _mfor liquid entrapped within the freezing zone, and the localized volume changeβ _Taccompanying the liquid-solid phase transformation at a given temperature. The first volume change is important in mold design, while the latter two are important factors in the formation of casting defects such as shrinkage pores, solidification cracks, and inverse segregation. Values ofβ _M, β_M, andβ _mare deduced for equilibrium conditions in the representative alloy systems Al-Cu, Bi-Sb, Fe-C and Pb-Sn. While the volume changeβ _Mmay vary only moderately with alloy composition,β _mis a strong function of composition and of the temperature of enclosure. The isothermal volume change,β _T, equal to the relative density difference between solid and liquid, varies during the freezing process and is strongly dependent upon composition. Isothermal volume changes and hence density differences as large as 20 pct are deduced for some Bi-Sb and Pb-Sn alloys.     

Simulation of freckles during vertical solidification of binary alloys

A mathematical model of solidification that simulates the formation of channel segregates or freckles is presented. The model simulates the entire solidification process starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. Predictions of the pattern and location of channels in different cooling situations are in good agreement with experimental observations. Formerly Graduate Student, University of Arizona     

Dendritic growth during directional solidification of hypoeutectic Fe-C-Si alloys

The liquid decanting technique has been used to study the morphology of dendrites in directionally solidified Fe-3.08 pct C-2.01 pct Si alloy. The experimental results indicated that the morphology of primary dendrites in the Fe-C-Si system is very similar to those obtained in some transparent metal model systems and in some other metal systems. In order to study the morphological transition between cellular and dendritic growth, directionally solidified samples were quenched in cold water at various stages of solidification and the morphology was examined on the polished and etched surface. It has been found that when the growth velocity decreased from 326.6 to 0.8 μn/s, the average dendrite tip radius increased from 1.12 to 33.1 μm. At a growth velocity of about 0.65 μm/s, a transition from dendritic to cellular growth occurred. Models for dendritic growth proposed by various investigators have been briefly reviewed and compared with the present experimental results. Significant disagreements were found for some of the available theoretical models. Possible explanations have been given for these disagreements.     

Cellular-to-dendritic transition during the directional solidification of binary alloys

The transition from a cellular to dendritic microstructure during the directional solidification of alloys is examined through experiments in a transparent system of succinonitrile (SCN)-salol. In a cellular array, a strong coupling of solute fields exists between the neighboring cells, which leads not only to multiple solutions of primary spacing, but also includes multiple solutions of amplitude, tip radius, and shape of the cell. It is found that these multiple solutions of different microstructural features in a cellular array, obtained under fixed growth conditions and compositions, play a key role in the cell-dendrite transition (CDT). The CDT is controlled not only by the input parameters of alloy composition (C ₀), growth rate (V), and thermal gradient (G), but also by microstructure parameters such as the local primary spacing. It is shown that the CDT is not sharp, but occurs over a range of growth conditions characterized by the minimum and maximum values of V/G. Within this transition range, a critical spacing is observed above which a cell transforms to a dendrite. This critical spacing is given by the geometric mean of the thermal, diffusion, and capillary lengths and is inversely proportional to composition in weight percent.     

A numerical study of oxidation behavior during reactive atomization and deposition

The oxidation behavior of droplets during reactive atomization and deposition (RAD) is analyzed on the basis of a numerical framework proposed here. Commercial 5083 Al is chosen as a model material; moreover, in the numerical model, nonspherical droplets are approximated as cylinders with a length/diameter ratio of 3. An equation that represents the growth rate of the oxide phases, together with models that describe the dynamic and thermal behavior of droplets, is implemented in an effort to elucidate the oxidation behavior of individual droplets. The numerical results reveal that the oxidation rate of a droplet is extremely high and that the oxide phase grows very rapidly initially, eventually attaining a steady state of limited oxide growth. The overall volume fraction of oxide phases in the RAD material increases with increasing atomization pressure, superheat temperature, and O₂ concentration, whereas it decreases with increasing melt flow rate. The oxygen concentrations in the RAD powders and deposited materials predicted on the basis of numerical analysis are in good agreement with the results from chemical analysis when O₂ concentration is lower than 16 vol pct.