Simulation of Solute Redistribution during Casting and Solutionizing of Multi-phase, Multi-component Aluminum Alloys F. Yi,* H. D. Brody* and J. E. Morral** * University of Connecticut, Storrs, CT 6269-336 USA ** The Ohio State University, Columbus, OH 432-78 USA Abstract Numerical simulations of solute redistribution and microstructure evolution during solidification, post-solidification cooling, and solution heat treatment have been extended to multi-phase, multi-component Al-Si-Cu-Mg alloys. The basic models that have been applied to binary and ternary systems have been modified to handle the extra degrees of freedom in quaternary and higher order systems, which are more representative of commercial casting alloys. During solidification Si and Mg diffusion is extensive and microsegregation of Si and Mg in the dendrite cores at the end of solidification is negligible. Diffusion of Cu through the dendrite cores controls the extent of microsegregation of Cu in the as-solidified alloy. The presence of small amounts of Mg enhances diffusion of Cu, and the diffusivity of Cu in multiphase interdendritic regions is several multiples of the diffusivity through the single-phase dendrite cores. Substantial solute redistribution occurs during post-solidification cooling in sand or permanent molds. Si, in particular, diffuses from dendrite cores to the interdendritic regions as the solubility of Si in the interdendritic -Al phase decreases sharply with decreasing temperature. During solution heat treatment the redistribution of solute that occurs during post-solidification cooling is reversed quickly. The nonequilibrium amounts of θ-phase and Q-phase that are distributed in the interdendritic regions between secondary dendrite arms at the end of solidification are reduced to their equilibrium amounts within a few hours. Nonequilibrium phases distributed in the grain boundaries and between primary dendrite branches require ten or more hours to reduce to their equilibrium amounts. Key words Aluminum castings, solution treatment, solidification simulation, aluminum alloys, diffusion. 36/
Introduction As part of a collaborative program to develop, verify and market an integrated system of software, databases, and design rules to enable quantitative prediction and optimization of the heat treatment of cast aluminum alloys, we are simulating solute redistribution during the solidification, post-solidification cooling, and solution heat treatment of Al- Si-Cu-Mg alloys.[,2] The ultimate goal is to simulate the casting and heat treatment processes in multicomponent multiphase alloys with sufficient accuracy to enable computer-aided-design and control of process parameters to achieve specified properties in critical locations. Currently, the simulation routines are used iteratively with experiment to check the influence of process and material parameters on microstructure evolution. In developing and applying models for solute redistribution to solidification and heat treatment processes a key step is assuming a geometry and critical dimension(s) for a characteristic volume element to represent the overall process. Typically a one-dimensional model is chosen and the characteristic dimension (d) of the volume element is more important than its shape (plate-like, cylindrical, or spherical) in determining the predictions of the model. Diffusivity of the solute in the primary dendritic phase is the key material parameter influencing the degree of as-cast microsegregation and the effectiveness of solution treatment in reducing microsegregation for typical commercial casting and solutionizing conditions.[,3] Models appropriate to solutionizing of castings use the as-cast solute distribution and phase fraction as the initial condition. As in solidification models, diffusion of solute through the dendrite cores and the dimension of the characteristic volume element control the rate of dissolution of nonequilibrium phases and homogenization of the matrix phase. Comprehensive solidification and heat treatment models have been developed for binary alloys.[4] Extension of the models to multi component alloys presents challenges to account for the extra degrees of freedom and the interactions between alloying elements to modify equilibrium phase relations and diffusivity. Experimental Models are developed iteratively with experimental studies to increase understanding of basic processes and their interaction with materials parameters; to build databases of phase relations, diffusivity, and process parameters; and to validate assumptions and predictions against measurements on test castings. As example, phase relations --- temperatures and order of phase appearance --- are determined by interrupted solidification. Diffusion coefficients are determined from electron microprobe measurements on diffusion couples. Quantitative metallography, scanning electron microscopy, and electron microprobe analyses of sections taken from end-chilled test plate castings are used to validate predictions of the model.[5] 36/2
Model The characteristic volume element used for most of the results presented here is the -d plate-like geometry with characteristic dimension d taken as one-half the secondary dendrite arm spacing. The characteristic volume element is divided into N equal diiferential elements of width λ = d. Considering the rate of solidification to be linear and the final N df S ( f ) eutectic reaction to be isothermal, the rate of solidification is = E dt θ f where θ f is the local solidification time and f E is the fraction eutectic microconstituent. Above the eutectic temperature the time for each θ f differential volume element to solidify is t S =. The eutectic N ( f E ) microconstituent freezes instantaneously. The contribution of dendrite coarsening to solute redistribution during solidification is not considered here. The local thermal cycle T = T(t) during post-solidification cooling and during solution heat treatment is input from measured cooling and heating curves herein (but could be input from heat transfer. Initially, the characteristic volume element is considered to be % liquid of composition C Oi where the subscript, i, refers to the solute elements Si, Cu, Mg and/or Fe. The liquidus temperature for the alloy is determined by interpolation for the initial alloy and each subsequently computed liquid composition by accessing the stored phase relations database (temperature and solute concentrations) used to represent the liquidus surface. Undercooling of the primary aluminum phase due to nucleation or curvature is assumed negligible. The solid phase or phases in equilibrium with the liquid are determined from the stored phase data and that composition is assigned to the differential volume element at the solid/liquid interface. Secondary phases solidify without undercooling at the point of saturation of the liquid. Two or more solid phases form within the solidifying volume element in the proportions dictated by the tie lines for the average composition of the solid phases. When solubility decreases in a volume element that is multi-phase there is no barrier to growth or dissolution of existing phases. On-the-other-hand, when a solid volume element becomes saturated with respect to a new secondary phase, the barrier to nucleation is assumed infinite (unless otherwise stated). When desired a solid state precipitation model can be coupled to the simulation. After each differential volume element solidifies, diffusion through the primary solid phase is computed, iteratively, for the time interval, t S. Then solute balances are computed that simultaneously satisfy the equilibrium phase relations. The concentration of the solute in the - phase is used to compute the solute flux in Fick s Laws and the average composition is used in solute balance computations. 36/3
Based on diffusion couple data [] obtained for ternary and quaternary alloys the diffusivities (m 2 /s) used for the -phase, the terminal FCC solid 6 solution around aluminum, are D = CuCu.45x exp 2, 3 ; RT 6 D = x 3, 6 SiSi 6.3 exp ; D = RT MgMg 8.57x exp 9, 4. RT The cross coefficients D CuSi, DSiCu, DCuMg, DMgCu,... are negligible. The variation of D CuCu with Cu content is negligible over the limited solubility range. Small additions of Mg (<.5%) increase the diffusivity of Cu in the -phase by a factor of 2 to 4. Also, diffusivity of Cu through the twophase silicon region is increased by a factor of 5 to 2. As sketched in Figure, an alternative 2-D volume element used here is rectangular in cross-section. The characteristic dimensions, d and d 2, are taken as one-half the primary dendrite arm spacing and one-half the secondary dendrite arm spacing, respectively. The differential volume element dimensions for solidification, λ and λ 2, are taken in the same ratio, which is 3/ for the results reported here. The differential volume elements used for diffusion computations are λ x λ. To account for divorced solidification, the sequence of solidification of the differential volume elements is modified, as illustrated in Figure 2. When the composition of the liquid phase becomes saturated with respect to silicon, the composition of the -phase and the equilibrium ratio of silicon phases are computed to satisfy, simultaneously, the solute balances and the stored phase equilibria data. Predetermined differential volume elements ahead of the /L interface are considered to transform to an silicon colony in a ratio determined by quantitative metallography. The observed fraction of -phase in the binary eutectic colonies is below the equilibrium value, the remainder of the -phase continues to form at the original /L interface. Results The -D model is applied first to simulation of solute redistribution during solidification for the ternary alloy Al-6.5%Si-3.5%Cu. The solidification path for the alloy is shown on the projections of the -liquidus and - solidus surfaces in Figure 3. Also shown in Figure 3 is the solidification curve, i.e. phase fraction versus temperature through the solidification range. Freezing begins at the liquidus with solidification of -phase, which is more dilute in Si and Cu than the liquid. As solidification proceeds through the L region the concentrations of silicon and copper increase in the solid and liquid phases. The line of two fold saturation (the eutectic valley) is reached when 42wt% -phase has solidified, As temperature decreases along the eutectic valley, -phase and essentially pure silicon solidify as a binary eutectic, which is about 9wt% -phase. The Cu concentrations continue to increase and the Si concentrations decrease slightly in the and liquid phases. At the ternary eutectic temperature the 36/4
remaining liquid transforms isothermally to -phase, -phase (CuAl 2 ), and silicon, in the ratio by weight 39/56/5. The predicted distribution of Cu and Si in the -phase at the end of the ternary eutectic solidification in an Al-7%Si-3.5%Cu alloy is shown in Figure 4. The Cu concentration in the -phase increases continuously through the primary -phase and two-phase silicon regions and reaches a plateau at the ternary eutectic concentration. The Cu distribution at the end of solidification is little changed from that predicted by the Gulliver-Scheil model.[3] The Si concentration is essentially uniform at the equilibrium ternary eutectic composition for the -phase, which is consistent with the data that the diffusivity of Si in the -phase at the liquidus temperature is four times that of Cu.[] Because the solubility for Si in the -phase decreases during solidification of the binary eutectic, the silicon particles in the silicon region grow larger and fine silicon precipitates can nucleate within the primary. The predicted distributions of Cu in the -phase after an Al-7%Si-3.5%Cu alloy has solidified and then cooled to 58K in the mold are shown in Figure 5 for two positions in an end-chilled plate casting. By measurement position has a dendrite arm spacing of 38µm, a local solidification time of 54s, and cools time from the eutectic to 58K in 848s. The comparable measurements for position 6 are 7µm, 769s, and 94s, respectively. Comparison of the Cu distributions in Figures 4 and 5 show postsolidification diffusion of copper into the primary phase to reduce the concentration gradient and diffusion of copper from the silicon region to the θsilicon region as the solubility of Cu in the -phase decreases with decreasing temperature. Comparisons of the predictions of the -D model in Figures 3-5 with the results of interrupted solidification studies and quantitative microscopy on sections from end-chilled plate castings indicate a major discrepancy.[,5] The apparent fraction of primary -phase in as-cast plates is over 7% as compared to the predicted 42% and in the interrupted solidification studies the two-phase silicon colonies are observed to grow in the liquid ahead of the /L interface with a silicon fraction much greater than the predicted %. Using quantitative metallography data as a guide, the divorced eutectic model, Figure 2, is being used to simulate solidification and solute redistribution. Figure 6 presents a result for Al-7%Si-3.5%Cu. The -D plate geometry and the 2-D plate geometry (Figure ) are being used to simulate phase formation and dissolution and solute redistribution during silidification and post-solidification solution treatment. Both the -D and 2-D simulations consider divorced binary eutectic solidification and enhanced Cu diffusion in the binary eutectic region (due to the silicon particles). Predicted rates of dissolution of θ-phase during solutionizing (at 55 O C) for a region close to the chill in an Al-7%Si-3.5%Cu test plate casting (38µm DAS), Figure 7, are consistent with observations of the dissolution of copper-rich θ-phase during solution heat treatment of Al-Si- 36/5
Cu and Al-Si-Cu-Mg alloys. The θ particles distributed in the interdendritic regions between secondary arms dissolve within two hours and θ-particles within clusters of eutectic microconstituent distributed at primary dendrite subboundaries and at grain boundary junctions require eight or more hours to dissolve. Similar results are found for the quaternary alloy Al-7%Si-3.5%Cu-.5%Mg. Solidification of primary -phase is followed by the binary eutectic silicon, the ternary eutectic siliconq (Al 5 Cu 2 Mg 8 Si 6 ), and finally the quaternary eutectic siliconqθ. The predicted distributions of Cu in the -phase for the -D model at the end of quaternary eutectic solidification are shown in Figure 8 for two cases, (i) using the expression D CuCu given above (LSD) and (ii) using 2 x D CuCu (ESD) to account for the enhanced Cu diffusivity with small additions of Mg. The predictions for Cu distribution in the quaternary alloy for a location near the chill in a test plate casting (38µm DAS) using (i) the divorced eutectic model (LSD), (ii) enhanced diffusivity for copper in the -phase due to the Mg addition (ESD), and (iii) enhanced diffusivity of Cu in the - phase within the two-phase silicon region (ESD2) are shown for the simulation of solidification and post-solidification cooling (to 3 O C) in Figure 9. Also shown in Figure 9 are a series of electron microprobe measurements across a typical dendrite arm.[6] The agreement is surprisingly good. Conclusions Experiment and predictions of simulations of solute redistribution and phase appearance for solidification and post-solidification cooling of multicomponent and multi-phase Al-Si-Cu-Mg alloys using (i) a -D model, (ii) a characteristic dimension equal to one-half the secondary arm spacing, (III) measured solute diffusivities and phase relations, (iv) enhanced diffusion of copper in the FCC -phase due to small additions of Mg and/or the presence of silicon particles, and (v) a model for divorced solidification of silicon colonies. A 2-D model with two characteristic dimensions for solution treatment of as-cast microstructre is consistent with observations. References. Brody H D and Morral J E, Solution Heat Treatment of Aluminum Alloys: Effect on Microstructure and Properties, Final Report, Univ. of Connecticut to Center for Heat Treating Excellence, 24. 2. Yao Z et al, Integrated Numerical Simulation and Process Optimization for Aluminum Alloy Solutionizing, ASM Heat Treating Society Conference Proceedings, 25. 3. Flemings MC, Solidification Processing, McGraw-Hill, New York,974. 36/6
4. Gandin CA et al, Modelling of solidification and heat treatment for the prediction of yield stress of cast alloys, Acta Materialia 5(5): 22, 9-927. 5. Fang J, Brody HD, Morral JE, Empirical Model for Tensile Property Prediction in Cast and Heat Treated Al-Si-Cu-Mg Alloys, This Volume, WFC#35. 6. Ma Y., University of Connecticut, Personal Communication, 26. Acknowledgements The authors are grateful to our sponsors: the Department of Energy under contract DOE DE-FC36-ID497 and the Center for Heat Treating Excellence. We are grateful to the members of the industry focus groups for these programs, chaired by Dr. Scott MacKenzie, Houghton, for the DOE project and Dr. Paul Crepeau, GM Powertrain, for the CHTE program and to the program teams at WPI, UConn, and OSU. Important contributions to this project have been made by the UConn and OSU team: Dr. X. Pan, Dr. D. Zhang, M. Qian, S. Adibhatla, C. Lin, and Y, Ma. Figures d λ -Phase λ d 2 L Figure : Two-dimensional characteristic volume element, schematic. The number of divisions in the -direction is the same as the number of divisions in the 2-direction. The ratio of dimensions to the differential volume element λ2 are λ in the same proportion as the characteristic spacings d 2. d Two-phase Si L Si Si Figure 2: Schematic representation of -D characteristic volume element for divorced solidification of silicon binary eutectic microconstituent. 36/7
35 3 25 Liquidus 6 5 4 Solidus 2 5 % Si 3 2 % Si 5 5 5 2 25 3 35 4 % Cu 2 3 4 5 6 7 8 % Cu 88 Temperature (K) 87 86 85 84 83 82 8 8 79 Fraction of -Phase Fraction of Silicon-Phase Fraction of θ-phase G-S Model DAS=8µm.2.4.6.8 Weight Fraction of Solid Phases during Solidification Figure 3: Solidification path along solidus and liquidus surfaces and solidification curve for ternary alloy Al-6.5%Si- 3.5%Cu, dendrite arm spacing equal to 8µm. Solute Concentration (wt. %) 5. 4.5 LSD Model DAS=8µm 4. 3.5 3. silicon / silicon 2.5 %Cu in -phase θ 2. %Si in -phase silicon.5..5..2.4.6.8 Fractional Distance from Center of Dendrite Arm (λ/d) Figure 4: Distribution of Cu and Si in the -phase after solidification to the ternary eutectic temperature for an Al-6.5%Si-3.5%Cu alloy. Weight % Cu in -Phase 4. 3.5 3. 2.5 2..5..5. As-cast Al-7%Si-3.5%Cu at 58 K Position Position 6..2.3.4.5.6.7.8.9 Figure 5: Copper concentration in the -phase across the characteristic volume element after postsolidification cooling to 58K for two positions in an endchilled Al-7%Si-3.5% Cu casting. Solid Fraction (λ/d) 36/8
Solute Distribution in Phase (Al-7%Si-3.5%Cu, DAS=38 Microns, at T eut ) Solute Concentration (Wt%) 6 5 4 3 2 Cu in -Phase Silicon in -Phase..2.3.4.5.6.7.8.9 Solid Fraction (λ/d) Si Si θ Figure 6: Cu and Si distribution after solidification to ternary eutectic temperature for Al-7%Si-3.5%Cu alloy using divorced eutectic model. Weight Percent of θ-phase during Solution Treatment (Al-7%Si-3.5%Cu, DAS=38 µm, T=55 O C) 4 Weight Percent of θ-phase 3.5 3 2.5 2.5.5 2-D Growth Model -D Growth Model 2 4 6 8 Solution Treatment Time (Hrs) Figure 7: Dissolution of θ-phase during solution treatment of Al-7%Si-3.5%Cu at 55 O C: Comparison of -D and 2-D models. 36/9
Cu Distribution in the -phase for 6 Al-7%Si-3.5%Cu-.5%Mg alloy at T eut Weight % Cu in - phase 5 4 3 2 Cu (ESD model) Cu (LSD model) Si Si Q Si θ Q..2.3.4.5.6.7.8.9 Solid Fraction (λ/d) Figure 8: Cu distribution in -phase for Al-7%Si-3 5%Cu-.5%Mg alloy after solidification to the quaternary eutectic temperature: Comparison of use of D CuCu (LSD) measured for ternary alloy without Mg and use of enhanced diffusivity (2xD CuCu ) for Mg addition (ESD). Cu Distribution in -phase (Al-7%Si-3.5%Cu-.5%Mg, DAS=38 Microns, T=573 K) 3 Weight %Cu in -phase 2.5 2.5.5 ESD2 ESD LSD..2.3.4.5.6.7.8.9 Solid Fraction (λ/d) Figure 9: Comparison of predicted Cu distribution in -phase for as-cast Al-7%Si-3.5%Cu-.5%Mg with microprobe data (points). Model ESD2 includes divorced solidification. enhanced diffusivity due to Mg addition and enhanced diffusion in silicon region. 36/