Modeling of solidification microstructures in concentrated solutions and intermetallic systems

Most of the theoretical models for the predictions of solidification microstructure and solute segregation are based on the assumption mat the solute distribution coefficient,k, is independent of temperature. For concentrated alloys and for alloys near intermetallic compounds,k may vary significantly with temperature. A theoretical analysis which shows the necessary modifications in the theoretical models which must be made ifk varies with temperature is developed. It is shown that for phase diagrams with linear liquidus and solidus segments, many of the results derived with constantk can be used if the solute distribution coefficientk is replaced by a modified parameterk* which includesk as well as the derivative ofk with composition. The application of the model to concentrated alloys and to compositions near intermetallic phases is discussed. It is shown that the variation ink with temperature can significantly alter the composition dependence of dendritic microstructural scales and change the solute segregation profiles in solidified alloys.     

Modeling of solidification microstructures in concentrated solutions and intermetallic systems

Most of the theoretical models for the predictions of solidification microstructure and solute segregation are based on the assumption mat the solute distribution coefficient,k, is independent of temperature. For concentrated alloys and for alloys near intermetallic compounds,k may vary significantly with temperature. A theoretical analysis which shows the necessary modifications in the theoretical models which must be made ifk varies with temperature is developed. It is shown that for phase diagrams with linear liquidus and solidus segments, many of the results derived with constantk can be used if the solute distribution coefficientk is replaced by a modified parameterk* which includesk as well as the derivative ofk with composition. The application of the model to concentrated alloys and to compositions near intermetallic phases is discussed. It is shown that the variation ink with temperature can significantly alter the composition dependence of dendritic microstructural scales and change the solute segregation profiles in solidified alloys.     

Effect of Alloy Composition on the Dendrite Arm Spacing of Multicomponent Aluminum Alloys

Predictions of secondary dendrite arm spacing (SDAS) for multicomponent aluminum alloys using a dendrite ripening model are compared with experimental observations. For six of the seven alloys studied, the predicted SDAS was within 20 pct of the measured SDAS. It was found that the final SDAS was dependent upon both the solidification time and the solute profile of the solidifying alloys. It is interesting that while the solidification times and the solute segregation during solidification varied significantly over the range of alloys, these two factors largely canceled each other out so that the predicted SDAS did not vary much between the alloys. The experimental and modeling results show that elements causing high constitutional undercooling near the beginning of solidification, e.g., Ti, which reduces the grain size substantially, have little effect on the SDAS. Instead, it was found that elements that strongly partitioned toward the end of solidification were more effective at restricting SDAS coarsening.     

Solidification of Nb-bearing superalloys: Part II. Pseudoternary solidification surfaces

Equilibrium distribution coefficients and pseudoternary solidification surfaces for experimental superalloys containing systematic variations in Fe, Nb, Si, and C were determined using quenching experiments and microstructural characterization techniques. In agreement with previous results, the distribution coefficient, k, for Nb and Si was less than unity, while the “solvent” elements (Fe, Ni, and Cr) exhibited little tendency for segregation (k ≈ 1). The current data were combined with previous results to show that an interactive effect between k _Nb and nominal Fe content exists, where the value of k _Nb decreases from 0.54 to 0.25 as the Fe content is increased from ≈2 wt pct to ≈47 wt pct. This behavior is the major factor contributing to formation of relatively high amounts of eutectic-type constituents observed in Fe-rich alloys. Pseudoternary γ-Nb-C solidification surfaces, modeled after the liquidus projection in the Ni-Nb-C ternary system, were proposed. The Nb compositions, which partially define the diagrams, were verified by comparison of calculated amounts of eutectic-type constituents (via the Scheil equation) and those measured experimentally, and good agreement was found. The corresponding C contents needed to fully define the diagrams were estimated from knowledge of the primary solidification path and k values for Nb and C.     

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.     

Numerical modelling of dendritic solidification in aluminium-rich AlCuMg alloys

By modification of a numerical iterative computer simulation worked out for binary alloys, the solidification behaviour of ternary alloys can be quantitatively predicted. The program finds the cooling curves, the amount of binary and ternary eutectic, the concentration distribution of the solute elements in the dendrite arms and the spacing of the dendrite arms during and after complete solidification. Comparison of the numerical predictions with experimental results obtained for five alloys from the aluminium rich corner of the AlCuMg system at four cooling rates shows very good agreement.     

A Comparative Study of the γ/γ′ Eutectic Evolution During the Solidification of Ni-Base Superalloys

The evolution of γ/γ′ eutectic during the solidification of Ni-base superalloys CMSX-10 and CMSX-4 was investigated over a wide range of cooling rates. The microsegregation behavior during solidification was also quantitatively examined to clarify the influence of elemental segregation on the evolution of γ/γ′ eutectic. In the cooling rate ranges investigated (0.9 to 138.4 K/min (0.9 to 138.4 °C/min)), the γ/γ′ eutectic fraction in CMSX-10 was found to be more than 2 times higher than that in CMSX-4 at a given cooling rate. However, the dependence of the γ/γ′ eutectic fraction on the cooling rate in both alloys showed a similar tendency; i.e., the γ/γ′ eutectic fraction increased with increasing the cooling rate and then exhibited a maximum plateau at and above the certain critical cooling rate in both alloys. This critical cooling rate was found to be dependent on the alloy composition and was estimated to be about 12 K/min (12 °C/min) and 25 K/min (25 °C/min) for CMSX-10 and CMSX-4, respectively. The calculated solid compositions based on the modified Scheil model revealed that even a small compositional difference of total γ′ forming elements in the initial composition of the alloy can play a significant role in the as-cast eutectic fraction during the solidification of Ni-base superalloys. The evolution of the γ/γ′ eutectic fraction with respect to the cooling rate could be rationalized by taking into account the effects of back-diffusion in solid and dendrite arm coarsening on decreasing the extent of microsegregation.     

铝液凝固过程中显微组织对溶质元素偏析的影响

以溶质元素分配系数小于1的元素Fe、Si、Ga、Zn为研究对象,通过分析工业试验条件下铝液凝固过程中杂质元素含量变化,以及对应的显微组织(包括晶粒形貌、尺寸和金属间化合物),并与热力学计算软件Factsage计算的Scheil-Gulliver冷却条件下杂质元素含量和析出相进行了比较。研究发现,铝液凝固初期固相中杂质元素含量最低,且均大于理论计算值,随着凝固的进行,杂质元素含量逐渐增高且与理论值偏差越来越大,出现以上现象的原因包括：1)铝液实际凝固过程中存在边界层效应,即从固相中排出的杂质元素没有完全扩散到液相中;2)铝液实际凝固过程中存在微观偏析现象,即沿着晶界处有Al-Fe-Si中间相析出。另外,发现本研究试验条件下铝液凝固组织有粗大柱状晶、细小柱状晶、等轴晶,粗大的柱状晶更有利于提高部分杂质元素的偏析提纯效率,通过控制提高强制冷却可以促进粗大柱状晶的形成。     

A castability model based on elemental solid-liquid partitioning in advanced nickel-base single-crystal superalloys

A castability model that accounts for the characteristic segregation behavior of constituent elements in Ni-base superalloys has been developed and experimentally verified in production scale casting trials. The model ranks alloy compositions with respect to their susceptibility to freckle formation during directional solidification. Thirty-nine distinct Ni-base single-crystal superalloys encompassing a broad range of compositions were investigated to assess the influence of the constituent elements on their solidification characteristics. Linear regression was applied to the fitted solid-liquid partition coefficients of the major constituent elements to develop formulas capable of describing elemental interactions. The high-density refractory elements Ta, W, and Re were found to segregate most severely during solidification. Increasing the amount of Cr and Mo in high-refractory single-crystal alloys reduced the extent of W and Re microsegregation during solidification. This effect was found to minimize the occurrence of freckle defects due to the corresponding decrease in the density inversion term, which is effectively the driving force for thermosolutal convective instabilities known to cause macroscopic grain defects during single-crystal solidification. Model predictions were validated using production scale casting trials where additions of 1.5 wt pct (1.9 at. pct) Cr and 3.0 wt pct (2.0 at. pct) Mo to a high-refractory superalloy more than halved the number of solidification-related grain defects formed. These findings suggest that elemental interactions between Cr, Mo, W, and Re need to be considered when optimizing alloys for high-temperature creep properties.     

脉冲电磁场凝固组织细化和均质化技术研究与应用进展

由于金属凝固过程中选分结晶的作用,不可避免地会出现成分不均匀现象。连铸过程中由于强制冷却,这种成分不均匀现象更为严重。这不仅影响了铸坯和铸锭后续加工性能,并影响了最终产品质量和性能的均匀性和稳定性。研究和生产实践表明,细化凝固组织是解决成分不均匀性的有效手段。脉冲电磁场因能耗低、施加方便、细晶效果显著,近年来得到了广泛关注,有望成为冶金界广泛应用的凝固组织细化和均质化技术。分别介绍脉冲电流、脉冲磁场和脉冲磁致振荡3种脉冲电磁场凝固组织细化和均质化技术的研究现状和应用进展。     

Effect of composition on the solidification behavior of several Ni-Cr-Mo and Fe-Ni-Cr-Mo alloys

The microstructural development of several Ni-Cr-Mo and Fe-Ni-Cr-Mo alloys over a range of conditions has been examined. A commercial alloy, AL-6XN, was chosen for analysis along with three experimental compositions to isolate the contribution of individual alloying elements to the overall microstructural development. Detailed microstructural characterization on each alloy demonstrated that the observed solidification reaction sequences were primarily dependent on the segregation behavior of molybdenum (Mo), which was unaffected by the large difference in cooling rate between differential thermal analysis (DTA) samples and welded specimens. This explains the invariance of the amount of eutectic constituent observed in the microstructure in the welded and DTA conditions. Multicomponent liquidus projections developed using the CALPHAD approach were combined with solidification path calculations as a first step to understanding the observed solidification reaction sequences. Discrepancies between the calculations and observed reaction sequences were resolved by proposing slight modifications to the calculated multicomponent liquidus projections.     

Study of microstructure and solute partitioning in a cast Ti-48Al-2Cr-2Nb alloy by quenching during directional solidification technique

One major hindrance to effective implementation of cast gamma TiAl-based intermetallic alloys in aircraft engines lies in the variability of their mechanical properties resulting from chemical and microstructural heterogeneities. In the present work, the buildup of microsegregation in a cast Ti-48Al-2Cr-2Nb alloy is investigated through experiments of quenching during directional solidification (QDS). The solidification process, as well as the partitioning of alloying elements, between the solid and liquid phases, is investigated. Considering experimental conditions, the α-hcp phase is found to be the primary solidifying phase. A low dendrite tip temperature of 1475 °C was estimated from thermal recordings. These observations could be explained considering the value of the thermal gradient (around 4 °C/mm). Quantitative values of partition coefficients are proposed for Al, Cr, and Nb. In addition to Al, Cr is found to segregate in interdendritic regions, whereas Nb tends to be retained in the Ti-rich inner dendrites. Considering experimental cumulative solute distributions, the buildup of microsegregation can be satisfactorily represented on the basis of Gulliver-Scheil assumptions. Due to high-temperature quenching, the QDS experiments are also found to be appropriate to the study of high-temperature phase transformations and microstructural development of TiAl-based alloys. The results of QDS experiments are discussed with regard to the range of microstructural and chemical heterogeneities determined within Ti-48Al-2Cr-2Nb investment castings. Finally, regarding solid-state phase transformations subsequent to solidification, the study attempts to explain the formation of B2 phase particles stabilized by the ternary additions. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 17–21, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

Experimental determination of ternary partition coefficients in Fe-Ni-X alloys

A directional solidification experiment to measure partition coefficients of ternary additions in Fe-Ni alloys is described. A model is developed to calculate the extent of solid state diffusion effects during and after solidification. Ternary diffusivities of Ge and Au in Fe-Ni were measured for use in the calculation procedure. The model is used to correct the measured partition coefficients for solid state diffusion effects. The resulting equilibrium partition coefficients, K _x ^o , for elementX in Fe-Ni-X alloys are 0.43 for Au, 0.58 for Ge, 0.12 for P, 0.87 for Ni, and 1.45 for Pt. These studies demonstrated that solid state diffusion effects are significant when the diffusivity of the third elementX, in Fe-Ni, is higher than 1 × 10⁻¹⁰ cm²/s at 1300 °C. The partition coefficient data is of particular interest in understanding the fractionation behavior of trace elements in iron meteorites.     

ND钢连铸坯两相区内的微观偏析模型

通过构建ND钢连铸坯凝固两相区内溶质的微观偏析模型, 不仅研究了C、S和P元素对固液两相区内钢的高温力学参数以及溶质再分配的影响, 还对P元素偏析比随冷却速率(C_R) 的变化规律进行了探究.通过分析模型结果表明: 初始C的质量分数在0.075%~0.125%之间时, 随着初始C含量的增加, P、S元素的偏析加剧, 凝固末端温度下降幅度变大, 导致脆性温度区间增大; 增加P和S元素的初始含量, P、S元素的偏析比降低, 但会加剧其在枝晶间残余液相中的富集, 直接导致零塑性温度(ZDT) 下降; ND钢中的Cu含量低于显著提高裂纹敏感性的临界含量, 且凝固过程中Cu元素的偏析比较低, 因此在ND钢凝固过程中Cu元素不能主导裂纹的诱发; 在一定的冷却速率波动范围内, P元素的偏析比随着冷却速率(C_R)的提高略有下降.      

On differential thermal analyzer curves for the melting and freezing of alloys

Using a heat-flow model of a differential thermal analyzer and thermal characteristics obtained by fitting experimental results for a pure metal, the response of the differential thermal analyzer is modeled for the melting and solidification of alloys. The enthalpy-temperature relation used for the alloy simulations is obtained by two different methods: (1) equilibrium and Scheil considerations derived solely from thermodynamic information and (2) solute-diffusion micromodels coupled to the differential thermal analysis (DTA) heat-flow equations. During the consideration of pure material melting, simple expressions are obtained for the effect of sample size and heating rate on the DTA melting onset temperature, peak temperature, and peak height, which assist in the proper calibration of a differential thermal analyzer. For alloys, the smearing effect of the DTA heat flow at different heating and cooling rates is demonstrated for various solidification-path features. In particular, the DTA peak temperature during melting, which is often selected as the liquidus temperature experimentally, is shown to be significantly higher than the liquidus temperature for small-freezing-range alloys and/or for alloys with slow solid diffusion. The DTA curves calculated for freezing with dendritic growth due to supercooling, quantify the errors associated with the determination of the liquidus temperature on cooling.     

Asymmetric Diffusional Solidification during Transient Liquid Phase Bonding of Dissimilar Materials

A theoretical analysis of diffusional solidification during transient liquid phase (TLP) bonding of dissimilar materials was performed in conjunction with experimental verification. A fully implicit, two-dimensional, finite element numerical simulation model, without the inherent symmetry assumption, was developed and used for the theoretical calculations, and good correlations between the model predictions and experimental results were observed. The study showed that an asymmetric distribution of residual interlayer liquid during a dissimilar joining of polycrystal and single crystal alloys is attributable to a mismatch between their lattice diffusion coefficients or solute solubility, irrespective of enhanced intergranular diffusion as was assumed previously. Also, notwithstanding increased solute diffusivity with temperature, it was found that an increase in bonding temperature can result in the prolongation of processing time t _f that is required to prevent the formation of deleterious eutectic during bonding of dissimilar materials. The occurrence of this seemingly anomalous behavior, however, reduces when a material is coupled with another type that exhibits a higher solute solubility or better capability of accommodating diffusing melting point depressant solute from the liquid interlayer.     

Prediction of hot tearing tendency for multicomponent aluminum alloys

It is of practical importance to be able to predict the hot tearing tendency for multicomponent aluminum alloys. Hot tearing is one of the most common and serious defects that occurs during the casting of commercial aluminum alloys, almost all of which are multicomponent systems. For many years, the main criterion applied to characterize the hot tearing tendency of an alloy system was based on the solidification interval. However, this criterion cannot explain the susceptibility-composition relation between the limits of the pure base metal and the eutectic composition. Clyne and Davies correlated the susceptibility-composition relationship in binary systems based on the concept of the existence of critical time periods during the solidification process when the structure is most vulnerable to cracking. The Scheil equation was used in their model using constant partition coefficient and constant liquidus slope estimated from the phase diagram. In the current study, the authors followed Clyne and Davies’ general idea, and directly coupled the Scheil solidification simulation with phase diagram calculation via PanEngine, a multicomponent phase equilibria calculation interface, and extended the model to higher order systems. The predicted hot tearing tendencies correlated very well with the experimental results of multicomponent aluminum alloys. This article is based on a presentation made in the John Campbell Symposium on Shape Casting, held during the TMS Annual Meeting, February 13–17, 2005, in San Francisco, CA.     

Simple model of microsegregation during solidification of steels

A simple analytical model of microsegregation for the solidification of multicomponent steel alloys is presented. This model is based on the Clyne-Kurz model and is extended to take into account the effects of multiple components, a columnar dendrite microstructure, coarsening, and the δ/γ transformation. A new empirical equation to predict secondary dendrite arm spacing as a function of cooling rate and carbon content is presented, based on experimental data measured by several different researchers. The simple microsegregation model is applied to predict phase fractions during solidification, microsegregation of solute elements, and the solidus temperature. The predictions agree well with a range of measured data and the results of a complete finite-difference model. The solidus temperature decreases with either increasing cooling rate or increasing secondary dendrite arm spacing. However, the secondary dendrite arm spacing during solidification decreases with increasing cooling rate. These two opposite effects partly cancel each other, so the solidus temperature does not change much during solidification of a real casting.