Experimental determination of mushy zone permeability in aluminum-copper alloys with equiaxed microstructures

An experimental apparatus for measuring the mushy zone permeability of aluminum-copper alloys with equiaxed microstructures has been constructed. Permeabilities have been measured for high solid fractions (0.68 to 0.91) and different dendrite morphologies. Microstructure characterizations on both the interdendritic and extradendritic length scales have been performed on the samples. The results are in fairly good agreement with the predictions of the Kozeny-Carman relation and with more recent theory that takes flow partitioning between interdendritic and extradendritic regions into account.     

Further discussions on the solute redistribution during dendritic solidification of binary alloys

After a review over former works about the solute redistribution during dendritic solidification, a new“local solute redistribution equation ”is deduced based on Flemings's model, where lim-ited diffusion in solid during solidification is carefully treated. Because a form parameter is also included, the equation can be used for the solidification processes with different shapes of den-drites. By solving the equation at the condition of directional solidification, more completef _s -C, functions for both needlelike and platelike dendritic solidifications with both linear and parabolic solidification rates are obtained. As examples, the volume fractions of nonequilibrium phase in Al-4.5 pct Cu alloy is evaluated with differentf _s -C _l functions. On the thinking that the dendrites in actual solidification process is usually between needlelike and platelike ones, the volume fraction of the nonequilibrium phase is suggested to be in the region between the one calculated by the model for platelike dendrites and that for needlelike dendrites. The relationship between the region and local solidification time is also presented by figures, which are compared with the data of former researchers.     

Measurement of liquid permeability in the mushy zones of aluminum-copper alloys

Measurements of liquid permeability in the mushy zones of Al-15.42 pct Cu and Al-8.68 pct Cu alloy samples were performed isothermally just above the eutectic temperature, using eutectic liquid as the fluid. A modified method was developed to determine the specific permeability as a function of time (K _s) during the test from the data collected on these alloys. Factors affecting permeability measurements are discussed. The permeabilities are observed to vary throughout the experiment. This is attributed to microstructural coarsening and channeling that occur in the sample during the experiment. Coarsening rates are determined for the isothermal coarsening tests without fluid flow, and the results are observed to be less than the rates indicated from permeability tests where fluid flow is present. Careful measurement of the volume fraction of liquid (g _L) shows that g _L decreases during the test. The permeability is then related to the microstructure of the sample using the Kozeny-Carman equation. The correlation between the measured K _S, g _L, and specific solid surface area (S _V) improves markedly when compared to previous studies, when microstructural parameters at the initial stage of the test are used.     

Mathematical modeling of solidification paths in ternary alloys: Limiting cases of solute redistribution

A simple mathematical framework is provided for calculating solidification paths of ternary alloys for equilibrium, paraequilibrium, and nonequilibrium conditions. The results are useful for estimating the possible range of primary solidification paths, the type of monovariant reaction expected to occur, and the relative amount of primary, monovariant eutectic and ternary eutectic constituents that form during solidification. Example calculations show that, for solidification of a ternary eutectic alloy under equilibrium conditions, the monovariant eutectic reaction will only occur when the nominal alloy concentration is above the maximum solid solubility. This result is similar to the binary case. For paraequilibrium conditions, a monovariant eutectic reaction is always expected to occur, but solidification can terminate before the invariant ternary eutectic reaction is reached. Finally, for nonequilibrium conditions, both the monovariant and invariant ternary eutectic reactions are always expected to occur, which is similar to the binary nonequilibrium case. The direction of liquid enrichment on the monovariant eutectic line can also be determined from the results.     

An analytical solution of directional solidification with mushy zone

An analytical heat transfer model is presented that describes the temperature distribution and the positions of solidus and liquidus isotherms in the unidirectional solidification of binary alloys. The proposed technique employs the mathematical expedient of replacing the interfacial thermal resistance by equivalent layers of material. The application of the model is demonstrated by comparison with experimental data and with a finite difference method.     

Thermal strain in the mushy zone for aluminum alloys

The parameters in a recently developed constitutive equation for macroscopic thermal strain in the mushy zone have been determined for the commercial alloys A356, AA2024, AA6061, and AA7075 in addition to an Al-4 wt pct Cu alloy. The constitutive equation for macroscopic thermal strain in the mushy zone reflects that there is no thermal strain in the solid part of the mushy zone at low solid fractions and that the thermal strain in the mushy zone approaches thermal strain in the fully solid material as the solid fraction increases toward 1. The development of thermal strain in the mushy zone is determined by combining experimentally measured contraction of a cast sample with thermomechanical stimulations. Experiments were performed at cooling rates in the range from 2 to 5.5 °C/s. The solid fractions when the tested alloys start to contract,g _s ^th, are in the range from 0.63 to 0.94. Grain refinement increasesg _s ^th for all the tested alloys. For most of the tested alloys the thermal strain in the mushy zone increases rapidly to the same level as thermal strain in fully solid material once the solid fraction becomes higher thang _s ^th.     

Structure formation during the sintering of aluminum-copper alloys

Conclusions In the stage of growth of Al-Cu compacts during liquid-phase sintering diffusion zones of solid solutions form on the surfaces of the aluminum particles, while a liquid phase appears at the grain boundaries. At a copper concentration in the mixture within the limits of solid-phase solubility the structure of the compacts does not change during holding at the sintering temperature. In the shrinkage stage, when the liquid phase is retained during the whole period of sintering, a polyhedral structure is formed, whose grain increases in size with increasing duration of the process. The principal mechanism of formation of the polyhedral cast structure is apparently crystallization of the melt on the undissolved particles during cooling. The subsequent coarsening of the structure with time during isothermalsintering is due to recrystallization of the solid phase through the melt.Translated from Poroshkovaya Metallurgiya, No. 3(279), pp. 19–23, March, 1986.     

The influence of convection during solidification on fragmentation of the mushy zone of a model alloy

Experiments have been conducted to observe fragmentation events in a model alloy (succinonitrile and acetone) solidifying in the presence of forced convection in the superheated melt. Measurements of fragmentation rates have been made, and an attempt was made to relate the results to the controllable parameters of the system. A microscope-video system recorded the mushy zone-melt interface, and the fragmentation process and fragmentation rates could be determined from a frame-by-frame analysis of the video images. Experiments were conducted for varying cooling rates, overall temperature differences, melt flow rates, and for two different concentrations of acetone (1.3 and 6.1 wt pct). Significant dendritic fragmentation occurred for all runs. In addition, the influence of buoyancy forces is clearly evident from particle motion near the mushy zone-melt interface. Fragmentation rates appear to correlate well with the magnitude of particle velocities near the interface, with increasing fragmentation being associated with higher particle velocity magnitude (either in the same or the opposite direction to the mean flow) for the 1.3 wt pct acetone mixture. However, the correlation is quite different for the higher concentration. The relationship between these results and the possible mechanisms for fragmentation are discussed. Although it appears that either constitutional remelting or capillary pinching are likely of importance, hydrodynamic shear forces or some other mechanism as yet undiscovered cannot be completely discounted, although circumstantial evidence suggests that mechanical shearing is inconsistent with observations made both here and already in published literature. The results provide a step in the development of solidification models that incorporate fragmentation processes in the mushy zone as an important mechanism of grain refinement and a potential source of macrosegregation in ingots and large castings.     

The influence of convection during solidification on fragmentation of the mushy zone of a model alloy

Experiments have been conducted to observe fragmentation events in a model alloy (succinonitrile and acetone) solidifying in the presence of forced convection in the superheated melt. Measurements of fragmentation rates have been made, and an attempt was made to relate the results to the controllable parameters of the system. A microscope-video system recorded the mushy zone-melt interface, and the fragmentation process and fragmentation rates could be determined from a frame-by-frame analysis of the video images. Experiments were conducted for varying cooling rates, overall temperature differences, melt flow rates, and for two different concentrations of acetone (1.3 and 6.1 wt pct). Significant dendritic fragmentation occurred for all runs. In addition, the influence of buoyancy forces is clearly evident from particle motion near the mushy zone-melt interface. Fragmentation rates appear to correlate well with the magnitude of particle velocities near the interface, with increasing fragmentation being associated with higher particle velocity magnitude (either in the same or the opposite direction to the mean flow) for the 1.3 wt pct acetone mixture. However, the correlation is quite different for the higher concentration. The relationship between these results and the possible mechanisms for fragmentation are discussed. Although it appears that either constitutional remelting or capillary pinching are likely of importance, hydrodynamic shear forces or some other mechanism as yet undiscovered cannot be completely discounted, although circumstantial evidence suggests that mechanical shearing is inconsistent with observations made both here and already in published literature. The results provide a step in the development of solidification models that incorporate fragmentation processes in the mushy zone as an important mechanism of grain refinement and a potential source of macrosegregation in ingots and large castings. C. J. PARADIES, formerly Graduate Research Assistant, Rensselaer Polytechnic Institute     

AH36钢两相区非平衡凝固路径的数值预测

应用多元合金两相区凝固显微偏析数学模型,对AH36钢在一定冷却条件下的非平衡凝固路径进行了数值计算,获得了相应的局部固相分数与局部温度之间的变化关系,为该钢种对应的连铸浇铸过程仿真及其它凝固过程仿真提供了必要而准确的耦合数据,具有重要的理论意义和广泛的适用性.     

连铸流动与凝固耦合模拟中糊状区系数的表征及影响

分析提出了连铸流动与凝固耦合数值模拟中, 钢液在两相区流动时的糊状区系数(A_mush)与渗透率的关系; 通过建立大方坯连铸结晶器三维耦合数值模型, 揭示了不同糊状区系数对钢液流动、传热与凝固进程的影响, 以及早期相关研究结果差异的源头.结果表明: 糊状区系数越大, 钢液在糊状区内的流动阻力越强, 凝固时钢液流动速度降低越快.采用较大的糊状区系数时, 糊状区呈较窄的"带状"分布在固液相之间; 当糊状区系数较小时, 糊状区范围变大, 钢液在结晶器内温降过快, 自由液面处出现过冷现象, 凝固坯壳局部发生重熔.结合实验数据验证与模型分析, 认为糊状区系数取值1×108~5×108 kg·m-3·s-1可以较可靠地揭示连铸结晶器内的实际凝固现象.      

Modeling freckle formation in three dimensions during solidification of multicomponent alloys

The formation of macrosegregation defects known as “freckles” was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-W alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.     

Modeling of the formation of under-riser macrosegregation during solidification of binary alloys

The formation of macrosegregation in a rectangular ingot with reduced cross section from the riser to the casting, chilled from the bottom, has been studied numerically. In addition to positive inverse segregation occurring near the chilled surface, very severe negative segregation around the under-riser region and moderate positive segregation near the top corners of the casting were found. Although large circulating vortexes are created by natural convection in the under-riser region during the early stage of solidification, the fluid flow in the mushy zone is dominated by solidification shrinkage. As a result, the final solute distribution in the casting is determined by the flow of solute-rich liquid in the mushy zone owing to the combined effects of solidification shrinkage and change of cross section from casting to riser. Detailed explanations regarding the effect of different flow phenomena on the formation of the segregations are provided. The effects of riser size and cooling condition at the bottom of the ingot on the formation of macrosegregation also were studied. The predicted negative and positive macrosegregations in the casting compared very well with the available experimental data.     

An analytical model for solute redistribution during solidification of planar,columnar, or equiaxed morphology

Existing models for solute redistribution (microsegregation) during solidification were reviewed. There are no analytical models that take into account limited diffusion in both the liquid and the solid phases. A new analytical mathematical model for solute redistribution was developed. Diffusion in liquid and in solid was considered. This model does not require a prescribed movement of the interface. It can be used for one-dimensional (1-D) (plate), two-dimensional (cylinder), or three-dimensional (3-D) (sphere) calculations. Thus, it is possible to calculate microsegregation at the level of primary or secondary arm spacing for columnar dendrites or for equiaxed dendrites. The solution was compared with calculations based on existing models, as well as with some available experimental data for the segregation of base elements in as cast Al-4. 9 wt pct Cu, INCONEL 718, 625, and plain carbon (0. 13 wt pct C) steel.     

Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone

A two-phase volume-averaged continuum model is presented that quantifies macrosegregation formation during solidification of metallic alloys caused by deformation of the dendritic network and associated melt flow in the coherent part of the mushy zone. Also, the macrosegregation formation associated with the solidification shrinkage (inverse segregation) is taken into account. Based on experimental evidence established elsewhere, volumetric viscoplastic deformation (densification/dilatation) of the coherent dendritic network is included in the model. While the thermomechanical model previously outlined (M. M’Hamdi, A. Mo, and C.L. Martin: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2081–93) has been used to calculate the temperature and velocity fields associated with the thermally induced deformations and shrinkage driven melt flow, the solute conservation equation including both the liquid and a solid volume-averaged velocity is solved in the present study. In modeling examples, the macrosegregation formation caused by mechanically imposed as well as by thermally induced deformations has been calculated. The modeling results for an Al-4 wt pct Cu alloy indicate that even quite small volumetric strains (≈2 pct), which can be associated with thermally induced deformations, can lead to a macroscopic composition variation in the final casting comparable to that resulting from the solidification shrinkage induced melt flow. These results can be explained by the relatively large volumetric viscoplastic deformation in the coherent mush resulting from the applied constitutive model, as well as the relatively large difference in composition for the studied Al-Cu alloy in the solid and liquid phases at high solid fractions at which the deformation takes place.     

Relationship between tensile and shear strengths of the mushy zone in solidifying aluminum alloys

Strength development in the mushy zone during solidification of three aluminum alloys (Al-4 wt pct Cu, Al-7 wt pct Si-1 wt pct Cu, and Al-7 wt pct Si-4 wt pct Cu) has been measured with two different techniques—horizontal tensile testing and direct shear cell testing. The strength results from the two methods correspond with one another to a much higher degree than suggested by the results presented in the literature. Tensile strength starts to develop at the maximum packing solid fraction, confirmed by the shear strength measurements. The maximum packing fraction represents the point where the internal network structure of the mushy zone is established and ligaments of the network must be broken to rearrange the dendrites. The data indicate a converging trend of the shear and tensile strength at high solid fractions, therefore indicating that the deformation mechanisms are also becoming similar. The results presented in this article suggest that it is possible to develop constitutive equations for the mechanical properties of the mushy zone over the entire solid fraction regime, i.e., from coherency to complete solidification. These equations could be used for the prediction of stress development as well as defect formation.     

Modeling of marangoni-induced droplet motion and melt convection during solidification of hypermonotectic alloys

A two-phase volume averaging approach to model Marangoni-induced droplet motion of the minority liquid phase and the convection in the parent melt during solidification of the hypermonotectic alloys is presented. The minority liquid phase decomposed from the parent melt as droplets in the miscibility gap was treated as the second-phase L ₂. The parent melt including the solidified monotectic matrix was treated as the first phase L ₁. Both phases were considered as different and spatially interpenetrating continua. The conservation equations of mass, momentum, solute, and enthalpy for both phases, and an additional transport equation for the droplet density, were solved. Nucleation of the L ₂ droplets, diffusion-controlled growth, interphase interactions such as Marangoni force at the L ₁-L ₂ interface, Stokes force, solute partitioning, and heat release of decomposition were taken into account by corresponding source and exchange terms in the conservation equations. The monotectic reaction was modeled by adding the latent heat on the L ₁ phase during monotectic reaction, and applying an enlarged viscosity to the solidified monotectic matrix. A two-dimensional (2-D) square casting with hypermonotectic composition (Al-10 wt pct Bi) was simulated. This paper focused on Marangoni motion, hence gravity was not included. Results with nucleation, droplet evolution, Marangoni-induced droplet motion, solute transport, and macrosegregation formation were obtained and discussed.