Effect of peritectic reaction on the migration of secondary dendrite arms in the presence of tertiary dendrites: analysis of a directionally solidified Sn–36 at.%Ni peritectic alloy

Directional solidification experiments have been performed on Sn–36 at.%Ni peritectic alloy in a constant temperature gradient at different growth velocities. Experimental result shows that a “sawtooth” morphology forms on secondary dendrite arms during the migration of secondary dendrites in the presence of tertiary dendrite arms. A theoretic model is therefore proposed to describe the formation of this “sawtooth” morphology in the peritectic solidification with tertiary dendrite arms taken into consideration. The migration of secondary dendrite arms is caused by remelting/solidification at the hot/cold sides of a liquid pool between secondary dendrite arms, which is a form of temperature gradient zone melting. And, the “sawtooth” morphology is ascribed to the difference in remelting velocity at the hot side of liquid pool during the migration of secondary dendrite arms due to the presence of tertiary dendrite arms. In addition, the proceeding of peritectic reaction can accelerate the formation of “sawtooth” morphology.     

Simulation of dendrite growth of Fe–C alloy using phase field method

采用相场法模拟了Fe--0.5%C合金等温凝固过程中单个枝晶和多个枝晶的生长, 研究了过冷度、各向异性、界面厚度、晶体取向以及扰动对枝晶形貌的影响, 获得了具有二次分枝的枝晶形貌, 再现了枝晶生长过程及枝晶臂之间的竞争生长. 模拟结果表明: 凝固过程中存在溶质富集和枝晶偏析, 枝晶主干溶质浓度最低, 枝晶臂之间的液相浓度最高. 随着过冷度的增大, 枝晶生长加快且分枝发达; 界面厚度直接影响枝晶的生长速度; 各向异性影响枝晶的形态; 晶体取向与坐标轴方向一致时枝晶优先生长;扰动的加入导致枝晶分枝的形成.     

用相场方法模拟Fe-C合金枝晶生长

采用相场法模拟了Fe-0.5%C合金等温凝固过程中单个枝晶和多个枝晶的生长,研究了过冷度、各向异性、界面厚度、晶体取向以及扰动对枝晶形貌的影响,获得了具有二次分枝的枝晶形貌,再现了枝晶生长过程及枝晶臂之间的竞争生长.模拟结果表明:凝固过程中存在溶质富集和枝晶偏析,枝晶主干溶质浓度最低,枝晶臂之间的液相浓度最高.随着过冷度的增大,枝晶生长加快且分枝发达;界面厚度直接影响枝晶的生长速度;各向异性影响枝晶的形态;晶体取向与坐标轴方向一致时枝晶优先生长;扰动的加入导致枝晶分枝的形成.     

Directional solidification of Cu-20Sn alloy at low speed: From peritectic coupled growth to banding

Bridgman-type directional solidification experiments have been carried out in Cu-20Sn peritectic alloy. Peritectic coupled growth and banding structures have been observed at low growth rates (1.5 and 2 μm/s) under a temperature gradient up to 40 K/mm. The peritectic coupled growth structure, containing rod dendrite primary α phase plus peritectic β phase, forms initially. As solidification proceeds, peritectic coupled growth is overgrown by banding or island banding structures. The formation of banding structure from coupled growth is explained by a model involving Sn concentration change at nucleation of the secondary phase ahead of the solid/liquid interface. It is found that the competitive growth between the α and β phases also plays a critical role on the formation of banding structures.     

Analysis on fluid permeability of dendritic mushy zone during peritectic solidification in a temperature gradient

Compared with the growing applications of peritectic alloys,none research on the fluid permeability K of dendritic network during peritectic solidification has been reported before.The fluid permeability K of dendritic network in the mushy zone during directional solidification of Sn-Ni peritectic alloy was investigated in this study.Examination on the experimental results demonstrates that both the temperature gradient zone melting (TGZM) and Gibbs-Thomson (G-T) effects have obvious influences on the morphology of dendritic network during directional solidification.This is realized through different stages of liquid diffusion within dendritic mushy zone by these effects during directional solidification.The TGZM effect is demonstrated to play a more important role as compared with the G-T effect during directional solidification.Besides,it is shown that the evolution of dendrite network is more complex during peritectic solidification due to the involvement of the peritectic phase.Through the specific surface Sv,analytical expression based on the Carman-Kozeny model was proposed to analyze the fluid permeability of dendritic mushy zone in directionally solidified peritectic alloys.In addition,it is interesting to find a rise in permeability K after peritectic reaction in both theoretical predication and experimental results,which is different from that in other alloys.The theoretical predictions show that this rise in fluid permeability K after pedtectic reaction is caused by the remelting/resolidification process on dendritic structure by the TGZM and G-T effects during peritectic solidification.     

用相场方法模拟镍的枝晶生长

采用相场模型,计算了纯镍的过冷溶液在凝固过程中的枝晶生长。在相场方程中,采用均匀网格的一般显示有限差分方法求解,通过数值模拟显示了枝晶的形貌,包括一次臂、二次臂,以及在枝晶生长过程中出现的“缩颈”现象。     

凝固方向对单晶高温合金枝晶组织的影响

用籽晶法制备了沿不同晶体取向凝同的镍基单晶高温合金试样,研究了单晶中枝晶形貌和一次枝晶臂距随凝固取向的变化规律.结果表明:凝同方向偏离[001]取向小于15°时,枝晶排列比较规则,一次枝晶臂距随偏离角度增大而减小;偏离角度为25°时,部分二次枝晶臂阻断了相邻一次枝晶干的生长,导致一次枝晶臂距增大.沿[011]和[111...     

强磁场下Zn-2 wt.%Cu合金定向凝固的初步研究

本文进行了10T强磁场下Zn-2wt.%Cu合金的定向凝固的初步研究.结果发现下拉速度较低时,无磁场时晶体以平界面方式生长,而施加磁场则产生带状组织,并且随着磁场的增加带状组织越来越明显,带状组织间距越来越小;当定向凝固速度较高,晶体以枝晶方式生长时,磁场促进枝晶的分枝,并扰乱枝晶规则生长;随定向凝固速度提高,磁场的作用逐渐减弱.     

On secondary dendrite arm coarsening in peritectic solidification

A model for isothermal coarsening of secondary dendrite arms in peritectic reaction and transformation (liquid + primary-phase → peritectic-phase) is proposed to evaluate the secondary dendrite arm spacing (λ₂) of the primary phase in directional solidification of peritectic alloys. The model defines three stages for thin-arm dissolution (or thick-arm coarsening), i.e. the initial, intermediate and final stages: the initial thin-arm dissolution through the primary phase is sustained solely by the Gibbs–Thomson effect; the intermediate thin-arm dissolution through the peritectic phase is driven by Gibbs–Thomson effect but retarded by the peritectic reaction and transformation; the final dissolution through the primary and peritectic phases is enhanced by the Gibbs–Thomson effect and the phase transformation. The kinetics of peritectic reaction and transformation were found to be crucial to determine the thin-arm dissolution, which were characterized by the reaction constant (f) and the diffusion coefficient of solute in solid peritectic-phase (D_S), respectively. The present model shows that λ₂V^m is constant for a given Pb–Bi peritectic alloy, where V is growth velocity, and the factor, m, ranges from 1/3 to 1/2, rather than that normally observed (e.g. 1/3) for single-phase solidification. It is also notable that the calculated λ₂ for a Zn–7.37 wt.% Cu peritectic alloy was reasonably consistent with our earlier experiments for various growth velocities.     

Effect of peritectic reaction on dendrite coarsening in directionally solidified Sn–36 at.%Ni alloy

Effect of peritectic reaction on dendrite coarsening was investigated in directionally solidified Sn–36 at.%Ni peritectic alloys at different growth rates (2~200 μm/s) under constant temperature gradient. A coarsening model was used to characterize the coarsening process in terms of both the secondary dendrite arm spacing (λ ₂) of the primary Ni₃Sn₂ phase and the specific surface area (S _V ) of dendrites. It was shown that peritectic reaction could retard the increase of λ ₂ and decrease of S _V during coarsening, which resulted from decelerating solute transport rate between adjacent dendrite arms caused by the peritectic phase enclosing the primary phase. The kinetics of the peritectic reaction that was found to be crucial to determine the coarsening process was characterized by the reaction constant (f) which not only changed with growth rates but also with solidification time in the real solidification process at a given growth rate.     

An examination of effects of solidification parameters on permeability of a mushy zone in castings

A model describing the development of dendritic structure and the resulting gradient of flow resistance to interdendritic liquid is presented. The Hagen–Pousielle version of D’Arcy’s equation for flow through a porous structure is developed as a function of cooling rate and liquid volume fraction. Applied to finite elements in a unidirectionally cooled casting model, permeability gradient, feeding flow-rate required to prevent porosity, and mushy-zone liquid pressure drop at this flow rate are evaluated for the simple Fe–2Cr–0.5C and Al–5Cu castings exhibiting asymptotic and linear temperature profiles, respectively. The model shows permeability of the dendritic structure in the mushy zone dropping sharply, approaching the root of solidification front (solidus). Also shown is the effect of relative magnitude of primary and secondary arm spacing. If secondary dendrite arm spacing approaches primary arm spacing, the permeability for flow normal to primary dendrite arms approaches or even surpasses the permeability for flow parallel to primary dendrite arms.     

The 3-dimensional morphology of dendrite during equiaxed solidification of an Al-5 wt.% Cu alloy

In a sample quenched during equiaxed solidification of an Al-5 wt.% Cu alloy, the multi-scales 3-dimensional morphology of equiaxed dendrite was observed. The slim primary stem and secondary branches constitute the frame of dendrite, and rows of dense tertiary branches further divide the 3-dimensional space. In the divided space, the quartic branches grow further. The dendritic branches,which are perpendicular to each other, can change their growth directions and coalesce into a whole. In the tertiary branches and quartic branches, the formation of double branch structures is induced by competitive growth. The branch that wins in the competitive growth will produce a cabbage-like structure by wrapping the failed branches. In addition, the side branch can also wrap the original parent branch to produce cabbage-like structures. Depending on the historical growth direction, the dendritic arms can form vein-like and spicate structures, and the shapes of single dendritic arm may be the cylinder, plate and trapezoid platform. According to the compositions and etching morphology, the single dendritic arm in the final solidification structures should coalesce from a fine porous structure. The porous structures at different length-scales are principally induced by the preferential growth. Based on 3-dimensional morphology of equiaxed dendrite, a new research object for the investigation of microsegregation was suggested.     

基于三维LBM-CA模型模拟Al-4.7%Cu合金的枝晶形貌和成分分布

建立了三维格子玻尔兹曼方法(LBM)-元胞自动机(CA)耦合数值模型,并用该模型模拟研究了Al-4.7%Cu(质量分数)固溶体合金的凝固过程。该耦合模型采用元胞自动机方法模拟枝晶的生长,同时采用基于分子动力学理论的格子玻尔兹曼方法模拟合金凝固过程中的温度场、流场以及溶质场。模拟结果再现了合金凝固过程中的三维枝晶形貌变化以及溶质富集过程,并将三维流场因素考虑进去,定量研究了自然对流、过冷度对单枝晶形貌和成分分布的影响。研究表明,在纯扩散条件下,枝晶呈现对称的生长现象,模拟自由枝晶稳态生长的尖端速度、尖端半径和过冷度的关系与Lipton-Glicksman-Kurz(LGK)理论模型吻合得较好。在自然对流条件下,枝晶的生长形貌呈现不对称性,即枝晶生长在迎流方向上得到了促进,在顺流方向上受到了抑制。熔体过冷度对枝晶生长的影响较大,过冷度的增加导致枝晶生长加快,二次枝晶增多且呈现出粗化现象,枝晶尖端固液界面处的溶质浓度偏高,加重了溶质偏析。     

Predicting dendrite arm spacing and their effect on microporosity formation in directionally solidified Al-Cu alloy

In the case of metallic alloys, which present dendritic structure, the mechanical properties of foundry products depend on primary and secondary arm spacing. For the prediction of microporosities it is necessary to characterize precisely the dendritic structure formed during solidification, to calculate the permeability and also to estimate the radius of the gas bubble to determine the pressure due to gas/metal surface tension. Therefore, it is important in a computational simulation of the solidification processes to use reliable equations to correlate the calculated thermal parameters with primary and secondary dendrite arm spacing. This study presents a numerical and experimental analysis of some models to predict the primary and secondary arm spacing as a function of thermal parameters. Comparison between the numerical and experimental results for Al 4.5 wt% Cu alloy allowed the selection of adequate equations to predict the dendritic spacing during unidirectional solidification.     

Macrosegregation and thermosolutal convection-induced freckle formation in dendritic mushy zone of directionally solidified Sn-Ni peritectic alloy

Compared with the growing applications of peritectic alloy,none research on the freckle formation during peritectic solidification has been reported before.Observation on the dendritic mushy zone of Sn-36 at.％Ni peritectic alloy during directional solidification at different growth velocities shows that the freckles are formed in two different regions:region Ⅰ before peritectic reaction and region Ⅱ after peritectic reaction.In addition,more freckles can be observed at lower growth velocities.Examination on the experimental results demonstrates that both the temperature gradient zone melting(TGZM)and Gibbs-Thomson(G-T)effects have obvious influences on the morphology of dendritic network during directional solidification.The current theories onKI Rayleigh number Ra characterizing the thermoso-lutal convection of dendritic mushy zone to predict freckle formation through the maximum of Ra can only explain the existence of region Ⅰ while the appearance of region Ⅱ after peritectic reaction cannot be predicted.Thus,a new Rayleigh number RaP is proposed in consideration of evolution of dendritic mushy zone by both effects and peritectic reaction.Theoretical prediction of RaP also shows a maximum after peritectic reaction in addition to that before peritectic reaction,thus,agreeing well with the freckle formation in region Ⅱ.In addition,more severe thermosolutal convection can be predicted by the new Rayleigh number RaP at lower growth velocities,which further demonstrates the reliability of RaP in describing the dependence of freckle formation on growth velocity.     

A Modified Cellular Automaton Model for the Quantitative Prediction of Equiaxed and Columnar Dendritic Growth

Since the characteristic of dendrite is an important factor determining the performance of castings, a twodimensional cellular automaton model with decentered square algorithm is developed for quantitatively predicting the dendritic growth during solidification process. The growth kinetics of solid/liquid interface are determined by the local equilibrium composition and local actual liquid composition, and the calculation of the solid fraction increment is based on these two compositions to avoid the solution of growth velocity. In order to validate the developed model, quantitative simulations of steady-state dendritic features over a range of undercooling was performed and the results exhibited good agreement with the predictions of LGK（Liptone Glicksman-Kurz） model. Meanwhile, it is demonstrated that the proposed model can be applied to simulate multiple equiaxed dendritic growth, as well as columnar dendritic growth with or without equiaxed grain formation in directional solidification of AleC u alloys. It has been shown that the model is able to simulate the growth process of multi-dendrites with various preferential orientations and can reproduce a wide range of complex dendritic growth phenomena such as nucleation, coarsening of dendrite arms, side branching in dendritic morphologies, competitive growth as well as the interaction among surrounding dendrites.     

Dendrite morphologies of the metastable phase from undercooled Fe-30at % Co melts and its stabilities

Five typical dendrite morphologies of the metastable bcc phase fromundercooled Fe-30 at % Co melt have been observed by TEMtechnique. The morphologies of the metastable phase exhibitedwell-developed dendrite with the primary trunk and second arms,well-developed second arms, radiated structure, lath structure,and bifurcated structure. The crystal growth mode and theformation of different dendrite morphologies were discussed onthe basis of the morphological patterns from undercooled melts.In the mean while, the breakage mode for the primary dendritewas suggested according to the observation of microstructures ofthe alloy solidified at various undercoolings. The EDS (EnergyDispersive Spectrum) analysis has confirmed enrichment of thesolute Co in metastable dendrite cores in comparison to thatpredicted from the view of equilibrium solidification. Furtherinvestigation after annealing showed that the solute diffusioncontrolled the stability of the metastable phase; thedisappearance of dendrite morphologies was mainly attributed tothe constituent homogenization within dendrite cores and thedecrease in the number of dendrite cores was chiefly owing tothe solute diffusion between dendrite cores and the subsequentlysolidified equilibrium phase.     

Characteristics of α-dendritic and eutectic structures in Sr-treated Al—Si casting alloys

The present study was carried out to determine the effect of alloy composition and solidification conditions on changes in the dendritic and eutectic structures in Al—Si alloys containing strontium. A series of experimental and industrial alloys viz., Al-7% Si, Al-12% Si, 319 and 356 were selected, to cover a variety of alloy freezing ranges. The techniques of thermal analysis, optical microscopy, and SEM/EDX and EPMA analyses were employed to obtain the results presented here. Depression in the eutectic Si temperature in Al-7% Si alloys occurs on addition of alloying elements such as Mg and Cu. Introduction of Sr to these alloys further depresses the eutectic temperature, with a corresponding increase in the volume fraction of the -Al phase. The primary dendrite solidification pattern changes from parallel rows to a branched form, producing an equiaxed type of structure and hence shorter primary dendrite lengths. This is expected to enhance the interdendritic feedability. The lengths of the secondary dendrite arms are controlled by the rejection of solute atoms in front of the growing dendrites during solidification. The higher the alloying content in the alloy (i.e., 319), the smaller the dendrite cell size. The longer solidification time in the 319 alloy also appears to have a considerable influence on the amount of porosity formed in the alloy, in addition to that of Sr.     

Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation – Part I: Model description

Part I of this two-part investigation presents a volume-averaging multiphase solidification model that accounts for mixed columnar-equiaxed solidification, non-dendritic and dendritic crystal growth, nucleation of equiaxed grains, columnar primary dendrite tip tracking, melt flow, sedimentation of equiaxed crystals, and their influence on macrostructure and macrosegregation. Five distinct thermodynamic phases (phase regions) are defined: solid dendrites in equiaxed grains, the interdendritic melt between equiaxed dendrites, solid dendrites in columnar trunks, the interdendritic melt between trunk dendrites, and the extradendritic melt. These five phase regions are quantified by their volume fractions and characterized by their solute concentrations. The five phase regions are grouped into three hydrodynamic phases: equiaxed grains consisting of solid dendrites and interdendritic melt, columnar trunks consisting of solid dendrites and interdendritic melt, and extradendritic melt. The extradendritic melt is separated from the interdendritic melt with a grain envelope, whose profile connects the primary, secondary or tertiary dendrite tips to form a ‘natural’ enclosure of the equiaxed grains or columnar trunks. The envelope is further simplified as a volume-equivalent sphere for equiaxed grains, or as volume-equivalent cylinder for columnar trunks by use of morphological shape factors. Expansion of the envelopes during solidification is determined by dendrite growth kinetics, using the Kurz–Giovanola–Trivedi model for growth of columnar primary dendrite tips and the Lipton–Glicksman–Kurz model for growth of columnar secondary dendrite tips (radial growth of the columnar trunk) and equiaxed primary dendrite tips. The solidification of the interdendritic melt is driven by the supersaturation of the interdendritic melt and governed by the diffusion in the interdendritic melt region. Illustrative process simulations and model verifications are presented in Part II.     

Morphological aspects of competitive grain growth during directional solidification of a nickel-base superalloy, CMSX4

Quenched directional solidification of specially oriented bi-crystals of the Ni-base superalloy CMSX4, was carried out in an attempt to understand the role of the dendritic morphology in the process of competitive grain growth. For the range of misorientations considered (primary 001 misoriented by up to 7° from the uniaxial thermal gradient), there was no evidence of overgrowth of the primary misoriented dendrite by the secondary arms on the leading aligned primary. In fact, it was observed that for this range of misorientations, the tip of the retarded primary suppresses the growth of secondaries on its leading neighbour. This subsequently simply restricts the growth of the mis-aligned crystal to its original boundary, rather than reducing its size and is suggested as a possible reason for the range of stable axial orientations encountered during directional solidification of CMSX4.