Modeling of equiaxed microstructure formation in casting

A general micro/macroscopic model of solidification for 2-D or 3-D castings, valid for both dendritic and eutectic equiaxed alloys, is presented. At the macroscopic level, the heat diffusion equation is solved with an enthalpy formulation using a standard FEM implicit scheme. However, instead of using a unique relationship between temperature and enthalpy (i.e., a unique solidification path), the specific heat and latent heat contributions, whose sum equals the variation of enthalpy at a given node, are calculated using a microscopic model of solidification. This model takes into account nucleation of new grains within the undercooled melt, the kinetics of the dendrite tips or of the eutectic front, and a solute balance at the scale of the grain in the case of dendritic alloys. The coupling between macroscopic and microscopic aspects is carried out using two time-steps, one at the macroscopic level for the implicit calculation of heat flow, and the other, much finer, for the microscopic calculations of nucleation and growth. This micro/macroscopic approach has been applied to one-dimensional and axisymmetric castings of Al-7 pct Si alloys. The calculated recalescences and grain sizes are compared with values measured for one-dimensional ingots cast under well-controlled conditions. Furthermore, the influence of casting conditions on temperature field, undercooling, grain size, and microstructural spacings is shown to be predicted correctly from axisymmetric calculations with regard to the expected experimental behavior.     

Phase‐Field Simulation of Solidifying Microstructure in the Presence of a Convective Field

Here we present a contribution to the microstructure based design of new steel alloys by a careful investigation of multiphase microstructure solidification in a convective field. To this end we present an extension of the quantitative phase‐field model proposed in [1] to investigate the influence of hydrodynamic convection on the growth of eutectic/peritectic alloys. We study directional solidification of a eutectic alloy under the influence of a shear flow ahead of the solidifying front. We mainly investigate the growth of a eutectic lamellar structure. We show that the imposed flow tilts the whole lamellar structure away from the flow direction. Moreover, we show that forced flow alters the growth morphology of Fe‐Ni peritectic alloys, having a strong influence on the nucleation of the peritectic phase. Based on these investigations, a scale relation between the strength of flow and the solid volume fraction is derived. Further we propose an application of these models as an alternative approach to study heterogeneous nucleation kinetics in the solidification of peritectic materials systems.     

Simulation of microstructure formation in technical aluminum alloys using the multiphase-field method

Simulation results of microstructure evolution in technical aluminum alloys are presented. The examples comprise solidification and further heat treatment of three different alloy classes, namely for the hypoeutectic alloy AA6061, the near eutectic alloy A356 and the highly alloyed, hypereutectic commercial alloy KS1295 being used in automotive applications. After a short introduction to the simulation models being applied — especially to the multiphase-field approach coupled to thermodynamic databases — the evolving microstructures are discussed in the context of the interplay between thermodynamics, kinetics, interfacial properties and nucleation.     

Solidification Analysis of an Al-19 Pct Si Alloy Using <Emphasis Type="Italic">In-Situ</Emphasis> Neutron Diffraction

In-situ neutron diffraction and thermal analysis techniques were used simultaneously to evaluate the kinetics of the nonequilibrium solidification process of an Al-19 pct Si binary alloy. Feasibility studies concerning the application of neutron diffraction for advanced solidification analysis were undertaken to explore its potential for high resolution phase analysis coupled with fraction solid/liquid analysis of phase constituents. Neutron diffraction patterns were collected in a stepwise mode during solidification between 983 K and 793 K (710 °C and 520 °C). The variation of intensity of the diffraction peaks was analyzed and compared to the results of conventional cooling curve analysis. Neutron diffraction was capable of detecting nucleation of the Si phase (primary and eutectic), as well as the Al phase during Al-Si eutectic nucleation. Moreover, neutron diffraction indicated the possibility of detecting the presence of Si peaks at near liquidus temperature and premature nucleation of α-Al prior to Al-Si eutectic temperature. The solid and liquid volume fractions were determined based on the change of intensity of neutron diffraction peaks over the solidification interval. Overall, the volume fraction determined was in good agreement with the results of the cooling curve thermal analysis, as well as calculations using the FactSage software. The potential of neutron diffraction for high resolution melt analysis required for advanced studies of grain refining, eutectic modification, etc. was illustrated. This study will help us better understand the solidification mechanism of Al-Si alloys used for various casting component applications.     

Eutectic Morphology of Al-7Si-0.3Mg Alloys with Scandium Additions

The mechanisms of Al-Si eutectic refinement due to scandium (Sc) additions have been studied in an Al-7Si-0.3Mg foundry alloy. The evolution of eutectic microstructure is studied by thermal analysis and interrupted solidification, and the distribution of Sc is studied by synchrotron micro-XRF mapping. Sc is shown to cause significant refinement of the eutectic silicon. The results show that Sc additions strongly suppress the nucleation of eutectic silicon due to the formation of ScP instead of AlP. Sc additions change the macroscopic eutectic growth mode to the propagation of a defined eutectic front from the mold walls opposite to the heat flux direction similar to past work with Na, Ca, and Y additions. It is found that Sc segregates to the eutectic aluminum and AlSi₂Sc₂ phases and not to eutectic silicon, suggesting that impurity-induced twinning does not operate. The results suggest that Sc refinement is mostly caused by the significantly reduced silicon nucleation frequency and the resulting increase in mean interface growth rate.     

Modeling of microstructural evolution with tracking of equiaxed grain movement for multicomponent Al-Si alloy

A new model for the simulation of microstructure evolution of multicomponent alloys with equiaxed dendritic and eutectic morphology has been developed based upon the mixture-theory model (continuum approach). The model can account for the effects of natural convection, solidification contraction, solidification kinetics, and grain movement on the solidification microstructure evolution. The novelty of this model is that it includes tracking of equiaxed dendritic and eutectic grains movement during solidification and, thus, eliminates the assumption of uniform grain size in a given volume element, which is standard in current advanced solidification models. This is achieved through the implementation of continuous nucleation laws and of a grain distribution function over the volume element, in addition to solid transport simulation through the energy equation. To track grain movement, rules of tracking grain movement are proposed. The model deals with nonequilibrium solidification and describes competitive growth of primary and eutectic phases. The proposed model was implemented to simulate the microstructural evolution of an Al-Si-Mg alloy (A356) during solidification. An equivalent pseudobinary approach was developed to calculate the solidification parameters required in modeling of this multicomponent alloy. Computational experiments with the new model have demonstrated that significant variations in the volumetric grain density exist throughout the casting because of natural convection. These differences can be traced with the proposed grain tracking technique but not with current solidification models.     

Influence of Phosphorus on the Nucleation of Eutectic Silicon in Al-Si Alloys

The role of phosphorus (P) in the heterogeneous nucleation of eutectic silicon (Si) and the evolution of eutectic grains in hypoeutectic aluminum-silicon alloys were investigated. Systematic additions of P in the range of 0.5 to 20 ppm to Al-7 wt pct Si alloys of different purities have shown that the morphology of the eutectic Si changes from a fine plate- to a coarse flake-like structure. The growth of eutectic grains was investigated by interrupting the eutectic reaction by quenching experiments. Moreover, the macroscopic growth mode of the eutectic grains was characterized by electron backscatter diffraction. An increase in P concentration from 2 to 3 ppm resulted in a transition of the macroscopic growth mode of the Al-Si eutectic in high purity alloys from growth with a planar front with a strong dependence of the thermal gradient, to nucleation in the vicinity of the primary Al dendrites and subsequent growth of distinct eutectic grains. It is suggested that AlP particles are the key impurities acting as potential nucleation sites for eutectic Si. This is further substantiated as with increasing P concentration nucleation and growth of the Al-Si occurred at higher temperatures close the equilibrium Al-Si eutectic solidification temperature at 850 K (577 °C). In addition, the recalescence undercooling ΔT _R,eu was reduced from 4.5 K (0.5 ppm P) to 1.5 K (20 ppm P) in high purity alloys. This was accompanied by a drastic increase of the nucleation rate of the eutectic grains.     

Comparison of nucleation and growth mechanisms in alloy solidification to those in metallic glass crystallisation — relevance to modeling

The development of microstructure during phase transformations is often best understood by considerations of nucleation in the parent material followed by growth of the new phase. This is a mature research field in alloy solidification, thanks to extensive investigations of nucleation and dendritic growth in cooling alloy melts. Bulk metallic glasses, on the other hand, typically do not form crystals on cooling from above the liquidus to below the glass transition temperature, resulting in very strong hard materials. As BMG toughness can be enhanced by a crystallising anneal, the study of nucleation and growth of crystals in viscous multi-component liquids has become an important topic for study. Such devitrification can lead to crystalline-glass composites or bulk nano-crystalline alloys, and the micro- or nano-structure is controlled by phenomena such as diffusion of solute and heat, and impingement dynamics. The relevance of solidification theories of nucleation, growth and impingement to crystallisation in amorphous alloys is discussed in this paper. The effects of the key differences between phase transformations in alloy casting processes and those in alloy devitrification on development of computational models for process simulation are highlighted.     

Dendritic growth of undercooled nickel-tin: Part II

High-speed optical temperature measurements were made of the solidification behavior of levitated metal samples within a transparent glass medium. Two undercooled Ni-Sn alloys were examined, one a hypoeutectic alloy and the other of eutectic composition. Recalescence times for the 9 mm diameter samples studied decreased with increasing undercooling from the order of 1.0 second at 50 K under-cooling to less than 10⁻³ second for undercoolings greater than 200 K. Both alloys recalesced smoothly to a maximum recalescence temperature at which the solid was at or near its equilibrium composition and equilibrium weight fraction. For the samples of hypoeutectic alloy that recalesced above the eutectic temperature, a second nucleation event occurred on cooling to the eutectic temperature. For samples which recalesced only to the eutectic temperature, no subsequent nucleation event was observed on cooling. It is inferred in this latter case that both the α and β phases were present at the end of recalescence. The thermal data obtained suggest a solidification model involving (1) dendrites of very fine structure growing into the melt at temperatures near the bulk undercooling temperature, (2) thickening of dendrite arms with rapid recalescence, and (3) continued, much slower recalescence accompanying dendrite ripening.     

Effect of shape variations on the structure of directionally solidified Al-Al3Ni composites

The effect on structure of some of the possible changes in shape of directionally solidified Al-Al₃Ni eutectic composites has been studied for two growth conditions. The shape changes investigated included both contraction and divergence in cross-section of the grown part, as well as 90 deg bends in the center-line of the composites. The experimental results showed that contractions in the solidifying cross section do not seriously affect the growth of composites, apart from some coarsening of the structure near the surface. Fiber branching took place in the case of gradual divergence in the solidifying cross section with the fibers deviating from the general growth direction by an angle determined by the shape of equitemperature contours during solidification. Sharp changes in growth direction, 90 deg bend, gave rise to nucleation of new grains of considerable misorientation and hypoeutectic alloys nucleated primary aluminum phase before the eutectic structure was established. The relatively large under cooling needed for nucleation gave rise to high local growth rates in the 90 deg bend area. As the Al₃Ni fibers grow at right angles to equitemperature contours during solidification, it is concluded that control of the composite structure can be achieved by controlling the growth conditions and mold design. Molten alloy-graphite reactions resulted in the formation of aluminum carbides which were more extensive at higher temperatures and longer exposure times.     

The impact of cooling rates on the microstructure of Al-U alloys

The impact of cooling rates on the microstructure of Al-U alloys was studied by optical, scanning electron, and transmission electron microscopy. A variety of solidification techniques were employed to obtain cooling rates ranging between 3 × 10⁻² and 10⁶ K/s. High-purity uranium (99.9 pct) and high-purity aluminum (99.99 pct), or “commercially pure” type Al-1050 aluminum alloys were used to prepare Al-U alloys with U concentration ranging between 3 and 22 wt pct. The U concentration at which a coupled eutectic growth was observed depends on the cooling rates imposed during solidification and ranged from 13.8 wt pct for the slower cooling rates to more than 22 wt pct for the fastest cooling rates. The eutectic morphology and its distribution depends on the type of aluminum used in preparing the alloys and on the cooling rates during solidification. The eutectic in alloys prepared from pure aluminum was evenly distributed, while for those prepared from Al-1050, the eutectic was unevenly distributed, with eutectic colonies of up to 3 mm in diameter. Two lamellar eutectic structures were observed in alloys prepared from pure aluminum containing more than 18 wt pct U, which solidified by cooling rates of about 10 K/s. One structure consisted of the stable eutectic between UAl₄ and Al lamella. The other structure consisted of a metastable eutectic between UAl₃ and Al lamella. At least three different eutectic morphologies were observed in alloys prepared from Al-1050.     

Microstructural characteristics of Ni-Sb eutectic alloys under substantial undercooling and containerless solidification conditions

Both Ni-36 wt pct Sb and Ni-52.8 wt pct Sb eutectic alloys were highly undercooled and rapidly solidified with the glass-fluxing method and drop-tube technique. Bulk samples of Ni-36 pct Sb and Ni-52.8 pct Sb eutectic alloys were undercooled by up to 225 K (0.16 T _E ) and 218 K (0.16 T _E ), respectively, with the glass-fluxing method. A transition from lamellar eutectic to anomalous eutectic was revealed beyond a critical undercooling ΔT ₁*, which was complete at an undercooling of ΔT ₂*. For Ni-36 pct Sb, ΔT ₁*≈60 K and ΔT ₂*≈218 K; for Ni-52.8 pct Sb, ΔT ₁*≈40 K and ΔT ₂*≈139 K. Under a drop-tube containerless solidification condition, the eutectic microstructures of these two eutectic alloys also exhibit such a “lamellar eutectic-anomalous eutectic” morphology transition. Meanwhile, a kind of spherical anomalous eutectic grain was found in a Ni-36 pct Sb eutectic alloy processed by the drop-tube technique, which was ascribed to the good spatial symmetry of the temperature field and concentration field caused by a reduced gravity condition during free fall. During the rapid solidification of a Ni-52.8 pct Sb eutectic alloy, surface nucleation dominates the nucleation event, even when the undercooling is relatively large. Theoretical calculations on the basis of the current eutectic growth and dendritic growth models reveal that γ-Ni₅Sb₂ dendritic growth displaces eutectic growth at large undercoolings in these two eutectic alloys. The tendency of independent nucleation of the two eutectic phases and their cooperative dendrite growth are responsible for the lamellar eutectic-anomalous eutectic microstructural transition.     

连续铸钢过程中结晶器的传热研究

 为了研究结晶器内壁温度的分布，设计了模拟结晶器工作过程的实验装置，并进行了实验。实验结果表明，结晶器内壁温度趋近于冷却水温度。基于实验，推导了结晶器边界等效导热系数。该系数用于解决金属和冷却水之间的传热，即反映结晶器的传热能力。用等效导热系数处理结晶器的边界传热，对包括结晶器在内的连铸凝固进程温度场进行数值模拟既简单又方便，并且计算结果与实验结果符合。还讨论了拉坯速度和冷却水流量对结晶器温度场的影响。     

Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part II. Computation problems and validation on INCONEL 718 superalloy castings

In Part I of the article, a new analytical model that describes solidification of equiaxed dendrites was presented. In this part of the article, the model is used to simulate the solidification of INCONEL 718 superalloy castings. The model was incorporated into a commercial finite-element code, PROCAST. A special procedure called microlatent heat method (MLHM) was used for coupling between macroscopic heat flow and microscopic growth kinetics. A criterion for time-stepping selection in microscopic modeling has been derived in conjunction with MLHM. Reductions in computational (CPU) time up to 90 pct over the classic latent heat method were found by adopting this coupling. Validation of the model was performed against experimental data for an INCONEL 718 superalloy casting. In the present calculations, the model for globulitic dendrite was used. The evolution of fraction of solid calculated with the present model was compared with Scheil’s model and experiments. An important feature in solidification of INCONEL 718 is the detrimental Laves phase. Laves phase content is directly related to the intensity of microsegregation of niobium, which is very sensitive to the evolution of the fraction of solid. It was found that there is a critical cooling rate at which the amount of Laves phase is maximum. The critical cooling rate is not a function of material parameters (diffusivity, partition coefficient,etc.). It depends only on the grain size and solidification time. The predictions generated with the present model are shown to agree very well with experiments.     

The solidification characteristics of Fe-rich intermetallics in Al-11.5Si-0.4Mg cast alloys

After the nucleation and sedimentation of primary Fe-rich phases, the microstructures of Al-11.5Si-0.4Mg cast alloys with 0.35–1.03Fe and 0.18–0.59Mn have been studied to investigate the solidification characteristics of Fe-rich phases. Depending on the iron and manganese contents as well as cooling rates, Fe-rich phases may solidify as predendritic (primary), pre-eutectic, coeutectic, and posteutectic intermetallics at the different stages of solidification through three types of reactions: (1) predendritic (primary), (2) eutectic, and (3) peritectic reactions. It seems that Fe-rich phases may nucleate on the wetted sides of double oxide films, while the gap of the dry sides of oxide films constitutes the cracks commonly observed in the Fe-rich phases and aluminum matrix. Conventional metallurgical observations also suggest that the Fe-rich phases nucleated early during the solidification might act as nuclei for those formed subsequently, although it has not been ruled out that these phases may share the same oxide substrates. It is probable that these nucleation events may all work as suggested in the possible nucleation hierarchy for Al-11.5Si-0.4Mg cast alloys.     

小方坯连铸机喷淋结晶器的研究

建立小方坯喷淋结晶器凝固传热数学模型，模拟计算了铸坯温度场、坯壳厚度、热流场，坯壳与铜壁间气隙厚度。计算坯壳厚度与实测坯壳厚度基本吻合；与普通水缝式结晶器相比，铸坯温度场均匀，坯壳厚度均匀，冷却强度有所提高。     

Nucleation-controlled microstructures and anomalous eutectic formation in undercooled Co-Sn and Ni-Si eutectic melts

Co-20.5 at. pct Sn and Ni-21.4 at. pct Si eutectic alloys have been levitated and undercooled in an electromagnetic levitator (EML) and then solidified spontaneously at different undercoolings. The original surface and cross-sectional morphologies of these solidified samples consist of separate eutectic colonies regardless of melt undercooling, indicating that microstructures in the free solidification of the eutectic systems are nucleation controlled. Regular lamellae always grow from the periphery of an independent anomalous eutectic grain in each eutectic colony. This typical morphology shows that the basic unit should be a single eutectic colony, when discussing the solidification behavior. Special emphasis is focused on the anomalous eutectic formation after a significant difference in linear kinetic coefficients is recognized for terminal eutectic phases, in particular when a eutectic reaction contains a nonfaceted disordered solid solution and a faceted ordered intermetallic compound as the terminal eutectic phases. It is this remarkable difference in the linear kinetic coefficients that leads to a pronounced difference in kinetic undercoolings. The sluggish kinetics in the interface atomic attachment of the intermetallic compound originates the occurrence of the decoupled growth of two eutectic phases. Hence, the current eutectic models are modified to incorporate kinetic undercooling, in order to account for the competitive growth behavior of eutectic phases in a single eutectic colony. The critical condition for generating the decoupled growth of eutectic phases is proposed. Further analysis reveals that a dimensionless critical undercooling may be appropriate to show the tendency for the anomalous eutectic-forming ability when considering the difference in linear kinetic coefficients of terminal eutectic phases. This qualitative criterion, albeit crude with several approximations and assumptions, can elucidate most of the published experimental results with the correct order of magnitude. Solidification modes in some eutectic alloys are predicted on the basis of the present criterion. Future work that may result in some probable errors is briefly directed to improve the model.     

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m² to peak values of 0.95 to 2.0 MW/m². A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m² °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (μm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.