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DOE OSTI2021

In situ synchrotron diffraction and modeling of non-equilibrium solidification of a MnFeCoNiCu alloy

The solidification mechanism and segregation behavior of laser-melted Mn 35 Fe 5 Co 20 Ni 20 Cu 20 was firstly investigated via in situ synchrotron x-ray diffraction at millisecond temporal resolution. The transient composition evolution of the random solid solution during sequential solidification of dendritic and interdendritic regions complicates the analysis of synchrotron diffraction data via any single conventional tool, such as Rietveld refinement. Therefore, a novel approach combining a hard-sphere approximation model, thermodynamic simulation, thermal expansion measurement and microstructural characterization was developed to assist in a fundamental understanding of the evolution of local composition, lattice parameter, and dendrite volume fraction corresponding to the diffraction data. This methodology yields self-consistent results across different methods. Via this approach, four distinct stages were identified, including: (I) FCC dendrite solidification, (II) solidification of FCC interdendritic region, (III) solid-state interdiffusion and (IV) final cooling with marginal diffusion. It was found out that in Stage I, Cu and Mn were rejected into liquid as Mn 35 Fe 5 Co 20 Ni 20 Cu 20 solidified dendritically. During Stage II, the lattice parameter disparity between dendrite and interdendritic region escalated as Cu and Mn continued segregating into the interdendritic region. After complete solidification, during Stage III, the lattice parameter disparity gradually decreases, demonstrating a degree of composition homogenization. The volume fraction of dendrites slightly grew from 58.3 to 65.5%, based on the evolving composition profile across a dendrite/interdendritic interface in diffusion calculations. Postmortem metallography further confirmed that dendrites have a volume fraction of 64.7 ± 5.3% in the final microstructure.

36 MATERIALS SCIENCE↗

NASA NTRS1974

Specimen analysis of the Skylab M553 Metals Melting and Solidification Experiment

The M553 Sphere Forming Experiment conducted in the M512 Furnace Facility during Skylab II was designed to study the effects of weightlessness on the solidification process. Results indicated that there was an outstanding record of solidification terracing and solute redistribution, and that this record may be better than obtainable terrestrially. The solute redistribution was found to be highly localized to prescribed crystallographic systems. It was also shown that for some experimental conditions in a space environment, the anticipated solid/liquid solidification process was perturbed and a solid/liquid/gas reaction took place during solidification. It is felt that these results will contribute to the understanding of terrestrial solidification and will contribute to future space processing considerations.

Larson, D., Jr.↗

NASA NTRS1980

Analysis and calculation of macrosegregation in a casting ingot. MPS solidification model. Volume 1: Formulation and analysis

The physical and numerical formulation of a model for the horizontal solidification of a binary alloy is described. It can be applied in an ingot. The major purpose of the model is to calculate macrosegregation in a casting ingot which results from flow of interdendritic liquid during solidification. The flow, driven by solidification contractions and by gravity acting on density gradients in the interdendritic liquid, was modeled as flow through a porous medium. The symbols used are defined. The physical formulation of the problem leading to a set of equations which can be used to obtain: (1) the pressure field; (2) the velocity field: (3) mass flow and (4) solute flow in the solid plus liquid zone during solidification is presented. With these established, the model calculates macrosegregation after solidification is complete. The numerical techniques used to obtain solution on a computational grid are presented. Results, evaluation of the results, and recommendations for future development of the model are given. The macrosegregation and flow field predictions for tin-lead, aluminum-copper, and tin-bismuth alloys are included as well as comparisons of some of the predictions with published predictions or with empirical data.

Maples, A. L.↗

NASA NTRS1981

Containerless undercooling and solidification in drop tubes

A containerless low-gravity environment, produced within a 32 m drop tube apparatus, has been used to undercool and solidify metals, alloys or glasses by eliminating crucible induced nucleation processes. Niobium droplets with diameters in the range of 2 to 5 mm have been undercooled by 525 K which corresponds to the maximum undercooling reported by Turnbull and others on fine dispersions of low melting point metals. Solidification at large undercooling resulted in single crystalline spheres with the formation of interdendritic shrinkage channels on the sample surface rather than interior shrinkage cavities. The grain refinement as observed for Ni samples undercooled and solidified in fused silica crucibles does not occur in free-falling drops of Nb. A calculated solidification speed of undercooled Nb is compared to Ni. A solidification speed of 320 m/s is found for the Nb drops. This solidification speed is greater than or comparable to the solidification speeds calculated in splat cooled samples. Thus, a drop tube apparatus can be useful in the preparation and study of high temperature metastable compounds or alloys in bulk form.

Lacy, L. L.↗

NASA NTRS1985

MPS solidification model. Analysis and calculation of macrosegregation in a casting ingot

Work performed on several existing solidification models for which computer codes and documentation were developed is presented. The models describe the solidification of alloys in which there is a time varying zone of coexisting solid and liquid phases; i.e., the S/L zone. The primary purpose of the models is to calculate macrosegregation in a casting or ingot which results from flow of interdendritic liquid in this S/L zone during solidification. The flow, driven by solidification contractions and by gravity acting on density gradients in the interdendritic liquid, is modeled as flow through a porous medium. In Model 1, the steady state model, the heat flow characteristics are those of steady state solidification; i.e., the S/L zone is of constant width and it moves at a constant velocity relative to the mold. In Model 2, the unsteady state model, the width and rate of movement of the S/L zone are allowed to vary with time as it moves through the ingot. Each of these models exists in two versions. Models 1 and 2 are applicable to binary alloys; models 1M and 2M are applicable to multicomponent alloys.

Poirier, D. R.↗

NASA NTRS1992

The influence of gravity level during directional solidification of immiscible alloys

During directional solidification of immiscible (hypermonotectic) alloys it is theoretically possible to establish a stable macroscopically-planar solidification front, and thus avoid sedimentation. Unfortunately, convective instabilities often occur which interfere with the directional solidification process. In this paper, stability conditions are discussed and results presented from directional solidification studies carried out aboard NASA's KC-135 zero-g aircraft. Samples were directionally solidified while the effective gravity level was varied from approximately 0.01 g for 25 s to 1.8 g for 45 s. Dramatic variations in microstructure were observed with gravity level during solidification.

Andrews, J. B.↗

NASA NTRS1993

Solidification of eutectic system alloys in space (M-19)

It is well known that in the liquid state eutectic alloys are theoretically homogeneous under 1 g conditions. However, the homogeneous solidified structure of this alloy is not obtained because thermal convection and non-equilibrium solidification occur. The present investigators have clarified the solidification mechanisms of the eutectic system alloys under 1 g conditions by using the in situ observation method; in particular, the primary crystals of the eutectic system alloys never nucleated in the liquid, but instead did so on the mold wall, and the crystals separated from the mold wall by fluid motion caused by thermal convection. They also found that the equiaxed eutectic grains (eutectic cells) are formed on the primary crystals. In this case, the leading phase of the eutectic must agree with the phase of the primary crystals. In space, no thermal convection occurs so that primary crystals should not move from the mold wall and should not appear inside the solidified structure. Therefore no equiaxed eutectic grains will be formed under microgravity conditions. Past space experiments concerning eutectic alloys were classified into two types of experiments: one with respect to the solidification mechanisms of the eutectic alloys and the other to the unidirectional solidification of this alloy. The former type of experiment has the problem that the solidified structures between microgravity and 1 g conditions show little difference. This is why the flight samples were prepared by the ordinary cast techniques on Earth. Therefore it is impossible to ascertain whether or not the nucleation and growth of primary crystals in the melt occur and if primary crystals influence the formation of the equiaxed eutectic grains. In this experiment, hypo- and hyper-eutectic aluminum copper alloys which are near eutectic point are used. The chemical compositions of the samples are Al-32.4mass%Cu (Hypo-eutectic) and Al-33.5mass%Cu (hyper-eutectic). Long rods for the samples are cast by the Ohno Continuous Casting Process and they show the unidirectionally solidified structure. Each flight and ground sample was made of these same rods. The dimensions of all samples are 4.5 mm in diameter and 23.5 mm in length. Each sample is put in a graphite capsule and then vacuum sealed in a double silica ampoule. Then the ampoule is put in the tantalum cartridge and sealed by electron beam welding. For onbard experiments, a Continuous Heating Furnance (CHF) will be used for melting and solidifying samples under microgravity conditions. Six flight samples will be used. Four samples are hypo-eutectic and two are hyper-eutectic alloys. The surface of the two hypo-eutectic alloy samples are covered with aluminum oxide film to prevent Marangoni convection expected under microgravity conditions. Each sample will be heated to 700 C and held at that temperature for 5 min. After that the samples will be allowed to cool to 500 C in the furnace and they will be taken out of the furnace for He gas cooling. The heating and cooling diagrams for the flight experiments are shown. After collecting the flight samples, the solidified structures of the samples will be examined and the mechanisms of eutectic solidification under microgravity conditions will be determined. It is likely that successful flight experiment results will lead to production of high quality eutectic alloys and eutectic composite materials in space.

Ohno, Atsumi↗

NASA NTRS1996

Microstructural Development during Directional Solidification of Peritectic Alloys

A thorough understanding of the microstructures produced through solidification in peritectic systems has yet to be achieved, even though a large number of industrially and scientifically significant materials are in this class. One type of microstructure frequently observed during directional solidification consists of alternating layers of primary solid and peritectic solid oriented perpendicular to the growth direction. This layer formation is usually reported for alloy compositions within the two-phase region of the peritectic isotherm and for temperature gradient and growth rate conditions that result in a planar solid-liquid interface. Layered growth in peritectic alloys has not previously been characterized on a quantitative basis, nor has a mechanism for its formation been verified. The mechanisms that have been proposed for layer formation can be categorized as either extrinsic or intrinsic to the alloy system. The extrinsic mechanisms rely on externally induced perturbations to the system for layer formation, such as temperature oscillations, growth velocity variations, or vibrations. The intrinsic mechanisms approach layer formation as an alternative type of two phase growth that is inherent for certain peritectic systems and solidification conditions. Convective mixing of the liquid is an additional variable which can strongly influence the development and appearance of layers due to the requisite slow growth rate. The first quantitative description of layer formation is a model recently developed by Trivedi based on the intrinsic mechanism of cyclic accumulation and depiction of solute in the liquid ahead of the interface, linked to repeated nucleation events in the absence of convection. The objective of this research is to characterize the layered microstructures developed during ground-based experiments in which external influences have been minimized as much as possible and to compare these results to the current the model. Also, the differences between intrinsic and externally influenced layer formation were explored. The choice of alloy system is critical to a study of the formation of layered microstructures. The ideal system would have a well-characterized phase diagram, equal densities of both elements in the liquid state to minimize compositionally-driven convective flows, a low peritectic temperature to simplify directional solidification and the achievement of a high temperature gradient in the liquid, a broad composition range for the peritectic reaction, and a reasonable hardness at room temperature to facilitate handling and metallographic preparation. The In-Sn system was selected initially due to a very low peritectic temperature and the nearly equal densities of In and Sn in the liquid state. Since the In-rich peritectic reaction had apparently not been utilized previously for solidification research, experiments were conducted to check the phase diagram in the region of interest. The alloys in this system proved to be difficult to handle and prepare in bulk form with the equipment available, so experiments were initiated with the Sn-Cd system. Layered microstructures had been observed previously in Sn-Cd.

Lograsso, Thomas A.↗

NASA NTRS2002

Toward Understanding Pore Formation And Mobility During Controlled Directional Solidification In A Microgravity Environment Investigation (PFMI)

The generation and inclusion of detrimental porosity, e.g., "pipes" and "rattails" can occur during controlled directional solidification processing. The origin of these defects is generally attributed to gas evolution and entrapment during solidification of the melt. On Earth, owing to buoyancy, an initiated bubble can rapidly rise through the liquid melt and "pop" at the surface; this is obviously not ensured in a low gravity or microgravity environment. Clearly, porosity generation and inclusion is detrimental to conducting any meaningful solidification-science studies in microgravity. Thus it is essential that model experiments be conducted in microgravity, to understand the details of the generation and mobility of porosity, so that methods can be found to eliminate it. In hindsight, this is particularly relevant given the results of the previous directional solidification experiments conducted in Space. The current International Space Station (ISS) Microgravity Science Glovebox (MSG) investigation addresses the central issue of porosity formation and mobility during controlled directional solidification processing in microgravity. The study will be done using a transparent metal-analogue material, succinonitrile (SCN) and succinonitrile-water "alloys", so that direct observation and recording of pore generation and mobility can be made during the experiments. Succinonitrile is particularly well suited for the proposed investigation because it is transparent, it solidifies in a manner analogous to most metals, it has a convenient melting point, its material properties are well characterized and, it has been successfully used in previous microgravity experiments. The PFMI experiment will be launched on the UF-2, STS-111 flight. Highlighting the porosity development problem in metal alloys during microgravity processing, the poster will describe: (i) the intent of the proposed experiments, (ii) the theoretical rationale behind using SCN as the study material for porosity generation and migration and, (iii) the experimental protocol for the investigation of the effects of the processing parameters. Photographs of the flight experimental hardware, and the novel sample ampoule, will be exhibited. The experimental apparatus will be described in detail and a summary of the scientific objectives will be presented.

Grugel, R. N.↗

NASA NTRS2003

Melt Flow Control in the Directional Solidification of Binary Alloys

Our main project objectives are to develop computational techniques based on inverse problem theory that can be used to design directional solidification processes that lead to desired temperature gradient and growth conditions at the freezing front at various levels of gravity. It is known that control of these conditions plays a significant role in the selection of the form and scale of the obtained solidification microstructures. Emphasis is given on the control of the effects of various melt flow mechanisms on the local to the solidification front conditions. The thermal boundary conditions (furnace design) as well as the magnitude and direction of an externally applied magnetic field are the main design variables. We will highlight computational design models for sharp front solidification models and briefly discuss work in progress toward the development of design techniques for multi-phase volume-averaging based solidification models.

Zabaras, Nicholas↗

NASA NTRS2003

Flight Planning for the International Space Station - Levitation Observation of Dendrite Evolution in Steel Ternary Alloy Rapid Solidification (LODESTARS)

During rapid solidification, a molten sample is cooled below its equilibrium solidification temperature to form a metastable liquid. Once nucleation is initiated, growth of the solid phase proceeds and can be seen as a sudden rise in temperature. The heat of fusion is rejected ahead of the growing dendrites into the undercooled liquid in a process known as recalescence. Fe-Cr-Ni alloys may form several equilibrium phases and the hypoeutectic alloys, with compositions near the commercially important 316 stainless steel alloy, are observed to solidify by way of a two-step process known as double recalescence. During double recalescence, the first temperature rise is associated with formation of the metastable ferritic solid phase with subsequent conversion to the stable austenitic phase during the second temperature rise. Selection of which phase grows into the undercooled melt during primary solidification may be accomplished by choice of the appropriate nucleation trigger material or by control of the processing parameters during rapid solidification. Due to the highly reactive nature of the molten sample material and in order to avoid contamination of the undercooled melt, a containerless electromagnetic levitation (EML) processing technique is used. In ground-based EML, the same forces that support the weight of the sample against gravity also drive convection in the liquid sample. However, in microgravity, the force required to position the sample is greatly reduced, so convection may be controlled over a wide range of internal flows. Space Shuttle experiments have shown that the double recalescence behavior of Fe-Cr-Ni alloys changes between ground and space EML experiments. This program is aimed at understanding how melt convection influences phase selection and the evolution of rapid solidification microstructures.

Flemings, Merton C.↗

NASA NTRS2003

Toward Understanding Pore Formation and Mobility during Controlled Directional Solidification in a Microgravity Environment Investigation (PFMI)

The generation and inclusion of detrimental porosity, e.g., pipes and rattails can occur during controlled directional solidification processing. The origin of these defects is generally attributed to gas evolution and entrapment during solidification of the melt. On Earth, owing to buoyancy, an initiated bubble can rapidly rise through the liquid melt and pop at the surface; this is obviously not ensured in a low gravity or microgravity environment. Clearly, porosity generation and inclusion is detrimental to conducting any meaningful solidification-science studies in microgravity. Thus it is essential that model experiments be conducted in microgravity, to understand the details of the generation and mobility of porosity, so that methods can be found to eliminate it. In hindsight, this is particularly relevant given the results of the previous directional solidification experiments conducted in Space. The current International Space Station (ISS) Microgravity Science Glovebox (MSG) investigation addresses the central issue of porosity formation and mobility during controlled directional solidification processing in microgravity. The study will be done using a transparent metal-analogue material, succinonitrile (SCN) and succinonitrile-water 'alloys', so that direct observation and recording of pore generation and mobility can be made during the experiments. Succinonitrile is particularly well suited for the proposed investigation because it is transparent, it solidifies in a manner analogous to most metals, it has a convenient melting point, its material properties are well characterized and, it has been successfully used in previous microgravity experiments. The PFMI experiment will be launched on the UF-2, STS-111 flight. Highlighting the porosity development problem in metal alloys during microgravity processing, the poster will describe: (i) the intent of the proposed experiments, (ii) the theoretical rationale behind using SCN as the study material for porosity generation and migration and, (iii) the experimental protocol for the investigation of the effects of the processing parameters. Photographs of the flight experimental hardware, and the novel sample ampoule, will be exhibited. The experimental apparatus will be described in detail and a summary of the scientific objectives will be presented.

Grugel, Richard N.↗

NASA NTRS2003

Magnetic Field Effects on Convection and Solidification in Normal and Microgravity

It has been well understood that convective flows induced by g-jitter forces associated with spacecraft are responsible for defects formation and irregularity in product quality during melt growth of single crystals in microgravity. This research is concerned about numerical simulations and experimental measurements for the purpose of developing a fundamental understanding of the g-jitter induced fluid flows and their effects on solidification in microgravity with and without the presence of additional damping forces that are derived from the applied DC magnetic fields. The numerical models include both 2-D and 3-D transient fluid flow, heat transfer, mass transfer and solidification under the combined action of g-jitter and magnetic fields. Numerical simulations using both the 2-D and 3-D models are conducted for both idealized, synthesized and real g-jitter forces, and 2-D simulations are tested against the experimental measurements taken on the thermal oscillator. 2-D solidification models have also been developed and simulations are conducted. Results show that the numerical model predictions compare well with the measurements. Analysis of these results illustrates that an applied magnetic field can have a drastic influence on the convective flows induced by g-jitter and can be particularly useful to suppress the effects resulting from the spiking of g-jitter signatures, which are considered the most detrimental effects on quality of crystals grown in space. Work in progress includes developing 3-D numerical models for solidification phenomena with the presence of both g-jitter and magnetic fields and measurements of flow fluid and its effect on solidification in both transparent fluid and low melting point melts to verify numerical predictions.

Li, Ben Q.↗

NASA NTRS2003

Improved Crystal Quality by Detached Solidification in Microgravity

The goals of our work on detached solidification have been to: 1) Develop a complete understanding of all of the phenomena of detached solidification; 2) Make it possible to achieve detached solidification reproducibly; and 3) Increase crystallographic perfection through detached solidification. Specifically, we aimed in this project to: 1) Identify a system and develop methods that would allow viewing of the melt surface and convection in the melt during detached solidification in microgravity; 2) Improve understanding of the origination and evolution of detachment through experiments and theoretical treatments; and 3) Achieve detachment on earth. The project resulted in 14 publications, 15 presentations, completion of 2 Ph.D. theses, and completion of 2 M.S. theses. Two additional papers are currently being reviewed for publication. Copies of most of the papers are included as appendices.

Regel, Liya L.↗

NASA NTRS2003

Simulating the Effect of Space Vehicle Environments on Directional Solidification of a Binary Alloy

Space microgravity missions are designed to provide a microgravity environment for scientific experiments, but these missions cannot provide a perfect environment, due to vibrations caused by crew activity, on-board experiments, support systems (pumps, fans, etc.), periodic orbital maneuvers, and water dumps. Therefore, it is necessary to predict the impact of these vibrations on space experiments, prior to performing them. Simulations were conducted to study the effect of the vibrations on the directional solidification of a dendritic alloy. Finite element ca!cu!attie?ls were dme with a simd2titcr based on a continuum model of dendritic solidification, using the Fractional Step Method (FSM). The FSM splits the solution of the momentum equation into two steps: the viscous intermediate step, which does not enforce continuity; and the inviscid projection step, which calculates the pressure and enforces continuity. The FSM provides significant computational benefits for predicting flows in a directionally solidified alloy, compared to other methods presently employed, because of the efficiency gains in the uncoupled solution of velocity and pressure. finite differences, arises when the interdendritic liquid reaches the eutectic temperature and concentration. When a node reaches eutectic temperature, it is assumed that the solidification of the eutectic liquid continues at constant temperature until all the eutectic is solidified. With this approach, solidification is not achieved continuously across an element; rather, the element is not considered solidified until the eutectic isotherm overtakes the top nodes. For microgravity simulations, where the convection is driven by shrinkage, it introduces large variations in the fluid velocity. When the eutectic isotherm reaches a node, all the eutectic must be solidified in a short period, causing an abrupt increase in velocity. To overcome this difficulty, we employed a scheme to numerically predict a more accurate value for the rate of change of fraction of liquid as the liquid in an element solidifies. The new method enables us to contrast results of simulations in which the alloy is subjected to no gravity or a steady-state acceleration versus simulations when the alloy is subjected to vibration disturbances; therefore, the effect of vibration disturbances can be assessed more accurately. To assess the impact of these vibration-perturbations, transient accelerometer data from a space shuttle mission are used as inputs for the simulation model. These on-orbit acceleration data were obtained from the Microgravity Science Division at Glenn Research Center (GRC- MSD) and are applied to the buoyancy term of the momentum equation in a simulation of a Pb-5.8 wt. % Sb alloy that solidifies in a thermal gradient of 4000 K/m and a translation velocity of 3 p d s . Figure 2 shows the vertical velocity of a node that begins in the all-liquid region and subsequently solidifies; the vibrations are applied at 5000 seconds in this simulation. An important difficulty, common to all solidification models based on finite elements or 2 The magnitudes of the velocity oscillations that are vibration-induced are very small and acceptable. The biggest concern is whether the concentration of the liquid near the dendrite tips is distorted because of the vibration-induced perturbations. Results for this case show no concentration oscillations present in the all-liquid region.

Westra, D. G.↗

NASA NTRS2008

Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions

The Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MSL-CETSOL and MICAST) are two investigations which supports research into metallurgical solidification, semiconductor crystal growth (Bridgman and zone melting), and measurement of thermo-physical properties of materials. This is a cooperative investigation with the European Space Agency (ESA) and National Aeronautics and Space Administration (NASA) for accommodation and operation aboard the International Space Station (ISS). Research Summary: Materials Science Laboratory - Columnar-to-Equiaxed Transition in Solidification Processing (CETSOL) and Microstructure Formation in Casting of Technical Alloys under Diffusive and Magnetically Controlled Convective Conditions (MICAST) are two complementary investigations which will examine different growth patterns and evolution of microstructures during crystallization of metallic alloys in microgravity. The aim of these experiments is to deepen the quantitative understanding of the physical principles that govern solidification processes in cast alloys by directional solidification.

Gandin, Charles-Andre↗

DOE OSTI2018

Effects of Inclusion Precipitation, Partition Coefficient, and Phase Transition on Microsegregation for High-Sulfur Steel Solidification

A microsegregation model coupled with inclusion precipitation, variable partition coefficient, and diffusion coefficient of the solute was developed to investigate solute microsegregation for high-sulfur steel solidification. The effects of the solidification path and phase transition on solute microsegregation were explored. The results showed that the solute concentration predicted by the variable partition coefficient was quite different from the solute concentration predicted by the constant partition coefficient, and the percentage differences of solutes Si, P, and S were − 35.5, − 25.0, and 43.0 pct, respectively. For high-sulfur steel solidification, the concentrations of solutes Mn and S would be reduced by 88.3 and 74.9 pct, respectively, due to the precipitation of MnS. The solidification path and phase transition has a significant effect on the solute partition coefficient and microsegregation. With the increase in C content, the fraction of δ-phase decreased while the fraction of the γ-phase increased, and the microsegregation ratio of solutes C and Si decreased while the microsegregation ratio of solute P increased. To predict microsegregation more accurately, all influencing factors of the partition coefficient, inclusion precipitation, and phase transition should be comprehensively considered.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Examination of Dendritic Growth During Solidification of Ternary Alloys via a Novel Quantitative 3D Cellular Automaton Model

A three-dimensional (3D) quantitative cellular automaton (CA) model was developed to simulate dendritic growth during solidification processing of ternary alloys. A detailed method was proposed to solve solute diffusion and calculate the solid fraction for ternary alloys during solidification. The present model has been shown to accurately predict dendrite morphologies and solute distributions of both single equiaxed dendrite and columnar dendrites during solidification. The model was also used to study the influence of the concentration of a third component (Mg in the Al-Si-Mg system) on dendritic growth. With increasing Mg concentration, the steady-state dendrite tip growth velocity was shown to decrease, resulting in a shorter primary dendrite length. The 3D CA simulation results agree well with the prediction of the LGK theoretical model. Multi-columnar dendrite growth was simulated with different cooling rates. Primary and secondary dendrite morphology was shown to have little variation at low cooling rates (1.0 to 2.0 K/s) and a constant undercooling. The average secondary dendrite arm spacing was shown to decrease with the increase of cooling rate within this range. The 3D CA simulation results are in good agreement with the experimental directional solidification experiments of a commercial A356 (Al-7 wt pct Si-0.3 wt pct Mg).

36 MATERIALS SCIENCE↗