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A transient, 3D model has been developed to study evolution and constitution of melt pool for a single-pass laser melting-based direct energy deposition process. Here, the powder material, Inconel 718, is deposited on a SS 316 substrate having different chemical composition. The conservation equations for mass, energy, momentum and species have been solved with respect to a reference frame fixed with the moving laser. To study the phase change process, an enthalpy-based technique has been utilized so that a single-domain solution of the problem gives the interface of solid and liquid as part of the solution. The melting of different compositional elements of IN 718 being deposited on the substrate, their vaporization above respective boiling points, and the momentum of carrier and shield gases have been incorporated into the model. The computational model can predict the distribution of species in melt pool and the geometry of the dilution zone. [ABSTRACT FROM AUTHOR]

Abstract Ultra pure metals have various applications, e. g. as electrical conductors. Crystallization from the melt, e. g. via zone melting, using the segregation of impurities at the solidification front is the basic mechanism behind different technical processes for the refining of metals and semi-metals. In this paper, we focus on a crystallization methodology with a gas cooled tube (“cooled finger”) dipped into a metallic melt in a rotating crucible. The necessary requirement for purification in a solidification process is a morphologically stable solidification front. This is the only way to enable macroscopic separation of the impurities, e. g. by convection. For cellular or dendritic solidification morphologies, the segregated impurities are trapped into the interdendritic melt and remain as microsegregations in the solidified metal. Morphological stability depends on the temperature gradient G at the solidification front, the solidification front velocity V front and thermodynamic alloy properties like the segregation coefficients of the impurity elements. To quantify the impact of these parameters on the morphological evolution, especially on the planar/cellular transition and thus on microsegregation profiles, phase field simulations coupled to a thermodynamic database are performed for an aluminium melt with three impurities, Si, Mn and Fe. In particular, we have investigated the morphology evolution from the start of solidification at the cooled finger towards a stationary growth regime, because in the technical process a significant fraction of the melt solidifies along the initial transient. To solve the transient long range temperature evolution on an experimental length scale, the temperature field has been calculated using the homoenthalpic approach together with a 1D temperature field approximation. The simulations provide the process window for an energy efficient purification process, i. e. low thermal gradients, and elucidate the benefit of melt convection.

What is nucleation core origin during alloy solidification, especially for equiaxed grains? Different dependence degrees of the magnitude or occurrence of element content variation could shed light on this long-standing issue in actual large ingots. Here, based on etched surface height and grayscale, element content distributions within the solid fraction in continuous casting billets and additive manufacturing samples are first obtained by only a two-dimensional surface. Then, combined with the phylogenetic trees, the rank correlation is applied to measure the dependence of content differences during initial solidification. Assessments of external dependence degrees are helpful to determine nucleation core origin and low internal dependence degree facilitates grain refinement. Moreover, in continuous casting, some nucleation cores in the central equiaxed grain zone are confirmed to originate from the edge-chilled zone and high equiaxed grain area ratio under a low superheat, which is attributed to the low ratio of temperature gradient to growth rate rather than remelting fewer cores originating from the chilled zone. In addition, the floating behavior of separated grains originating from the chilled zone can be affected by gravity force, but these grains should be more active when increasing the casting superheat that may weaken the influence of gravity to a certain extent. [ABSTRACT FROM AUTHOR]

In this paper, the effects of composition on the mutual exchange of core-shell structure in immiscible Al-Bi-Sn alloys have been studied. The morphology can be classified into three types, Al85Bi6Sn9 and Al75Bi9Sn16 formed a perfect core-type structure, in which the shell is an Al-rich phase and the core is a Sn/Bi-rich phase; Al60Bi14.4Sn25.6 formed an irregular multilayer core-type structure; and Al45Bi19.8Sn35.2 formed a core-type structure, in which the shell is a Sn/Bi-rich phase and the core is an Al-rich phase; the mutual change of core and shell in Al-Bi-Sn occurs when the composition changes, and the variation in composition leads to changes in the volume fraction of each phase, and one phase with a minor volume fraction will form a core. This study provides some methods for the preparation of core-type structure productions. [ABSTRACT FROM AUTHOR]

A novel solution approach is proposed for the numerical simulation of the solidification process of binary Al-Si hypoeutectic alloys during upward and downward solidification modes. Undercooling is always observed during solidification, but the phenomenon could not be considered in the present-day numerical solution. In this approach, the temperature distribution in the mushy zone was used to define the fraction of solid, which enabled the evaluation of the effect of dendrite tip undercooling on the characteristics of the binary alloy solidification. The present numerical algorithm was found to significantly reduce the computation time. Transient temperature distribution and solidification time from the numerical analysis, with consideration of natural convection due to temperature and concentration gradients, have been successfully simulated and validated with experiment results. Numerical results with consideration of dendrite tip undercooling have better agreement with experimental results. The effect of dendrite tip undercooling on the fluid flow (velocity profile), G, R and λ1 for both upward and downward solidification modes of Al-Si alloys have been investigated and discussed. Consideration of undercooling was found to increase G and reduce R in both solidification modes. During downward solidification, considering undercooling significantly increased flow velocity and decreased λ1. The primary dendrite arm spacing could be validated with results from uni-directional solidification experiments only when dendrite tip undercooling was considered. [ABSTRACT FROM AUTHOR]

Ultra pure metals have various applications, e. g. as electrical conductors. Crystallization from the melt, e. g. via zone melting, using the segregation of impurities at the solidification front is the basic mechanism behind different technical processes for the refining of metals and semi-metals. In this paper, we focus on a crystallization methodology with a gas cooled tube ("cooled finger") dipped into a metallic melt in a rotating crucible. The necessary requirement for purification in a solidification process is a morphologically stable solidification front. This is the only way to enable macroscopic separation of the impurities, e. g. by convection. For cellular or dendritic solidification morphologies, the segregated impurities are trapped into the interdendritic melt and remain as microsegregations in the solidified metal. Morphological stability depends on the temperature gradient G at the solidification front, the solidification front velocity V front and thermodynamic alloy properties like the segregation coefficients of the impurity elements. To quantify the impact of these parameters on the morphological evolution, especially on the planar/cellular transition and thus on microsegregation profiles, phase field simulations coupled to a thermodynamic database are performed for an aluminium melt with three impurities, Si, Mn and Fe. In particular, we have investigated the morphology evolution from the start of solidification at the cooled finger towards a stationary growth regime, because in the technical process a significant fraction of the melt solidifies along the initial transient. To solve the transient long range temperature evolution on an experimental length scale, the temperature field has been calculated using the homoenthalpic approach together with a 1D temperature field approximation. The simulations provide the process window for an energy efficient purification process, i. e. low thermal gradients, and elucidate the benefit of melt convection. [ABSTRACT FROM AUTHOR]

In the last two decades, X-ray imaging techniques have been used increasingly to study metal solidification in real-time as, thanks to advances in X-ray sources (synchrotron and laboratory-based) and detector technology, images can now be obtained with spatio-temporal resolutions sufficient to record key phenomena and extract quantitative information, primarily relating to crystal growth. This paper presents an overview of the research conducted at the University of Oxford over the last 6 years as a partner in the UK's Future Liquid Metal Engineering (LiME) Manufacturing Hub. The focus is on in situ X-ray radiography to investigate the solidification of Al alloys, including the formation of primary α -Al crystals, and the formation and growth of secondary intermetallic phases. Technologically, the thrust is to understand how to control as-cast phases, structures and element distributions, particularly elements associated with recycling, as a means to facilitate greater recirculation of aluminium alloys. We first present studies on refinement of primary α -Al, including extrinsic grain refinement using inoculation and intrinsic refinement based on dendrite fragmentation. Second, we describe studies on intermetallic phase formation and growth, because intermetallic fraction, morphology and distribution are frequently a limiting factor of alloy mechanical properties and recyclability. Then we present some of the latest progress in studying liquid flow during solidification and associated hot tear formation. Finally, future research directions are described. [ABSTRACT FROM AUTHOR]

A widespread implementation of large scale additive manufacturing (AM) processes, such as wire arc-directed energy deposition (WA-DED) AM can transform the current manufacturing supply chain networks. Naturally, such implementation requires control of the microstructural attributes, such as texture and phase evolution in the processed alloys. Currently, the texture evolution in fusion-based AM (F-BAM) processes is majorly rationalized by the phenomena occurring only during solidification. However, such rationalization is insufficient for understanding the evolution of primary and secondary crystallographic orientations, and consequently, fails to offer a comprehensive understanding and control of overall texture in F-BAM processed alloys. To this end, we report a single crystal (SX)-like texture in WA-DED processed SS316L for the first time. Furthermore, we assess the physical phenomena that may lead to such unique microstructural evolution during WA-DED AM. Subsequently, using microstructural characterization spanning the build height and thermomechanical simulations we investigate the effect of competitive growth and epitaxial growth occurring during solidification and thermally induced plastic deformation occurring post solidification on the overall texture of WA-DED processed SS316L. A spatial variation in solidification pathway is also established and correlated with variation in undercoolings across the build. Tensile tests revealed a strong orientation dependence of deformation mechanisms with over 110% elongation to failure of specimens deformed along <011>. Such anisotropy is rationalized using Schmid's analysis of dislocation slip and deformation twinning. Overall, the mechanisms outlined in this work will facilitate an enhanced understanding and subsequent control of texture evolution, solidification behavior and mechanical behavior of WA-DED processed steels. [Display omitted] • A SX-like texture is reported in a directed energy deposition processed SS316L. • Phenomena occurring during and post solidification affect texture in DED. • Tip temperatures of γ and δ phases and solidification modes vary with build height. • Stray-grain formation is rationalized using spatially varying thermokinetics. • Orientation dependent behavior of leading/trailing partials leads to anisotropy. [ABSTRACT FROM AUTHOR]

What is nucleation core origin during alloy solidification, especially for equiaxed grains? Different dependence degrees of the magnitude or occurrence of element content variation could shed light on this long-standing issue in actual large ingots. Here, based on etched surface height and grayscale, element content distributions within the solid fraction in continuous casting billets and additive manufacturing samples are first obtained by only a two-dimensional surface. Then, combined with the phylogenetic trees, the rank correlation is applied to measure the dependence of content differences during initial solidification. Assessments of external dependence degrees are helpful to determine nucleation core origin and low internal dependence degree facilitates grain refinement. Moreover, in continuous casting, some nucleation cores in the central equiaxed grain zone are confirmed to originate from the edge-chilled zone and high equiaxed grain area ratio under a low superheat, which is attributed to the low ratio of temperature gradient to growth rate rather than remelting fewer cores originating from the chilled zone. In addition, the floating behavior of separated grains originating from the chilled zone can be affected by gravity force, but these grains should be more active when increasing the casting superheat that may weaken the influence of gravity to a certain extent.

A novel solution approach is proposed for the numerical simulation of the solidification process of binary Al-Si hypoeutectic alloys during upward and downward solidification modes. Undercooling is always observed during solidification, but the phenomenon could not be considered in the present-day numerical solution. In this approach, the temperature distribution in the mushy zone was used to define the fraction of solid, which enabled the evaluation of the effect of dendrite tip undercooling on the characteristics of the binary alloy solidification. The present numerical algorithm was found to significantly reduce the computation time. Transient temperature distribution and solidification time from the numerical analysis, with consideration of natural convection due to temperature and concentration gradients, have been successfully simulated and validated with experiment results. Numerical results with consideration of dendrite tip undercooling have better agreement with experimental results. The effect of dendrite tip undercooling on the fluid flow (velocity profile), G, R and λ1 for both upward and downward solidification modes of Al-Si alloys have been investigated and discussed. Consideration of undercooling was found to increase G and reduce R in both solidification modes. During downward solidification, considering undercooling significantly increased flow velocity and decreased λ1. The primary dendrite arm spacing could be validated with results from uni-directional solidification experiments only when dendrite tip undercooling was considered.

In situ X-radiography imaging during the isothermal solidification of a 200 µm thin Al-24 at.% Ge sample was performed to determine dendritic growth rates, liquid concentrations and projected solid fractions. The experimental data allowed to follow dendrite tip growth velocities with high accuracy all the way from the initial transient growth related decrease of velocity via the expected increase of velocity during free dendrite growth to its final decrease during neighbor interacted growth. Concentration profiles in front of individual dendrite tips were measured to analyze the increase in far-field solute concentration due to solute accumulation. By time-resolved imaging of almost the entire 12 mm diameter sample, the global melt concentration could be derived. This enabled to estimate the initial nucleation undercooling of this un-refined alloy, which was so far unresolved. The experimental results are compared to a three-dimensional dendrite needle network model that simulates the experimental conditions, such as hexagonal dendrite structures and confined sample geometry. Although the simulation results are very sensitive to variations of the parameters undercooling and dendrite selection constant, one model parameter set is found that reproduces all experimentally measured solidification characteristics. The thorough experiment-model comparison indicates that the dendritic growth rates in this experimental configuration can be lower by a factor of 7 depending on undercooling than in the non-confined case. Image, graphical abstract [ABSTRACT FROM AUTHOR]

We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings.

In the last two decades, X-ray imaging techniques have been used increasingly to study metal solidification in real-time as, thanks to advances in X-ray sources (synchrotron and laboratory-based) and detector technology, images can now be obtained with spatio-temporal resolutions sufficient to record key phenomena and extract quantitative information, primarily relating to crystal growth. This paper presents an overview of the research conducted at the University of Oxford over the last 6 years as a partner in the UK’s Future Liquid Metal Engineering (LiME) Manufacturing Hub. The focus is on in situ X-ray radiography to investigate the solidification of Al alloys, including the formation of primary α-Al crystals, and the formation and growth of secondary intermetallic phases. Technologically, the thrust is to understand how to control as-cast phases, structures and element distributions, particularly elements associated with recycling, as a means to facilitate greater recirculation of aluminium alloys. We first present studies on refinement of primary α-Al, including extrinsic grain refinement using inoculation and intrinsic refinement based on dendrite fragmentation. Second, we describe studies on intermetallic phase formation and growth, because intermetallic fraction, morphology and distribution are frequently a limiting factor of alloy mechanical properties and recyclability. Then we present some of the latest progress in studying liquid flow during solidification and associated hot tear formation. Finally, future research directions are described.

• Convection modeling in a mesoscale/multiscale solidification model is presented. • We study microstructure evolution of equiaxed dendritic crystals under forced flow. • We study columnar microstructure formation at different gravity levels. • The results obtained by the mesoscale model are compared to phase-field simulations. • We show that the mesoscale model accurately reproduces the microstructure evolution. Quantitative modeling of solidification microstructures growing under the influence of convection is a challenging multiscale problem. It is of particular interest in processes where strong flow is present, such as centrifugal casting of Ti–Al alloys, where hypergravity strongly reinforces the buoyancy-driven flow. We present the coupling of the mesoscopic envelope model for dendritic solidification with fluid flow. We use the model to investigate columnar and equiaxed dendritic growth of the β -solidifying Ti–45 at.%Al under the influence of flow. The calculations are compared to phase-field results in 2D. For equiaxed growth the case of forced flow is treated. For columnar growth, the influence of buoyancy-driven flow on the growing structure and on the primary dendrite arm spacing is characterized for gravity levels ranging from 0 to ± 15 g. The computational cost of the mesoscopic simulations is around two orders of magnitude lower than that of phase field. We show that the mesoscopic model can accurately reproduce the microstructure characteristics, such as grain shape and primary arm spacing (PDAS), as long as the dendrite tip remains parabolic. When flow effects in columnar growth are strong enough to change the tip shape and induce tip splitting events, the mesoscopic envelope model does not reproduce the resulting branched microstructures. It does however predict the corresponding PDAS reduction at the correct gravity level. [ABSTRACT FROM AUTHOR]

A 3D mesoscopic envelope model is used to numerically simulate the experimental X-ray observations of isothermal equiaxed dendritic solidification of a thin sample of Al-20 wt % Cu alloy. We show the evolution of the system composed of multiple grains growing under influence of strong solutal interactions. We emphasize the three-dimensional effects in the thin sample thickness on the growth kinetics, focusing on three aspects: (i) the impact of the third dimension on the solute diffusion, (ii) the influence of the orientation of the preferential grain growth directions <100> on the interactions with the confining sample walls, and (iii) the influence of the grain position along the sample thickness. We demonstrate the importance of considering the three-dimensional structure of the thin samples despite the small thickness. We further show that the mesoscopic envelope model can accurately describe the shape and the time-evolution of the equiaxed grains growing under influence of strong solutal interactions. Image 1 [ABSTRACT FROM AUTHOR]

To utilize the full potential of additive manufacturing routes for metallic part production, understanding how microstructure and texture develop as functions of alloying additions and process conditions is critical. Use of cellular automata (CA) with alloy solidification theory can provide a useful augmentation to experimental microstructure observations, as it can accurately and efficiently reproduce nucleation and growth of cubic crystal structures common to binary and ternary alloy solidification. We apply CA to model constrained solidification under thermal gradient magnitudes and solidification velocities representative of those commonly encountered along the melt pool boundary in Laser Engineered Net Shaping (LENS®), a specific alloy-based additive process. Various sets of alloying elements, quantities, and nucleation parameters are used to show the model's ability to predict realistic trends in nucleation and growth of single phase β -Ti alloys. 2D and 3D model implementations are qualitatively and quantitatively compared, and alloy composition (element and quantity) is shown to play a critical role on the columnar to equiaxed transition (CET) through changes to the interfacial response function. Simulation results are further used to define a parameter that correlates with the CET over a range of imposed conditions, linking alloy solidification theory to the CA prediction of microstructure. This CA model can serve as a useful tool when designing sets of alloying additions that would produce given microstructures, while coupled application of this CA to process scale simulations of additive process temperature fields will facilitate design of both specific alloy compositions and sets of process conditions for microstructure control. [ABSTRACT FROM AUTHOR]

A new two-dimensional modeling approach combining the cellular automaton(CA) and the lattice Boltzmann model(LBM) was developed to simulate heat transport, fluid flow, solute diffusion, and dendritic growth in the process of the Al-4.7%Cu solidification of the single-phase solid solution alloy. And the changes of dendritic morphology and constituent under convection were analyzed. The present model improved the solutal distribution approach at the solid-liquid (S/L) interface, which made the change of solute more consistent with the actual transport. The simulation results demonstrate that dendritic morphology is strongly influenced by forced convection, comparing with that without accounting for convection. Under the forced convection, the dendrite grain sizes tend to be similar; the constituent in the interdendritic region is more homogeneous; and the composition in the whole solidification region exhibits a certain gradient trend from upstream to downstream.

The use of a phase field approach to simulate solidification of metallic alloys has many computational advantages, but if obtaining quantitative results relies on the interface between phases being physically realistic, the computational advantage is much reduced. We propose here a method for compensating for a computationally convenient large interface width by simply transferring a numerically derived 1D steady state anti-trapping current to a general non-steady 2D simulation. The method proposed is not restricted to dilute or ideal materials and has a high degree of interface width independence, illustrated here with two models, illustrating a broad applicability for the approach. [ABSTRACT FROM AUTHOR]

Understanding the interplay among process parameters, microstructure, and presence of defects is critical to optimizing Additive Manufacturing (AM) routes for producing specialty alloy parts with unique geometry, properties, and compositional features. However, since it is not feasible to obtain experimental results for every possible set of AM process, process conditions, and alloy composition, computational modeling is becoming an increasingly important tool for understanding key physical processes, with the hope of developing a framework for AM materials design. One such physical process of interest is the dendritic solidification within grains; we implement a Cellular Automata (CA) model for coupled solute transport and growth of cellular and dendritic β -Ti alloy colonies under thermal conditions typically encountered in AM processes. Quantitative agreement with analytical models of the undercooling-solidification velocity relationship was achieved, as well as qualitative agreement with trends in primary dendrite arm spacing (PDAS), secondary arm development, and compositional profile with changes in solidification conditions. The roles of solute diffusivity, interfacial energy, and alloying addition are considered as well. Under rapid solidification conditions, extension to include local non-equilibrium for solute allowed for the modeling of solute trapping along dendrite stems as well as qualitative representation of the dendritic to banded morphology transition. To quantitatively reproduce non-equilibrium solidification at the dendritic colony scale and more accurately estimate rapid solidification microstructures, use of multiple grids or more complex CA rules would be in order. [ABSTRACT FROM AUTHOR]

We present methods and results for the simulation of faceted and dendritic crystal growth. Using a thermodynamically realistic isothermal alloy model for AlSi we demonstrate, in confirmation of experimental observations, a change in morphology from perfectly faceted hexagons at smaller undercooling to dendritic growth at larger undercoolings. We also demonstrate that there exists a cut off temperature which separates the two distinct morphologies, and indeed hybrid morphologies. These results suggest that the mechanism for morphology variation observed experimentally primarily lies in anisotropic surface free energy modelling, which we adopt in preference to kinetic anisotropy. [ABSTRACT FROM AUTHOR]

Grain refiner is often added to aluminum and magnesium alloys during solidification processing to encourage the development of a fine equiaxed grain structure. Numerical modeling of such processes face the challenge of considering the effect of free floating grains that nucleate on grain refiner particles, are advected in the bulk fluid flow, and eventually coalesce to form a permeable, rigid solid structure. While several models have been developed to consider the advection of solid grains, the attachment of these grains is uniformly treated on a discrete, cell-by-cell basis. In a previous study, channel segregates were observed in the predicted composition field of equiaxed solidification simulations and were found to exhibit an extreme grid dependence. These channels were examined in the present study in detail for two different grain attachment models, one that assumed coalescence occurs at a constant and uniform volume fraction solid, and one that considered the effects of the local solid velocity field. The mechanism of the initiation and propagation of these channels was explored, and their physical relevance considered. It was concluded that these defects were primarily numerical artifacts arising from the discrete nature of the grain attachment models, and therefore, necessarily occurred on the length scale of the grid spacing. Development of an alternative attachment model that avoid this numerical problem is the subject of ongoing research. [ABSTRACT FROM AUTHOR]

We investigate and assess the capability of the mesoscopic envelope model of dendritic solidification to represent the growth of columnar dendritic structures. This is done by quantitative comparisons to phase-field simulations in two dimensions. While the phase-field model resolves the detailed growth morphology at the microscale, the mesoscopic envelope model describes a dendritic grain by its envelope. The envelope growth velocities are calculated by an analytical dendrite-tip model and matched to the numerical solution of the solute concentration field in the vicinity of the envelope. The simplified representation of the dendrites drastically reduces the calculation time compared to phase field. Larger ensembles of grains can therefore be simulated. We show that the mesoscopic envelope model accurately reproduces the evolution of the primary branch structure, the undercooling of the dendrite tips, and the solidification path in the columnar mushy zone. We further show that it can also correctly describe the transient adjustments of primary spacing, both by spacing increase due to elimination of primary branches and by spacing reduction due to tertiary rebranching. Elimination and tertiary rebranching are also critical phenomena for the evolution of grain boundaries between columnar grains that have a different crystallographic orientation with respect to the temperature gradient. We show that the mesoscopic model can reproduce the macroscopic evolution of such grain boundaries for small and moderate misorientation angles, i.e., up to 30°. It is therefore suitable for predicting the texture of polycrystalline columnar structures. We also provide guidelines for the calibration of the main parameters of the mesoscopic model, required to obtain reliable predictions. [ABSTRACT FROM AUTHOR]

We present a method for coupling current phase field models of alloy solidification into general continuum modelling. The advantages of this approach are to provide a generic framework for phase field modelling, give a natural and thermodynamically consistent extension to non-isothermal modelling, and to see phase field models in a wider context. The bracket approach, introduced by Beris and Edwards, is an extension of the Poisson bracket of Hamiltonian mechanics to include dissipative phenomena. This paper demonstrates the working of this formalism for a variety of alloy solidification models including multi phase, multi species with thermal and density dependency. We present new models by deriving temperature equations for single and more general phase field models, and give a density dependent formulation which couples phase field to flow. [ABSTRACT FROM AUTHOR]

[Display omitted] • A well-defined casting case study in solidification of various Al-Cu alloys. • Two different modelling methods used for simulation: Cellular Automata and Front Tracking. • The FT model shows the evolution of undercooled liquid with columnar growth. • The CA model predicts the columnar-equiaxed transition directly. • Agreement is excellent between the simulations from both models. Developing computational tools appropriate for modelling physical phenomena, such as alloy solidification, requires making optimisation decisions on the time and spatial scales that can be resolved with finite computational resources. Here we report on development of a model of grain nucleation and growth, based on a Cellular Automata (CA) approach, that can directly simulate columnar and equiaxed solidification, and their competition to trigger a columnar-equiaxed transition (CET), at the scale of a casting. Previous work has been to develop a Front Tracking (FT) model of columnar solidification and an equiaxed index capable of predicting the relative likelihood of CET formation in a casting case study. This FT model has been validated by extensive experimental studies. Here we apply the new CA model and compare the predictions to those of the FT model. The close agreement between the two models serves to verify the new CA model. The study also presents insights into the thermophysical phenomena affecting grain structure evolution in alloy solidification and confirms the validity and utility of the equiaxed index. [ABSTRACT FROM AUTHOR]

The mesoscopic envelope model is a recent multiscale model that is intended to bridge the gap between purely microscopic and macroscopic approaches for the study of dendritic solidification. It consists of the description of a dendritic grain by an envelope that links the active dendrite branches. The envelope growth is deduced from an analytical microscopic model of the dendrite tip growth kinetics matched to the numerical solution of the mesoscopic solute concentration field in the vicinity of the envelope. The branched dendritic structure inside the envelope is described in a volume-averaged sense by phase fractions and averaged solute concentrations. We present a careful quantitative analysis of the influence of numerical and model parameters on the accuracy of the model predictions. We further perform a validation study through comparisons of 3D simulations to experimental scaling laws giving the shape and the internal solid fraction of freely growing binary alloy dendrites and to analytical solutions for the primary dendrite tip speed. We provide generally valid guidelines for the calibration of the mesoscopic model, enabling reliable control of the accuracy of model predictions over a wide range of undercoolings. The model is applied to simulate strong solutal interactions in large ensembles of equiaxed grains. The potential for mesoscopic simulations to provide refined modeling of microstructures in volume-averaged macroscopic models via scale bridging is demonstrated. [ABSTRACT FROM AUTHOR]

Modeling the as-solidified grain structures that form during alloy processing is a critical component in understanding process-property relationships, particularly for additive manufacturing (AM) where grain structure is very sensitive to processing conditions. While cellular automata (CA)-based models have proven able to predict aspects of microstructure for several alloys and AM process conditions, long run times and large resource sets required limit the utility and the problem size to which existing CA models can be applied. As part of the ExaAM project, an initiative within the Exascale Computing Project (ECP) to develop, test, and optimize an exascale-capable coupled and self-consistent model of AM parts, we developed ExaCA (https://github.com/LLNL/ExaCA) for the liquid–solid phase transformation in the wake of AM melt pools. The CA-based code is parallelized using MPI and the Kokkos programming model, the latter enabling simulation on both CPUs and GPUs within a single-source implementation. We detail the steps taken to transform a baseline, MPI-based CA code into one that is performant on CPUs and GPUs. Performance testing of ExaCA on Summit (a pre-exascale machine at Oak Ridge National Laboratory) was used to quantify CPU–GPU speedup comparing with equal numbers of nodes. Testing showed comparable CPU performance to the MPI-only CA code and a 5-20x speedup when running AM-based test problems using GPUs. The improved performance of CA through GPU utilization and the performance portable nature of ExaCA will enable accurate part-scale modeling by harnessing the power of current and future generations of high performance computing resources. Future work will include improving the strong scaling of ExaCA on GPUs by reducing load imbalance associated with the locality of the problem, and continuing performance optimization across exascale hardware. [Display omitted] [ABSTRACT FROM AUTHOR]

The paper presents the potential of an efficient front tracking method on a fixed control-volume grid in micro–macroscopic numerical modeling of both binary alloy solidification and a solid–liquid phase transition of single-component or doped optically functioning materials. In the former case, the method, basing on the assumption that an envelope of columnar dendrite tips moves locally according to a single crystal growth law, allows more precise identification of zones of different dendritic structures developing within the two-phase region, and thus more detailed analysis of some closing models. It is shown, by exploiting the commonly used benchmark problem that a porous medium model of the columnar mush must be carefully chosen since it strongly affects the predicted macro-segregation pattern. In the case of solidification of a single-component or doped semi-transparent material the combination of the front tracking method with the immersed boundary technique provides a new simulation method, which can handle different thermo-physical and optical properties of liquid and solid phases, processes of emission, absorption, reflection and refraction or transmission of thermal radiation at a diffusive or specular distinct solid–liquid interface detected by the front tracking technique. The method has been used in a detailed parametric analysis where the impact of different optical configurations of both phases and their various optical properties as well as variable transmissivity of solid–liquid interface on the phase change process development has been addressed. [ABSTRACT FROM AUTHOR]

• Re-analysis of the local solute redistribution equation of macrosegregation. • Identification of anomalies in 50 years of literature. • Extension to non-zero microscale back diffusion and equiaxed solidification. • Significance for the formation freckles, A-segregates and V-segregates. In this paper, we reassess the local solute redistribution equation (LSRE) of macrosegregation which, since it first appeared in 1960s, has served as a cornerstone for understanding the composition variations that occur in the solidification of alloys. We highlight some anomalies in earlier literature, in particular as regards the prediction of remelting as a precursor to the formation of channel segregates (freckles, A-segregates and V-segregates) in casting processes. Also, we suggest extensions to the LSRE for situations where solute diffusion in the solid phase is not negligible, as well as when the mode of solidification is unconsolidated equiaxed dendritic, rather than columnar/consolidated equiaxed dendritic. In addition, the significance of the equation for latter-day numerical computations of macrosegregation is also discussed. [ABSTRACT FROM AUTHOR]

Riser sizing optimization is based on the analysis of riser operation. Casting solidification simulation software allows this analysis to be done without the consumption of materials, energy and labor. This paper presents a methodology to analyze riser operation to optimize riser size during metalcasting. This three-part paper includes: (1) establishing the test criteria during the riser operation analysis; (2) exemplification of the riser operation analysis by simulation, using a steel casting; and (3) experimental verification of the results. The findings suggest that the riser operation analysis must be based on solidification time maps (and not on the temperature maps at the end of solidification), on the time of interruption of communication between riser and casting and on the amount of the useful liquid alloy available in the riser until the casting solidifies. Our study shows that the solidification analysis must be undertaken on the basis of the real solidification modulus and not on the geometric solidification modulus. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the flow pattern of non-linear magneto convection that can be realized in a horizontal mushy layer and in the presence of joule heating, which is the amount of heat produced by the induced magnetic field. We consider the appropriate system of equations and the associated boundary conditions for the flow in the mushy layer subjected to a vertical magnetic field of uniform strength. Under certain assumptions and conditions, we determine the stable finite-amplitude solutions of the resulting system using a perturbation approach and stability analysis. We find, in particular, that for a wide range of values of the joule heating parameter and sufficiently small amplitude of the flow, the only stable convective flow is in the form of subcritical down-hexagons with down-flow at the cells'' centers and up-flow at the cells'' boundaries. This result is in sharp contrast to the case in the absence of joule heating where instead the subcritical up-hexagons with up-flow at the cells'' centers and down-flow at the cells'' boundaries can be stable. In the presence of joule heating the stable subcritical down-hexagons were found to be enhanced with increasing the strength of the externally imposed magnetic field. [Copyright &y& Elsevier]

The numerical analysis of a new model of metal crystallization is performed. The novelty of the model, which has recently appeared in publications, consists in modeling that is simultaneously carried out at several scale levels, from micro-to macroscales. Although experimental studies of metal crystallization revealed many details of metal crystallization, there is no comprehensive theoretical view on this phenomenon. In the model employed in this work, the space of the crystallizing alloy is assumed to be a porous medium, in which the disturbance propagation is described by Biot's type of equations. The formation of crystal nuclei is described by a modified Cahn-Hilliard equation. A numerical scheme is constructed and its convergence is demonstrated. It is shown that various crystallization modes can be set by varying the parameters. We intend to investigate a multidimensional variant in our subsequent research, using multiprocessor computer complexes. [ABSTRACT FROM AUTHOR]

Abstract: A transient nonlinear inverse heat transfer problem arising from alloy solidification processes is considered. In practice, the solidus and liquidus interface motions and thus the mushy zone thicknesses are pre-given to control the material quality. To achieve the desired front motions, the required time-dependent boundary conditions have to be predicted on both mold sides simultaneously. In this study, the enthalpy method is used for the derivation of governing equations. Hence, the inverse problem will be solved only in a single spatial and temporal domain. The conjugate gradient method with adjoint equation is applied for the resulting minimization problem. The method is applied as comparison for pure material with other previous studies. Then, alloy material with different front velocities is set up to investigate the solidification process. The obtained results show a close agreement between the desired and computed front motions and mushy zone thickness. [Copyright &y& Elsevier]

We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings. [ABSTRACT FROM AUTHOR]