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Nowadays, surface modification of austenitic stainless steels has become a necessity for the scientific and industrial communities. Cladding made of tungsten inert gas (TIG) is one efficient way to modify the surfaces of these steels. The study aims to probe the influence of TIG cladding current intensities (80-160A), and thus heat energy input on microstructures of NiTi coatings deposited on AISI-316 austenitic stainless steel. 1 mm diameter pre-placed NiTi wires with a cladding travel speed of 87 mm/min. were used to deposit a distinct clad layer-substrate interfacial bonding in all the coated samples. Scanning electron and optical microscopies revealed different microstructures throughout the clad layers, mostly NiTi-based solid solution dendrites with minor phase precipitates distributed through the matrix. The energy dispersive spectroscopy proved that the amounts of chromium and iron elements diluted from the substrate into the molten NiTi layer increase (53.9 wt.% and 13.7 wt.% respectively) with increasing cladding current intensity at the expense of Ni and Ti contents. The diluted elements can lead to the formation of a B2 (NiTiFeCr) dendritic structure during solidification. X-ray diffraction testing revealed the presence of different phases and compounds forming the coating layers mainly NiTi solid solution, γ(Fe,Ni), Cr0.19Fe0.7Ni0.11 and Cr1.36Fe0.52. [ABSTRACT FROM AUTHOR]

The effects of chemical composition and solidification rate on the solidification behavior of high-Cr white irons were investigated through directional solidification. Increasing the solidification rate in hypoeutectic alloys caused finer dendrite-arm spacing, as expected. The eutectic structure, which formed in the interdendritic region, was comprised of M7C3 and austenite; however, secondary dendrite arms of hypoeutectic alloys contained a few M7C3 particles that solidified prior to the eutectic structure. The transition from cellular to dendritic solidification occurred at a solidification rate between 50 µm/s and 100 µm/s in a near-eutectic alloy. In the near-eutectic alloy with cellular solidification, a directionally arrayed in-situ composite of M7C3/austenite formed within the cell. Speckle-like features appeared in the intercellular region due to M23C6 carbide precipitation during subsequent cooling after freezing. Like dendrite-arm spacing in hypoeutectic alloys, the inter-speckle spacing and the inter-fiber spacing became finer with an increasing solidification rate in the cellular solidification range. [ABSTRACT FROM AUTHOR]

Introduction Solidification processes are present in a wide range of manufacturing methods and applications, from metallurgy to food processing. In recent years, PhaseField models have been increasingly used to simulate and predict the formation and evolution of material microstructure and phase change interfacial kinetics. In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys based on the Kobayashi model. Material and Methods At first, the Kobayashi phase-field model, which describes the solidification of a pure material from an undercooled melt, is introduced in detail. In discretization process of this model, the time derivatives are approximated via finite difference method. Then the local meshless moving Kriging method is applied for discretization of the model in space direction. The moving Kriging method is a truly meshless method in which the unknown function can be approximated locally, and this leads to the sparsity of the coefficient matrix. As the shape functions possess the Kronecker delta function property, boundary conditions can be implemented without any difficulties. Results and discussion The model is simulated for various values of its parameters. Numerical simulations illustrate the applicability and effectiveness of the proposed method. Conclusion As a consequence, it is found that the method is very efficient and accurate for phase-field models compared with other conventional methods. Therefore, this method can be considered as an attractive alternative to existing meshbased methods in solving phase-field models. [ABSTRACT FROM AUTHOR]

The effects of chemical composition and solidification rate on the solidification behavior of high-Cr white irons were investigated through directional solidification. Increasing the solidification rate in hypoeutectic alloys caused finer dendrite-arm spacing, as expected. The eutectic structure, which formed in the interdendritic region, was comprised of M7C3 and austenite; however, secondary dendrite arms of hypoeutectic alloys contained a few M7C3 particles that solidified prior to the eutectic structure. The transition from cellular to dendritic solidification occurred at a solidification rate between 50 µm/s and 100 µm/s in a near-eutectic alloy. In the near-eutectic alloy with cellular solidification, a directionally arrayed in-situ composite of M7C3/austenite formed within the cell. Speckle-like features appeared in the intercellular region due to M23C6 carbide precipitation during subsequent cooling after freezing. Like dendrite-arm spacing in hypoeutectic alloys, the inter-speckle spacing and the inter-fiber spacing became finer with an increasing solidification rate in the cellular solidification range.

• A novel meshless approach for phase-field modelling of dendritic growth. • Reduction of discretisation-induced anisotropy by the scattered nodes. • Increase in computational efficiency by a space-time adaptive approach. A novel adaptive numerical approach is developed for an accurate and computationally efficient phase-field modelling of dendritic solidification. The adaptivity is based on the dynamic quadtree domain decomposition. A quadtree decomposes the computational domain into rectangular sub-domains of different sizes. Each sub-domain is extended to ensure overlap communication between neighbouring sub-domains. In each sub-domain, uniform distribution of computational nodes is generated. The product between the node density and the sub-domain area is fixed to ensure the h-adaptivity. The adaptive approach provides the highest density of computational nodes at the solid-liquid interface and the lowest density in the bulk of the phases. The meshless radial basis function generated finite difference (RBF-FD) method is applied for the spatial discretisation of the partial differential equations which arise from the phase-field model. The RBF-FD method is especially appealing since it allows straightforward spatial discretisation of partial differential equations on scattered node distributions. The use of scattered node distribution reduces the discretisation-induced anisotropy in the phase-field modelling of dendritic growth. The forward Euler scheme is used for temporal discretisation. The adaptive time-stepping is employed to speed up the calculations further. The performance of the novel numerical approach is tested for dendritic solidification of supercooled pure melts and supersaturated dilute binary alloys at arbitrary preferential growth directions. The impact of the numerical parameters on the accuracy and computational efficiency is thoroughly analysed. It is shown that the RBF-FD method, defined on scattered node distribution, together with the space-time adaptive approach, represents an accurate and efficient technique for solving the phase-field models of dendritic solidification. [ABSTRACT FROM AUTHOR]

Dendrite fragmentation commonly occurs by pinch-off of sidearms at the narrow neck with the parent stem. Comprehensive measurements of the local neck dynamics are performed using in-situ synchrotron radiography experiments in which a flat sample of a Ga–35wt%. In alloy is solidified under both steady and transient growth conditions with minimal effects of melt convection. The measurements reveal two characteristic limits where the neck radius follows universal self-similar t 1 / 3 power laws, with a positive rate constant in the limit of steady growth and a negative rate constant in the isothermal pinch-off limit. The temporal power law for steady growth found here relates the sidearm neck radii to the tip radius of the primary dendrite stem, and the neck radius probability density distribution is shown to be symmetric. For the more general case of decelerated growth, it is observed that the neck initially widens along the steady growth limit, is then increasingly limited by the pinching tendency, and for sufficiently large decelerations converges ultimately to the pinch-off limit. A dynamical model is derived that predicts the behavior of the sidearm neck radius under arbitrary decelerating growth conditions. The highly variable nature of dendrite fragmentation is explained by the stochastic properties of the initial sidebranch development process. The model can be used to estimate the number of dendrite fragments forming during a certain time interval at any location behind the primary tips. [Display omitted] [ABSTRACT FROM AUTHOR]

Sliver is a typical grain defect in single crystal Ni-based superalloy castings produced by Bridgman directional solidification. However, its formation mechanism has yet to be fully understood. In this study, the formation of sliver defects was investigated with respect to the defect morphological features, the microstructure of defect initiation points, and the solidification conditions. Experiment results showed that sliver defects were originated from fragmentation of dendrite trunks and could developed to various morphologies. The misorientation range of sliver grains was between 3.2° to 12°. Microstructural analysis results indicated that the dendrites fragmented abruptly without significant plastic deformation. And the dendrite fragmentation could be facilitated by oxide inclusions and solidification pores. It was also found that the sliver defects were prone to occur at the interface where primary dendrite converge to the mold inner wall. Based on the low misorientation level of sliver grains in the experimental observation, the critical solid volume fraction range for fragmentation was suggested to be 0.6–0.8. The dendrite fragmentation was attributed to the non-uniform stress distribution in dendrite during solidification. In addition, the effect of airfoil geometry of a typical blade casting and defect prevention methodology were discussed.

The Pore Formation and Mobility Investigation at the International Space Station provided information on the morphological evolution during remelting and directional solidification under microgravity conditions for Succinonitrile-0.24 wt% water binary alloys. Unlike the terrestrial experiments where the growth is affected by natural convection, constrained diffusive growth is observed in the microgravity experiments. This study aims to provide an experimental benchmark of dendritic growth applicable for validation of theoretical and numerical dendrite growth models. The results of the experiment were compared with the cellular automata and the phase field models, which are two classes of numerical methods widely used by scholars in the field of dendritic solidification, in both two and three dimensions. The resulting morphologies and tip velocities from the models were compared with the Pore Formation and Mobility Investigation experimental results. The combination of experimental and simulation results shows fair agreement and together can be used as a benchmark solution for tip velocity and evolution of dendritic microstructures. • A validation benchmark for dendrite growth in microgravity conditions is presented. • The experimental results are compared with two numerical models. • Both numerical models were able to successfully predict the dendrite tip velocity. [ABSTRACT FROM AUTHOR]

• A new method for meshfree phase-field simulation of dendritic solidification is presented using smoothed particle hydrodynamics. • Radial basis functions and moving least squares are used for constructing the weight functions. • Easy discretization of the interface thickness independently from the thermal field particle resolution. • Easy imposition of Neumann boundary conditions at arbitrary domain boundaries with and without internal cavities. We present a robust and efficient approach to meshfree phase-field (PF) simulation of dendritic solidification on arbitrary domain geometries using smoothed particle hydrodynamics (SPH). We use radial basis functions (RBFs) and moving least squares (MLS) as alternative approaches for constructing kernel approximation functions exhibiting a higher order of consistency than traditional kernel functions used in SPH. In the proposed smoothed particle hydrodynamics-phase field method (SPH–PFM), proper discretization of the PF order parameter at the diffuse interface region can be easily accomplished independently from the particle spacing resolution used for computing the thermal field distribution. We use an implicit geometry construction approach to automatically generate virtual boundary particles to impose Neumann-type boundary conditions at the domain boundaries. We solve the Allen–Cahn equation locally at particles constructed at a narrow band around the interface region. Additionally, only first-order derivatives of the meshfree approximation functions are needed in our implementation to solve the governing equations. Mathematical formulation and detailed analysis will be presented and discussed where we investigate the effect of the meshfree approximation scheme on the final morphology of the grown dendrite. [ABSTRACT FROM AUTHOR]

• Titanium crystal-melt interfacial properties obtained from atomistic simulations. • Atomistically-informed phase field simulation studies of titanium solidification. • Anisotropy of crystal-melt interfacial properties affects titanium microstructure. • Parameter-free phase field modeling of solidification of undercooled titanium. The effects of kinetic and capillary anisotropies on crystal morphology and growth rate during solidification of titanium are studied using atomistically-informed phase field simulations. Molecular dynamics (MD) is employed to calculate the anisotropic kinetic coefficient and crystal-melt interface free energy using the free solidification and capillary methods. The phase field simulation results for solidification velocity and interface temperature are in quantitative good agreement with experimental and analytical data for undercoolings below 150 K. As the role of interface kinetic effects increases with undercooling the use of a modified phase field model allowed the extension of its quantitative prediction capability to higher undercoolings. In addition, the effect of MD calculated kinetic and capillary anisotropy parameters on dendrite shape and tip and solidification velocity was investigated. [ABSTRACT FROM AUTHOR]

Highlights • An extended free dendritic growth model is developed for binary alloys. • Results show that it is necessary to introduce the diffusion relaxation effect. • Results indicate the effect of the nonisothermal nature of interface is significant. • The effect of the nonisosolutal nature of interface is very slight and negligible. Abstract Through considering both the relaxation effect of local nonequilibrium solute diffusion in bulk liquid and the effect of nonisothermal and nonisosolutal nature of the solid–liquid interface, a further improved version of free dendritic growth model was proposed, for binary alloys. Comparative analysis indicates that the effect of the nonisothermal nature of the interface is significant and this effect should be taken into account in modeling the free dendritic growth. It is also concluded that the effect of the nonisosolutal nature of interface is very slight and really negligible. Thus, the simplified version of free dendritic growth model taking into account the nonisothermal nature of the interface and with an isosolutal interface assumption is reasonable. Furthermore, experimental comparison demonstrates that it is necessary to introduce the diffusion relaxation effect for achieving a good agreement between the model predictions with the available experiment data, especially at high undercoolings, for the Cu 70 Ni 30 alloy. [ABSTRACT FROM AUTHOR]

In this paper, we use the newly proposed meshfree interface finite element method (MIFEM) for numerical simulation of dendritic solidification with fluid flow. In the MIFEM, meshfree points without connectivity are imposed directly at the zero-isocontour of an implicit function defining the interface which is allowed to arbitrarily intersect the finite elements. The MIFEM utilizes the constructed interface points for meshfree solution of a variational level set equation based on the Ginzburg–Landau energy functional minimization such that the reinitialization procedure is completely eliminated. To account for inter-element discontinuities, field variables at interface-embedded elements are computed by extending the approximation using the meshfree interface points as additional degrees of freedom directly corresponding to the interface. This is achieved by meshfree interpolation at the interface region via radial basis functions which inherently satisfies the Kronecker-delta and the partition of unity conditions allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. We use the MIFEM for solving the interfacial evolution equation and the set of mass, momentum, and energy conservation equations describing the dendritic solidification process with fluid flow. Mathematical formulation and implementation to multiple case studies will be presented and discussed. [ABSTRACT FROM AUTHOR]

Melt processing offers a cost effective method for producing metal matrix nanocomposite (MMNC) components; however, the influence of nanoparticles on the evolving microstructure during solidification is still not well understood. In this study, the effect of SiC nanoparticles on α-Mg dendrite evolution in a Mg-25Zn-7Al (wt.%) alloy was investigated through 4D (three dimensions plus time) synchrotron tomographic quantification of solidification experiments conducted at different cooling rates with and without nanoparticles. Key features of the solidifying primary α-Mg dendritic grains were quantified, including grain morphology, size distribution, and dendrite tip velocity. To obtain the high-contrast tomography dataset necessary for structure quantification, a new image reconstruction and processing methodology was implemented. The results reveal that the addition of nanoparticles increases grain nucleation whilst restricting dendritic growth and altering the dendritic grain growth morphology. Using LGK model calculations, it is shown that these changes in solidification microstructure occur as a result of nanoparticle-induced restriction in Zn's effective diffusivity ahead of the dendrite tips, reducing tip velocity. The results both suggest the key phenomena required to be simulated when numerically modelling solidifying Mg-based MMNC and provide the data required to validate those models. [ABSTRACT FROM AUTHOR]

The microstructural evolution in mushy zones of alloys due to temperature gradient zone melting (TGZM) is studied by simulations using a two-dimensional quantitative cellular automaton (CA) model and in situ observations of directional solidification with a transparent organic SCN-ACE alloy. The present model is an extension of a previous CA model by involving the mechanisms of both solidification and melting. The present CA model is adopted to simulate the temporal evolution of the position and velocity of a liquid pool migrating in the solid matrix of a SCN–0.3 wt% ACE alloy under conditions that the pulling velocity is either lower or higher than the critical pulling velocity. The CA simulated position and velocity curves agree well with analytical solutions. Simulations are also performed for the microstructural evolution of columnar dendrites in a SCN–2.0 wt% ACE alloy held in a stationary temperature gradient using the present CA model and a previous CA model that does not include the melting mechanism under otherwise identical conditions for comparison. The results show how melting is essential to dendrite arm migration in a temperature gradient. The time-averaged velocities of arm migration obtained from the present CA simulations increase with increasing temperature gradient and with decreasing the length between the initial arm position and the liquidus. This agrees reasonably well with experimental measurements and analytical predictions. The mechanisms of dendrite arm migration are investigated in detail by comparing the local equilibrium and actual liquid compositions at solid/liquid interfaces. The simulations render visualizing the complex interactions among local temperature, solute distribution/diffusion, and solidification/melting during the TGZM process. [ABSTRACT FROM AUTHOR]

The local dynamics of dendritic sidearms during coarsening are studied by combining in-situ radiography observations with numerical and analytical models. A flat sample of a Ga-In alloy is partially solidified and then held isothermally in a vertical temperature gradient. The evolving dendritic microstructure is visualized using synchrotron X-ray imaging at the BM20 (ROBL) beamline at ESRF, France. During the coarsening stage, the temporal evolution of the geometrical features of sidebranches is captured by automated image processing. This data is then used to quantify the dynamics of two basic evolution mechanisms for sidebranches: retraction and pinch-off. The universal dynamics of sidearm necks during pinch-off are exploited to determine the product of liquid diffusivity and capillarity length D d 0 , as a parameter that is crucial in the calibration of quantitative models. By employing an idealized phase-field model for the evolution of a single sidebranch, the behavior of selected sidebranches is reproduced from the experiments in a consistent way. [ABSTRACT FROM AUTHOR]

[Display omitted] • Increase in solute composition ratio or temperature reduce γ of Mg-Al-Zn system. • γ Basal > γ PrismaticIIA > γ PrismaticIA was identified for Mg-Al-Zn system. • Primary dendrite growth orientation of [0001] is identified for Mg-Al-Zn system. In this study anisotropic solid–liquid interfacial energy, γ, of Mg-Al-Zn system is evaluated based on capillary fluctuation method. To investigate effects of temperature and solute compositions on γ, five simulation cases, Cases I-V, are designed and divided into two group, Group I consist of Cases I-III for evaluation on solute compositions, while Group II consist of Cases I, IV and V for evaluation on temperatures. Interfacial energy stiffness of six differently oriented interfaces is evaluated, average interfacial energy, γ 0 , and anisotropic parameters of the interfaces are obtained. This study determined melting point of Mg as 964 ± 5 K, which matches the standard value of 923 K. Evaluation on γ 0 , and γ in high symmetric orientations γ Basal , γ PrismaticIA and γ PrismaticIIA suggests, for Cases I-V, lower γ 0 values within 15.74–18.19 mJ/m2 compared with elemental Mg could be related with the insufficiency of selected interatomic potential to describe the solid–liquid interface, and relation of γ Basal > γ PrismaticIIA > γ PrismaticIA was identified. Comparisons within Group I indicate the increase of relative average equilibrium composition, c ¯ i / c ¯ j , will improve solute adsorption of element i on interface, which causes γ 0 , γ Basal , γ PrismaticIA and γ PrismaticIIA to decrease. As for Group II, temperature increase will result in decline of γ 0 , γ Basal , γ PrismaticIA and γ PrismaticIIA , similar trend was found in Al-Sm alloy systems. Primary dendrite growth orientations for Cases I-V were determined as [0001], analysis shown increase in either temperature or c ¯ i / c ¯ j stabilize this preference further towards [0001]. [ABSTRACT FROM AUTHOR]

The specific area of the solid-liquid interface of an assembly of dendrites is an important integral measure of the morphology of the microstructure forming during alloy solidification. It represents the inverse of a characteristic length scale and is needed for the prediction of solidification defects and material properties. In the present study, the evolution of the interfacial area of dendrites is analysed using 3D phase-field simulations. A general evolution equation is developed for the specific interface area as a function of time and solid volume fraction that accounts for the effects of growth, curvature-driven coarsening and interface coalescence. The relation is validated using data from previously performed synchrotron X-ray tomography and isothermal coarsening experiments. It is found to be valid for arbitrary and even varying cooling rates and for a wide range of binary alloys. The rate constant in the evolution equation is successfully related to alloy properties. [ABSTRACT FROM AUTHOR]

Adopting of a simple, but dependable analytic thermodynamic solution model in the simulation of phase transformation kinetics reduces the complexity of computation and the need for extensive thermodynamic data and hence is desired in the practical application of kinetic theories in materials processing. A simple subregular solution model with linear temperature dependency, which can calculate G curves with limited information extracted from an equilibrium phase diagram, is presented and applied to the calculation of (1) the binary Ag-Cu phase diagram with metastable phase boundaries and (2) the kinetics of free dendritic growth in supercooled Ag-Cu melts. The simple T- dependent subregular solution model can duplicate the published Ag-Cu phase diagram with the predicted metastable extensions to the same accuracy as that of calculations with highly structured models that require more computation and wider range of thermodynamic data. Its integration with a free dendritic growth model permits the calculation of correct values of the driving force at non-Henrian interfacial solute concentrations that occur in rapid solidification. The use of the simple T -dependent subregular solution model to calculate the interfacial driving force greatly improves the mathematical stability in the transition stage from mass transfer-limited growth to heat transfer-limited crystal growth. [ABSTRACT FROM AUTHOR]

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields up to 6 T were measured using a high-speed camera. The growth velocities for undercoolings below 120 K are depressed under low magnetic fields, but are recovered progressively under high magnetic fields. This retrograde behavior arises from two competing kinds of magnetohydrodynamics in the melt and becomes indistinguishable for higher undercoolings. The measured data is used for testing of a recent theory of dendritic growth with convection. A reasonable agreement is attained by assuming magnetic field-dependent flow velocities. As is shown, the theory can also account for previous data of dendritic growth kinetics in pure succinonitrile under normal gravity and microgravity conditions. These tests demonstrate the efficiency of the theory which provides a realistic description of dendritic growth kinetics of pure substances with convection. [ABSTRACT FROM AUTHOR]

The solidification process of three metamagnetic Ni–Co–Mn–Sn alloys has been investigated by DTA and DSC calorimetry, X-ray diffraction, optical and electron microscopy. The as-cast microstructures are composed of three phases: austenite L2 1 /6-layered martensite, D0 3 phase and γ phase (disordered fcc). Subsequent annealing treatments at 900 °C completely dissolve the D0 3 phase in the three alloys and also the γ phase in alloys with low Co content (6.4 and 7.2 at.%). However, for 9 at.% Co the stability of γ -phase extends to temperatures close to the melting point and becomes very sensitive to the Mn and Sn content. No traces of the B2–L2 1 order–disorder transition have been obtained in the alloys investigated. The multiphase solidification can be interpreted as a peritectic process where D0 3 is the primary solidified phase with dendritic growth, followed by the peritectic reaction of this phase with the residual liquid to form the austenite L2 1 , whereas the γ -phase precipitates from the austenite L2 1 upon further cooling. [ABSTRACT FROM AUTHOR]

Shining a tightly-focussed but low-powered laser beam on an absorber dispersed in a biological fluid gives rise to spectacular growth of dendritic patterns. These result from localized drying of the fluid because of efficient absorption and conduction of optical energy by the absorber. We have carried out experiments in several biologically relevant fluids and have analysed patterns generated by different types of absorbers. We observe that the growth velocity of branches in the dendritic patterns can decrease below the value expected for natural drying. [ABSTRACT FROM AUTHOR]

In the present paper, the Stefan problem is solved by enriching an underlying NURBS-based isogeometric approximation with an explicitly defined (sharp) interface on which a hybrid function/derivative condition is isoparametrically described. Since the geometry of the enrichment is explicitly defined, normals and curvatures are explicitly computed at any point on the interface. Thus, the enriched approximation naturally captures the interfacial discontinuity in temperature gradient and naturally enables the imposition of Gibbs–Thomson condition. The blending of the enrichment with the underlying approximation requires an estimate of distance to the enriching geometry from a quadrature point and the parametric value of the footpoint on the enriching geometry. These quantities are computed efficiently in the present paper using an algebraic estimate of distance coupled with an algebraic point projection method. These algebraic schemes rely on implicitization of the parametric curve, and are shown to be more efficient and robust than Newton–Raphson iterations. Procedures for adaptive time stepping, refinement and coarsening of geometry are developed to increase the stability and efficiency of the developed methodology. Several numerical examples of classical and dendritic Stefan problem are presented to demonstrate the methodology. [ABSTRACT FROM AUTHOR]

An extended Cahn–Hilliard model (ECHM) was compared with the conventional phase-field model (CPFM) for simulating the operating state of a dendrite tip during the two-dimensional solidification of pure undercooled melts over a wide range of interfacial energy anisotropy. ECHM differs from CPFM in terms of how interfacial energy anisotropy is introduced. In ECHM, anisotropy comes solely from the anisotropic nature of the fourth-rank tensor terms included in free energy density, and not from assuming an orientation-dependent gradient energy coefficient ɛ ( θ ), which is the case in CPFM. ECHM resulted in dendrites growing with a rounded tip, even when anisotropy ( δ ) was greater than its critical value ( δ c ), but the tip radius at large anisotropy ( δ ⩾ δ c ) was limited by the interface width. In contrast to CPFM, ECHM did not engender an anomalous increase in the tip radius with bulk undercooling at small anisotropy ( δ < δ c ). In the simulation by ECHM, the tip velocity increased continuously with increasing δ beyond δ c . When compared in terms of the selection parameter σ ∗ of the dendrite tip, data obtained from ECHM fitted better to the σ ∗ ∝ δ 7/4 relationship over a wider range of δ than those obtained from CPFM. The present comparative study suggests that ECHM hinders the transition of the dendritic growth kinetics from diffusion-limited to interface-kinetic-limited, which occurs in the case of CPFM as the tip velocity increases with an increase in either undercooling or anisotropy. [ABSTRACT FROM AUTHOR]

Through introducing the nonisothermal and nonisosolutal nature of the solid–liquid interface, due to interface curvature and interface kinetics, a free dendritic growth model was proposed for binary alloys. Comparative analysis of the present model and the corresponding model assuming an isothermal and isosolutal interface indicates that there is a higher interfacial temperature predicted by the present model. This is attributed to the two factors: (i) sidewise thermal diffusion; and (ii) solutal diffusion in the bulk liquid, with the boundary condition of the nonisothermal and nonisosolutal interface. An agreement between the model predictions with the available experiment data was obtained for the Cu 70 Ni 30 alloy. It is finally concluded that the effect of the nonisothermal nature of the interface on the dendritic solidification behavior is significant and thus this effect should be taken into account in modeling free dendritic growth of binary alloys. Furthermore, it is also indicated that the effect of the nonisosolutal nature of the interface is small for the Cu 70 Ni 30 alloy. [ABSTRACT FROM AUTHOR]

We investigated the competitive growth of dendrites at the converging grain boundaries (GBs) of bicrystals during the directional solidification of an Al–Cu alloy by means of two-dimensional phase-field simulations. In particular, the focus was on the recently observed phenomenon of unusual overgrowth during the directional solidification of a Ni-based superalloy, where the favorably oriented (FO) dendrites are overgrown by the unfavorably oriented (UO) ones. The phase-field simulations were accelerated by parallel computations on graphics processing units. The simulation results showed that unusual overgrowth occurs in Al–Cu alloys, indicating that this phenomenon is a common one in metallic materials. It was also concluded that the differences in the diffusion layers in front of the FO and UO dendrites had a dominant effect on the competitive growth of dendrites at the converging GB as well as on the unusual overgrowth. In addition, unusual overgrowth was observed in all the FO dendrites with a spacing that allowed the dendrite array to grow stably without necessitating a change in the number of dendrites. The FO dendrite at the GB is overgrown by the UO dendrite when the spacing between the FO dendrite at the GB and the next FO dendrite is approximately equal to the critical minimum spacing. However, the unusual overgrowth was not observed for UO dendrites with a large inclination angle. In this case, all the UO dendrites are blocked by the FO dendrite at the GB, and the FO dendrites migrate toward the UO dendrites. [ABSTRACT FROM AUTHOR]

Numerous models for the simulation of dendritic solidification with Cellular Automaton based methods have been published in the last two decades. A large variety of different concepts have been investigated, an important fraction of them with the intent to reduce the anisotropic influence of the frequently employed Cartesian grid. The present review offers a systematization of the published models by identifying the basic components of a Cellular Automaton model describing dendritic solidification of alloys. These components are found to be three evolution algorithms, that is, one for each of the three central cell state variables, and an algorithm for the calculation of the interface geometry. The different approaches to these four algorithms are presented and evaluated with special regard toward possible potential for future research. Two of these algorithms are found to be of special interest for further model development: (1) both of the most commonly adopted geometry calculation methods, cell counting and level set with Finite Differences, are expected to yield high errors, suggesting the development of alternative approaches and (2) the algorithm for the change of state has the largest impact on the anisotropic influence of the grid. Alternative approaches, such as the decentered square algorithm, may lead to considerable improvement in simulation quality. [ABSTRACT FROM AUTHOR]

Abstract: We address the directional solidification of inclined structures by combining numerical and experimental studies performed in situations capable of yielding a detailed relevant comparison between them. We especially seek to determine the growth directions and the stability of microstructures at various Péclet numbers when the crystal axes and the thermal gradient involve a misorientation. For this we perform experiments and simulations in the closest possible conditions referring to similar physical parameters and to a monocrystal growing in a thin sample by a single layer of homogeneously spaced microstructures. Implementing a 3D phase-field numerical code proves necessary to accurately model the solidification structures. A quite satisfactory agreement, both on qualitative and quantitative grounds, is found between experiments and 3D simulations, on both the growth directions of microstructures and the transition to the degenerate mode. This agreement provides a confirmation of the growth direction law evidenced experimentally and a fine validation of the 3D phase-field numerical model. [Copyright &y& Elsevier]