Solidification Of Binary Alloy Research Articles

Modeling binary alloy solidification by a random projection method

This paper addresses the numerical modeling of the solidification of a binary alloy that obeys a liquidus–solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based on a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus–solidus diagram. We provide some numerical illustrations which assess the good behavior of the method: maximum principle, stability under CFL condition, numerical convergence toward self‐similar solutions, ability to handle two melting fronts.

Effects of Casting Speed and Runner Angle on Macrosegregation of Aluminium-Copper Alloy.

Abstract During the solidification of binary metal alloys, chemical heterogeneities at product scale over a long distance range (1cm-1m) develop and this has detrimental effect on the resulting mechanical properties of cast products. Macrosegregation is of great concern to alloy manufacturers and end users as this problem persist. In this study, the use of process parameters namely casting speed and runner angle to reduce macro-segregation in aluminum-copper-zinc binary alloy solidification is reported. The results from optical microscope, scanning electron microscope and energy dispersive spectrometry show that these parameters significantly influenced the development, size and volume of macro-segregation. The combination of parameters namely the pouring height between 96 mm/s, 100mm/s, and runner angles between 1200, 1500 produced less segregations with improved mechanical properties within standard specification. The tensile strength (110 MPa), modulus of elasticity (6800 MPa) and 2.5 % elongation obtained in this study are within standard (88- 124 MPa), 7100 MPa and (1-25 %) respectively for this class of alloy.

Compositional dependency of double-diffusive layers during binary alloy solidification: Full-field measurements and quantification

Density variations arising from thermal and compositional gradients in multi-component fluids can lead to natural convection flows. The double-diffusive layer is one such flow phenomenon, commonly observed in oceanic and phase change systems. The solidification of high Prandtl number fluids offers a suitable platform to study multi-diffusive convection owing to continuously evolving temperature and compositional fields. In this work, an experimental investigation was conducted to study the influence of transport phenomena on the double-diffusive layer formation, by performing full-field measurements of concentration and flow velocities during bottom-cooled solidification of a hyper-eutectic aqueous mixture. Using a Mach-Zehnder interferometer, the first-ever real-time, quantitative observations of solutal mixing, plume formation, and the evolution of the double-diffusive layers by forming a stepped compositional distribution have been reported. In addition, the associated flow velocities were measured using the particle image velocimetry technique which clearly characterizes the compositional and thermal natural convection patterns along the vertical and horizontal directions, respectively. The study revealed a life-cycle for the existence of the double-diffusive layers, wherein they undergo onset, development, and disappearance depending on the initial composition, and identified critical Rayleigh numbers for each of these stages. The experimental observations were further supported with analytical scale estimates of the critical length, time, and velocities of the system. The quantitative results elucidate the conditions, including a newly hypothesized threshold composition difference, which led to the formation as well as the disappearance of the layers.

Dynamic instability of the steady state of a planar front during non-equilibrium solidification of binary alloys

The dynamic stability of the steady state arising during rapid solidification of a binary alloy with a planar front is examined. Earlier work (Galenko and Danilov, 2000) that was derived under the assumption of dilute solutions and linearized phase diagrams is extended and generalized to the case of non-linear phase diagrams and concentrated alloys. The present treatment confirms the validity of the earlier derived criteria for the stability of a steady state of a planar front independently of any thermodynamic model describing non-equilibrium solidification of binary alloys.It is found that in temperature and concentration ranges where the solidus concentration increases with increasing solidification velocity, the steady state of the planar front is dynamically unstable. It is discussed how such a dynamic instability of the steady state of a solidifying planar front has an effect on its morphological stability. This is a possible explanation for the discrepancy between morphological stability theory and published experimental data (Hoglund et al., 1998) obtained from rapidly solidified Si-Sn melts.

A finite element formulation for macrosegregation during alloy solidification using a fractional step method and equal-order elements

A finite element formulation of the “minimal” solidification model is presented for the prediction of macrosegregation during two-dimensional (2D) columnar solidification of binary alloys. A fractional step method is extended to solve the thermosolutal convection that has a damping in the mushy zone during solidification. Using this method, the velocity and pressure are decoupled and interpolated by linear equal-order triangular elements, resulting in decoupled systems that can be solved simply and efficiently. For convection-diffusion equations of energy, solute and momentum, the consistent streamline upwind Petrov-Galerkin (SUPG) method and the second-order Crank-Nicolson scheme are used for the discretization and integration over the spatial domain, respectively. A solution procedure is designed to couple the resolutions of conservations of energy, solute and momentum, as well as the microsegregation model at an overall computational efficiency and accuracy. The formulation is first validated and then applied to predict macrosegregation during solidification of Pb-18 wt%Sn and Sn-10 wt%Pb alloys in a rectangular mold. The formation of macrosegregation is investigated, and comparisons with another finite element method (FEM) based code are made.

Competitive grain growth during directional solidification of a polycrystalline binary alloy: Three-dimensional large-scale phase-field study

Competitive grain growth during the directional solidification of a polycrystalline binary alloy is investigated by performing systematic three-dimensional large-scale phase-field simulations with the GPU supercomputer TSUBAME2.5 at the Tokyo Institute of Technology. Contrary to two-dimensional investigations, in which an unusual growth of unfavorably oriented (UO) grains has been observed frequently in preference to favorably oriented (FO) ones, the grain selection in the present three-dimensional simulations follows essentially the Walton and Chalmers model, in which FO grains are predominant. The UO dendritic grains persist for longer times than the UO cellular grains, and the FO dendritic grains remain smaller than the FO cellular ones. The change in the number of grains follows a power law, with an exponent that is much lower than that of the Kolmogorov's model describing a purely geometrical growth selection.

Modeling of binary alloy solidification under conditions representative of Additive Manufacturing

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.

Interaction between primary dendrite arm spacing and velocity of fluid flow during solidification of Al–Si binary alloys

A new and more efficient numerical algorithm to simulate the solidification of binary metallic alloys, wherein for the first time, the undercooling of the liquidus temperature prior to solidification event and optimized thermo-physical properties was incorporated, has been recently developed and validated by various experiments. Subsequently, experiments were carried out to evaluate the validity of various theoretical models in the literature used to predict the dendrite arm spacing (DAS) and quantify the critical interaction between fluid flow and transient DAS during unsteady state solidification. Typically, models of solidification processes such as casting, welding and galvanizing assume a constant value of fluid flow to predict the DAS and in many cases unable to obtain validation. This practice is erroneous and the transient fluid flow developed during solidification has a significant effect on the transient DAS, thermal gradient (G), solidification velocity (R) and morphology of the mushy zone. The Bouchard–Kirkaldy model (DAS prediction) coupled with the Lehmann model to incorporate fluid flow velocity was the only valid theoretical model in binary alloy solidification.

Squeeze-film flow between a flat impermeable bearing and an anisotropic porous bed

We consider a theoretical model of the squeeze film in the presence of a porous bed. The gap between the porous bed and the bearing is assumed to be filled with a Newtonian fluid. We use the Navier-Stokes equation in the fluid region and the Darcy equation in the fluid filled porous region. Lubrication approximation is used to derive the corresponding evolution equation for the film thickness. We use G. S. Beavers and D. D. Joseph [“Boundary conditions at a naturally permeable wall,” J. Fluid. Mech. 30, 197–207 (1967)] and M. Le Bars and M. G. Worster [“Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification,” J. Fluid. Mech. 550, 149–173 (2006)] condition at the liquid porous interface and present a detailed analysis on the corresponding impact. We assume that the porous bed is anisotropic in nature with permeabilities K2 and K1 along the principal axes. Accordingly, the anisotropic angle ϕ is taken as the angle between the horizontal direction and principal axis with permeability K2. We show that the anisotropic permeability ratio and the anisotropic angle make a significant influence on the contact time, flux, velocity, etc. Contact time to meet the porous bed when a bearing approaches under a constant prescribed load is estimated. We present some important findings (relevant to the knee joint) based on the anisotropic properties of the human cartilage. For a prescribed constant load, we have estimated the time duration, during which a healthy human knee remains fluid lubricated.

Peritectic phase transformation in the Fe–Mn and Fe–C system utilizing simulations with phase-field method

The present investigation focuses on the solidification of peritectic binary alloys in the systems Fe–Mn and Fe–C by utilizing phase-field simulations. Isothermal and directional solidification conditions were simulated with this approach and the following aspects were investigated: the phases evolution during the peritectic transformation close to the peritectic temperature for the Fe–Mn alloys with 9.5 and 11.0wt.%, the kinetics of the γ-phase growth simultaneously into the liquid and into the δ-phase during the peritectic transformation for several alloys under isothermal conditions in the Fe–Mn peritectic plateau, the γ-phase thickness during the peritectic reaction in the Fe–Mn system and, finally, the behavior of the remaining δ-phase amount at the end of solidification for different cooling rates in the Fe–C peritectic alloy. The model approach was checked by comparison with literature data. It was concluded that the present approach is consistent in yielding quantitative results for the interested phase transformation.

Effect of rotational vibrations on directional solidification of high-temperature binary SiGe alloys

Numerical investigation of flows and heat and mass transfer during the directional solidification of high temperature SiGe alloys in the presence of rotational vibrations has been performed. It has been shown that the structure of a vibration-induced flow has the form of a vortex localized near the crystallization front and the direction of this flow is such that the fluid moves along the front from the symmetry axis to the wall of the crucible. With the increase of the vibration parameter the intensity of the vortex grows, and the concentration gradient on the crystallization front near the crucible wall increases. This causes an increase in the crystallization temperature in this region, the temperature of the melt in this area becomes lower compared to the crystallization temperature, and hence the melt becomes overcooled. For the germanium-silicon system, changes in the gravity force lead to the changes in the flow and heat and mass transfer regimes, which are accompanied by a hysteresis. The analysis of the obtained numerical results has revealed that rotational vibrations are responsible for the disappearance of the zone of non-uniqueness.

Modelling of macrosegregation with mesosegregates in a binary metallic cast by the diffuse approximate meshless method

The solidification of binary metallic alloy (Sn-10%Pb) is simulated in 2D with a diffuse approximate meshless method. The macrosegregation with mesosegregates is described by a coupled set of volume-averaged partial differential equations. The incompressible Newtonian fluid is described by coupled mass and momentum equations and the mushy zone is treated as a Darcy porous media. The energy transport is described with enthalpy formulation and the species transfer is incorporated by considering the Lever rule approximation. The thermo-solutal Boussinesq hypothesis is applied in order to account for the double-diffusive effects in the melt. The mathematical model is solved by a diffusive approximate method on local subdomains with Euler time stepping. Pressure-velocity coupling is incorporated by applying the fractional step method. The instabilities due to the convective terms are smoothed out by applying the upwinding technique. The results are presented on a regular node arrangement and are compared to other benchmark results. The present paper demonstrates that the results calculated with the diffuse approximate meshless method are in good agreement with reference results.

Influence of crystal growth kinetics on prediction of macro segregation by micro-macroscopic simulation of binary alloy solidification

Using the micro-macroscopic computer simulation model of binary alloy solidification, based on a single domain control-volume calculations, and involving the tracking of columnar dendrite tips envelope for distinguishing different grain structures within the two-phase liquid-solid region, the paper reports the outcomes of the detailed analysis addressing the question of the influence of enhanced KGT crystal growth models on the predicted macro-segregation pattern in the Al-4wt.%Cu alloy cast. In particular, the analysis concerns the impact of a proper selection of the stability constant for the KGT model (based on a crystal-melt surface energy anisotropy strength and linear scaling law of the marginal stability theory) on the predicted dendrite tip under-cooling, volumetric solid fraction and actual solute concentration along the front of columnar dendrite tips. Differences in the resulting evolution of both: the under-cooled melt region within the mushy zone and the solute concentration fields calculated for the considered various kinetics of a grain growth are also reported and discussed.

Thermal characterisation with modelling for a microgravity experiment into polycrystalline equiaxed dendritic solidification with in-situ observation

The Multiple Equiaxed Dendrite Interaction (MEDI) experiment was launched on the MASER-13 sounding rocket campaign to investigate polycrystalline equiaxed solidification in the transparent phase change material Neopentylgycol-30wt.%(d)Camphor. This material is of interest as an energy-storage material and as a transparent analogue system of solidification in hypoeutectic metal alloys with a Face Centred Cubic lattice. The liquid sample was cooled under a controlled rate of 0.75 K/min with sufficient time to allow semi-solid conditions to develop under microgravity conditions with the absence of gravity-driven convection. This manuscript provides details on the experimental apparatus and procedures. In addition, the experimental method has been augmented with a numerical model to assist with the characterisation of the essential thermal aspects of the experiment. The model followed a volume-averaging, continuum approach for mushy-zone development. A fast algorithm for computing non-isothermal crystallisation kinetics was applied to the case of binary alloy solidification. To build confidence, a formal numerical verification procedure was performed. The model converged sufficiently with second order accuracy as expected. Application of the model gave close agreement between experimental thermocouple readings and numerical simulation data with a Root Mean Square of 0.2 K for the error. A 2D thermal model is sufficient with a suitable heat loss coefficient at the sample-viewing window boundary. Thermal gradients within the sample and along the growth direction were uniform and approximately 0.3 K/mm. Lateral thermal gradients in the sample ranged from zero at the median plane to 0.3 K/mm at the boundary with the containing structure. However, temperature variation in the lateral direction was predicted to be less than 0.22 K.

Sound velocity during solidification in binary eutectic systems

We applied an ultrasound technique to an advanced material process by investigating the behavior of sound velocity during solidification of binary alloy melts over a wide range of temperatures and compositions. To gain a basic understanding of the relationship between the sound velocity and phase change in binary eutectic systems, the sound velocity was measured in Pb-Sn and Bi-Sn alloys by the pulse transmission method. Based on the measurement results, we established a link between the sound velocity variation and the complex solidification process, including the initial appearance of undercooling and eutectic reaction. During solidification, alloys usually pass through a transient mushy state between the liquid and solid phases. Since the solid fraction is uniquely related to the sound velocity, we demonstrate that it is possible to identify the solid fraction in the mushy state using the sound velocity. At the eutectic point, a sudden change was observed in relation to the eutectic reaction, in which the sound velocity exhibited an abrupt transition under isothermal conditions. This sudden change in the sound velocity was evident even when the initial composition was below the maximum solid-solution limit, such as when the solute distribution coefficient was relatively large. This result suggests that the presence of a eutectic in the final solidified texture can be predicted using our sound velocity measurement system. Finally, we present a novel sound velocity phase diagram that provides a real-time state determination system using ultrasound during solidification process, such as casting.

Numerical modeling of solidification process taking into account the effect of air gap

The paper presents a method of numerical modeling of binary alloy solidification process in a permanent mold in a two-dimensional area. The model takes into account the influence of the gas gap of variable width existing between the mold and the casting on the rate of solidification process. The numerical model is based on the finite element method (FEM) with independent spatial discretization of the casting and the mold. The displacements of these regions resulting from a thermally dependent changes of their volumes are also taken into account. The adopted approach involves the use of two separated meshes, where the temporary temperature fields are obtained. The thermal interaction between the casting and the mold is described by the appropriate boundary condition. The solution is obtained sequentially in each time step independently for the each region.

Mathematical modeling of macrosegregation during solidification of binary alloy by Control Volume Finite Element Method

• A mathematical model for solidification with CVFEM is implemented in a computer code. • Coupled heat and mass transfer in solidification of lead-tin alloy is described. • Thermo-solutal convection and freckle formation in phase-change are reported. • Effects of cavity aspect ratio and cooling direction in solidification are studied. • Macrosegregation maps for Pb-48%Sn alloy in rectangular cavities is investigated. Unsteady coupled natural convective heat and mass transfer with liquid to solid phase change is described to analyze the macrosegregation of a Pb–Sn alloy in a rectangular two-dimensional cavity. The effect of cooling direction is investigated, by comparing the numerical simulation of solidification in rectangular molds with one vertical side cooled and with bottom wall cooling, both with the cold wall temperature changing with time. Fluid mechanics, heat and mass transfer coupled equations with unsteady, convective, diffusion and sources terms are solved with the Control Volume Finite Element Method (CVFEM) in cavities with aspect ratios A = H / B = 1 / 3 , 0.6 and 3. Results for the evolution of the distribution of streamlines, solidification front, isotherms and iso-concentrations are obtained with a code developed to characterize coupled fluid, heat and mass transport phenomena. Complex physical processes such as thermo-solutal convection during solidification, freckle formation and the final pattern of macrosegregation are described in terms of the cavity aspect ratio by the mathematical model. A good description of freckle formation and its relation to direction of cooling and aspect ratio has been obtained by the transient-convective–diffusive mathematical model solved by CVFEM.

Eutectic Solidification in Zn-Sn Binary Alloys: An Experiment for High Schools

Eutectic Solidification in Zn-Sn Binary Alloys: An Experiment for High Schools

Stability of a planar interface during solidification of a dilute binary alloy, W. W. Mullins and R. F. Sekerka, J. Appl. Phys., 35, 444-451(1964) : Morphological Stability

Stability of a planar interface during solidification of a dilute binary alloy, W. W. Mullins and R. F. Sekerka, J. Appl. Phys., 35, 444-451(1964) : Morphological Stability

Exploring the design of eutectic or near-eutectic multicomponent alloys: From binary to high entropy alloys

Eutectic and near-eutectic high entropy alloys (HEAs) have recently attracted a great deal of interest because of their promising properties, such as an excellent castability and unique combination of good ductility and high strength. However, in the absence of a phase diagram, it remains a non-trivial task to find a eutectic or near-eutectic composition for a HEA system, which usually demands a tremendous amount of efforts if a trial-and-error approach is followed. In this paper, we briefly review the thermodynamics that governs the eutectic solidification in regular binary and ternary alloys, and proceed to the discussion for the design of eutectic HEAs. Based on the data reported, we then propose an improved strategy which may enable an efficient search for the eutectic or near eutectic HEA compositions.