Solidification Front Research Articles

Investigation on nonequilibrium crystallization of highly undercooled Cu–Ni–Co alloys

Deep undercooling rapid solidification experiments of Cu–Ni–Co alloys were carried out using the molten glass purification cycle superheat method. 130 K, 177 K and 277 K undercooling degrees were obtained and analysed for Cu55Ni43Co2 alloy. The crystallographic information obtained by EBSD and the dynamics of the solidification front taken by high speed photography were analysed and it was concluded that both the formation of relatively rounded equiaxed grains during the first refinement and the subsequent formation of finer subcrystals were due to the release of a large amount of solidification energy during the solidification process. The re-glow stage releases a large amount of latent heat of solidification resulting in the remelting of the dendrites. TEM tests were carried out on Cu55Ni43Co2 alloy with a maximum undercooling of 277 K. It was found that part of the substructure showed a high density dislocation network. By analysing the effect of increasing undercooling on the microstructure evolution, combined with the EBSD and TEM characterisation data, it was found that the stress-induced recrystallization mechanism was the dominant factor in the grain refinement mechanism at large undercooling.

Phase-field investigation on the microstructural evolution of eutectic transformation and four-phase reaction in Mo-Si-Ti system

By using phase-field method, we investigate the morphological evolution of three-phase eutectic transition and four-phase reaction in Mo-Si-Ti system through 2-D and 3-D simulations. For the eutectic transition, we focus on the two-phase growth of lamellar pair from an isothermally undercooled melt: L→Ti(Mo)5Si3+β(Mo,Si,Ti), and obtain a microstructure selection map for (mi) stable, (mii) unstable, and (miii) oscillatory growth (metastable mode), in terms of the Mo-composition and lamellar spacings. The underlying reason for these three different morphologies is clarified by analyzing the growth rate of the solidification front. In addition, we scrutinize the influence of interfacial energy on the solidification morphology and observe three different types of growth mode: (gi) curving, (gii) stable, and (giii) unstable growth. For the four-phase reaction, L+Mo(Ti)3Si→Ti(Mo)5Si3+β(Mo,Si,Ti), we observe the remelting of Mo(Ti)3Si phase and the formation of a lamellar pair consisting of Ti(Mo)5Si3 and β(Mo,Si,Ti) on the surface of the Mo(Ti)3Si phase after an interface of the lamellae pair phases is formed. A certain orientation angle with respect to the solidification direction is obtained for the lamellar pair growth during the four-phase reaction. In both eutectic phase transformation and four phase reaction, a comparison between the 2D and 3D simulations reveals the influence of the third dimension on the development of the lamellar pair.

Scaling of inter-pore spacing of lotus-type pores

Abstract The present study is to scale the inter-pore spacing and bubble radius required for controlling the porosity of the lotus-type pores in the solid during a unidirectional solidification. The porosity in solid degrade properties of material in welding, casting and additive manufacturing, etc. On the other hand, the ordered cylindrical pores in the material are often used to improve the functional properties, such as the tensile and compression stresses, the impact and acoustic energy absorption, the permeability, and the thermal and electrical conductivity, etc. Different from the traditional minimum undercooling criterion to estimate the porosity and size of lotus-type pores, this study relevantly combines the Gibbs-Thomson equation, the Young-Laplace equation, the nucleation theory, and the Henry’s law or Sieverts’ law to scale the inter-pore spacing and the critical radius of the lotus-type pores, which are considered as the same order of the wavelength and the amplitude of the morphological instability of the solidification front, respectively. This work revises the minimum undercooling criterion which ignores the nucleating bubble on the solidification front, and conducts irrelevant evaluation of the curvature of the solidification front. The present work finds the revised scaling results and available experimental data to be in good agreement. The sizes of the pores and the porosity in the solid can be successfully controlled in advance.

Three-dimensional sharp and conservative VOF method for the simulation of binary solidification

We present a 3D adaptive octree based numerical method for the simulation of binary solidification, with the temperature and the concentration fields being strongly coupled at the solidification front. The volume of fluid approach (VOF) is used to advance the front, which is geometrically reconstructed as a sharp interface separating the liquid and the solid domains. On basis of this, the embedded boundary method (EBM), together with the finite volume method, is employed to discretize the temperature and concentration fields at two sides of the interface in a sharp manner. The major novelty of the present study is displayed in several aspects: It is the first attempt to develop fully sharp schemes for the simulation of binary solidification in the VOF framework, while previous VOF-type methods consider the jump conditions at the interface as source terms; second the geometrically reconstructed interface and the EBM enable us to capture those discontinuities accurately without any artificial smearing, and particularly, we will show how to construct a second-order scheme for the flux jump condition of the temperature field across the interface; finally compared to other sharp schemes, we will show that the present method has natural advantages to adapt with the fluid flow solvers, because the hybrid VOF-EBM method guarantees good performance in solving the complex solid-fluid coupling problems based on the finite volume framework. Owing to all these advantages, we will show that regardless of pure substance or binary solution, all the numerical results agree well with the benchmark results. In particular, we apply the numerical method to model the solidification of a Ni-Cu alloy, which is thought to be very challenging owing to the high Lewis number. Besides, coupling to the fluid flow solver, we demonstrate that this method can predict the solidification/melting of an ice cylinder/sphere accurately in a salted solution under forced convection, by which the fluid, temperature and concentration equations are all solved sharply.

Toward sustainability for upcycling SoG-Si scrap by an immersion rotational segregation purification process

Recycling solar grade silicon (SoG-Si) scrap is critical for the sustainability of solar energy and fulfilling to close material loops in circular economics. A major challenge is to control trace impurities efficiently in short time for upgrading scrap to a level of SoG-Si. Here, a new immersion rotational separation purification (IRSP) process is developed to enhance trace impurities removal and the crystal growth from remelted metal by driving the rotating shear flow to improve the efficiency of solute and heat transfer. In a departure from conventional practice that forces extremely low solidification rate limited by the diffusion layer depth at approximately equilibrium solidification interface, here IRSP achieves the deep removal of impurities and the increase of solidification rate by the non-equilibrium rotating solidification interface. In the non-equilibrium solidification process caused by mold rotation, the rotating shear flow not only reduces the diffusion layer depth to improve impurity removal efficiency, but also increases the temperature gradient of the melt at the solidification front that is conducive to the increase of crystal growth rate. The new method is applicable to molten Si and the production of SoG-Si (99.9998%) has been demonstrated, which is able to improve the quality of recycled SoG-Si requiring a low energy input. It is expected that this process helps close high purity Si material loops, reduce resource consumption and the carbon footprint of the photovoltaic industry.

Controlling solute channel formation using magnetic fields

Solute channel formation introduces compositional and microstructural variations in a range of processes, from metallic alloy solidification, to salt fingers in ocean and water reservoir flows. Applying an external magnetic field interacts with thermoelectric currents at solid/liquid interfaces generating additional flow fields. This thermoelectric (TE) magnetohydrodynamic (TEMHD) effect can impact on solute channel formation, via a mechanism recently drawing increasing attention. To investigate this phenomenon, we combined in situ synchrotron X-ray imaging and Parallel-Cellular-Automata-Lattice-Boltzmann based numerical simulations to study the characteristics of flow and solute transport under TEMHD. Observations suggest the macroscopic TEMHD flow appearing ahead of the solidification front, coupled with the microscopic TEMHD flow arising within the mushy zone are the primary mechanisms controlling plume migration and channel bias. Two TE regimes were revealed, each with distinctive mechanisms that dominate the flow. Further, we show that grain orientation modifies solute flow through anisotropic permeability. These insights led to a proposed strategy for producing solute channel-free solidification using a time-modulated magnetic field.

Formation mechanism of heterogeneous microstructures and shape memory effect in NiTi shape memory alloy fabricated via laser powder bed fusion

Additive manufacturing involves the process of track-by-track melt pools accompanied by the localized rapid melting/solidification, which can determine unique nonequilibrium microstructures. In this study, we report formation of heterogeneous nonequilibrium microstructures in near-equiatomic NiTi fabricated via laser powder bed fusion (LPBF) additive manufacturing, and further discuss their underlying formation mechanisms and influences on shape memory effect of the LPBF NiTi. Specifically, the heterogeneous microstructures include the core (HCP α-Ti)-shell (Ti2Ni) structural nano-sized precipitation phases in columnar grains, which were resulted from high undercooling and cooling rate during LPBF solidification, the intermediate R phase in cellular and columnar grains, which was stemmed from residual thermal stress during LPBF, the nano-sized cellular substructure in columnar grains with boundaries decorated with Ti2Ni precipitates, which was originated from enriched Ti atoms at the solidification front during directional and orderly solidification of melt pools, together with the abundant dislocations. Interestingly, the two-way shape memory strain of 0.8% in LPBF NiTi was obtained by cycle loading–unloading-heating–cooling training process. These findings achieved in this work enrich the knowledge on formation mechanism of heterogeneous microstructures in LPBF NiTi SMAs, and further pave the way for engineering applications of two-way shape memory effect of LPBF NiTi shape memory alloys.

Migration Behavior of Inclusions at the Solidification Front in Oxide Metallurgy.

Distribution of inclusions plays an essential role in inducing intracrystalline ferrite, and the migration behavior of inclusions during solidification has a significant influence on their distribution. The solidification process of DH36 (ASTMA36) steel and the migration behavior of inclusions at the solidification front were observed in situ using high-temperature laser confocal microscopy. The annexation, rejection, and drift behavior of inclusions in the solid-liquid two-phase region were analyzed, providing a theoretical basis for regulating the distribution of inclusions. Analysis of inclusion trajectories showed that the velocity of inclusions decreases significantly as they near the solidification front. Further study of the force on inclusions at the solidification frontier shows three situations: attraction, repulsion, and no influence. Additionally, a pulsed magnetic field was applied during the solidification process. The original dendritic growth mode changed to that of equiaxed crystals. The compelling attraction distance for inclusion particles with a diameter of 6 μm at the solidification interface front increased from 46 μm to 89 μm, i.e., the effective length for the solidification front engulfing inclusions can be increased by controlling the flow of molten steel.

Multi-scale Multi-physics Phase-field coupled Thermo-mechanical approach for modeling of powder bed fusion process

The present study investigates the thermomechanical simulation of powder bed fusion (PBF) process, focusing on the characterization of the melt pool. With the aim of comprehensively understanding the complex multi-physics phenomena inherent to the PBF process, our objective is to establish a robust and refined computational framework that is capable of systematic evaluation of the dynamic evolution of the melt pool geometry and temporal characteristics across the various stages of its formation. For this purpose, the Allen-Cahn phase field formulation is integrated with the elastoplastic material model based on J2 plasticity theory and the model implementation is conducted based on a finite element method (FEM) framework using the Multi-physics Object-Oriented Simulation Environment (MOOSE). As an objective, the model tends to depict the intricate, nonlinear, and non-equilibrium nature of the melt pool, encompassing multi-physics process of the PBF, while assuming powder particles as a homogenized continuum medium and neglecting complex interactions between the particles and their surroundings. This includes the separation of geometry into two domains (i) the powder layer and (ii) the substrate, the melting and solidification of the material, the phase-changing process, and the resulting induced distortion and residual stresses. Additionally, the model incorporates a phase indicator to account for the degree of solidification or consolidation of powder, whose evolution describes diffusion, solidification and shrinkage phenomena. This approach enables the tracking of the movement of the melting front of the metallic material induced by a heat source, effectively dividing the domain into regions of soft and hard solid states with a diffusive interface in between. Furthermore, to enhance the model's fidelity, an adaptive mesh refinement (AMR) strategy is employed to precisely capture important aspects of the phase changing process, such as characteristics of the solidification front and powder melting. To assess the model's performance, it is tested by simulating the processing of a three-dimensional Inconel 625 thin plate, as well as a benchmark example, where the influence of parameters such as temperature and phase change on the mechanical response of the system during the solidification process is elucidated.

Solute segregation affected by transport properties during a bubble entrapment in upward solidification

Abstract The effects of transport properties on segregation of a dissolvable gas, for example, carbon dioxide in water in the presence of an entrapping bubble during upward unidirectional solidification is numerically investigated. Microporosity and inter-related solute segregation are two common defects detrimental to mechanical properties of components, especially to fatigue performance, strength and ductility. In this work, transport processes between the bubble, liquid and solid affected by mass, momentum, energy, and concentration Eqs. are solved by finite element schemes provided from the commercial COMSOL code. The results find that solute concentration in solid and liquid surrounding the pore increases with decreasing Henry's law constant and gravitational acceleration, and increasing surface tension and solid thermal conductivity. Solute gas concentration on the top free surface is insensitive to that in the pore rather than that in liquid and solid away from the pore. Apex cap becomes non-spherical affecting solidification rate and shape of the solidification front as ambient pressure at the top free surface and gravitational acceleration increase. Contact angle versus location of the solidification front predicted from this work and Abel's Eq. agrees well. Solute segregation encountered by pore formation is controllable.

Effect of Laser Beam Profile on Thermal Transfer, Fluid Flow and Solidification Parameters during Laser-Based Directed Energy Deposition of Inconel 718.

The profile of the laser beam plays a significant role in determining the heat input on the deposition surface, further affecting the molten pool dynamics during laser-based directed energy deposition. The evolution of molten pool under two types of laser beam, super-Gaussian beam (SGB) and Gaussian beam (GB), was simulated using a three-dimensional numerical model. Two basic physical processes, the laser-powder interaction and the molten pool dynamics, were considered in the model. The deposition surface of the molten pool was calculated using the Arbitrary Lagrangian Eulerian moving mesh approach. Several dimensionless numbers were used to explain the underlying physical phenomena under different laser beams. Moreover, the solidification parameters were calculated using the thermal history at the solidification front. It is found that the peak temperature and liquid velocity in the molten pool under the SGB case were lower compared with those for the GB case. Dimensionless numbers analysis indicated that the fluid flow played a more pronounced role in heat transfer compared to conduction, especially in the GB case. The cooling rate was higher for the SGB case, indicating that the grain size could be finer compared with that for the GB case. Finally, the reliability of the numerical simulation was verified by comparing the computed and experimental clad geometry. The work provides a theoretical basis for understanding the thermal behavior and solidification characteristics under different laser input profile during directed energy deposition.

Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy Approach.

By taking enthalpy-an internal energy of a diffusion-type system-as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.

Effect of novel concentric annular fins on the melting and solidification process of stearic acid in thermal energy storage devices

The latent heat thermal energy storage device provides an alternative solution to the problem of imbalance between energy supply and demand. To enhance heat transfer, a series of latent heat thermal energy storage devices with novel concentric annular fins are proposed, as the design accelerates the melting and solidification processes of stearic acid. Based on the finite volume method, the enthalpy-porosity approach is employed to numerical simulation the charging/discharging process. Effects of the number and arrangement of concentric annular fins on the liquid fraction, melting and solidification front, melting uniformity, temperature uniformity, velocity uniformity and total melting and solidification time during melting and solidification are studied. Results showed that the melting and solidification rate increases with increasing fin number. The total melting and solidification times were reduced by 72.83% and 86.39%, respectively, for the case with 9 concentric annular fins compared to the bare tube. Both melting performance and temperature uniformity were improved. Further, the effect of fin arrangement on the melting and solidification performance was investigated with the same total volume of fins. Results revealed that the heat transfer performance of progressively shorter fin structures < uniformly distributed fins < progressively longer fins < performance of non-uniformly distributed fin arrangement. The non-uniform fin arrangement reduces the total melting and solidification time of stearic acid by 85.46% and 90.11%, respectively, compared to bare tube. This work provides new insights into the understandings of the transient phase change process and the strategies for guiding the design for thermal energy storage devices using annular fins.

Numerical Simulations and Thermal Diagnostic of Ledge Formation in Hall–Heroult Aluminum Electrolysis Cell with a Solidification Front at the Cryolite-Metal Baths Interface for Reduction of Heat Losses

Numerical Simulations and Thermal Diagnostic of Ledge Formation in Hall–Heroult Aluminum Electrolysis Cell with a Solidification Front at the Cryolite-Metal Baths Interface for Reduction of Heat Losses

Experimental investigation of a thermal response behavior of d-mannitol as phase change material

The credibility of any phase change material (PCM) must be meticulously examined prior to using it as an efficient energy storage medium for any practical application. The present work focuses on experimental thermal response analysis of the d-mannitol as PCM during the charging and discharging process for medium to high-temperature applications. An 8.6% reduction in melting enthalpy during experimentation is reported while comparing characterization outcomes during the 100th and 11th cycles. However, no significant mass reduction is experienced while heating the d-mannitol at a temperature 100 °C higher than that of its melting point. It shows the thermal stability and suitability of d-mannitol as an efficient energy storage material. Infrared thermography and digital imageries complement each other to understand the thermal response behavior of the sample during experimental visualization. During charging and discharging experiments, radial inward movement of melting and solidification fronts is reported. Nevertheless, the axial movement of PCM is upward and downward in the melting and solidification processes, respectively. Analysis reveals that convection is the leading mode of heat storage during charging, while conduction dominates during discharging. Further, d-mannitol exhibits higher energy and exergy efficiency of charging (67.9% and 49.2%) compared to the energy and exergy efficiency of discharging (60.1% and 34%).

Numerical investigation of solidification behavior and inclusion transport with M-EMS in continuous casting mold

The present study deals with the development of a multiphase numerical model of the continuous casting process of steel bloom. Two SEN configurations that differ in port angles are considered for the study of flow pattern, temperature distribution, solidification thickness, interface fluctuation and inclusion behavior during the process. The influence of mold electromagnetic stirring (M-EMS) on the various output parameters is examined. The results show that the upper circulation loop formed in the 15° port angle case is responsible for higher inclusion removal, high interface level, and low solidification thickness in the meniscus region compared to that of the 30° case. The presence of M-EMS completely changes the flow pattern below SEN. Strong rotational flow coupled with oppositely directed swirl flow provides high tangential velocity near the solidification front and high axial velocity in the core region. It results in fluctuation in shell thickness along the casting direction and decreasing the superheated steam penetration. However, flow patterns remain unaffected above the SEN as upwards swirl flow is not able to reach this region. On applying the M-EMS, inclusion entrapment in solidifying shell increases for both 15° and 30° cases. In contrast, inclusion removal at the interface decreases for 15° case and increases for 30° case.

Thermo4PFM: Facilitating Phase-field simulations of alloys with thermodynamic driving forces

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. We present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library. Program summaryProgram Title: Thermo4PFMCPC Library link to program files:https://doi.org/10.17632/8j3ntp5c7k.1Developer's repository link:https://github.com/ORNL/Thermo4PFMLicensing provisions: BSD 3-clauseProgramming language: C++/OpenMPNature of problem: Accurate modeling of solidification in metallic alloys requires thermodynamic data associated with possible material phases. That data can be used in phase-field modeling (PFM) to evaluate the driving force responsible for phase changes and solidification front motion. Integrating that data into PFM requires the solution of a small system of coupled nonlinear differential equations — the Kim-Kim-Suzuki equations — that needs to be solved at every point of a discretization mesh.Solution method: Thermo4PFM implements a Newton-based solver for the Kim-Kim-Suzuki equations for a few special cases (binary and ternary alloys with two or three phases) for CALPHAD-based models of the bulk energy of the phases. The software is written in C++ and uses the Curiously Recurring Template Pattern and OpenMP offload capabilities to take advantage of GPU accelerators, when available, on modern High Performance Computing resources. It also uses the boost Property Tree library to parse input CALPHAD data.

Multi-fidelity Bayesian optimization to solve the inverse Stefan problem

In this work, we propose an efficient solution of the inverse Stefan problem by multi-fidelity Bayesian optimization. We construct a multi-fidelity Gaussian process surrogate model by combining many low-fidelity estimates of a solidification problem with only a few high-fidelity measurements. To solve the inverse problem, we employ the Gaussian process model in a Bayesian optimization approach based on a multi-fidelity knowledge gradient acquisition function. To account for the specific structure of the target function, we reformulate it as a composite function and thus significantly improve the stability of the optimization procedure. Target values can be switched easily, and previously obtained samples and surrogate models can be reused. The proposed method iteratively improves the recommended solution of the inverse problem. Explicitly adding recommended points of previous iterations to the solution procedure enhances the convergence properties of the algorithm.We demonstrate the applicability of the algorithm by solving the inverse problem for a planar solidification front in a single-fidelity setting. Process parameters are identified for targeted crystal-growth velocities during directional dendritic solidification. The relation between these velocities and process parameters, such as undercooling, thermal diffusivity, capillarity, and capillary anisotropy, defines the thermo-mechanical properties of the solidified part in metal-based additive manufacturing. Material design is based on the corresponding inverse problem. Cost-efficiency of solving the inverse problem is improved by introducing a fidelity hierarchy based on coarse-grid approximations of high-fidelity numerical simulations. The open-source simulation framework ALPACA for multiphase flows allows to generate data at all fidelities. We demonstrate the superior convergence properties of the presented multi-fidelity approach by comparison with an approach solely based on high-fidelity measurements of the tip velocity.

An optimal control problem for single-spot pulsed laser welding

We consider an optimal control problem for a single-spot pulsed laser welding problem. The distribution of thermal energy is described by a quasilinear heat equation. Our emphasis is on materials which tend to suffer from hot cracking when welded, such as aluminum alloys. A simple precursor for the occurrence of hot cracks is the velocity of the solidification front. We therefore formulate an optimal control problem whose objective contains a term which penalizes excessive solidification velocities. The control function to be optimized is the laser power over time, subject to pointwise lower and upper bounds. We describe the finite element discretization of the problem and a projected gradient scheme for its solution. Numerical experiments for material data representing the EN AW 6082-T6 aluminum alloy exhibit interesting laser pulse patterns which perform significantly better than standard ramp-down patterns.

Investigation on Solidification in Cu-20wt%Fe Alloy through In Situ Observation

The performance of Cu-Fe alloy is related to the solidification structure, which is directly determined by the microstructure evolution during solidification. The solidification sequence, solid–liquid interface variation, and microstructural evolution of Cu-20wt%Fe alloy at three cooling rates (0.3, 1.5, and 5.0 °C/s) were investigated. The results indicate that the remelting of primary γ-Fe dendrites was directly observed through the solidification experiment, and the partial γ-Fe dendrite was fragmented owing to remelting. The Fe phase morphology changed from the cellular structure to the typical finer and longer dendrite structure with the cooling rate increasing. As the cooling rate increased, the constitutional undercooling caused by the decrease in the Fe atom concentration and the increase in the Cu atom concentration increased in the solidifying interface. There was a parabolic relationship between the growth rate of the dendrite tip and time. Meanwhile, the growth of the primary γ-Fe phase was inhibited by the insufficient diffusion of Fe and Cu at the solidification front, which resulted in a decrease in the Fe phase volume fraction, and the Fe content in the Fe dendritic phase decreased slightly.