Solidification Of Metallic Alloys Research Articles

Quantification of melt pool dynamics and microstructure during simulated additive manufacturing

The dynamics of laser spot melting and metallic alloy solidification are investigated through synchrotron x-ray radiography, 3D electron backscatter diffraction data, and computational fluid dynamics (CFD) simulations on a model NiMoAl alloy. Solidification velocities are measured from in-situ images to validate a CFD model of the spot melt. TriBeam tomography is used to reconstruct the melt pool in 3D, characterize the microstructure, and validate the CFD model melt pool dimensions. 3D geometrically necessary dislocation (GND) density calculations reveal extensive deformation at the sample surface. GND calculations integrated with the CFD model reveal that the halo of small, equiaxed grains adjacent to the fusion line is a result of recrystallization that occurred in the heat affected zone. By combining in-situ and ex-situ data modalities across a variety of temporal and spatial length scales, the microstructure formation mechanisms and their relationship to melt pool solidification are quantified.

Error homogenization in physics-informed neural networks for modeling in manufacturing

Physics-informed neural networks (PINNs) have demonstrated effectiveness in solving partial differential equations (PDEs) associated with manufacturing scenarios, due to their physically interpretable training logic. One limitation has been that PINNs often exhibit heterogenous error maps and high-error “hot spots” throughout the solution domain, which reduce not only the solutions’ accuracy but also their overall consistency with the physical laws. This study addresses this limitation by presenting an efficient and error-aware PINN ensembling technique for error homogenization in solving manufacturing problems. Specifically, a PINN is first established by constraining its training process through a manufacturing specific PDE and corresponding boundary conditions to ensure physical consistency. Next, the loss landscape in the neighborhood of three PINNs trained with varying network parameter initialization is sampled to generate a PINN ensemble. Finally, the outputs of the ensemble members are combined through an inverse error-weighted average to yield the prediction of the PDE solution. Evaluation using the Allen-Cahn PDE, which describes phase separation in the solidification of metallic alloys, shows that the developed method reduces the average prediction error by 63% and error standard deviation by 30% across the solution space, demonstrating its effectiveness for PINN error reduction and homogenization. Additionally, the method has also demonstrated 96% reduction in the computational time as compared to conventional ensembling methods.

An image processing pipeline for in situ dynamic x-ray imaging of directional solidification of metal alloys in thin cells

An image processing pipeline for in situ dynamic x-ray imaging of directional solidification of metal alloys in thin cells

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.

John David Hunt. 12 December 1936—8 December 2012

John Hunt was a scholar of the solidification of metallic alloys, and published seminal works that are of influence today in the design of alloy casting, welding and additive manufacturing processes. John was raised in the West Country of England, and following school did National Service in the Royal Air Force. He entered the University of Cambridge in 1957, being awarded an honours BA in metallurgy in 1960, and a PhD for studies of solidification of eutectic alloys in 1963. John met Ann Carroll during his Cambridge studies; they married in 1961 and later had three children. From 1963 to 1965 John carried out research with Ken Jackson at Bell Laboratories, New Jersey, USA. They published groundbreaking papers on solidification and pioneered the use of transparent organic analogues. John returned to England and, following a year working at the UK Atomic Energy Authority at Harwell, he joined the faculty at the University of Oxford in 1966. During a 36-year academic career at Oxford, John made significant contributions to the scientific understanding of solidification on many topics, including dendritic array growth, eutectic and peritectic solidification, the columnar-to-equiaxed transition and twin roll casting. As well as being a talented experimentalist, he published many groundbreaking theoretical analyses and also pioneered the use of numerical methods for the simulation of solidification phenomena. He was an accomplished educator of undergraduate and postgraduate students, and a fellow of St Edmund Hall, Oxford. John was a family man, and kept geese and pigs, grew apples and made legendary cider at his old farmhouse home north of Oxford.

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.

Modeling Framework for the Simulation of an Electric Smelting Furnace Considering Freeze Lining Formation

The use of freeze linings to protect pyrometallurgical furnaces from chemically corrosive molten slags is a widespread technique in industrial processes. The main goal of the present study is to establish a modeling framework that considers fluid flow, heat transfer, and slag solidification to simulate freeze-lining formation and its dependency on operating conditions. A mixture continuum solidification model, which had been used for the solidification of metal alloys, was employed. Several parametric studies have been conducted to better understand the smelting process. The results demonstrate that the model can capture freeze-lining formation and predict the global energy balance and flow behavior of the smelting furnace. The freeze-lining thickness was shown to depend on heat removal intensity during the process and slag bath chemistry. A direct relationship between the average temperature in the refractory and freeze-lining thickness was also observed. This is an important indicator for furnace operators in controlling the furnace operation parameters. This improved knowledge offers the potential to further optimize furnace operations and reduce energy costs and environmental impacts. A discussion was presented on the different modeling assumptions considered and potential future model refinements.

Pulsed and Static Magnetic Field Influence on Metallic Alloys during Solidification

Electromagnetic methods can be used to affect the solidification of metallic alloys. Combined alternating and static (DC) magnetic fields can induce pressure waves in liquid metals in a contactless manner, refining grain structure, preventing component segregation, and dispersing added particles. Here, the possibility of using a pulsed magnetic field in combination with a DC magnetic field to improve the solidification structure of metals is investigated. This enables achieving higher pressure amplitude and liquid movement within the whole crucible volume at the same power consumption. This can be a prospective way to achieve a fine-grained and a more homogeneous microstructure of metallic alloys as well as disperse added particles. In this work, analytical description of the phenomena and numerical modeling of the pressure amplitude and melt motion has been performed. A series of experiments have been carried out to demonstrate the effect of such interaction on the solidified metal microstructure. It is found that a combination of pulsed and DC magnetic fields creates strong compression and expansion of the liquid metal. Metals solidified under such interaction exhibit finer grain structure in Sn-Pb alloy and improved TiB2 particle distribution in 6061 aluminum alloy.

Modeling of dendritic solidification and numerical analysis of the phase-field approach to model complex morphologies in alloys

Dendrites are one of the most widely observed patterns in nature, and occur across a wide spectrum of physical phenomena—from snow flakes to river basins; from bacterial colonies to lungs and vascular systems; and in solidification and growth patterns in metals and crystals. The ubiquitous occurrence of these “tree-like” structures can be attributed to their excellent space-filling properties, and at times, dendritic structures also spatially manifest fractal-like distributions. As is the case with many fractal-like geometries, the complex multi-level branching structures in dendrites pose a modeling challenge, and a full resolution of dendritic structures is computationally very demanding. In the literature, extensive theoretical models of dendritic formation and evolution, essentially as extensions of the classical moving boundary Stefan problem exist. Much of this understanding is from the analysis of dendrites occurring during the solidification of metallic alloys, as this is critical for understanding microstructure evolution during metal manufacturing processes that involve solidification of a liquid melt. Motivated by the problem of modeling microstructure evolution from liquid melts of pure metals and metallic alloys during metal additive manufacturing, we developed a comprehensive numerical framework for modeling a large variety of dendritic structures that are relevant to metal solidification. In this work, we present a numerical framework encompassing the modeling of Stefan problem formulations relevant to dendritic evolution using a phase-field approach and a finite element method implementation. Using this framework, we model numerous complex dendritic morphologies that are physically relevant to the solidification of pure melts and binary alloys. The distinguishing aspects of this work are—a unified treatment of both pure metals and alloys; novel numerical error estimates of dendritic tip velocity; and the study of error convergence of the primal fields of temperature and the order parameter with respect to numerical discretization. To the best of our knowledge, this is a first of its kind study of numerical convergence of the phase-field equations of dendritic growth in a finite element method setting. Further, using this numerical framework, various types of physically relevant dendritic solidification patterns like single equiaxed, multi-equiaxed, single columnar and multi-columnar dendrites are modeled in two-dimensional and three-dimensional computational domains.

Analysis of the Solidification Process of Metal Alloys Under Microgravity Conditions

The solidification of metal alloys under low gravity conditions mainly deviates in four physical properties compared with samples solidified on earth. The coarseness of the structure and the solidification temperature increase. The latent heat and the solubility of alloying elements in solids are changed. Experimental results are presented and analyzed in order to find a unified theoretical understanding. The differences in the measured quantities between experiments performed in space and on earth were calculated and are presented in this article. Kinetic, thermodynamic, and thermophysical relations were used to analyze those values. The change in the melting point was found to be a result of an increase in the vibrational amplitude of the atoms in the solid. The increase in the latent heat results from an increase in the vibration of atoms in the liquid. The changes in the solubility are a result of an increase in heat of fusion of the alloying element. Furthermore, the increase in the coarseness of the structure is explained as an increase in the atom’s vibration. The analysis highlights that the atom’s vibration increases with decreasing gravity; especially, the amplitude will increase. The explanation for this is given by a decrease in the binding energy between the atoms with decreasing gravity. The decrease in binding energy for liquids is larger than for solids.

Concurrent model for sharp and progressive columnar to equiaxed transitions validated by directional solidification experiments processed in microgravity conditions

Columnar and equiaxed structures, which occur during solidification of metallic alloys, influence the texture and properties of castings, welded joints and additively manufactured components. During transient solidification, where grain refiner particles provide the predominant nucleation mechanism, a Columnar to Equiaxed Transition (CET) occurs when conditions that had originally favoured directional columnar growth change to those favouring equiaxed. Constitutional undercooling ahead of the columnar front can permit equiaxed nucleation and growth. By carrying out experiments in microgravity conditions, liquid flows due to thermal and solutal buoyancy effects are suppressed. In these diffusion-controlled conditions, we have observed examples of both sharp (clear) and progressive (gradual) CET. The experimental outcomes, especially the observation of a progressive CET, has highlighted the need for a continuum model that allows for competitive columnar and equiaxed structure development; hence, the Concurrent Columnar to Equiaxed Transition (C2ET) model is proposed. The C2ET is thermally transient and relies on the well-known concept of extended growth for impingement mechanics; thereby, greatly reducing numerical complexity. Importantly, the proposed approach removes the need for a specific equiaxed-blocking criterion, which is often proposed as an essential requirement in other CET models. The C2ET model is validated by four experimental solidification scenarios: two velocity jumps and two thermal-gradient decreases. The velocity jumps induced sharp CETs; whereas, thermal-gradient decreases gave progressive CETs. The C2ET model gave good agreement for the columnar and equiaxed transition zones for both sharp and progressive CET. Results are compared with the classic Hunt model. Unlike Hunt’s model, the C2ET model predicted all macrostructure transitions faithfully using a single (or consistent) set of nucleation input parameters across all four scenarios. Since, the same level of grain refinement was used in each experiment, a consistent set of nucleation parameters was expected. The validated approach can enable effective simulation at lower computational cost for industrial processes that rely on a solidification processing step.

Unique surface patterns emerging during solidification of liquid metal alloys.

It is well-understood that during the liquid-to-solid phase transition of alloys, elements segregate in the bulk phase with the formation of microstructures. In contrast, we show here that in a Bi-Ga alloy system, highly ordered nanopatterns emerge preferentially at the alloy surfaces during solidification. We observed a variety of transition, hybrid and crystal-defect-like patterns, in addition to lamellar and rod-like structures. Combining experiments and molecular dynamics simulations, we investigated the influence of the superficial Bi and Ga2O3 layers during surface solidification and elucidated the pattern-formation mechanisms, which involve surface-catalysed heterogeneous nucleation. We further demonstrated the dynamic nature and robustness of the phenomenon under different solidification conditions and for various alloy systems. The surface patterns we observed enable high-spatial-resolution nanoscale-infrared and surface-enhanced Raman mapping, which reveal promising potential for surface- and nanoscale-based applications.

Thermodynamic Effect of Pressure on Nucleation Activation Energy

The first stage of the solidification of metal alloys is nucleation, during this stage is defined the number of grains present in the final structure, just as the conditions in which the same will grow. The application of pressure in the solidification is mostly studied as an operational parameter, and its effects are described and commented extensively in literature. The objective of this paper is to study the effect of pressure on nucleation, still not to describe but to explain it, for this purpose the pressure is treated as a thermodynamic variable. From this analysis it was possible to determine the real influence of pressure on the activation energy, being clear that its effect is equivalent and co-dependent to that of the undercooling, and can thus cause considerable variations in the activation energy, much larger than what is proposed in previously published papers that approach the subject, causing a considerable stimulus on nucleation. It was also observed that the curve that represents the effect of pressure on the activation energy proposed in this paper, has a similar form to the curves that describe how the pressure refines structures, resulting from the process of solidification under pressure reported in literature.

Impact of gravity on directional solidification of refined Al-20wt.%Cu alloy investigated by in situ X-radiography

Gravity effects such as natural convection in the liquid phase and buoyancy forces acting on the solid phase have a strong influence on the grain structure and microstructure formation dynamics during the solidification of metal alloys. It is thus very useful to undertake experimental studies that will provide benchmark data for a deeper understanding of the role of such gravity effects. In this paper, we study the formation of the equiaxed grain structure during refined Al-20wt.%Cu solidification in a temperature gradient for three different configurations: horizontal, vertical upward and vertical downward solidification. The key grain characteristics, namely grain size, grain elongation and grain growth orientation, were determined for all experiments. A comparative analysis was performed to identify the dominant effects of gravity using the experiment in horizontal configuration as reference case. The impact of buoyancy on the grain structure formation was highlighted for the experiment in vertical upward configuration, inducing a final grain structure with a wider grain size distribution. For the experiment in vertical downward configuration, the final grain structure is composed of thinner and longer grains. The origin of these differences was linked to the impact of grain flotation and solute flows on the equiaxed microstructure development.

Progress in modelling solidification microstructures in metals and alloys. Part II: dendrites from 2001 to 2018

ABSTRACT This is the first account of the history of modelling dendritic and cellular solidification. While Part I reviewed the progress up to the year 2000 [Kurz W, Fisher DJ, Trivedi R. Progress in modelling solidification microstructures in metals and alloys: dendrites from 1700 to 2000. Intern Mater Rev. 2019;64:311–354], Part II retraces our modelling capabilities developed during the early years of the present century. Advances in in-situ X-ray observations of solidification of metallic alloys are also presented. While the most important contributions are mentioned, the authors are aware that such a historical review must leave many worthy articles by the wayside. This overview considers dendrite tip growth and morphology, rapid solidification, melt flow, fragmentation, columnar-to-equiaxed transition, dendrite spacings, coalescence, grain competition, and cellular growth. Modelling across the length scales from nano- up to macroscopic solidification phenomena by massive phase field computations or multiscale approaches show the potential for the simulation of real processes such as additive manufacturing, single crystal casting, welding or advanced solidification processes.

Solidification of Metallic Alloys: Does the Structure of the Liquid Matter?

In 1952, Frank (Proc R Soc Lond Ser-Math Phys Sci 215:43–46, 1952) already postulated that Icosahedral Short Range Order (ISRO) of atoms in the liquid could possibly explain the large nucleation undercoolings measured in metallic alloys by Turnbull and Fisher (J Chem Phys 17:71–73, 1949). About thirty years later, this conjecture was proven to be key for the understanding of Quasicrystals (QC) formation (Shechtman et al. in Phys Rev Lett 53:20, 1951–3, 1984). More recently, it has been found that a few tens to thousand ppm of solute elements in Al-base and Au-base alloys can influence the nucleation and growth of the primary fcc phase via mechanisms involving ISRO and QC formation. ISRO has also been found to limit the mobility, and thus diffusion, of atoms in the liquid. This can lead to out-of-equilibrium conditions, e.g., the formation of metastable phases or supersaturated solid solution, at reduced velocity compared to alloys where ISRO is not predominantly present. Finally, there are several experimental evidences that ISRO is also responsible for twinned dendrites formation in Al alloys. The present contribution summarizes these recent findings and points out the implications that these might have in the field of solidification and additive manufacturing.

Sensitivity of macroscopic transport calculations to uncertain microscale relationships during metal alloy solidification

The formation of grains during metallic solidification results in a multiphase system consisting of many moving interfaces. Models have been formulated in terms of variables describing the microscopic details of interface motion during solidification, but the computational cost prohibits their extension to the length scale of industrial castings. For this reason, macroscopic transport equations are mathematically formulated using averaging methods to replace the instantaneous description of interfaces. The most common approach is the volume-averaged, Eulerian approach relying on both the proper derivation of macroscopic field equations as well as uncertain interfacial conditions used to account for the average behavior of the interphase transfer occurring on the sub-grid length scale. In this work, common models used to describe the microsegregation occurring during solidification are evaluated in terms of the uncertainty of parametric inputs invoked in each model and their effect on macroscale predictions. We show that the qualitative macroscale predictions are not significantly changed by using more sophisticated microsegregation models, however significant uncertainty in input parameters used to describe the unresolved sub-grid interface is accumulated. Therefore, the use of simplified models is preferred until the uncertainty in model inputs can be reduced.

Multi-Step Crystallization of Self-Organized Spiral Eutectics.

A method for the solidification of metallic alloys involving spiral self-organization is presented as a new strategy for producing large-area chiral patterns with emergent structural and optical properties, with attention to the underlying mechanism and dynamics. This study reports the discovery of a new growth mode for metastable, two-phase spiral patterns from a liquid metal. Crystallization proceeds via a non-classical, two-step pathway consisting of the initial formation of a polytetrahedral seed crystal, followed by ordering of two solid phases that nucleate heterogeneously on the seed and grow in a strongly coupled fashion. Crystallographic defects within the seed provide a template for spiral self-organization. These observations demonstrate the ubiquity of defect-mediated growth in multi-phase materials and establish a pathway toward bottom-up synthesis of chiral materials with an inter-phase spacing comparable to the wavelength of infrared light. Given that liquids often possess polytetrahedral short-range order, our results are applicable to many systems undergoing multi-step crystallization.

Competitive Growth of Degenerate Pattern and Dendrites During Directional Solidification of a Bicrystal Metallic Alloy

A degenerate pattern is seaweed-like morphology with its tip splitting continuously, differing from that the regular dendrite has a stable tip. Here, we carried out bicrystal (BC)-assembled experiments to investigate the competitive growth between a degenerate pattern and regular dendrites in a directionally solidified Al-4.5 wt pct Cu alloy. Using the electron backscattered diffraction (EBSD) technique, we characterized a degenerate pattern that solidified with a (100)[001]45 deg orientation and a dendrite growth comprising (100)[001]0 deg or (100)[001]15 deg orientations. The experimental results for the competitive growth show that the dendrites could overgrow the degenerate pattern completely at V = 15 and 25 µm/s. The grain boundary (GB) in between these two morphologies is not smooth, and its inclination angle θGB is slightly increased with an increase in the growth velocity. For the converging GBs, we find that the dendrites overgrow the degenerate pattern either by generating new primary arm dendrites through tertiary branching or being blocked by the growth of the existing primary arm dendrites, depending on the misorientation arrangement between these two morphologies. The limited growth stability of the degenerate pattern in comparison with the dendrite contributes to deepening the understanding of why the degenerate pattern is not widely prevailing in metallic alloy solidification microstructures.

Multi-dimensional characterization and controlling of microstructure evolution during solidification of metallic alloys

Metallic alloys are important structural and functional materials and have been widely applied in industry. The performance of metallic alloys strongly depends on the microstructures after solidification. Many effective methods are introduced to control the microstructure evolution during solidification, including grain refining, adding rare earth (RE) elements, applying electric current and/or magnetic field, etc. However the inherent mechanisms affecting the microstructure formation are still unclear due to the limitation of real time and multidimensional characterization technique. With the development of the third generation synchrotron radiation light source, a real time imaging technology in 2D (two dimensional) or 3D (three dimensional) view with strong penetrability, high spatial and temporal resolution, nondestructive features has been developed to break those limitations. In this paper, some application cases during solidification performed in our group are reported in different alloys and using different solidification controlling techniques. Different solidification behaviors in those cases are revealed and discussed.