Modelling binary alloy solidification with adaptive mesh refinement
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Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.
The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.
Refractory alloys are known for their high temperature capabilities and are intended for use at ultra-high temperatures above even 1200°C, which exceeds the capabilities of conventional superalloys. Additive manufacturing (AM) is an attractive alternative processing route because refractory alloys are difficult to fabricate through traditional methods; AM can form a near net-shape part with a tailored microstructure. This work seeks to evaluate the solidification behavior of refractory alloys under AM conditions and establish corresponding solidification models. Two binary alloys, Mo30Nb and Nb7.5Ta, as well as the commercial Nb alloy, C103, and one refractory high entropy alloy (RHEA), MoNbTaTi, were subjected to single track melts in a laser powder bed fusion (LPBF) machine. Each melt track was evaluated in the scanning electron microscope (SEM), which determined that some AM conditions used led to non-ideal behavior. Electron backscatter diffraction (EBSD) revealed that the Nb7.5Ta, C103, and MoNbTaTi all exhibited new grain nucleation to various extents while the Mo30Nb exhibited primarily epitaxial growth. This was found to be inconsistent with solidification models that were developed for each alloy and each set of AM conditions to predict the columnar to equiaxed transition behavior (CET) of the experimental microstructures. This disparity was largely attributed to the input parameters for the solidification model, which were developed using Thermo-Calc and SYSWELD. These input parameters include the alloy specific Gibbs-Thomson coefficient and thermophysical properties, the solute specific liquidus slopes and partitioning coefficients, as well as the process specific thermal gradients. Each input parameter was evaluated to determine the likely changes required for the modeled values to generate solidification models that better correspond to what was observed experimentally.
In this study, laser rapid solidification technique was used to refine the microstructure of ternary Al–Cu–Si and binary Al–Cu eutectic alloys to nanoscales. Micropillar compression testing was performed to measure the stress–strain response of the samples with characteristic microstructure in the melt pool regions. The laser-remelted Al–Al2Cu–Si ternary alloy was observed to reach the compressive strength of 1.59 GPa before failure at a strain of 28.5%, which is significantly better than the as-cast alloy with a maximum strength of 0.48 GPa at a failure strain of 4.8%. The laser-remelted Al–Cu binary alloy was observed to reach the compressive strength of 2.07 GPa before failure at a strain of 26.5%, which is significantly better than the as-cast alloy with maximum strength of 0.74 GPa at a failure strain of 3.3%. The enhanced compressive strength and improved compressive plasticity were interpreted in terms of microstructural refinement and hierarchical eutectic morphology.
Large-batch numerical, CALculation of PHAse Diagrams (CALPHAD)-based solidification cracking calculations are performed and then analyzed with machine learning methods to generate models that relate chemistry of refractory alloys to cracking susceptibility. Kou’s solidification cracking index is used to study the refractory alloys including O, N, C binary mixtures with Mo, Ta, Nb, and W, the molybdenum-based TZM, Niobium-based C103, and Tantalum-based T111 and Ta-10 W, as well as hypothetical refractory ternary alloys. Findings strongly validate Kou’s Crack Susceptibility Index (CSI) against Varestraint test data for Nb- and Ta-based alloys, establishing CSI thresholds where refractory alloys with CSI < 15,000 K are likely weldable, CSI > 15,000 K are prone to cracking, and CSI > 25,000 K are likely unweldable (or unprintable). Furthermore, interstitial elements C, N, and O significantly increase crack susceptibility, with some existing material specifications coinciding with peak cracking susceptibility concentrations. Finally, machine learning-derived elemental potency factors enable rapid prediction of CSI from alloy chemistry for C103, TZM, Ta-10 W, and T-111 alloys. These results provide practical guidance for feedstock selection, powder reuse limits, and alloy specification amendments for welding and additive manufacturing applications.
This study investigates the as-cast and aged microstructures, thermal stability, ambient temperature strengthening, and creep resistance of three ternary Al–Ce–Ni alloys (wt%): near-eutectic Al–10Ce–5Ni (with both eutectic and hypoeutectic regions), hypoeutectic Al-7.5Ce-3.75Ni (with numerous primary Al dendrites), and hypereutectic Al-12.5Ce-6.25Ni (with coarse, blocky primary Al3Ni and Al11Ce3 precipitates and some primary Al dendrites). Depending on the alloy composition and local solidification conditions, the following eutectic morphologies are found: (i) coarse Al–Ce eutectic colonies where Al 11 Ce 3 is in the form of “Chinese script”, (ii) intermingled regions of binary Al–Ce and Al–Ni eutectic colonies, with finer Al 3 Ni and Al 11 Ce 3 fibers, (iii) large ternary eutectic colonies, where the binary Al 3 Ni and Al 11 Ce 3 phases are alternating or intertwining within the individual, fine fibers (diameters of ~60–170 nm, depending on solidification rates), and (iv) ternary eutectic zones (between primary Al dendrites), where fine Al 3 Ni and Al 11 Ce 3 build up a 3D-interconnected network. The high volume fraction of intermetallic phases and extremely fine eutectic spacing/fiber diameter both contribute to high ambient strengthening (higher as-cast microhardness than binary Al–Ce or Al–Ni), and also provide enhanced creep resistance at 300 and 350 °C. Additionally, the alloys are coarsening-resistant up to 425 °C for extended periods, with a gradual decrease in microhardness. The alloys aged at 400 °C to 1050 h show fiber fragmentation and coarsening of the resulting particles, with the faster-diffusing Ni driving more rapid coarsening of the Al 3 Ni particles which engulf finer, more stable Al 11 Ce 3 particles. Severe overaging (performed at 590 °C for 24 h) leads to Al 3 Ni and Al 11 Ce 3 spheroids which remain submicron-sized in eutectic colonies, but micron-sized at colony boundary and at Al dendrite-eutectic interface. Creep resistance at 300 °C of overaged Al–10Ce–5Ni remains substantial, consistent with load-transfer based composite strengthening being an important strengthening mechanism in these alloys, making them excellent candidates for replacement of heavier steel or titanium parts operating under stress up to 300 °C.
Currently, additive manufacturing (AM) technology is extensively used to manufacture aerospace components because of the unique advantages of the technique in producing custom designs, complex geometries in a near-net fashion that significantly reduces the manufacturing cost, and improved energy efficiency. However, the thermodynamic properties of existing aerospace alloys and the thermal conditions that prevail in most of the powder-bed based additive manufacturing processes lead to undesirable columnar / columnar-dendritic microstructures that promote solidification cracking during the process, and the development of anisotropy in the mechanical properties of the as-built components. Time consuming, energy-intensive post AM treatments are required to recover the mechanical properties of the wrought components for which the existing alloy compositions were designed for. However, novel alloy compositions, that exploit the AM thermal conditions to produce fine, equiaxed grain structures in the as-built condition, with mechanical properties equal to or exceeding those of the wrought work-horse alloy, Ti-6Al-4V has recently been demonstrated in Ti-Cu alloys. Significant energy savings up to 66% can be obtained for a typical aerospace component through digitally designing the AM process, process parameters, and alloy composition. The current project focused on developing a fundamental understanding of the evolution of the columnar to equiaxed transition (CET) occurring during solidification under AM thermal conditions in Ti-Cu and Ti-Cu-X alloys using high-fidelity phase field (PF) simulations using the leadership class computing facilities that exist in the national laboratories. The simulations were able to capture the effect of alloy and process conditions on CET, and clearly showed the beneficial effect of a ternary solute addition to Ti-Cu binary alloys on CET. The simulations indicated that bulk nucleation in the liquid ahead of the solidifying epitaxial front was promoted by a large, transient, thermal undercooling promoted by the mismatch between the growth rate of the dendrite tips in the epitaxial front and the imposed solidification rate. AM experiments performed at Raytheon Technologies Research Center using the same thermal conditions used in the PF simulations indicated the formation of equiaxed grains, although the grain size was bigger than the ones reported in the literature. On the other hand, the equiaxed grain size predicted by PF simulations were smaller than the grain size of Ti-Cu alloys reported in the literature. The industry will follow up the existing work in a future program that would involve further optimization of the process for the Ti-Cu-X alloys to demonstrate the application of the process and the alloy to a specific aerospace component.
The nano-cellular dendritic microstructure formed during rapid directional solidification in powder bed fusion additive manufacturing creates unique properties such as simultaneous improvement in strength and ductility. However, process control of microsegregation features remains challenging due to low sensitivity of critical solidification mechanisms to process parameters. This study leverages microalloying to achieve large changes in dendrite composition, microstructure, and interdendritic zone width during laser powder bed fusion without modifying process parameters. CALPHAD simulations predict that the addition of Zr significantly steepens the solidus line of the dilute Cu-Cr alloy system, leading to enhanced Cr rejection into the melt and greater than 95% reduction in solubility of Cr in the solidified Cu matrix. Experimental validation using time-of-flight secondary ion mass spectrometry and Kelvin probe force microscopy reveals that the ternary alloy containing 0.01 wt% Zr exhibited wider interdendritic regions compared to the binary, a significantly higher number of Cr-rich particles within interdendritic regions, near-complete ejection of oxygen impurities from the matrix, and greater nanoscale work function contrast. These features indicate more aggressive Cr segregation in the presence of Zr and a purer Cu matrix and provide a potentially robust method for engineering the nano-cellular dendritic solidification microstructure.
Heterostructured materials comprised of relatively soft/hard disparate phases typically exhibit composite strengthening but lack plastic deformability at ambient temperatures. However, heterostructured systems comprised of nanoscale phases can simultaneously enhance yield strength and strain hardening, thereby promoting uniform distribution of plastic flow. In this review, the atomic-scale deformation mechanisms in model systems of eutectic alloys, Al-Al 2 Cu and Al-Si, refined to nanoscales via laser rapid solidification are discussed, and compared with literature on multi-component (high entropy) eutectics such as Ni-Al-Fe-based with Cr and/or Co additions. The nano-lamellar Al-Al 2 Cu structures exhibit unit defect mechanisms not reported in monolithic Al 2 Cu intermetallic: localized shear on {0 1 1} and shear-induced faults on {1 2 1} planes, constrained by closely-spaced dislocation arrays in Al confined by Al/Al 2 Cu interfaces. The unexpected plasticity mechanisms are enabled by slip continuity in nanoscale Al-Al 2 Cu eutectics associated with the orientation relationship and interface habit planes. In nano-fibrous Al-Si eutectic, tensile ductility at strength approaching 600 MPa is observed resulting from dislocation plasticity in the nano-Al channels and cracking in Si nanofibers. Molecular dynamics simulations show that Al dislocations easily cross-slip (screw) or climb (edge) along Al-Si interfaces, making slip transmission difficult. The propagation of nano-cracks is suppressed by surrounding strain hardening Al, retaining good ductility of the sample, in spite of lack of direct slip transmission. Finally, the critical unit mechanisms of slip transmission and interface-enabled plasticity observed in nanoscale eutectic binary systems can also explain the strength-ductility relationship in multi-component eutectics and homogeneously distributed plastic flow with increasing microstructural heterogeneity.
This study reports the first use of in-situ synchrotron X-ray diffraction (SXRD) to study the effects of ultrasonic melt processing (USMP) on phase and grain size evolution during solidification in a commercial Al–Si–Mg casting alloy. USMP is a technique that, when applied to aluminum as it solidifies, can be used to refine the local microstructure of large-scale castings. Analysis of the in-situ SXRD data to estimate the average grain size of primary α-Al grains during USMP demonstrates that USMP slows the growth rate of α-Al grains and reduces grain size by 36 pct. Furthermore, there is also evidence that USMP causes the primary α-Al grains to move relative to the X-ray beam; such motion increases the probability of primary α-Al grains colliding and fragmenting. This movement becomes constrained at the onset of the Al–Si binary eutectic, suggesting that USMP ceases to effectively refine the microstructure once the Al–Si binary eutectic begins to form. Complementary laboratory-scale X-ray diffraction (XRD) data were used to correlate the lattice parameters of the α-Al and Si (D-A4) phases with temperature to estimate cooling rate during solidification. Thus, this study can guide the design of novel castings with spatially distributed fine-grained regions produced using local ultrasonic processing.
Cast Monel alloys are used in applications requiring a combination of good mechanical properties and excellent resistance to corrosion. Despite prevalent industrial use, relatively few studies have been conducted to investigate the relationships between composition, solidification behavior, and microstructure. Given that these alloys are used in the cast and welded conditions, these factors have a significant influence over the material properties. Here, in this work, microstructural characterization, electron probe microanalysis, X-ray diffraction, and differential scanning calorimetry were used to study how changes in Si and Nb concentrations affected the solidification path and microstructure of Monel alloys. It was found that increasing Nb concentration stabilized higher amounts of MC carbides and suppressed graphite formation during solidification. It was also found that the high nominal concentration and segregation of Si to the liquid led to the formation of Ni 31 Si 12 and other silicides via terminal eutectic reactions at the end of solidification. A pseudo-binary solidification diagram was constructed using experimental data and was applied to predict the mass fraction of solidified eutectic as a function of composition. The modeled microstructures were found to be in good agreement with experimentally measured phase fractions.
Here, a hypoeutectic, Fe-modified Al–Ce–Ni alloy (Al–6Ce–3Ni-0.7Fe, wt.%) is studied in terms of microstructure, thermal stability, ambient temperature strengthening, and creep resistance. The as-cast microstructure consists of primary Al dendrites and interdendritic binary eutectic regions (Al–Al11Ce3 and/or Al–Al9(Fe,Ni)2), with micron/submicron lamellar spacing, depending on the location along the height of the ingot. The cast alloy exhibits excellent coarsening resistance at 400 °C, with mostly unchanged microstructure and microhardness after 6 weeks of aging, indicating good thermal stability of Al11Ce3 and Al9(Fe,Ni)2. Orowan strengthening and load transfer are identified as strengthening mechanisms at ambient and elevated temperature. A high volume fraction of the intermetallic phases (providing load transfer) and relatively coarse eutectic spacing (for modest Orowan strengthening) result in a moderate as-cast microhardness of 566 ± 32 MPa. Creep resistance at 300 and 350 °C is similar to a binary Al-12.5Ce eutectic alloy (with twice the Ce content) because of two countering effects: Al–6Ce–3Ni-0.7Fe shows a higher volume fraction of strengthening intermetallic phases, but it also exhibits a large fraction of primary Al dendrites which weaken the alloy. By contrast, the alloy, when laser-remelted at the surface, has a fully eutectic microstructure without primary aluminum dendrites achieved by high undercooling on solidification, with a refined network of eutectic phases that doubles the microhardness as compared to the cast alloy. Whereas coarsening is faster due to the shorter diffusion distances between the eutectic phases, hardness remains ~30% higher than the as-cast alloy after ~6 weeks aging at 400 °C.
The relative stability of the different tri-aluminide (Al 3 M) phases in three binary systems (M = Zr, Nb and V) was assessed for their potential to form fine cubic L1 2 precipitates in additively manufactured alloys. Supersaturated thin films of Al-(8–30) at% M were sputtered and heat treated during in-situ x-ray diffraction (XRD) measurements to observe the temperature ranges of stability for each phase. As-sputtered films were then processed with laser tracks simulating additive manufacturing solidification conditions, and the formation of phases in the laser tracks was correlated with density functional theory (DFT) and nucleation rate calculations. We found that the metastable L1 2 structure is highly competitive with the stable DO 23 structure in the Al-Zr system, but much less stable than the DO 22 structure in the Al-Nb system, and both the DO 22 and Al 8 V 5 structure in the Al-V system. Furthermore, these experimental results were found to be in good agreement with the DFT and kinetic calculations, as we determined that the metastable L1 2 in Al-Zr only requires a small amount of undercooling to favor its nucleation over the stable DO 23 , suggesting additive manufacturing can be a viable pathway to develop Al-Zr alloys strengthened by a high volume fraction of L1 2 Al 3 Zr phase.
Additive manufacturing of aluminum alloys is largely dominated by a near-eutectic Al-Si compositions, which are highly weldable, but have mechanical properties that are not competitive with conventional wrought Al alloys. In addition, there is a need for new Al alloys with improved high temperature properties and thermal stability for applications in the automotive and aerospace fields. In this work, we considered laser powder bed fusion additive manufacturing of two alloys in the Al–Ce–Mg system, designed as near-eutectic (Al–11Ce–7Mg) and hyper-eutectic (Al–15Ce–9Mg) compositions with respect to the binary L → Al + Al 11 Ce eutectic reaction. The addition of magnesium is used to promote solid solution strengthening. A custom laser scan pattern was used to reduce the formation of keyhole porosity, which was caused by excessive vaporization due to the high vapor pressure of magnesium. The microstructure and tensile mechanical properties of the alloys were characterized in the as-fabricated condition and following hot isostatic pressing. The two alloys exhibit significant variations in solidification structure morphology. These variations in non-equilibrium solidification structure were rationalized using a combination of thermodynamic and thermal modeling. Both alloys showed higher yield strength than AM Al-10Si-Mg for temperatures up to 350 °C and better strength retention at elevated temperatures than additively manufactured Scalmaloy.
Throughout this work, a database for the Cr-Ni-V system was constructed by modeling the binary Cr-V and ternary Cr-Ni-V systems using the CALPHAD approach aided by density functional theory (DFT)-based first-principles calculations and ab initio molecular dynamics (AIMD) simulations. To validate this new database, a functionally graded material (FGM) using Ni-20Cr and elemental V was fabricated using directed energy deposition additive manufacturing (DED AM) and experimentally characterized. The deposited Ni-20Cr was pure fcc phase, while increasing the amount of V across the gradient resulted in the formation of sigma phase, followed by the bcc phase. The experimentally measured phase data was compared with computational predictions made using a Cr-Ni-V thermodynamic database from the literature as well as the database developed in the present work. The newly developed database was shown to better predict the experimentally observed phases due to its accurate modeling of binary systems within the database and the ternary liquid phase, which is critical for accurate Scheil calculations.
Excellent irradiation damage resistance demonstrated by multi-principal elemental alloys (MPEAs) has sparked significant interest among researchers, prompting exploration into their vast compositional space, to validate their suitability for nuclear applications. A combined approach of thermodynamic and empirical parameters calculations alongside CALPHAD (CALculation of PHAse Diagrams) for phase formation predictions enable high-throughput material selection for sophisticated applications like nuclear, overcoming laborious and time-consuming experiments. Key thermodynamic and empirical parameters for eight novel equiatomic MPEAs, based on seven low thermal neutron cross section refractory elements, for predicting phase formation were calculated, and equilibrium and non-equilibrium simulations in CALPHAD were employed to comprehensively model the systems. Pseudo binary phase diagram simulations showed that Zr, V or equiatomic CrV additions to the base MoNbTi alloy (MoNbTi-Zr, MoNbTi-V and MoNbTi-CrV alloys) favor the formation of isomorphous body-centered cubic (BCC) phase at high temperatures, while Cr, Al, equiatomic ZrV, or equiatomic CrAl additions (MoNbTi-Cr, MoNbTi-Al, MoNbTi-ZrV or MoNbTi-CrAl alloys) limit the solubility of them. Equilibrium CALPHAD simulations at 750 oC were consistent with XRD results on MoNbTi, MoNbTiZr and MoNbTiCr alloys, and partially for others. Notably, elemental segregation observed in the backscattered electron (BSE) scanning electron microscopy (SEM) images of the alloys was accurately simulated through non-equilibrium Scheil solidification calculations in CALPHAD, further verified by experiments. The precipitation of TiCr2 Laves phase in Cr containing MoNbTiCr and MoNbTiCrAl was accurately predicted while discrepancies were noted in MoNbTiCrV. The equilibrium simulations also provided insights into phase compositions at specific temperatures offering a pathway for tailoring the desired microstructure and properties of these systems. Empirical parameters calculations successfully predicted random solid solution in the base MoNbTi alloy, and with an exception in MoNbTiV and MoNbTiAl, predicted intermetallic precipitation in the rest, especially, Laves phase precipitation in Cr containing alloys.
Additive Manufacturing (AM) has opened new frontiers for the design of refractory high-entropy alloys (HEAs) for high-temperature applications. The thermal conductivity of the AM feedstock is among the most important thermo-physical properties that control the melting and solidification process. Despite its significance, there remains a notable gap in both computational and experimental research concerning the thermal conductivity of HEAs. Here, we use density functional theory (DFT) to systematically investigate the alloying effects on the transport properties of Ti-Cr-Mo-W-V-Nb-Ta RHEAs, including electrical and thermal conductivities and Seebeck coefficient. The relaxation time of charge carriers is a key underlying parameter determining thermal conductivity that is exceedingly challenging to predict from first principles alone, and we thus follow the approach by Mukherjee, Satsangi, and Singh [Chem Mater 32, 6507 (2022)] to optimize the relaxation time for RHEAs. Here we validated thermal conductivity predictions on elemental solids, binary and ternary alloys, and RHEAs and compared them against thermodynamic (CALPHAD) predictions and our experiments with good correlations. To understand observed trends in thermal conductivity, we assessed the phase stability, electronic structure, phonon, and intrinsic- and tensile strength of down-selected RHEAs. Our electronic structure and phonon results connect well with the observed compositional trends for thermal transport in RHEAs. Our DFT assessment and CALPHAD predictions provide a unique design guide for RHEAs with tailored thermal conductivity, a critical consideration for AM and thermal-management applications.