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For solidification rates at or near equilibrium solidification conditions the effects of chrome (Cr) and nickel (Ni) on stainless steel solidification modes and microstructures are well detailed. However, fusion-based additive manufacturing (FBAM) processes that rely on faster, more rapid solidification rates call for a more in-depth understanding of the effects of rapid solidification on the solidification behavior and how these change with variations in alloy composition. Eleven custom stainless steel (SS) alloys with unique compositions based on 316L were made using targeted alloying element additions to generate feedstock with Cr/Ni eq ratios ranging from 0.9 to 2.1. Two-piston splat quenching (SQ) was used to produce rapid solidification conditions similar to those achieved in powder bed fusion processes in a fraction of the time and cost of traditional methods. Employing heat transfer simulations, SEM, TEM, and STEM characterization techniques, the SQ process was found to consistently produce solidification rates estimated to be between ~ 0.4 and 1.6 m/s. Five unique solidification microstructures were identified within the rapidly solidified SQ samples (primary austenite, massively transformed ferrite to austenite, primary austenite and massively transformed ferrite to austenite, primary ferrite, and primary ferrite and massively transformed ferrite to austenite). Both the primary ferrite solidification mode and primary ferrite phase were found to form at lower Cr/Ni eq values than previously predicted. SQ samples with compositions that were within the compositional specifications for 316L SS, an alloy which is commonly used in FBAM processes, demonstrated a wider range of potential solidification modes and microstructures that could form at rapid solidification rates than expected. Finally, by using SQ as a means to simulate rapid solidification conditions similar to those observed in FBAM processes, potential new alloy compositions can be screened faster and more cost effectively than purchasing and running test batches of the metallic powder.
High-entropy alloys (HEAs) are promising candidates for advanced structural applications due to their excellent mechanical properties. Additive manufacturing (AM), with its rapid solidification conditions, enables the creation of unique nonequilibrium microstructures. To fully leverage the synergy between AM and HEAs, understanding how processing affects structure and properties is essential. Here, how solidification rate influences microstructure evolution and phase transformation pathway in laser additively manufactured AlCrFe2Ni2 eutectic HEAs is investigated. By increasing the laser scan speed and hence the solidification rate, distinct solidification modes evolving from coupled eutectic to anomalous eutectic and eventually to single-phase solidification are revealed. These transitions result in distinct microstructures and a wide range of mechanical properties. Thermodynamic modeling and molecular dynamics simulations reveal that low cooling rates allow for sufficient atomic diffusion and phase separation, facilitating coupled eutectic growth. In contrast, rapid cooling suppresses diffusion and destabilizes the solid–liquid interface, promoting anomalous or single-phase solidification. This integrated experimental and computational approach provides a multiscale understanding of solidification mechanisms in HEAs and underscores how kinetic effects can over-ride thermodynamic predictions under nonequilibrium conditions. Furthermore, these results demonstrate that AM can serve as a powerful tool to design HEAs with tailored microstructures and properties.
The localized corrosion of laser surface melted (LSM) 316L stainless steel is investigated by a combination of potentiodynamic anodic polarization in 0.1M HCl and microscopic investigation of the initiation and propagation of localized corrosion. The pitting potential of LSM 316L is significantly lower than the pitting potential of wrought 316L. The LSM microstructure is highly banded as a consequence of the high laser power density and high linear energy density. The bands are composed of zones of changing modes of solidification, cycling between very narrow regions of primary austenite solidification and very wide regions of primary ferrite solidification. Pits initiate in the outer edge of each band where the mode of solidification is primary austenite plane front solidification and primary austenite cellular solidification. The primary austenite regions have low chromium concentration (and possibly low molybdenum concentration), which explains their susceptibility to pitting corrosion. The ferrite is enriched in chromium, which explains the absence of pitting in the primary ferrite regions. The presence of the low chromium regions of primary austenite solidification explains the lower pitting resistance of LSM 316L relative to wrought 316L. The influence of banding on localized corrosion is applicable to other rapidly solidified processes such as additive manufacturing.
The addition of boron to steel alloys results in an increase in both hardenability and casting defects. The casting difficulties are predicted to stem from a metatectic reaction, δ + γ → L + γ, where a fully solidified material begins to locally remelt as the temperature decreases. Another possible source of casting defects is a boride-rich phase that is predicted to remain liquid at low temperatures. To experimentally determine which reaction is the likely source of the casting defects, the predicted reactions and the effect of solute elements on those reactions are investigated. Levitation zone melting is used to control segregation in a ternary Fe–C–B alloy and a commercial 22MnB5 alloy. Carbon segregation and a peritectic reaction result in a peritectic jump during directional solidification where the first directionally solidified (DS) zone undergoes δ-bcc solidification followed by a peritectic jump to steady state planar solidification of γ-fcc in the second DS zone. The presence of other solute elements in the zone melted 22MnB5 alloy lead to a breakdown in the planar solidification front before steady state solidification could be achieved in the second DS zone. With a cellular solid/liquid interface, boron-rich intercellular liquid formed low melting iron boro-carbide particles. The controlled solidification conditions in a levitation zone melter were unable to prevent ~0.003 wt% boron from segregating to high enough levels to form boride particles. Therefore, it is likely that during commercial casting, the formation of the low melting boride phase from interdendritic segregation is a key source of the casting issues.
Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).
A major limitation of additive manufacturing (AM) processes is that local conditions of material deposition frequently lead to unintentional heterogeneities in microstructure and properties within a single component, despite nominally uniform process conditions. Up to now, there has been no way to a priori determine the distribution of these heterogeneities, requiring expensive trial-and-error approaches to fabrication, testing, and characterization. Here, a physics-based framework for creating a digital representation of the laser powder bed fusion (PBF) process is proposed to predict the variation in solidification behavior that leads to heterogeneous microstructures in an as-built part. By leveraging in situ process data stored in the part’s digital thread, the scan path and process parameters were input into a heat transfer model which predicted solidification data at the melt pool scale. A two-step unsupervised clustering algorithm was used to first cluster the local solidification conditions (12.5µm 3 voxels) and then to cluster the regional behavior on the scale of multiple scan passes and print layers (250µm 3 super-voxels). This process was used to identify regions with similar solidification characteristics for multiple locations in a Stainless Steel 316-L component. The corresponding as-built part was sectioned and characterized using electron backscatter diffraction (EBSD). Quantitative analysis of the pole figures confirmed that the predicted regions of heterogeneity in the solidification conditions corresponded with differences in the observed microstructure. In conclusion, this work shows a viable path for estimating the microstructural heterogeneity for additively manufactured parts to either limit microstructural variation throughout a part or to enable functionality-based variation of the microstructure.
In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.
A widespread implementation of large scale additive manufacturing (AM) processes, such as wire arc-directed energy deposition (WA-DED) AM can transform the current manufacturing supply chain networks. Naturally, such implementation requires control of the microstructural attributes, such as texture and phase evolution in the processed alloys. Currently, the texture evolution in fusion-based AM (F-BAM) processes is majorly rationalized by the phenomena occurring only during solidification. However, such rationalization is insufficient for understanding the evolution of primary and secondary crystallographic orientations, and consequently, fails to offer a comprehensive understanding and control of overall texture in F-BAM processed alloys. To this end, we report a single crystal (SX)-like texture in WA-DED processed SS316L for the first time. Furthermore, we assess the physical phenomena that may lead to such unique microstructural evolution during WA-DED AM. Subsequently, using microstructural characterization spanning the build height and thermomechanical simulations we investigate the effect of competitive growth and epitaxial growth occurring during solidification and thermally induced plastic deformation occurring post solidification on the overall texture of WA-DED processed SS316L. A spatial variation in solidification pathway is also established and correlated with variation in undercoolings across the build. Tensile tests revealed a strong orientation dependence of deformation mechanisms with over 110% elongation to failure of specimens deformed along <011>. Such anisotropy is rationalized using Schmid's analysis of dislocation slip and deformation twinning. Importantly, overall, the mechanisms outlined in this work will facilitate an enhanced understanding and subsequent control of texture evolution, solidification behavior and mechanical behavior of WA-DED processed steels.
The Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy aims to develop and qualify additively manufactured materials for nuclear applications. One key challenge to this is the microstructural variability observed in the additively manufactured products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-throughput experimental and modeling techniques to accelerate qualification. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the additive manufacturing process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture microstructural variability is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning models to develop a digital twin for additive manufacturing that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation. The melting and subsequent solidification that occurs during the additive process is a complex phenomenon that requires multiscale multiphysics analysis. This work package focuses on understanding the role of process variabilities on the unique microstructural characteristics of additively manufactured materials. Microstructural features at the subgrain level, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. Idaho National Laboratory’s Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for additively manufactured materials in an efficient, reliable, and cost-effective way. This work focuses on capturing the microstructural variabilities at the subgrain level that are often missing in the part-scale models. In fiscal year 2025, we significantly advanced upon our work in the last fiscal year, in terms of the predictive capabilities of the physics-based and ML models, by adding the capabilities to capture subgrain-level micro-segregation during solidification using phase-field model and to predict the time-dependent dynamics of the AM process through the MOGPAR model. The alloy solidification model in MOOSE incorporates the thermodynamic properties and free energy relevant to 316 stainless steel. The model demonstrates the Cr and Ni segregation that occurs during solidification, including that the rate of solidification. The microstructural evolution model is connected to the process conditions via the surrogate model developed in this work. This enables predictions of the final microstructure in conjunctions with the manufacturing process. This work supports AMMT's rapid qualification goals by laying the foundation for an efficient and cost-effective model establishing the PSPP correlation for AM. The generated microstructures and predicted micro-segregation can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work helps to identify the key microstructural features at the subgrain level that are significant in property and performance predictions of additively manufactured components. This work will also provide inputs to the large-scale process variability models to reevaluate and validate assumptions and simplifications made in the part-scale models. Furthermore, through active learning this work can help identify the data need from both modeling and experimental sides for development of a robust digital twin for additive manufacturing and accelerate the AMMT's qualification efforts.
Cast Monel alloys are used in many industrial applications that require a combination of good mechanical properties and excellent resistance to corrosion. Despite relative widespread use, there has been limited prior research investigating the fundamental composition–structure–property relationships. Here in this work, microstructural characterization, thermal analysis, electron probe microanalysis, tensile testing, and Varestraint testing were used to assess the effects of variations in nominal composition on the solidification path, microstructure, mechanical properties, and solidification cracking susceptibility of cast Monel alloys. It was found that Si segregation caused the formation of silicides at the end of solidification in grades containing at least 3 wt pct Si. While increases to Si content led to significant improvements in strengthening due to the precipitation of β 1 -Ni 3 Si, the silicide eutectics acted as crack nucleation sites during tensile loading which severely reduced ductility. The solidification cracking susceptibility of low-Si Monel alloys was found to be relatively low. However, increases to Si concentration and the onset of associated eutectic reactions increased the solidification temperature range and drastically reduced cracking resistance. Increases in the Cu and Mn concentrations were found to reduce the solubility limit of Si in austenite which promoted additional eutectic formation and exacerbated the reductions in ductility and/or weldability.
Cellular automata (CA) models of as-solidified grain structure, originally developed and applied to casting, have become a common means of predicting grain structure resulting from Additive Manufacturing (AM) processes. The majority of these models are based on the decentered octahedron approach, which attempts to correct for the effect of grid anisotropy on the prediction of competitive solidification of dendritic grains. However, AM solidification occurs under cooling rates ($\dot{T}$) and thermal gradients (G) that are orders of magnitude larger than those encountered in casting, and no systematic investigation on the effect of the CA model cell size (Δx) and time step (Δt) on AM microstructure predictions has been performed. Here, in this study, such an investigation is first performed via simulation of individual grains of various crystallographic orientations with a fixed, unidirectional G, showing that CA prediction of the steady-state undercooling matched the expected values based on the interfacial response function at small G and deviated from the expected values at large G. Simulation of competitive growth of multiple grains showed a weakening of the predicted texture as G and Δx became large. Simulation of solidification under AM conditions, where G and $\dot{T}$ vary spatially across the melt pools, showed that not only does grain selection weaken and deviate from expectations at large Δx, but grains with crystallographic $\langle$100$\rangle$ aligned with the grid directions are more adversely affected by the temperature field discontinuities than grains with other crystallographic orientations. Despite the fact that the exact grain competition results depended on Δt, the overall texture development was notably less sensitive to Δt than Δx, provided that a reasonable value of Δt is selected based on the ratio of Δx to the maximum local solidification velocity in the simulation domain. Finally, from the directional solidification and AM simulation results, an analysis of computational cost compared to simulation resolution is performed based on an equation derived to quantify the relatively inaccuracy in grain selection based on the model and temperature field inputs. From this analysis, it is concluded that there is a need for algorithmic improvements to improve CA grain competition accuracy for large G processing conditions as sufficiently small Δx to resolve the necessary competition is intractable for many AM processing conditions.
Permanent magnets made from Sm(Fe,Co) 12 -based compounds are being actively pursued through nanostructuring and powder metallurgy. This study was aimed at the development of hard magnetic properties in bulk as-cast alloys and in melt-spun alloys for very low wheel speeds. Slower solidification rates and alloying with Zr promote the tetragonal ThMn 12 -type crystal structure, whereas higher solidification rates and alloying with B replace the ThMn 12 structure type with the TbCu 7 structure type. When introduced simultaneously, Zr and B dramatically reduce the alloy solidification rates required for both the refinement of the 1:12 crystallites and their replacement with the 1:7 phase. In bulk arc-melted alloys, this allowed for a microstructure of separated 1:12 crystallites 1–3 μm in size, although, because of the ferromagnetic nature of a minority phase, the coercivity of these fine-grained alloys reached only 0.73 kOe. A moderately accelerated solidification further refined the 1:12 crystallites and increased the coercivity; a Sm 0.7 Zr 0.4 (Fe,Co) 10.8 Ti 0.7 B 0.5 alloy exhibited a coercivity of 1.5 kOe and a maximum energy product of 3.4 MGOe when it was melt-spun into a 0.26-mm-thick ribbon. A more rapid solidification suppressed the 1:12 phase and after annealing at 800–850 °C, the alloys modified with Zr and B developed reasonably high coercivity and maximum energy product even when melt-spun at a wheel speed of 6 m/s. For the above-mentioned alloy, these values were 4.1 kOe and 7.8 MGOe, respectively. Further, a similarly processed very-Sm-lean Sm 0.5 Zr 0.6 (Fe,Co) 10.6 Ti 0.7 B 0.7 alloy exhibited a remanence of 8.8 kG and an energy product of 7.4 MGOe.
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.
The presence and morphology of Fe-containing intermetallic phases affect the mechanical properties of aluminum alloys, especially in secondary Al–Si-based cast alloys. Although strontium (Sr) addition of 50 to 500 ppm is known to refine the needle-type eutectic silicon structure, the influence of Sr on the formation of Fe-intermetallic phases remains unclear. The present work investigates the combined additions of Sr and Mn to Al–9Si–0.6Fe–0.35Mg (All compositions are in wt pct except otherwise stated.) alloys on the formation of Fe-intermetallic phases at different solidification rates from ~ 1.5 to ~ 60 °C/s. Long and branched-type AlFeSi phase with size ranging from 50 to 120 µm are more common when solidified at the rate of 1.5 °C/s regardless of Sr and Mn additions. However, at the fast solidification rate of 60 °C/s, a 60 ppm Sr addition significantly reduced the average length of needle-shaped AlFeSi phase to less than 3 to 5 µm. Thermodynamic simulations have been performed using CALculation of PHAse Diagrams (CALPHAD) models to predict the formation of various phases and their possible interactions during solidification. The results indicated that the combination of a high solidification rate and about 60 ppm of Sr is beneficial to refining the δ-Al 3 FeSi 2 phase in Al–Si–Mg alloys containing 0.6 pctFe. As a result, this unexpected finding of Fe-intermetallic refinement by low Sr addition (~60 ppm) provides an important guide in designing secondary alloys for sustainable casting applications.
This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).
To understand the process-microstructure relationships in additive manufacturing (AM), it is necessary to predict the solidification characteristics in the melt pool. This study investigates the influence of Marangoni driven fluid flow on the predicted melt pool geometry and solidification conditions using a continuum finite volume model. A calibrated laser absorptivity was determined by comparing the model predictions (neglecting fluid flow) against melt pool dimensions obtained from single laser melt experiments on a nickel super alloy 625 (IN625) plate. Using this calibrated efficiency, predicted melt pool geometries agree well with experiments across a range of process conditions. When fluid mechanics is considered, a surface tension gradient recommended for IN625 tends to overpredict the influence of convective heat transfer, but the use of an intermediate value reported from experimental measurements of a similar nickel super alloy produces excellent experimental agreement. Despite its significant effect on the melt pool geometry predictions, fluid flow was found to have a small effect on the predicted solidification conditions compared to processing conditions. We find that this result suggests that under certain circumstances, a model only considering conductive heat transfer is sufficient for approximating process-microstructure relationships in laser AM. Extending the model to multiple laser passes further showed that fluid flow also has a small effect on the solidification conditions compared to the transient variations in the process. Furthermore, limitations of the current model and areas of improvement, including uncertainties associated with the phenomenological model inputs are discussed.
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.