We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure ...evolution and solidification that have been compared and/or validated with experiments. They show the potential of phase-field modeling to make quantitative predictions of the link between processing and microstructure. Finally, some current challenges in extending the application of phase-field models within the context of integrated computational materials engineering are mentioned.
•We review solidification modeling advances from the atomic to the continuum scale.•We discuss interface properties and coalescence in light of atomistic calculations.•At the continuum scale, we ...focus on phase-field modeling with selected examples.•At the grain scale, we highlight a new multiscale approach for dendritic growth.•We summarize some remaining challenges in solidification modeling across scales.
We summarize recent advances in modeling of solidification microstructures using computational methods that bridge atomistic to continuum scales. We first discuss progress in atomistic modeling of equilibrium and non-equilibrium solid–liquid interface properties influencing microstructure formation, as well as interface coalescence phenomena influencing the late stages of solidification. The latter is relevant in the context of hot tearing reviewed in the article by M. Rappaz in this issue. We then discuss progress to model microstructures on a continuum scale using phase-field methods. We focus on selected examples in which modeling of 3D cellular and dendritic microstructures has been directly linked to experimental observations. Finally, we discuss a recently introduced coarse-grained dendritic needle network approach to simulate the formation of well-developed dendritic microstructures. This approach reliably bridges the well-separated scales traditionally simulated by phase-field and grain structure models, hence opening new avenues for quantitative modeling of complex intra- and inter-grain dynamical interactions on a grain scale.
Spatially extended cellular and dendritic array structures forming during solidification processes such as casting, welding, or additive manufacturing are generally polycrystalline. Both the array ...structure within each grain and the larger scale grain structure determine the performance of many structural alloys. How those two structures coevolve during solidification remains poorly understood. By in situ observations of microgravity alloy solidification experiments onboard the International Space Station, we have discovered that individual cells from one grain can unexpectedly invade a nearby grain of different misorientation, either as a solitary cell or as rows of cells. This invasion process causes grains to interpenetrate each other and hence grain boundaries to adopt highly convoluted shapes. Those observations are reproduced by phase-field simulations further demonstrating that invasion occurs for a wide range of misorientations. Those results fundamentally change the traditional conceptualization of grains as distinct regions embedded in three-dimensional space.
Tourret's fascination with Japan started at an early age. Like most kids of his generation. He grew up devouring manga, watching anime, and playing Japanese videogames. Years later, he came to ...realize that Japan was home to countless pioneering discoveries. In the field of metallurgy, this is perhaps best illustrated by the country's legendary bladesmithing. Close to his scientific interests, namely in computational modeling of crystal growth, milestone contributions from Japan go from Kobayashi's first-ever computer-generated phase-field dendrites to massively parallelized simulations of entire dendritic "forests" at record-breaking scale.
We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical ...networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. We focus on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. The computationally efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.
Dendrite fragmentation is an important phenomenon in microstructural development during solidification. For instance, it plays a key role in initiating the columnar-to-equiaxed transition (CET). ...Here, we use x-ray radiography to study dendrite fragmentation rate in a Sn-39.5 wt.% Bi alloy during directional solidification. Experiments were performed in which solidification was parallel and anti-parallel to gravity, leading to significantly different fragmentation rates. We quantify the distribution of fragmentation rate as a function of distance from the solidification front, time in the mushy zone, and volume fraction of solid. While the observed fragmentation rate can be high, there is no evidence of a CET, illustrating that it requires more than just fragmentation to occur.
Recent advances in materials processing technologies highlight the need to understand solidification kinetics in multicomponent alloys. Using a finite interface dissipation phase field model, we ...investigate planar front solidification rates in ternary alloys, used as a model system, as a function of various mass transport processes and nonequilibrium conditions. Simulation results reveal that the off-diagonal diffusion coefficients play an important role in controlling the solid–liquid (S–L) interface velocity and solute partition coefficients. Specifically, under various rapid solidification conditions negative values for the off-diagonal diffusion coefficients increase the solute partition coefficients due to the depletion of liquid phase concentrations ahead of the S–L interface. Given an undercooling, the S–L interface velocity increases with decreasing the off-diagonal diffusion coefficients. In broad terms, our work quantifies the role of coupled mass transport processes and nonequilibrium effects in solidification rates of multicomponent alloys.
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•Phase field modeling was used to study solidification in multicomponent alloys.•The model accounts for cross-diffusion and rapid solidification conditions.•Off-diagonal diffusivities greatly influence partition coefficients.•Decreasing off-diagonal diffusivities increase solid–liquid interface velocity.
Abstract
Grain growth competition during solidification determines microstructural features, such as dendritic arm spacings, segregation pattern, and grain texture, which have a key impact on the ...final mechanical properties. During metal additive manufacturing (AM), these features are highly sensitive to manufacturing conditions, such as laser power and scanning speed. The melt pool (MP) geometry is also expected to have a strong influence on microstructure selection. Here, taking advantage of a computationally efficient multi-GPU implementation of a quantitative phase-field model, we use two-dimensional cross-section simulations of a shrinking MP during metal AM, at the scale of the full MP, in order to explore the resulting mechanisms of grain growth competition and texture selection. We explore MPs of different aspect ratios, different initial (substrate) grain densities, and repeat each simulation several times with different random grain distributions and orientations along the fusion line in order to obtain a statistically relevant picture of grain texture selection mechanisms. Our results show a transition from a weak to a strong ⟨10⟩ texture when the aspect ratio of the melt pool deviates from unity. This is attributed to the shape and directions of thermal gradients during solidification, and seems more pronounced in the case of wide melt pools than in the case of a deeper one. The texture transition was not found to notably depend upon the initial grain density along the fusion line from which the melt pool solidifies epitaxially.
Cellular Automaton (CA) simulations of two-dimensional growth competition among columnar dendritic grains are carried out for a succinonitrile - 0.4 wt% acetone alloy. This is achieved by computing ...the Grain Boundary (GB) orientation during directional solidification of a bi-crystal in a frozen temperature gradient approximation, each crystal being defined by its own orientation. Comparisons are subsequently conducted with recent Phase Field (PF) results derived under the same conditions as well as with the Geometrical Limit (GL) criterion and the Favorably Orientated Grain (FOG) criterion. The GL criterion is defined mathematically considering infinitely small branching within each grain in directions perpendicular to the main dendrite arms growth directions. The FOG criterion states survival of the grain having the growth direction best aligned with the temperature gradient. The GB orientation is investigated by CA simulations as a function of the cell size, the cell neighborhood and the position used to compute the growth velocity. Results reveal that sufficiently small cells lead to the convergence of the GB orientation towards the GL criterion, while sufficiently large cells lead to the FOG criterion. Within a range of intermediate cell size, excellent agreement is found with a revised version of the FOG criterion (rev-FOG) extracted from PF simulations over a wide range of grain orientations. The cell size needs to be of the order of the maximum step between primary stationary dendrite tips of the two competing grains. The Moore neighborhood provides better results than the von Neumann neighborhood. Noticeable improvement is also observed when computing the growth velocity at the leading dendrite tip positions compared to using the cell center approximation. With computational times several orders of magnitudes lower than PF, the CA method offers a realistic and useful alternative for direct simulations of solidification grain structures in casting processes. This work is also an example of upscaling between models, showing how PF dedicated to model phenomena at the scale of the solid-liquid interface and sidebranching competition can be used to evaluate and calibrate CA developed for large scale simulations.
Growth competition between dendritic bi-crystals of orientations α1 and α2 is simulated with a Phase Field (PF) model and with a Cellular Automaton (CA) model. Maps of the grain boundary orientation angle, θ, are computed for the full spectrum of bi-crystals orientation (α1, α2). Quantitative PF vs. CA comparison is provided based on a statistical analysis of the maps. Display omitted
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