The interface thickness in the phase-field (PF) method limits its simulation scales. Consequently, large-scale PF simulations become prohibitively expensive for resolving the extremely fine microstructures that typically form during rapid solidification processing. This challenge is significant in predicting microstructure evolution in metal additive manufacturing and has been identified by the United States Department of Energy’s Exascale Computing Project. To address this, we develop a multi-GPU and MPI-based massively parallel simulation code, utilizing state-of-the-art algorithms, software, and libraries, for large-scale three-dimensional (3D) PF simulations. We report the first GPU-parallel PF simulations on Frontier (currently the second TOP500 exascale cluster) and Summit machines, taking dendritic growth as an example problem. We evaluate the parallel performance of our implementation using scaling studies with more than 24000 GPUs (among the largest known computations to date) and the acceleration performance using large-scale simulations of dendritic growth in 3D. Finally, massively parallel GPUs in these supercomputers enabled the first coupled multiscale simulations of laser melting and subsequent dendritic solidification on the scale of a full melt-pool, demonstrating the feasibility of performing PF simulations with a point total over 2 billion grid points within an acceptable time.

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. This surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the γ^'' phase at high Nb concentrations and the δ phase at low Nb concentrations.

Phase field (PF) simulations are computationally expensive but remain a key analysis tool to understand the complex mechanisms of additive manufacturing (AM) processes. Each PF simulation-aided analysis requires thousands of node hours on leadership-class supercomputers. One of the main goals of these analyses is the study of microstructure evolution during the build process which begins with the onset of nucleation. Nucleation occurs under certain thermomechanical conditions which are not known a priori and many PF simulations are required to identify ranges of input thermo-mechanical parameters that can result in the onset of nucleation. Since many of the simulations do not result in nucleation, an analysis campaign often ends up wasting tremendous amounts of precious computing resources executing nucleation-absent simulations. The goal of this work is to design and train deep learning models to inform a PF simulation about the likelihood of the occurrence of nucleation in a future simulation time-step based on the state summary over a finite number of past time-steps of a running simulation. If the prediction determines that the running simulation is unlikely to reach nucleation in the allotted time, then its execution is stopped immediately ultimately resulting in vast reduction in wasted computations when accrued over all the PF simulations typically performed in a single or multiple analysis campaign(s). The paper presents the performance of a machine learning pipeline that uses a convolutional neural network (CNN) model to learn an embedding which is then used with a self-attention network to build a multi-task deep learning model to predict the likelihood of nucleation. The model also predicts the input parameters used in a simulation. Performance is compared with a baseline pipeline that uses an off-the-shelf LeNet-5 model to learn the initial embedding. Despite their smaller size, performance results indicate significant improvement in accuracy of the proposed models compared to the larger baseline models.

the Big Area Additive Manufacturing (BAAM) for polymer matrix composites was presented as the background motivation for the workshop. Following, the extension of underlying technology to low-cost metals was proposed with the following goals: (i) High deposition rates (approaching 100 lbs/h); (ii) Low cost (<$10/lbs) for steel, iron, aluminum, nickel, as well as, higher cost titanium, (iii) large components (major axis greater than 6 ft) and (iv) compliance of property requirements. The above concept was discussed in depth by representatives from different industrial sectors including welding, metal fabrication machinery, energy, construction, aerospace and heavy manufacturing. In addition, DOE’s newly launched High Performance Computing for Manufacturing (HPC4MFG) program was reviewed. This program will apply thermo-mechanical models to elucidate deeper understanding of the interactions between design, process, and materials during additive manufacturing. Following these presentations, all the attendees took part in a brainstorming session where everyone identified the top 10 challenges in large-scale metal AM from their own perspective. The feedback was analyzed and grouped in different categories including, (i) CAD to PART software, (ii) selection of energy source, (iii) systems development, (iv) material feedstock, (v) process planning, (vi) residual stress & distortion, (vii) post-processing, (viii) qualification of parts, (ix) supply chain and (x) business case. Furthermore, an open innovation network methodology was proposed to accelerate the development and deployment of new large-scale metal additive manufacturing technology with the goal of creating a new generation of high deposition rate equipment, affordable feed stocks, and large metallic components to enhance America’s economic competitiveness.

During the Flash process, the cross section of a plain-carbon or a low-alloy steel is austenitized through rapid heating and transformed on rapid cooling to a predominantly martensite + bainite structure with small amounts of retained austenite. Unlike conventional heat treating, homogeneity is intentionally avoided during Flash processing of steels. The Flash process assembly consists of a pair of rolls that transfer the steel sheets through the heating and cooling stage of the thermal cycle. The initial microstructure of the steel consists of ferrite (body-centered cubic iron) + carbide ((Fe,X)mCn) mixture. The heating rate through the peak temperature is a function of temperature and reaches a peak of about 300-400K/s and the cooling rate has a maximum value of 3000-4000K/s. The on-heating phase transformations include carbide dissolution, austenite (face-centered cubic iron) nucleation and growth, and diffusion of carbon and other substitutional elements in the steel. The on-cooling phase transformations include formation of martensite (body-centered tetragonal phase containing supersaturated solute) and bainite (ferrite plates with or without fine carbides). In this project, the focus is on Fe-C-Cr steels that are currently Flash processed for armor applications. The modeling effort proposed here will help optimize the Flash thermal cycle for these low alloy steels to achieve the target performance, which is an ongoing effort at SFP Works. A significant feature of Flash processed Fe-C-Cr steels is the presence of scatter in the through-thickness in the sheet. The variability in hardness results from a variability in the bainite + martensite microstructure that is sensitive to the local chemical concentration of C and Cr. Such a chemical inhomogeneity is intentionally obtained in the Flash process. Although such a microstructural gradient is presumably responsible for the exceptional properties of the Flash processed steel, it is very important to quantify the gradients as a function of Flash variabilities in processing parameters and the input microstructure. Understanding the mechanistic pathway that leads to microstructural gradients could be ground-breaking and instrumental for achieving better process control and optimized microstructural state to meet application-specific strength-ductility requirements. Since the final microstructure depends on setting up precise solute concentration gradients through a rapid heating process, and transforming these regions into various phases, it is important to understand how small changes in steel chemistry, input microstructure (carbide size and distribution), and process variables (Flash thermal cycle) will impact the solute concentration gradients.

High fidelity simulations of grain formation in alloys are an indispensable tool for process-to-mechanical-properties characterization. Such simulations, however, can be computationally expensive as they require fine spatial and temporal discretizations. Their cost becomes an obstacle to parametric studies and ensemble runs and ultimately makes downstream tasks like optimal control and uncertainty quantification challenging. To enable such downstream tasks, we introduce GrainNN, an efficient and accurate reduced-order model for epitaxial grain growth in additive manufacturing conditions. GrainNN is a sequence-to-sequence long-short-term-memory (LSTM) deep neural network that evolves the dynamics of manually crafted features. Its innovations are (1) an attention mechanism with grain-microstructure-specific transformer architecture; and (2) an overlapping combination of several clones of the network to generalize to grain configurations that are different from those used for training. This design enables GrainNN to predict grain formation for unseen physical parameters, grain number, domain size and geometry. Furthermore, GrainNN not only reconstructs the quantities of interest but also can be pointwise accurate. In our numerical experiments, we use a polycrystalline phase field method to both generate the training data and assess GrainNN. For multiparametric, ensemble simulations with many grains, GrainNN can be orders of magnitude faster than phase field simulations, while delivering 5%–15% pointwise error. This speedup includes the cost of the phase field simulations for generating training data.

Additive manufacturing (AM), or 3D printing, of metals is transforming the fabrication of components, in part by dramatically expanding the design space, allowing optimization of shape and topology. However, although the physical processes involved in AM are similar to those of welding, a field with decades of experimental, modeling, simulation, and characterization experience, qualification of AM parts remains a challenge. The availability of exascale computational systems, particularly when combined with data-driven approaches such as machine learning, enables topology and shape optimization as well as accelerated qualification by providing process-aware, locally accurate microstructure and mechanical property models. We describe the physics components comprising the Exascale Additive Manufacturing simulation environment and report progress using highly resolved melt pool simulations to inform part-scale finite element thermomechanics simulations, drive microstructure evolution, and determine constitutive mechanical property relationships based on those microstructures using polycrystal plasticity. We report on implementation of these components for exascale computing architectures, as well as the multi-stage simulation workflow that provides a unique high-fidelity model of process–structure–property relationships for AM parts. In addition, we discuss verification and validation through collaboration with efforts such as AM-Bench, a set of benchmark test problems under development by a team led by the National Institute of Standards and Technology.

have been developing and validating an advanced physics-based process model. The specific goal is to develop a physics-based framework of an AM process and reliably predict fatigue properties of built-up structures as based on detailed solidification microstructures. Microstructures are predicted using process control parameters including energy source power, scan velocity, deposition pattern, and powder properties. The multi-scale multi-physics model requires solution and coupling of governing physics that will allow prediction of the thermal field and enable solution at the microstructural scale. The state-of-the-art approach to solve these problems requires a huge computational framework and this kind of resource is only available within academia and national laboratories. The project utilized the parallel phase-fields codes at Oak Ridge National Laboratory (ORNL) and Lawrence Livermore National Laboratory (LLNL), along with the high-performance computing (HPC) capabilities existing at the two labs to demonstrate the simulation of multiple dendrite growth in threedimensions (3-D). The LLNL code AMPE was used to implement the UTRC phase field model that was previously developed for a model binary alloy, and the simulation results were compared against the UTRC simulation results, followed by extension of the UTRC model to simulate multiple dendrite growth in 3-D. The ORNL MEUMAPPS code was used to simulate dendritic growth in a model ternary alloy with the same equilibrium solidification range as the Ni-base alloy 718 using realistic model parameters, including thermodynamic integration with a Calphad based model for the ternary alloy. Implementation of the UTRC model in AMPE met with several numerical and parametric issues that were resolved and good comparison between the simulation results obtained by the two codes was demonstrated for two dimensional (2-D) dendrites. 3-D dendrite growth was then demonstrated with the AMPE code using nondimensional parameters obtained in 2-D simulations. Multiple dendrite growth in 2-D and 3-D were demonstrated using ORNL's MEUMAPPS code using simple thermal boundary conditions. MEUMAPPS was then modified to incorporate the complex, time-dependent thermal boundary conditions obtained by UTRC's thermal modeling of single track AM experiments to drive the phase field simulations. The results were in good agreement with UTRC's experimental measurements.

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the gamma matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of delta precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of delta precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the delta interface. We propose a phenomenological model to describe the diffusion-controlled growth kinetics of the delta phase under a solute concentration gradient.

In the present work, a combined study with polarized neutron imaging (PNI) and neutron-grating interferometry based dark field imaging (DFI) experiments on grain oriented high permeability steel sample with 3% Si and 0.35 mm thickness is reported. With the combination of these two experimental techniques it was possible to obtain the complex picture of magnetic domain distribution and domain walls in the electric steel samples. With the PNI technique, the observed fringe pattern contrast may be correlated with basic magnetic domains. These magnetic domains are oriented anti-parallel with respect to each other and the different magnetic field in each domain may lead to fringe pattern contrast. The magnetic domains are disrupted at the grain boundaries, observed as discontinuities in the fringe pattern contrast. In comparison, with DFI measurements, we visualized scattering contrast from magnetic domain walls. A clear correlation between basic domains (from PNI) and domain walls (using DFI) is observed. In the current study we also demonstrate the potential of combining two differential experimental techniques to visualize and obtain collective information about magnetic domains and domain walls. (C) 2019 Elsevier B.V. All rights reserved.

The θʹ to θ phase transformation that occurs during overaging in Al-Cu alloys is detrimental for their mechanical properties. Experiments suggest that the onset of this transformation is dependent on the temperature and duration of thermal exposure, but the microstructural conditions which trigger this transformation are still unclear. In this study, the critical conditions associated with the onset of θʹ to θ phase transformation are predicted using thermodynamic analysis. We compare the predicted microstructural conditions with both new and previously reported microstructural observations, and also test the predictions using phase field modeling. This multi-pronged approach suggests that the tendency of a θʹ particle to transform into the θ phase depends primarily on temperature, particle size, and particle aspect ratio. We define a “critical” aspect ratio below which θʹ to θ phase transformation becomes thermodynamically favored and show how this critical aspect ratio increases with both temperature and particle volume. With this approach, the intimate link between phase stability, morphological stability, and coarsening resistance for θʹ precipitates in Al-Cu alloys is illustrated.

The solidification microstructure in IN718 during additive manufacturing was modeled using phase field simulations. The novelty of the research includes the use of a surrogate Ni–Fe–Nb alloy that has the same equilibrium solidification range as IN718 as the model system for phase field simulations, the integration of the model alloy thermodynamics with the phase field simulations, and the use of high-performance computing tools to perform the simulations with a high enough spatial resolution for realistically capturing the dendrite morphology and the level of microsegregation seen under additive manufacturing conditions. Heat transfer and fluid flow models were used to compute the steady state temperature gradient and an average value of the solid-liquid (s-l) interface velocity that were used as input for the phase field simulations. The simulations show that the solidification morphology is sensitive to the spacing between the columnar structures. Spacing narrower than a critical value results in continued growth of a columnar microstructure, while above a critical value the columnar structure evolves into a columnar dendritic structure through the formation of secondary arms. These results are discussed in terms of the existing columnar to dendritic transition (CDT) theories. The measured interdendritic Nb concentration, the primary and secondary arm spacing is in reasonable agreement with experimental measurements performed on the nickel-base superalloy IN718.

While most Al–Cu and Al–Si–Cu alloys strengthened by the metastable θ′ phase exhibit extensive microstructural degradation above 200 °C, recent experimental work has demonstrated that θ′ precipitates can be stabilized to 350 °C by microalloying additions of Mn and Zr, resulting in improved mechanical properties at elevated temperatures. The present work utilizes phase field modeling to study the relationship between microalloying solute elements and the coarsening resistance of θ′. Simulations are designed to parse out the relative influence of various stabilization mechanisms on microstructural evolution of θ′ precipitates at elevated temperatures. Specifically, a ternary alloying element is added to a virtual microstructure to study the operation and effectiveness of stabilization mechanisms including solute drag, diffusion barriers, interfacial energy reduction, and lattice strain modification. Simulation results are compared with atom probe tomography observations. The simulations rationalize experimental observations of microstructural evolution and solute segregation in Al–Cu–Mn–Zr alloys, and reveal the interlinked thermodynamic and kinetic mechanisms that determine the elevated temperature stability of θ′ precipitates.

A high order level set model is developed for deterministic simulation of dendritic growth in unstable solidifying systems. The model captures motion of the front implicitly on a structured finite difference grid, enables calculation of its geometric properties and also applies boundary conditions on the immersed interface. Interfacial capillary effect is incorporated in the model through the Gibbs-Thomson condition. Canonical problems for evaluating grid convergence of the numerical method and validation tests for stability of a growing nucleus in the presence of isotropic surface tension are presented. The growth morphology of solidifying nuclei in undercooled metallic melts is quantitatively analyzed. Effects of crystal anisotropy and melt undercooling on the front geometry, propagation speed and formation of branched dendritic structures are examined. The complex morphological changes, such as remelting of secondary perturbations under specific conditions of undercooling, are also captured during the quantitative analysis.

The time-of-flight neutron diffraction data collected in-situ on Oak Ridge National Laboratory's (ORNL, Oak Ridge, TN, USA) VULCAN and Los Alamos National Laboratory's (LANL, Los Alamos, NM, USA) High-Pressure-Preferred-Orientation (HIPPO) diffractometers have been analyzed complementarily to show the texture evolution during annealing of a cold-rolled Al-2%Mg alloy. The texture analysis aimed to identify the components present in the initial rolling (or deformation) texture and in the thermally-activated recrystallization texture, respectively. Using a quasi-Monte-Carlo (QMC) approach, a new method has been developed to simulate the weighted texture components, and to obtain inverse pole figures for both rolling and normal directions. As such, distinct recrystallization pathways during annealing in isochronal conditions, can be revealed in terms of the evolution of the texture components and their respective volume fractions. Moreover, the recrystallization kinetics associated with the cube and random texture components are analyzed quantitatively using a similar approach developed for differential scanning calorimetry (DSC).

Bragg-edge imaging, which is also known as neutron radiography, has recently emerged as a novel crystalline characterization technique. Modelling of this novel technique by incorporating various features of the underlying microstructure (including the crystallographic texture, the morphological texture, and the grain size) of the material remains a subject of considerable research and development. In this paper, Inconel 718 samples made by additive manufacturing were investigated by neutron diffraction and neutron radiography techniques. The specimen features strong morphological and crystallographic textures and a highly heterogeneous microstructure. A 3D statistical full-field model is introduced by taking details of the microstructure into account to understand the experimental neutron radiography results. The Bragg-edge imaging and the total cross section were calculated based on the neutron transmission physics. A good match was obtained between the model predictions and experimental results at different incident beam angles with respect to the sample build direction. The current theoretical approach has the ability to incorporate 3D spatially resolved microstructural heterogeneity information and shows promise in understanding the 2D neutron radiography of bulk samples. With further development to incorporate the heterogeneity in lattice strain in the model, it can be used as a powerful tool in the future to better understand the neutron radiography data.

The upper limit of service temperature for many Al-Cu alloys is determined by the thermal stability of strengthening theta' (Al2Cu) precipitates. Above a certain temperature, theta' precipitates will undergo morphological evolution and transform into the detrimental, equilibrium theta phase, leading to a rapid drop in strength. Certain alloying elements have recently been reported to increase the thermal stability of theta' precipitates, by mechanisms that are yet unclear. Herein, we investigate the effect of modified interfacial energy and solute chemical mobility on the thermal stability of theta' via high-throughput phase field study. We identify a critical theta' aspect ratio to predict the onset of theta formation. Using this criterion, we predict the time required for theta' to theta phase transformation as a function of temperature, Cu diffusivity, and the interfacial energy of theta' precipitates. The predicted times compare favorably with reported times for theta formation under similar experimental conditions. These phase field simulations predict that a moderate reduction in Cu mobilityis adequate to stabilize the as-aged microstructure up to 300 degrees C, while substantial reductions to both interfacial energy and Cu mobility are needed to achieve similar stability at 400 degrees C. Experimental microstructural evolution results in commercial (319) and thermally stabilized (RR350) cast aluminum alloys are presented to complement the simulations.

1. ABSTRACT Additive Manufacturing (AM) refers to a process by which digital three-dimensional (3-D) design data is converted to build up a component by depositing material layer-by-layer. United Technologies Corporation (UTC) is currently involved in fabrication and certification of several AM aerospace structural components made from aerospace materials. This is accomplished by using optimized process parameters determined through numerous design-of-experiments (DOE)-based studies. Certification of these components is broadly recognized as a significant challenge, with long lead times, very expensive new product development cycles and very high energy consumption. Because of these challenges, United Technologies Research Center (UTRC), together with UTC business units have been developing and validating an advanced physics-based process model. The specific goal is to develop a physics-based framework of an AM process and reliably predict fatigue properties of built-up structures as based on detailed solidification microstructures. Microstructures are predicted using process control parameters including energy source power, scan velocity, deposition pattern, and powder properties. The multi-scale multi-physics model requires solution and coupling of governing physics that will allow prediction of the thermal field and enable solution at the microstructural scale. The state-of-the-art approach to solve these problems requires a huge computational framework and this kind of resource is only available within academia and national laboratories. The project utilized the parallel phase-fields codes at Oak Ridge National Laboratory (ORNL) and Lawrence Livermore National Laboratory (LLNL), along with the high-performance computing (HPC) capabilities existing at the two labs to demonstrate the simulation of multiple dendrite growth in three-dimensions (3-D). The LLNL code AMPE was used to implement the UTRC phase field model that was previously developed for a model binary alloy, and the simulation results were compared against the UTRC simulation results, followed by extension of the UTRC model to simulate multiple dendrite growth in 3-D. The ORNL MEUMAPPS code was used to simulate dendritic growth in a model ternary alloy with the same equilibrium solidification range as the Ni-base alloy 718 using realistic model parameters, including thermodynamic integration with a Calphad based model for the ternary alloy. Implementation of the UTRC model in AMPE met with several numerical and parametric issues that were resolved and good comparison between the simulation results obtained by the two codes was demonstrated for two dimensional (2-D) dendrites. 3-D dendrite growth was then demonstrated with the AMPE code using non-dimensional parameters obtained in 2-D simulations. Multiple dendrite growth in 2-D and 3-D were demonstrated using ORNL’s MEUMAPPS code using simple thermal boundary conditions. MEUMAPPS was then modified to incorporate the complex, time-dependent thermal boundary conditions obtained by UTRC’s thermal modeling of single track AM experiments to drive the phase field simulations. The results were in good agreement with UTRC’s experimental measurements. arms seen in single track experiments using alloy 718, the simulations overestimated the width of the primary columns. Uncertainties in the simulation parameters and the thermodynamics of the alloy were responsible for the deviation. Simulations captured the partitioning of Nb to the inter-cellular and interdendritic liquid. However, the simulations overestimated the Nb segregation compared to experimental findings due to uncertainties in phase field model parameters and in the coupling of the phase field with the continuum heat transfer simulations.