The spatial distribution and morphology of precipitates formed during aging are key factors that determine the precipitation hardening response of various magnesium-rare earth alloys. In recent years, the use of high-performance computing clusters and massively parallel frameworks has enabled quantitative simulations of the evolution of individual and multiple precipitates at relevant length and time scales. However, predictive modeling of precipitate evolution remains challenging, in part because many key thermodynamic and kinetic parameters governing the underlying physics are either unknown or have a high degree of uncertainty. In this work, we developed a workflow in which experimental data were used to parameterize a phase-field model to perform two-dimensional (2D) simulations of concurrent nucleation and evolution of β_1 precipitates in magnesium-neodymium alloy during aging. Matrix composition and precipitate number density at different aging times were obtained from atom probe tomography and transmission electron microscopy measurements, respectively. We applied a stereological method to estimate the three-dimensional (3D) number densities from experimental cross-sectional transmission electron micrographs. The estimated 3D number density data were then converted to effective 2D number densities. The effective 2D number density and composition data were used to determine the required model parameters by minimizing the discrepancy between simulation and experimental results. The parameterized model allows for quantitative phase-field simulations of nucleation and growth of β_1 precipitates, which can be employed to optimize aging time to achieve a target number density of precipitates. This work highlights an approach to overcome the challenges associated with parameterizing a coupled phase-field and nucleation model.

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.

Additive manufacturing (AM), as a digital process, can generate a detailed digital thread linking a part's design and manufacturing to its operational performance. As AM systems advance, an increasing amount of process data is stored in manufacturing databases. In principle, this data can be utilized by simulation-based digital twin approaches, such as real-time process control and asynchronous post-processing guidance. However, few tools currently exist for systematically integrating digital thread data with computational tools. Here, we propose a software package, called Myna, for connecting data from powder bed fusion processes to simulation tools. The utility of such a platform is demonstrated using build data from the Oak Ridge National Laboratory Manufacturing Demonstration Facility "Peregrine v2023-10" public dataset to automatically configure and run 54 semi-analytical 3DThesis melt pool simulations, 78 numerical Additive FOAM melt pool simulations, and 3 ExaCA microstructure simulations. The simulated, spatially registered microstructures are then compared directly with electron backscatter diffraction characterization of the corresponding as-built part locations. The resulting simulated microstructure showed variation as a function of process parameters, particularly stripe width; however, the experimental data had little variation between the microstructure texture and grain size resulting from different processing conditions. Analysis of the discrepancies suggest that it is possible a two-phase ferritic-austenitic solidification model is needed to accurately predict grain size and texture for certain stainless steel 316L feedstock compositions under powder bed fusion conditions, providing direction for future research. As illustrated here, due to the number and complexity of the simulations involved in AM process-structure-property predictions, automated methods to connect process data and simulations will remain necessary tools for testing hypotheses and implementing digital twin applications.

Metal additive manufacturing (AM) offers a unique opportunity for production of advanced materials and complex geometries. However, variability in microstructure and properties challenges conventional approaches to design, process optimization, qualification, and materials selection. Modeling and simulation can improve understanding of AM processing and materials, but also poses major challenges for existing computational methods. Simultaneously, modern scientific computing hardware has become increasingly complex, most notably with the adoption of hybrid architectures such as Graphical Processing Units (GPUs). If appropriately utilized, emerging computational capabilities provide an opportunity to reveal new insight into AM processing and the resulting material structure and properties. In this review we describe the computational AM landscape, identify critical gaps, and highlight opportunities to impact the development and application of AM. First, the requirements and challenges of representative AM problem statements will be defined. These problems range from scientific studies to industrial applications and are designed to capture the breadth of challenges facing the AM community. Next, the current state of AM modeling and simulation is evaluated, broken down by enabling hardware and software, process simulation, microstructure simulation, and property simulation. Each section describes the diversity of simulation approaches and associated trade-offs in physical fidelity and computational expense. Each area is then assessed based on their suitability and readiness for current and developing computational architectures. Lastly, the greatest opportunities for future research and application are highlighted, including gaps in modeling capabilities, opportunities for near-term application, and key scientific challenges.

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.

Co-design across the Exascale Computing Project has been critical for both enabling science applications and bringing disparate communities together. Developing and porting applications to the various high-performance computing architectures on pre-exascale and exascale computers has been quite challenging due to the diversity of hardware features and software stacks. The Co-design Center for Particle Applications (CoPA) has developed and enhanced the Cabana and Parallel, Rapid O(N), and Graph-Based Recursive Electronic Structure Solver (PROGRESS)/Basic Matrix Library (BML) libraries to facilitate the creation of new particle applications, make existing particle applications exascale capable, and allow teams to explore new capabilities. Particle methods from the atomistic, mesoscale, and continuum through cosmological scales have been built with Cabana, along with new possibilities for application coupling. Similarly, the PROGRESS/BML library has enabled quantum particle applications with linear algebra solvers to use advanced hardware. Across these CoPA-developed libraries, the co-design abstraction layer combines performance portability with math library support to facilitate the separation of concerns and directly support science runs.

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. We present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library.Program summaryProgram Title: Thermo4PFM CPC Library link to program files: https://doi .org /10 .17632 /8j3ntp5c7k.1Developer's repository link: https://github .com /ORNL /Thermo4PFMLicensing provisions: BSD 3-clauseProgramming language: C++/OpenMPNature of problem: Accurate modeling of solidification in metallic alloys requires thermodynamic data associated with possible material phases. That data can be used in phase-field modeling (PFM) to evaluate the driving force responsible for phase changes and solidification front motion. Integrating that data into PFM requires the solution of a small system of coupled nonlinear differential equations - the Kim-Kim -Suzuki equations - that needs to be solved at every point of a discretization mesh. Solution method: Thermo4PFM implements a Newton-based solver for the Kim-Kim-Suzuki equations for a few special cases (binary and ternary alloys with two or three phases) for CALPHAD-based models of the bulk energy of the phases. The software is written in C++ and uses the Curiously Recurring Template Pattern and OpenMP offload capabilities to take advantage of GPU accelerators, when available, on modern High Performance Computing resources. It also uses the boost Property Tree library to parse input CALPHAD data.(c) 2023 Elsevier B.V. All rights reserved.

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.

We study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K × 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

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.

In this prospective paper, we first review the existing simulation tools to simulate microgalvanic corrosion during free immersion. Then, we describe a recently developed application that employs PRISMS-PF, an open-source, high-performance phase-field modeling framework. The model employed in the application accounts for the electrochemical reaction at the metal/electrolyte interface and ionic migration in the electrolyte to determine the evolution of the corrosion front. We present the implementation details for the application and discuss its features such as super-linear parallel scaling performance for a sufficiently large system. Finally, we demonstrate the capability of the application by simulating corrosion of the matrix phase of an alloy near a secondary phase particle in two and three dimensions. Graphical abstract

Understanding how alloy composition and thermal history determine the corrosion behavior is crucial to designing alloys with lower corrosion rates. We employ a model that combines the phase-field and smoothed boundary methods [1] to investigate the effect of second phases and particles on the corrosion behavior of Mg alloys. In this model, the dissolution rate at the metal/electrolyte interface is determined by the coupling of mass transport within the electrolyte and the Butler-Volmer electrochemical kinetics at the interface. The model is implemented in the PRISMS-PF framework [2,3], an open-source framework for phase-field modeling that employs a matrix-free finite element method. Simulations of corrosion are conducted with varying microstructure and compositions with associated corrosion parameters representative of Mg alloys. Specifically, we show how our approach can describe the experimentally observed microgalvanic effects due to the presence of impurities and second phases. Finally, we show the results of a parametric study of the dependence of the rate for various combination of the corrosion parameters for each phase. This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering as part of the Center for PRedictive Integrated Structural Materials Science (PRISMS Center) at University of Michigan. [1] A.F. Chadwick, J.A. Stewart, R.A. Enrique, S. Du, K. Thornton, Numerical Modeling of Localized Corrosion Using Phase-Field and Smoothed Boundary Methods, J. Electrochem. Soc. 165 (2018) C633–C646. [2] S. DeWitt, S. Rudraraju, D. Montiel, W. B. Andrews, K. Thornton, PRISMS-PF: A General Framework for Phase-Field Modeling with a Matrix-Free Finite Element Method. Submitted to npj Comput. Mater. [3] http://prisms-center.github.io/phaseField/

A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

Scientific communities struggle with the challenge of effectively and efficiently sharing content and data. An online portal provides a valuable space for scientific communities to discuss challenges and collate scientific results. Examples of such portals include the Micromagnetic Modeling Group (μMAG) [1], the Interatomic Potentials Repository (IPR) [2, 3] and on a larger scale the NIH Genetic Sequence Database (GenBank) [4]. In this work, we present a description of a generic web portal that leverages existing online services to provide a framework that may be adopted by other small scientific communities. The first deployment of the PFHub framework supports phase-field practitioners and code developers participating in an effort to improve quality assurance for phase-field codes. Funding statement: D.W. wishes to acknowledge the Materials Genome Initiative funding allocated to the National Institute of Standards and Technology. S.J.D wishes to acknowledge funding from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award #DE-SC0008637 as part of the Center for PRedictive Integrated Structural Materials Science (PRISMS Center) at University of Michigan. P.W.V. is grateful for the financial assistance under the award 70NANB14H012 from the National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD).

The Center for Predictive Integrated Structural Materials Science (PRISMS Center) is creating a unique framework for accelerated predictive materials science and rapid insertion of the latest scientific knowledge into next-generation ICME tools. There are three key elements of this framework. The first is a suite of high-performance, open-source integrated multi-scale computational tools for predicting microstructural evolution and mechanical behavior of structural metals. Specific modules include statistical mechanics, phase field, crystal plasticity simulation and real-space DFT codes. The second is the Materials Commons, a collaboration platform and information repository for the materials community. The third element of the PRISMS framework is a set of integrated scientific “Use Cases” in which these computational methods are linked with experiments to demonstrate the ability for improving our predictive understanding of magnesium alloys, in particular, the influence of microstructure on monotonic and cyclic mechanical behavior. This paper reviews progress toward these goals and future plans.

The uniform electrodeposition of certain materials, such as Li metal, remains elusive because the mechanisms controlling growth instability are not fully understood. To determine the conditions that lead to either stable or unstable deposition, we develop a phase-field model for the growth of multiple deposits in a binary electrolyte and examine the behavior as the kinetic parameters are varied. We find that the second Damköhler number, defined as the ratio between the reaction and the mass transfer fluxes, is an indicator of deposition instability. Our results suggest that controlling reaction kinetics and initial roughness are essential in achieving stable electrodeposition.