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1. Investigating the Precipitation Kinetics and Hardening Effects of γ” in Inconel 625 Using a Combination of Meso-Scale Phase-Field Simulations and Macro-Scale Precipitate Strengthening Calculations

   https://doi.org/10.1115/IMECE2020-23328  

   Yenusah, Caleb O.; Ji, Yanzhou; Liu, Yucheng; Stone, Tonya W.; Horstemeyer, Mark F.; Chen, Lei (November 2020, Proceedings of the ASME 2020 International Mechanical Engineering Congress and Exposition)

   null (Ed.)

   Abstract Precipitation strengthening of alloys by the formation of secondary particles (precipitates) in the matrix is one of the techniques used for increasing the mechanical strength of metals. Understanding the precipitation kinetics such as nucleation, growth, and coarsening of these precipitates is critical for evaluating their hardening effects and improving the yield strength of the alloy during heat treatment. To optimize the heat treatment strategy and accelerate alloy design, predicting precipitate hardening effects via numerical methods is a promising complement to trial-and-error-based experiments and the physics-based phase-field method stands out with the significant potential to accurately predict the precipitate morphology and kinetics. In this study, we present a phase-field model that captures the nucleation, growth, and coarsening kinetics of precipitates during isothermal heat treatment conditions. Thermodynamic data, diffusion coefficients, and misfit strain data from experimental or lower length-scale calculations are used as input parameters for the phase-field model. Classical nucleation theory is implemented to capture the nucleation kinetics. As a case study, we apply the model to investigate γ″ precipitation kinetics in Inconel 625. The simulated mean particle length, aspect ratio, and volume fraction evolution are in agreement with experimental data for simulations at 600 °C and 650 °C during isothermal heat treatment. Utilizing the meso-scale results from the phase-field simulations as input parameters to a macro-scale coherency strengthening model, the evolution of the yield strength during heat treatment was predicted. In a broader context, we believe the current study can provide practical guidance for applying the phase-field approach as a link in the multiscale modeling of material properties. 

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2. Emulating the evolution of phase separating microstructures using low-dimensional tensor decomposition and nonlinear regression

   https://doi.org/10.1557/s43577-022-00443-x  

   Iquebal, Ashif S.; Wu, Peichen; Sarfraz, Ali; Ankit, Kumar (January 2023, MRS Bulletin)

   The phase-field method is an attractive computational tool for simulating microstructural evolution during phase separation, including solidification and spinodal decomposition. However, the high computational cost associated with solving phase-field equations currently limits our ability to comprehend phase transformations. This article reports a novel phase-field emulator based on the tensor decomposition of the evolving microstructures and their corresponding two-point correlation functions to predict microstructural evolution at arbitrarily small time scales that are otherwise nontrivial to achieve using traditional phase-field approaches. The reported technique is based on obtaining a low-dimensional representation of the microstructures via tensor decomposition, and subsequently, predicting the microstructure evolution in the low-dimensional space using Gaussian process regression (GPR). Once we obtain the microstructure prediction in the low-dimensional space, we employ a hybrid input–output phase-retrieval algorithm to reconstruct the microstructures. As proof of concept, we present the results on microstructure prediction for spinodal decomposition, although the method itself is agnostic of the material parameters. Results show that we are able to predict microstructure evolution sequences that closely resemble the true microstructures (average normalized mean square of 6.78×10^−7) at time scales half of that employed in obtaining training data. Our data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. 

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3. Determination of γ/γ′ interface free energy for solid state precipitation in Ni–Al alloys from molecular dynamics simulation

   https://doi.org/10.1063/5.0217993  

   Tavenner, Jacob P; Mendelev, Mikhail I; Neuberger, Raymond; Arroyave, Raymundo; Otis, Richard; Lawson, John W (July 2024, The Journal of Chemical Physics)

   Interface free energy is a fundamental material parameter needed to predict the nucleation and growth of new phases. The high cost of experimentally determining this parameter makes it an ideal target for calculation through a physically informed simulation. Direct determination of interface free energy has many challenges, especially for solid–solid transformations. Indirect determination of the interface free energy from the nucleation data has been done in the case of solidification. However, a slow on molecular dynamics (MD) simulation time scale atomic diffusion makes this method not applicable to the case of nucleation from the solid phase when precipitate composition is different from that in matrix. To address this challenge, we outline the development of a new technique for determining the critical nucleus size from an MD simulation using a recently developed method to accelerate solid-state diffusion. The accuracy of our approach for the Ni–Al system for Ni3Al (γ′) precipitates in a Ni–Al (γ) matrix is demonstrated well within experimental accuracy and greatly improves upon previous computational methods [Herrnring et al., Acta Mater. 215(8), 117053 (2021)]. 

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4. Comparisons between Two-Dimensional and Three-Dimensional Fabric Characterizations Based on Scalar Parameters for Sands

   https://doi.org/10.1061/9780784482803.001  

   Sun, Quan; Zheng, Junxing (February 2020, Geo-Congress 2020)

   Hambleton, J. P. (Ed.)

   Soil particles that have been deposited through water or air generally align their largest projected surface area normal to the depositional direction, which generates a cross-anisotropic fabric of granular soils. Researchers have used both two-dimensional (2D) and three-dimensional (3D) images to determine scalar fabric parameters of granular soils, including void ratio, coordination number, and average branch vector length. This study aims to evaluate the accuracy and effectiveness of 2D images to characterize fabric in 3D soils based on scalar parameters. The X-ray computed tomography (X-ray CT) is used to reconstruct the 3D volumetric images of three air-pluviated sand specimens, including crushed limestone, Griffin sand, and glass beads. Then, six slices are obtained by vertically cutting the 3D volumetric image in an angle increment of 30 degrees. The 3D and 2D images are analyzed to determine scalar fabric parameters. The results show that coordination numbers and average branch vector lengths computed from 2D images underestimate these values in 3D granular soils. The void ratios computed from 2D images vary a large range depending on slicing directions, which cannot provide reliable fabric characterizations for 3D granular soils. 

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5. Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution

   https://doi.org/10.1088/2632-2153/ad3e4b  

   Fan, Shaoxun; Hitt, Andrew L.; Tang, Ming; Sadigh, Babak; Zhou, Fei (May 2024, Machine Learning: Science and Technology)

   Abstract Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided. 

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