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1. Statistically conditioned polycrystal generation using denoising diffusion models

   https://doi.org/10.1016/j.actamat.2024.119746  

   Buzzy, Michael O; Robertson, Andreas E; Kalidindi, Surya R (April 2024, Acta Materialia)

   Synthetic microstructure generation algorithms have emerged as a key tool for enabling large ICME and Materials Informatics efforts. In particular, statistically conditioned generative models allow researchers to systematically explore complex design spaces encountered in microstructure design. In spite of the engineering importance of polycrystalline materials, generative frameworks for these systems remain extremely limited. This stunted development – in comparison to the N-phase microstructure generation problem – occurs because of the complexities inherent to the representation of the polycrystalline orientation fields. For example, these fields exhibit multiple crystal- and sample-level symmetries. In prior work, these difficulties have resulted in instabilities in deep generative models for polycrystalline microstructures. In this work, we propose the use of a Reduced-Order Generalized Spherical Harmonic (ROGSH) basis to address the challenge described above. The proposed approach accounts for the complex sample- and crystal-level symmetries, and produces well behaved and low dimensional representations whose space has a meaningful Euclidean measure. We then demonstrate the ROGSH basis’s remarkable ability to produce stable denoising diffusion models by using our recently established Local–Global generative framework to create visually realistic synthetic polycrystalline microstructures. Furthermore, we demonstrate that the generation process can be conditioned on both first- and second-order spatial statistics of the polycrystalline orientation fields. 

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2. Generative Adversarial Networks and Mixture Density Networks-Based Inverse Modeling for Microstructural Materials Design

   https://doi.org/10.1007/s40192-022-00285-0  

   Mao, Yuwei; Yang, Zijiang; Jha, Dipendra; Paul, Arindam; Liao, Wei-keng; Choudhary, Alok; Agrawal, Ankit (November 2022, Integrating Materials and Manufacturing Innovation)

   Abstract There are two broad modeling paradigms in scientific applications: forward and inverse. While forward modeling estimates the observations based on known causes, inverse modeling attempts to infer the causes given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the causes that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, health care and materials science. Exploring the relationships from properties to microstructures is one of the inverse problems in material science. It is challenging to solve the microstructure discovery inverse problem, because it usually needs to learn a one-to-many nonlinear mapping. Given a target property, there are multiple different microstructures that exhibit the target property, and their discovery also requires significant computing time. Further, microstructure discovery becomes even more difficult because the dimension of properties (input) is much lower than that of microstructures (output). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling of structure–property linkages in materials, i.e., microstructure discovery for a given property. The results demonstrate that compared to baseline methods, the proposed framework can overcome the above-mentioned challenges and discover multiple promising solutions in an efficient manner. 

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3. Convolutional Neural Networks for the Localization of Plastic Velocity Gradient Tensor in Polycrystalline Microstructures

   https://doi.org/10.1115/1.4051085  

   Montes de Oca Zapiain, David; Shanker, Apaar; Kalidindi, Surya R. (January 2022, Journal of Engineering Materials and Technology)

   Abstract Recent work has demonstrated the potential of convolutional neural networks (CNNs) in producing low-computational cost surrogate models for the localization of mechanical fields in two-phase microstructures. The extension of the same CNNs to polycrystalline microstructures is hindered by the lack of an efficient formalism for the representation of the crystal lattice orientation in the input channels of the CNNs. In this paper, we demonstrate the benefits of using generalized spherical harmonics (GSH) for addressing this challenge. A CNN model was successfully trained to predict the local plastic velocity gradient fields in polycrystalline microstructures subjected to a macroscopically imposed loading condition. Specifically, it is demonstrated that the proposed approach improves significantly the accuracy of the CNN models when compared with the direct use of Bunge–Euler angles to represent the crystal orientations in the input channels. Since the proposed approach implicitly satisfies the expected crystal symmetries in the specification of the input microstructure to the CNN, it opens new research directions for the adoption of CNNs in addressing a broad range of polycrystalline microstructure design and optimization problems. 

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4. Graph neural networks for an accurate and interpretable prediction of the properties of polycrystalline materials

   https://doi.org/10.1038/s41524-021-00574-w  

   Dai, Minyi; Demirel, Mehmet F.; Liang, Yingyu; Hu, Jia-Mian (July 2021, npj Computational Materials)

   Abstract Various machine learning models have been used to predict the properties of polycrystalline materials, but none of them directly consider the physical interactions among neighboring grains despite such microscopic interactions critically determining macroscopic material properties. Here, we develop a graph neural network (GNN) model for obtaining an embedding of polycrystalline microstructure which incorporates not only the physical features of individual grains but also their interactions. The embedding is then linked to the target property using a feed-forward neural network. Using the magnetostriction of polycrystalline Tb_0.3Dy_0.7Fe₂alloys as an example, we show that a single GNN model with fixed network architecture and hyperparameters allows for a low prediction error of ~10% over a group of remarkably different microstructures as well as quantifying the importance of each feature in each grain of a microstructure to its magnetostriction. Such a microstructure-graph-based GNN model, therefore, enables an accurate and interpretable prediction of the properties of polycrystalline materials. 

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5. Local microstructure and micromechanical stress evolution during deformation twinning in hexagonal polycrystals

   https://doi.org/10.1557/jmr.2020.14  

   Kumar, Mariyappan Arul; Beyerlein, Irene J. (February 2020, Journal of Materials Research)

   Deformation twinning is a prevalent plastic deformation mode in hexagonal close-packed (HCP) materials, such as magnesium, titanium, and zirconium, and their alloys. Experimental observations indicate that these twins occur heterogeneously across the polycrystalline microstructure during deformation. Morphological and crystallographic distribution of twins in a deformed microstructure, or the so-called twinning microstructure, significantly controls material deformation behavior, ductility, formability, and failure response. Understanding the development of the twinning microstructure at the grain scale can benefit design efforts to optimize microstructures of HCP materials for specific high-performance structural applications. This article reviews recent research efforts that aim to relate the polycrystalline microstructure with the development of its twinning microstructure through knowledge of local stress fields, specifically local stresses produced by twins and at twin/grain–boundary intersections on the formation and thickening of twins, twin transmission across grain boundaries, twin–twin junction formation, and secondary twinning. 

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