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Integrating Materials and Manufacturing Innovation

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12.02.2024 | Thematic Section: Harnessing the Power of Materials Data

MICRO2D: A Large, Statistically Diverse, Heterogeneous Microstructure Dataset

verfasst von: Andreas E. Robertson, Adam P. Generale, Conlain Kelly, Michael O. Buzzy, Surya R. Kalidindi

Erschienen in: Integrating Materials and Manufacturing Innovation | Ausgabe 1/2024

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Abstract

The availability of large, diverse datasets has enabled transformative advances in a wide variety of technical fields by unlocking data scientific and machine learning techniques. In Materials Informatics for Heterogeneous Microstructures capitalization on these techniques has been limited due to the extreme complexity of generating or curating sizeable heterogeneous microstructure datasets. Historically, this difficulty can be attributed to two main hurdles: quantification (i.e., measuring microstructure diversity) and curation (i.e., generating diverse microstructures). In this paper, we present a framework for curating large, statistically diverse mesoscale microstructure datasets composed of 2-phase microstructures. The framework generates microstructures which are statistically diverse with respect to their n-point statistics—the primary emphasis is on diversity in their 2-point statistics. The framework’s foundation is a proposed set of algorithms for synthesizing salient 2-point statistics and neighborhood distributions. We generate statistically diverse microstructures by using the outputs of these algorithms as inputs to a statistically conditioned Local-Global Decomposition generation procedure. Finally, we demonstrate the proposed framework by curating MICRO2D, a diverse, large-scale, and open source heterogeneous microstructure dataset comprised of 87, 379 2-phase microstructures. The contained microstructures are periodic and \(256 \times 256\) pixels. The dataset also contains salient homogenized elastic and thermal properties computed across a range of constituent contrast ratios for each microstructure. Using MICRO2D, we analyze the statistical and property diversity achievable via the proposed framework. We conclude by discussing important areas of future research in microstructure dataset curation.

Vorheriger Artikel A Common Data Dictionary and Common Data Model for Additive Manufacturing

Nächster Artikel AM Bench 2022 Macroscale Tensile Challenge at Different Orientations (CHAL-AMB2022-04-MaTTO) and Summary of Predictions

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Specifically, PCA is distance preserving only when the entire basis is maintained [112]. However, in practice, truncated PC representations provide useful dimensionality reduction while being approximately distance preserving [87, 88, 92].

We emphasize the similarity of this requirement to that given by Niezgoda et al. [71] above.

The mixture weights must sum to 1. In this work, all weights in a single parameterization were set to the same value.

In this work, we set this value to \(\epsilon =10^{-8}\).

Empirical observations strongly indicate that large parts of the parameter space are not important for many engineering systems (e.g., [94, 123]). For example, in general, peaks closer to zero, i.e., with \(\varvec{\mu }_i\) near zero, are more prevalent and important in real autocorrelations.

This will likely be true even if optimal space filling is accomplished over the parameter space, because of the nonlinear generation transformation step described earlier.

This approximation is a generalization of PYMKS’ standard generative model [125].

The parameterization is numerically implemented as a standard eigenvalue decomposition of the covariance matrix where the eigenvector matrices are the euler rotation matrices.

For example, the class ’VoidSmallBig’ is nonstationary, breaking the stationarity assumption that accompanies many stochastic quantification frameworks. Similarly, the sharp edges in the Voronoi classes and the small features in the NBSA class will be difficult for localization models [126], in particular those utilizing Fourier filters [127].

The exact parameter values—along with all the code necessary to generate the dataset—can be found in the GitHub repository identified at the end of the paper.

In particular, we noticed that if we did not employ volume fraction stratification the final autocorrelation dataset was strongly skewed toward higher volume fractions. We hypothesize that this is a fingerprint of the spacefilling under the \(L_2\)-norm.

The total number of microstructures is less than 100, 000 (i.e., \(10 \times 10,000\)) because several volume fraction and neighborhood combinations resulted in unstable generation, e.g., see NBSA in Table 1.

In the dataset, each class is stored separately to simplify studying subsets of the dataset.

We selected this specific discretization to balance the degree of achievable diversity against practical considerations. This resolution was sufficiently high to allow us to incorporate two important lengthscales: both salient individual features and long range patterns. However, it is sufficiently low to remain inline with the discretizations preferred by the microstructure informatics community (e.g., in Process-Structure–Property modeling [37, 72, 73, 79, 81‐83] and synthetic generation [58, 65, 76, 80, 128]). Additionally, we construct our heuristic strategies to ensure that the chosen discretization is sufficient to represent the generated systems. Primarily, we do this by ensuring that the correlation length of the generated statistics is less than half the domain size and by generating periodic microstructures. It is well established in the micromechanics community that periodic RVEs and SVEs provide highly stable estimates of homogenized properties even using relatively small domains [84, 129]. We note that the proposed framework is not restricted to this discretization and datasets containing smaller, larger, or even 3D microstructures can readily be generated without significantly altering the codebase referenced at the end of this paper. However, more advanced generation strategies will need to be established if one is interested in incorporating more than two feature lengthscales.

Other microstructures, like grain boundary structures, could be generated by the local diffusion model [64, 76].

The TAMU microstructures are rescaled down to \(256 \times 256\) for comparison.

The average relative \(L_2\) reconstruction error of the projection is \(0.0071 \pm 0.0077\) for the spinodal dataset. This is comparable with the reconstruction error of MICRO2D, Appendix B. Therefore, the dataset is well represented by the basis. Additionally, including the spinodal dataset in training the PC basis did not change the structure of the latent space.

We use an analysis congruent to the analysis reported in Robertson et al. [64]. Only the subset of 3-point statistics in which the first shift is equal to 3 are considered.

Additionally, we computed localized elastic strain fields that are not included in the dataset due to the extreme memory cost. Interested readers should contact the authors.

In practice, such second order variability arises in many important material classes and is important to study to achieve desirable properties (e.g., rafting in nickel superalloy [137, 138]).

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Titel: MICRO2D: A Large, Statistically Diverse, Heterogeneous Microstructure Dataset
verfasst von: Andreas E. Robertson
Adam P. Generale
Conlain Kelly
Michael O. Buzzy
Surya R. Kalidindi
Publikationsdatum: 12.02.2024
Verlag: Springer International Publishing
Erschienen in: Integrating Materials and Manufacturing Innovation / Ausgabe 1/2024
Print ISSN: 2193-9764
Elektronische ISSN: 2193-9772
DOI: https://doi.org/10.1007/s40192-023-00340-4

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