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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. 

Abstract Polishing of additively manufactured products is a multi-stage process, and a different combination of polishing pad and process parameters is employed at each stage. Pad change decisions and endpoint determination currently rely on practitioners’ experience and subjective visual inspection of surface quality. An automated and objective decision process is more desired for delivering consistency and reducing variability. Toward that objective, a model-guided decision-making scheme is developed in this article for the polishing process of a titanium alloy workpiece. The model used is a series of Gaussian process models, each established for a polishing stage at which surface data are gathered. The series of Gaussian process models appear capable of capturing surface changes and variation over the polishing process, resulting in a decision protocol informed by the correlation characteristics over the sample surface. It is found that low correlations reveal the existence of extreme roughness that may be deemed surface defects. Making judicious use of the change pattern in surface correlation provides insights enabling timely actions. Physical polishing of titanium alloy samples and a simulation of this process are used together to demonstrate the merit of the proposed method.