Machine Learning Approaches in Crystal Plasticity
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Date
2022-04-27
Authors
Ibragimova, Olga
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
The continued advancements in material development and design require understanding the relationships between microstructure and flow behaviour. Crystal plasticity (CP) is a high-fidelity computational method that helps unravel these relationships and assist in the development of high-performance materials. CP can capture the material behavior subjected to any applied loading as well as the local stress and strain partitioning and localisation in a given microstructure. The high-fidelity of the crystal plasticity models comes at the cost of computational demand. This research addresses the significant computational demand of CP simulations and uses machine learning methods to achieve rapid and accurate predictions of material plastic behaviour. This research project uses two different crystal plasticity models: the CP model under a fully constrained Taylor assumption and the crystal plasticity finite element model. This thesis covers two different machine learning applications to high-fidelity predictions of model behaviour.
The first application presents a machine learning- and crystal plasticity-based framework to predict stress-strain behaviour and texture evolution for a wide variety of materials within the face-centred cubic family (FCC). First, the process of the framework design is described in detail. The proposed framework incorporates an ensemble of artificial neural networks (ANN) and a crystal-plasticity based algorithm. Next, the dataset constituent of crystal plasticity simulations was collected. The dataset consisting of examples of monotonic deformation cases, was prepared for training using mathematical transformations, and finally used to train ANNs used in the framework. Then, the framework was demonstrated to predict full stress-strain and texture evolution of different FCC single crystals under uniaxial tension, compression, simple shear, equibiaxial tension, tension- compression-tension, compression-tension-compression, and, finally, for some arbitrary non-monotonic loading cases. The proposed framework predicts the stress-strain response and texture evolution with high accuracy. The results demonstrated in this research show that the proposed machine learning- and crystal plasticity-based framework exhibits a tremendous computational advantage over the conventional crystal plasticity model. Finally, one of the most important contributions of this work is to show the framework’s feasibility. The work demonstrates that machine learning methods can help predict complex strain paths without training machine learning models on the extremely large set of possible non-monotonic loading scenarios. This part of the thesis presents a macro-level model that allows predictions for single and polycrystals.
The second part of this research project presents a micro-level type of model and utilizes convolutional neural networks (CNNs) in conjunction with the crystal plasticity finite element method (CPFEM). The inputs to the CNN model are material hardening parameters (initial hardness and initial hardening modulus), a global tensile strain value, and microstructure with varying number of grains, grain size, grain morphology and texture. This input selection allows performing simulations for a wide range of materials, as defined by microstructure and flow curves. The outputs of the CNN are the local stress and strain values. The proposed framework involves the following stages: feature engineering, generation of synthetic microstructures, CPFEM simulations, data extraction and preprocessing, CNN design and selection, CNN training, and validation of the trained network. The trained CNN was successfully demonstrated to predict local stress and strain evolution for the completely new dataset (test set) containing synthesised microstructures. The test set predictions were evaluated, and the median-, highest-, and lowest-error predictions were presented and discussed. Overall, the CNN demonstrated excellent agreement with CPFEM simulations, thus validating its accuracy. Then, the CNN was applied to predict the stress and strain evolution for AA5754 and AA6061 microstructures obtained using electron backscatter diffraction. These two microstructures were entirely new for the CNN and displayed size and grain morphology different from the synthesised microstructures. For both microstructures, the obtained stress and strain evolution predictions demonstrated excellent agreement with CPFEM simulations, thus confirming the flexibility of the trained CNN model. Then, the framework was extended to predict strain localisation and was evaluated on an AA6061 microstructure. The results demonstrate a clear computational advantage of CNN without losing accuracy.
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Keywords
machine learning, artificial neural networks, crystal plasticity, non-monotonic loadings, texture, convolutional neural networks, finite element method