Wednesday 2:00 PM

March 2, 2022

Room: 256A

Location: Anaheim Convention Center

Understanding fatigue damage initiation is crucial for predicting lifetime of components, especially when loaded in high cycle regime. However, the mechanisms responsible for this phenomenon are less understood, primarily due to the experimental data scarcity that reveals them. Moreover, the available data is tough to be analyzed because of the following properties: multi-modality, incompleteness, and high-dimensionality.We present a knowledge graph that reveals time evolution of initial fatigue damage. The data includes both microstructural and micromechanical features acquired/simulated prior to experiments. Different data-driven methods were employed for predicting grain-level damage initiation from these features. Graph-based or CNN-based approaches and combinations thereof were used to include and unify topological and morphological information. Conventional ML approaches were kept as a baseline. Including topological and morphological information was observed to be helpful for the task. Interpretability studies on the data-driven models revealed features that are relevant for prediction of initial fatigue damage.

Developing physics-based models that account for material variability is challenging, particularly in the area of mechanical behavior, where microstructural variations dictate the strength of polycrystalline metals. However, a combination of machine learning and dislocation dynamics can predict strength as a function of microstructural features/variations. We generated a large database of strength (for random sets of microstructural features), and then applied a combination of the “mixture method” and neural networks to quantify the relative importance of microstructure features, and calculate the strength distribution for a given set of microstructural features. The results show excellent agreement with experiments and demonstrate that the conventional Hall-Petch relationship is a statistically valid manifestation for correlating the strength to the average grain size. This work provides a new perspective for predicting polycrystalline strength, while accounting for microstructural variations,resulting in a tool to guide the design of materials with superior strength.

Machine learning (ML) algorithms have been successfully implemented to derive constitutive relationships for a variety of materials. However, their application has been limited due to concerns over low interpretability, lack of theoretical considerations, and/or poor generalization. A method to incorporate thermodynamic principles and reduce spurious correlations within ML derived constitutive models is presented. The approach utilizes a hyperplasticity formulation based on thermodynamic potentials and a dissipation function. A Gibbs energy potential and dissipation function are optimized to simulated mechanical testing data and subsequent uncertainty analysis of the optimized functions provides a means to establish a physics regularization component within an algorithm's fitness evaluation procedure. Genetic programming based symbolic regression was selected for a proof-of-concept implementation using simulated testing data and is demonstrated with an open-source package, Bingo. However, the method is generally applicable for use in other ML algorithms.

Traditional material constitutive models have the advantages of being interpretable, flexible, and computationally tractable, but can be limited in their accuracy by the assumptions required to formulate them. Future data-driven constitutive models should maintain these characteristics while improving accuracy by taking advantage of data that can be readily generated. In an attempt to address this need, the use of genetic programming for symbolic regression (GPSR) is demonstrated. GPSR uses machine learning to create inherently interpretable models trained on experimental or simulation data. In this study, finite element (FE) simulations of representative microstructures are used to extend the Gurson damage model for porous ductile materials. Assumptions made in the original Gurson model are systematically relaxed to understand changes in the models to enable interpretability. The results show an improved accuracy from Gurson’s prediction, and the resulting model form allows conjecture of decreased material strength due to void interaction and non-symmetric void-shapes.

In a previous study, representative volume elements for microstructurally small cracks (RVEMSC) were established for heterogeneous, linear-elastic materials via a finite element (FE)-based framework. The framework involved the simulation of various heterogeneous microstructures and proved to be prohibitively expensive for applying to more complex material systems. Despite important outcomes from the study, two major shortcomings of the framework were the large number of required FE simulations and the inefficient, brute-force approach of selecting microstructures to simulate. In this work, convolutional neural networks (CNNs) are harnessed to address the FE-based framework’s shortcomings and expedite the determination of RVEMSC. As compared to the previous brute-force selection of microstructures, CNNs provide a more informed selection of microstructural configurations that are critical with respect to RVEMSC size, thereby improving the efficiency of determining RVEMSC in future studies.

Crystal plasticity simulations are useful for machine learning and uncertainty quantification, multiscale modelling and to analyse complex experimental data (e.g. High Energy Diffraction Microscopy). However, validity and accuracy of these simulations depend on the choice of the constitutive law. Hence, we focus on the differences in the field predictions with the variation of the hardening laws in the constitutive models. We studied the Voce law and dislocation density based hardening law using a 3D fast Fourier transform-based elasto-viscoplastic formulation for tensile deformation of copper. Results show that, although average characteristics are similar, stress and texture predictions vary spatially with increasing strain. For the Voce law, dislocation density calculated from the threshold stress is comparatively higher than the predictions of the dislocation density based hardening law. Finally, incorporation of the orientation dependent dynamic recovery (like cross slip) within the dislocation density models is important for the spatiotemporal analysis of field variables.

Emulating complex problems of fracture mechanics requires the use of existing, or newly developed high-fidelity models. These models typically work by solving intricate systems where computational costs and time requirements scale up with problem complexity. A possible solution to circumvent these challenges involves reduced-order modeling techniques, such as Machine Learning (ML). A recently developed ML method for emulating large-scale complex physics while reducing computational costs is Graph Neural Networks (GNNs). GNNs work by integrating supervised ML along with graph theory. This work develops a GNN based framework for emulating fracture in brittle materials due to multiple crack interaction, and coalescence. The framework consists of four GNNs: the first three for predicting Mode-I and Mode-II stress intensity factors, and identifying propagating microcracks, respectively; and the final GNN for predicting subsequent crack-tip positions. The trained GNN framework emulates crack propagation and coalescence for systems involving 5 to 19 microcracks with good accuracy.

The phase-field method is a powerful and versatile computational approach for modeling the evolution of the microstructure and properties of a wide variety of physical, chemical and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve useful degree of accuracy. In this talk, I will discuss advanced in developing computationally inexpensive and accurate, data-driven surrogate models that directly learn the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. I will discuss the advantages/disadvantages of combining various techniques that integrate low-dimensional description of the microstructure, obtained directly from phase-field simulations, with history-dependent deep neural network. Lasty, I will give examples on the performance and accuracy of the established machine-learning, accelerated framework to predict the non-linear microstructure evolution as compared to high-fidelity phase-field. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.