Advantages and Limitations of using Physics Informed Deep Learning to Model Crystal Plasticity
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Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach
Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.
36 MATERIALS SCIENCE↗
Data-driven modeling of dislocation mobility from atomistics using physics-informed machine learning
Dislocation mobility, which dictates the response of dislocations to an applied stress, is a fundamental property of crystalline materials that governs the evolution of plastic deformation. Traditional approaches for deriving mobility laws rely on phenomenological models of the underlying physics, whose free parameters are in turn fitted to a small number of intuition-driven atomic scale simulations under varying conditions of temperature and stress. This tedious and time-consuming approach becomes particularly cumbersome for materials with complex dependencies on stress, temperature, and local environment, such as body-centered cubic crystals (BCC) metals and alloys. In this paper, we present a novel, uncertainty quantification-driven active learning paradigm for learning dislocation mobility laws from automated high-throughput large-scale molecular dynamics simulations, using Graph Neural Networks (GNN) with a physics-informed architecture. We demonstrate that this Physics-informed Graph Neural Network (PI-GNN) framework captures the underlying physics more accurately compared to existing phenomenological mobility laws in BCC metals.
36 MATERIALS SCIENCE↗
2024 Second Half Semi Annual Report: Modeling plasticity-mediated flow in metals with pressurized cavities
The objective is to better predict the bulk-scale mechanical behavior of porous metals that have over pressurized cavities (e.g., irradiated metals with helium bubbles) by quantifying the complex coupling among cavity aspects (e.g., size distribution, inhomogeneous overpressure values, spatial arrangement) and metal properties (e.g., rate-dependency, crystallographic lattice). This requires up-scaling local mechanical fields from the single crystal scale and will be accomplished using a homogenization approach that combines full-field numerical simulations, analytical formalisms, and physics-informed machine learning to produce symbolically-defined constitutive equations (e.g., gauge functions). These equations will satisfy the objective because they enable computationally efficient predictions that approach the accuracy of computationally expensive full-field numerical simulations, abide by theoretical requirements (e.g., conservation of energy, work conjugacy), and retain the transparency of analytical models.
36 MATERIALS SCIENCE↗
Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals
As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.
36 MATERIALS SCIENCE↗
Physics-informed machine-learning model of temperature evolution under solid phase processes
We model temperature dynamics during Shear Assisted Proccess Extrusion (ShAPE), a solid phase process that plasticizes feedstock with a rotating tool and subsequently extrudes it into a consolidated tube, rod, or wire. Control of temperature is critical during ShAPE processing to avoid liquefaction, ensure smooth extrusion, and develop desired material properties in the extruded products. Accurate modeling of the complicated thermo-mechanical feedbacks between process inputs, material temperature, and heat generation presents a significant barrier to predictive modeling and process design. In particular, connecting micro-structural scale mechanisms of heat generation to macro-scale predictions of temperature can become computationally intractable. In this work we use a neural network (NN) model of heat generation to bridge this gap, by combining it with a simplified model of the temperature dynamics due to conduction and convection to capture the macro scale evolution of temperature. We inform the construction of the NN heat generation model using crystal plasticity simulations at the micro-structural scale to model the effects of process inputs on generation of heat. We achieved close fits of the temperature dynamics model to a diverse experimental data-set. Further, the relationships learned by the NN model between process inputs and heat generation showed qualitative agreement with those predicted by crystal plasticity simulations.
36 MATERIALS SCIENCE↗
Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning
The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.
Jaehyun Cho↗
Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning
The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.
Jaehyun Cho↗
Predicting Failure Using Deep Learning SAND Report
Accurate prediction of ductile failure is critical to Sandia’s NW mission, but the models are computationally heavy. The costs of including high-fidelity physics and mechanics that are germane to the failure mechanisms are often too burdensome for analysts either because of the person-hours it requires to input them or because of the additional computational time, or both. In an effort to deliver analysts a tool for representing these phenomena with minimal impact to their existing workflow, our project sought to develop modern data-driven methods that would add microstructural information to business-as-usual calculations and expedite failure predictions. The goal is a tool that receives as input a structural model with stress and strain fields, as well as a machine-learned model, and output predictions of structural response in time, including failure. As such, our project spent substantial time performing high-fidelity, three-dimensional experiments to elucidate materials mechanisms of void nucleation and evolution. We developed crystal-plasticity finite-element models from the experimental observations to enrich the findings with fields not readily measured. We developed engineering length-scale simulations of replicated test specimens to understand how the engineering fields evolve in the presence of fine-scale defects. Finally, we developed deep learning convolutional neural networks, and graph-based neural networks to encode the findings of the experiments and simulations and make forward predictions in time for structural performance. This project demonstrated the power of data-driven methods for model development, which have the potential to vastly increase both the accuracy and speed of failure predictions. These benefits and the methods necessary to develop them are highlighted in this report. However, many challenges remain to implementing these in real applications, and these are discussed along with potential methods for overcoming them.
97 MATHEMATICS AND COMPUTING↗
SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials
This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.
42 ENGINEERING↗