Development and applications of machine learning frameworks for dynamic emulation of aerospace multiphysics problems and characterization of microstructure

Abstract

Future challenges in aerospace problems, spanning space exploration and military aircraft, demand advancements in several areas, including in-space 3D printing, high-performance missile technology, and rapid structural failure modeling for aircraft and rockets. However, materials used in these applications, such as additively manufactured (AM) materials and Energetic Materials (EM), exhibit defects at atomistic and microstructural scales, impacting their structural integrity and failure behavior. Addressing these challenges requires improved computational models for material characterization and dynamic failure simulation. Machine learning (ML) methods offer a promising approach to develop such models and enhance data processing efficiency. In this study, we propose various ML frameworks and techniques to aid in the development of efficient computational models for characterizing and simulating failure response in heterogeneous 3D printed materials and EMs. The first framework proposed is an autonomous ML model for fast characterization of pores, particles, grains and grain boundaries (GBs) from microstructural images of additively manufactured (AM) materials. To automate the process, the first ML model involves a classifier Convolutional Neural Network (CNN) to detect microstructures of pores or powder particles, versus GBs. For microstructures of pores or particles, a Convolutional Encoder-Decoder Network (CEDN) is used for generating binary segmentation images. Using an object detection ML network (YOLOv5), the particles’ or pores’ number, size and location are predicted with high accuracy. For GBs, Red-Green-Blue (RGB) segmentations are generated using an additional optimized CEDN. The Deep Emulator Network SEarch (DENSE) method (which employs the Covariance Matrix Adaptation - Evolution Strategy (CMA-ES)) is implemented to optimize the RGB CEDN in terms of computational speed. The characterization framework showed a significant improvement in analysis time when compared to conventional methods. The extracted defects can be used to rapidly estimate material properties in new unique heterogeneous AM material configurations. Lastly, the predicted defects and estimated material properties can be used as input to computational models to simulate their failure dynamics. Towards this effort, moving to simulation models of material failure, we then develop a Graph Neural Network (GNN) framework for simulating the failure response of brittle materials with multiple initial microcracks (5 to 19 microcracks) subjected to tension. First, a conventional eXtended Finite Element Model (XFEM-based) fracture model was used to generate training, validation, and test datasets. The number of cracks (5 to 19), their initial positions and orientations (0o, 60o, and 120o) were varied. The graph representation involved vertices placed at each crack-tip and edges connecting each crack-tip to its neighboring crack-tips within a 750mm radius. To achieve high prediction accuracy, the framework architecture is established using a sequence of physics-informed GNN-based predictions. The first prediction stage determines Mode-I and Mode-II stress intensity factors (stress distribution), the second stage predicts which microcracks will propagate (quasi-statics), and the final stage propagates crack-tip positions to the next time instant. The trained GNN framework is capable of simulating crack propagation, coalescence and corresponding stress distribution with speed-ups 6x–25x faster compared to an XFEM-based simulator. Next, while Microcrack-GNN was able to emulate crack propagation in problems involving multiple cracks with length of 300mm, orientations of 0o, 60o, and 120o, in a 2000mm × 3000mm domain under tensile load, the framework did not consider other problem-specific inputs. For instance, problems involving shear loadings, arbitrary crack orientations, arbitrary crack lengths, and different domain sizes were not predicted. An important challenge in supervised ML applications is the need for large training datasets. Extending Microcrack-GNN to handle these varying problem-specific inputs using traditional approaches would require generating large datasets for each parameter change. Therefore, to circumvent the issue of needing large training datasets for new initial conditions and loading cases, we use Transfer Learning (TL) approaches from ML theory to extend Microcrack-GNN’s capability. The new framework, ACCelerated Universal fRAcTure Emulator (ACCURATE), is generalized to a variety of crack problems using a sequence of TL update steps. The TL update steps are defined by sequentially training on significantly smaller datasets for: (i) arbitrary crack lengths, (ii) arbitrary crack orientations, (iii) square domains, (iv) horizontal domains, and (v) shear loadings. Using significantly small training datasets (20 simulations for each TL update step), ACCURATE achieves high prediction accuracy in Mode-I and Mode-II stress intensity factors, and crack paths for these problems. A key addition of ACCURATE is its ability to predict crack growth and stress evolution with high accuracy for unseen cases involving the combination of new boundary sizes with arbitrary crack lengths and crack orientations, for both tensile and shear loading. Additionally, we demonstrate a significant acceleration in simulation time of up to 2 orders of magnitude faster (200x) compared to the XFEM-based fracture model. The ACCURATE framework provides a universal computational fracture mechanics model that can be easily modified or extended in future work. Following this GNN framework along with TL, where the graph representation is formulated using vertices at each crack-tip, we then considered a mesh-based fracture simulator for phase field (PF) fracture models. As such, we develop a mesh-based GNN framework for emulating PF simulations of crack propagation. A key addition of this work is the introduction of Adaptive Mesh Refinement (AMR) to the graph representation itself. The framework (ADAPT-GNN) exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. ADAPT-GNN is able to add nodes and edges dynamically as the mesh is refined. We predict the evolution of displacement fields (u,ν) and scalar damage field (or crack field, ϕ) with good accuracy compared to a conventional PF fracture model. The stress field (σ) is as also computed using the predicted displacements and PF parameter. In terms of computational efficiency improvement, ADAPT-GNN is 15-36x faster compared to serial execution of the PF model. While ADAPT-GNN showed significant speed-up and overall good prediction accuracy, the framework involved limitations. Mesh-based GNNs such as ADAPT-GNN require a large number of message-passing (MP) steps and suffer from over-smoothing for problems involving very fine mesh. To mitigate challenges with conventional mesh-based GNNs such as ADAPTGNN, we develop a multiscale mesh-based GNN framework mimicking a conventional iterative multigrid solver, coupled with adaptive mesh refinement (AMR). We use the framework to accelerate PF fracture problems involving coupled partial differential equations with a near singular operator due to near-zero modulus inside the crack. We define the initial graph representation using all mesh resolution levels. We perform a series of downsampling steps using Transformer MP GNNs to reach the coarsest graph followed by upsampling steps to reach the original graph. We use skip connectors from the generated embedding during coarsening to prevent over-smoothing. We use Transfer Learning (TL) to significantly reduce the size of training datasets needed to simulate different crack configurations and loading conditions. The trained framework showed accelerated simulation times, while maintaining high accuracy for all cases compared to physics-based PF fracture model. This work provides a new approach to accelerate a variety of mesh-based engineering multiphysics problems. In future efforts, the microstructure characterization framework can be used in conjunction with the developed mesh-based GNNs to accelerate computational failure models for heterogeneous AM materials with defects such as pores, particles, grains and GBs. Lastly, in an effort to aid in the development of new high-performance missiles we also integrate ML methods for Heterogeneous Energetic Materials (HEM). In the realm of HEMs, where structural defects like pores are prevalent, predicting initiation metrics such as pressure, temperature, and particle velocity becomes complex due to the diverse arrangements of these defects. Current prediction methods rely heavily on experimental data and computational simulations, which are limited by the need for exhaustive testing across various pore configurations. To overcome this limitation, we introduce a novel ML framework to forecast critical velocities in PBX-9501 samples featuring multiple pores of varying sizes, quantities, and spatial distributions. In this framework, we employ the Computational Hydrocode (CTH) to simulate the shock response of each sample upon impact by a flyer plate, followed by the utilization of an automated bisection algorithm to compute critical velocities. We then develop two ML models, CNNs and GNNs, for predicting critical impact velocities. We perform rigorous evaluation of these models to assess their performance in predicting critical velocities across scenarios involving diverse spatial distributions, pore quantities, and pore sizes. The ultimate objective of this work is to develop ML-guided models capable of directly predicting critical velocities for unseen pore structures without the need for CTH simulations. By doing so, this framework lays the groundwork for accelerated comprehension of how different pore configurations influence shock sensitivity in HEMs.