Deep learning model to predict fracture mechanisms of graphene

Materials fracture is a fundamental challenge in nanomaterial applications, particularly in 2D materials like graphene. Molecular dynamics (MD) simulations provide atomistic-level fracture modeling, complementing experimental techniques like HRTEM. However, MD simulations are computationally expensive, hindering their scalability for materials design. Machine learning (ML), especially deep learning, offers a powerful alternative for capturing complex physical phenomena and achieving multiscale modeling across spatial and temporal domains. Deep learning has shown success in various materials science areas, including soft materials, proteins, and nanomaterials. Recent work developed a ConvLSTM-based deep learning model for predicting fracture patterns in crystalline Lennard-Jones materials, demonstrating excellent predictive power across different loading conditions and orientations. This study applies this model to graphene, a technologically relevant material with higher chemical complexity and covalent bond breaking central to its fracture mechanics, investigating the parameter calibration process for accurate fracture predictions and showcasing the potential of ML for increasingly complex material systems.

Existing literature highlights the challenges in understanding and predicting fracture in 2D materials like graphene. Molecular dynamics simulations, while offering atomistic detail, are computationally expensive for large-scale studies. The use of machine learning, specifically deep learning, in materials science is growing, with applications in various fields. Previous studies have applied ML to predict fracture stress in graphene with defects. A recent study demonstrated the effectiveness of a ConvLSTM model in predicting fracture patterns in simpler Lennard-Jones materials. This current research builds upon this previous work by applying it to the more complex material system of graphene, aiming to validate its applicability to real-world materials with complex fracture behavior.

The study employed MD simulations of graphene fracture to create a training dataset for the ML model. Graphene samples (32 × 24 nm) were simulated with various orientations (0° to 30° in 10° increments), each orientation simulated 11 times to account for random molecular vibrations. Periodic boundary conditions were used in the tensile direction, and a 3-Å thick border restricted motion to the tensile direction. The resulting fracture paths were averaged for each orientation. The ConvLSTM-based model, previously used for Lennard-Jones materials, was employed. The model consists of convolutional layers to extract geometric features, an LSTM layer to capture sequential relationships, and a dense layer for classification. The MD simulation data (fracture path images) was preprocessed and split into input (X[t]) and output (y[t]) matrix pairs. Different input and output widths were explored to determine optimal parameters (input width of 32 and output width of 2). Model training used an Adam optimizer. The model's predictive power was evaluated by comparing predictions with the average MD fracture paths for both training and unseen orientations. Quantitative comparisons included fractal dimension calculations (box counting method) and crack length/energy analysis. The model's generalization ability was tested by applying it to pristine surfaces and more complex systems, such as graphene bicrystals and larger-scale samples with varying orientations, as well as samples with pre-existing point defects.

The study found that the input width significantly impacts the accuracy of fracture path predictions, with larger widths (32 pixels) leading to more accurate and complex predictions closely aligned with MD results. The output width (2 pixels) was found to be optimal and corresponded to the graphene armchair unit cell length, demonstrating structural relevance. The calibrated ML model accurately predicted fracture behavior for both training and unseen graphene orientations, showing good agreement in terms of envelope angle and branching behavior. Quantitative analysis of fractal dimensions showed a small but consistent underestimation in ML predictions compared to MD. Crack length and energy were slightly overestimated by the model. Importantly, the model could predict crack nucleation on pristine surfaces despite being trained on pre-notched samples. Furthermore, the model accurately predicted fracture in graphene bicrystals, capturing the onset of crack branching at specific misorientation angles. The model showed the ability to predict the fracture behavior in complex large-scale graphene samples with various orientations and gradients of orientation. The model also successfully predicted the influence of point defects on fracture paths, aligning with previously reported findings of flaw tolerance in nanocrystalline graphene. The observed change in fracture behavior at a defect size of 3.2 nm corresponds to the critical size at which nanocrystalline graphene loses its flaw tolerance.

The findings demonstrate the successful application of deep learning to predict complex fracture behavior in graphene, showing good agreement with computationally expensive MD simulations. The careful calibration of model parameters, particularly input and output widths, is crucial for accurate predictions. The model's ability to generalize to unseen orientations and complex systems highlights its potential as a valuable tool for materials design. The quantitative discrepancies in fractal dimension and crack energy suggest areas for future improvements, potentially by increasing model resolution or incorporating more diverse training data. The model's success in predicting the effects of defects complements experimental observations of flaw tolerance in nanocrystalline graphene. The ability to model increasingly complex systems, such as bicrystals and samples with varying orientations at scale, opens up exciting possibilities for designing materials with desired fracture properties.

This research successfully demonstrates the use of a deep learning model to predict the fracture behavior of graphene, including its dependence on crystal orientation, showing agreement with MD simulations. Careful parameter selection was crucial for accurate predictions. The model's generalizability to unseen configurations and complex structures makes it a promising tool for materials design. Future studies could focus on improving accuracy, incorporating diverse data, and applying the model to other materials and defect types.

The study used a specific MD simulation setup and interatomic potential (AIREBO). Different potentials might yield different results. The model's accuracy is limited by the resolution of the input images and the size of the training dataset. The underestimation of fractal dimension and slight overestimation of crack energy represent areas for potential improvement. The model's ability to predict the effect of complex defects might be enhanced by including these in the training data.