Convolutional Neural Networks for Expediting the Determination of Minimum Volume Requirements for Studies of Microstructurally Small Cracks, Part II: Model Interpretation

A significant question in the study of microstructurally small cracks (MSCs) is: What is the minimum microstructural volume that should be included in studies involving MSCs? To answer this, representative volume elements for microstructurally small cracks (RVEMSC), or the minimum volume of microstructure required around an MSC to achieve convergence of crack-front parameters with respect to volume size, were previously determined using finite element (FE) simulations. The large computational expense of determining RVEMSC via FE simulations motivated the implementation of convolutional neural networks (CNNs) to expedite the determination of RVEMSC (Part I). In addition to expediting the determination of RVEMSC, trained CNNs provide the opportunity to gain insights about RVEMSC predictions through various interpretation methods, which we investigate in the current work. First, an inspection of CNN predictions reveals trends learned by the CNN. Second, an input sampling grid study offers insights into the volume of microstructure around an MSC that most influences predictions of RVEMSC. Third, an input feature sensitivity analysis compares the influence of microstructural and geometrical features on RVEMSC predictions. Fourth, visual inspections of saliency maps reveal the local microstructure that is most important to the CNN when predicting RVEMSC. The CNN interpretation results show that microstructural features are more critical than geometrical features to the CNN predictions. Despite inherent limitations in interpreting saliency maps, the results demonstrate that the CNN can learn to identify various microstructural arrangements at individual crack-front points. Overall, this study highlights the importance of considering a variety of microstructural instantiations when determining RVEMSC, as RVEMSC should be a conservative minimum volume requirement that applies across a wide range of microstructural instantiations.