Convolutional neural networks for expediting the determination of minimum volume requirements for studies of microstructurally small cracks, Part I: Model implementation and predictions

Abstract

Convolutional neural networks (CNNs) are implemented to expedite the determination of representative volume elements for microstructurally small cracks (RVEMSC). By definition, RVEMSC is the minimum volume of microstructure required around a microstructurally small crack (MSC) to achieve convergence of crack-front parameters with respect to volume size. In a previous study, RVEMSC was determined using a computationally expensive finite-element (FE) framework involving the simulation of many microstructural instantiations. With the aim of increasing the computational efficiency of determining RVEMSC, CNNs are leveraged herein to reduce the number of FE simulations required to determine RVEMSC. Using data from the previous FE-based RVEMSC study, CNNs are trained to predict RVEMSC,ip values, which quantify crack-front parameter convergence with respect to volume size for microstructural instantiation i evaluated at individual crack-front points p, given local microstructural and geometrical information. Predicted RVEMSC,ip values are subsequently used to estimate RVEMSC values. Studies are carried out to determine the optimal amount of training data, assess CNN-based RVEMSC estimation performance, and demonstrate the use of CNNs as microstructural-instantiation screening tools by enabling downselection of microstructures that are considered critical in terms of volume requirements. Individual and ensemble CNN predictions are compared. While CNNs are not found to be accurate enough to replace all FE simulations, CNNs are found to be effective as a rapid screening tool for improving the efficiency of the FE-based RVEMSC determination framework and for expediting future RVEMSC studies.