Machine-Learning Prediction of Atomistic Stress along Grain Boundaries

Abstract

The atomistic stress state along a grain boundary can be treated as a representation of the Cauchy stress tensor for the calculation of continuum traction fields, which ultimately governs the ability of grain boundaries to generate, absorb, or transmit dislocations. Such quantitative grain boundary descriptors are mostly confined to molecular dynamics (MD) simulations, where the notion of atomistic stress can be defined through virial theorem. Here, we use artificial neural networks for machine learning (ML), fed with a limited training dataset from MD simulations, to predict the local atomistic stresses from atomic position information across a series of equilibrium <110> symmetrical-tilt Cu grain boundary structures. Accuracy of the ML algorithm is found to depend on the type, sequence, and distortion of the grain boundary structural units. Accounting for these characteristics in the training dataset enables accurate predictions of the local atomistic stress distributions across the family of grain boundary structures. This ML-based constitutive modeling paves the way for direct interpretation of the equivalent stress state of atomistic structures beyond the MD domain, including those from high-resolution transmission electron microscopy (HRTEM) imaging and Density Functional Theory (DFT) modeling.