A multiscale model of grain boundary structure and energy: From atomistics to a continuum description

Grain boundaries play an important role in the mechanical and physical properties of polycrystalline metals. While continuum macroscale simulations are appropriate for modeling grain boundaries in coarse-grained materials, only atomistic simulations provide access to the details of the grain boundary (GB) structure and energy. Hence, a multiscale description is required to capture these GB details. The objective of this paper is to consolidate various approaches for characterizing grain boundaries in an effort to develop a multiscale model of the initial GB structure and energy. The technical approach is detailed using various 〈 1 0 0 〉 , 〈 1 1 0 〉 and 〈 1 1 1 〉 symmetric tilt grain boundaries in copper and aluminum. Characteristic features are: (i) GB energies obtained from atomistic simulations and boundary period vectors from crystallography, (ii) structural unit and dislocation descriptions of the GB structure and (iii) the Frank–Bilby equation to determine the dislocation content. The proposed approach defines an intrinsic net defect density scalar that is used to accurately compute the GB energy for these GB systems. The significance of the present work is that the developed atomistic-to-continuum approach is suitable for realistically inserting the initial GB structure and energy into continuum level frameworks.