A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals

Abstract

In recent years, numerous partitioned-domain methods have been developed to describe dislocation behavior at length scales that are usually inaccessible to most classical atomistic methods. These methods retain full atomistic detail in regions of interest while using a continuum description to reduce the computational burden elsewhere. In most of these methods, however, lattice defects in the continuum are either implemented via constitutive relations, lattice elasticity with dislocation field interactions, or are not permitted at all. In such approaches, the transit of dislocations across the atomistic/continuum interface appeals to approximate heuristics intended to minimize the effects of the interface due to the change from atomistic to continuum degrees of freedom. The concurrent atomistic-continuum (CAC) method, originally developed for addressing dynamic dislocation behavior by Xiong et al. (2011), permits dislocations to propagate in a continuum domain that employs a piecewise continuous finite element description with interelement displacement discontinuities. The method avoids ghost forces at interface between atomistically resolved and coarse-grained domains. CAC has subsequently been used to investigate complex dislocation behavior in face-centered cubic (FCC) metals (Xiong et al., 2012b,a,c, 2015). In this paper, we propose a quasistatic 3-D method to carry out sequential energy-minimized simulations at 0 K. This facilitates study of structure evolution along minimum energy pathways, avoiding over-driven conditions of high rate molecular dynamics. Parallelization steps in code implementation are described. Applications are presented for the quasistatic CAC method in FCC metal plasticity. Comparisons are made with a fully-resolved atomistic method for generalized stacking fault energy, core structure and stress field of a single 60° mixed type dislocation, surface indentation, and 60° mixed type dislocation migration through the interface between atomistic and coarse-grained domains. It is shown that 3-D CAC simulations are useful in substantially reducing the number of degrees of freedom while preserving key characteristics of dislocation structure, stacking faults, and plasticity, including the net Burgers vector and long range fields of interacting dislocations.