Finite element analysis of an atomistically derived cohesive model for brittle fracture

Abstract

In order to apply information from molecular dynamics (MD) simulations in problems governed by engineering length and time scales, a coarse graining methodology must be used. In previous work by Zhou et al (2009 Acta Mater. 57 4671–86), a traction-separation cohesive model was developed using results from MD simulations with atomistic-to-continuum measures of stress and displacement. Here, we implement this cohesive model within a combined finite element/cohesive surface element framework (referred to as a finite element approach or FEA), and examine the ability for the atomistically informed FEA to directly reproduce results from MD. We find that FEA shows close agreement of both stress and crack opening displacement profiles at the cohesive interface, although some differences do exist that can be attributed to the stochastic nature of finite temperature MD. The FEA methodology is then used to study slower loading rates that are computationally expensive for MD. We find that the crack growth process initially exhibits a rate-independent relationship between crack length and boundary displacement, followed by a rate-dependent regime where, at a given amount of boundary displacement, a lower applied strain rate produces a longer crack length. Our method is also extended to larger length scales by simulating a compact tension fracture-mechanics specimen with sub-micrometer dimensions. Such a simulation shows a computational speedup of approximately four orders of magnitude over conventional atomistic simulation, while exhibiting the expected fracture-mechanics response. Finally, differences between FEA and MD are explored with respect to ensemble and temperature effects in MD, and their impact on the cohesive model and crack growth behavior. These results enable us to make several recommendations to improve the methodology used to derive cohesive laws from MD simulations. In light of this work, which has critical implications for efforts to derive continuum laws from MD simulations, it is shown care must be taken when using a similar approach, and effects of ensemble, temperature and strain rate must be considered.