A comparison of finite element and atomistic modelling of fracture

TL;DR

This study compares atomistic and finite element models of fracture in silicon polycrystals, revealing that cohesive laws alone are insufficient for accurate continuum modeling due to atomic-scale effects.

Contribution

It provides a detailed methodology for deriving cohesive laws from atomistic simulations and highlights the limitations of cohesive zone models in polycrystal fracture.

Findings

Atomistic simulations fracture at lower stress levels.

Atomic-scale irregularities influence fracture initiation.

Cohesive laws alone do not fully capture fracture behavior.

Abstract

Are the cohesive laws of interfaces sufficient for modelling fracture in polycrystals using the cohesive zone model? We examine this question by comparing a fully atomistic simulation of a silicon polycrystal to a finite element simulation with a similar overall geometry. The cohesive laws used in the finite element simulation are measured atomistically. We describe in detail how to convert the output of atomistic grain boundary fracture simulations into the piecewise linear form needed by a cohesive zone model. We discuss the effects of grain boundary microparameters (the choice of section of the interface, the translations of the grains relative to one another, and the cutting plane of each lattice orientation) on the cohesive laws and polycrystal fracture. We find that the atomistic simulations fracture at lower levels of external stress, indicating that the initiation of fracture in the atomistic simulations is likely dominated by irregular atomic structures at external faces, internal edges, corners, and junctions of grains. Thus, cohesive properties of interfaces alone are likely not sufficient for modelling the fracture of polycrystals using continuum methods.