Grain boundary energies and cohesive strength as a function of geometry

TL;DR

This paper investigates how grain boundary energies and cohesive laws vary with geometry, revealing discontinuities at rational repeat distances, and introduces a dislocation-based model to describe these phenomena.

Contribution

It demonstrates that cohesive laws are discontinuous functions of grain boundary geometry and develops a dislocation decoration model to describe energy cusps and fracture toughness.

Findings

Cohesive laws are discontinuous at rational grain boundary repeat distances.

A dislocation decoration model captures energy cusps at high symmetry boundaries.

Asymptotic fracture toughness near discontinuities is characterized.

Abstract

Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract grain boundary energies and cohesive laws of grain boundary fracture in 2D with a Lennard-Jones potential for all possible geometries which can be simulated within periodic boundary conditions with a maximum box size. We introduce a model where grain boundaries are represented as high symmetry boundaries decorated by extra dislocations. Using it, we develop a functional form for the symmetric grain boundary energies, which have cusps at all high symmetry angles. We also find the asymptotic form of the fracture toughness near the discontinuities at high symmetry grain boundaries using our dislocation decoration model.