An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem

TL;DR

This paper rigorously analyzes a 2D atomic spring model to understand how crystals fracture under tension, revealing universal cleavage behavior and conditions for crack formation and orientation.

Contribution

It provides a rigorous discrete-to-continuum analysis of crystal cleavage, identifying universal laws and detailed crack geometries in a 2D model.

Findings

Minimal energy leads to universal cleavage law

Cracks form along a unique hyperplane beyond critical load

Symmetric orientations may prevent cleavage

Abstract

A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that, in the discrete-to-continuum limit, the minimal energy of a crystal under uniaxial tension leads to a universal cleavage law and energy minimizers are either homogeneous elastic deformations or configurations that are completely cracked and do not store elastic energy. Beyond critical loading, the specimen generically cleaves along a unique optimal crystallographic hyperplane. For specific symmetric crystal orientations, however, cleavage might fail. In this case a complete characterization of possible limiting crack geometries is obtained.