Atomistic Simulations of Materials Fracture and the Link between Atomic and Continuum Length Scales

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Abstract
The macroscopic fracture response of real materials originates from the competition and interplay of several atomic‐scale mechanisms of decohesion and shear, such as inter‐planar cleavage and dislocation nucleation and motion. These phenomena involve processes over a wide range of length scales, from the atomic to the macroscopic. We briefly review the attempts to span these length scales in dislocation and fracture modeling by (1) fully atomistic large‐scale simulations of millions of atoms or more, approaching the continuum limit from the “bottom‐up”; (2) directly coupling atomic‐scale simulations and continuum mechanics, in a “top‐down” approach; and (3) by defining a set of variables common to atomistic simulations and continuum mechanics and feeding the results of atomistic simulations into continuum‐mechanics models in the form of constitutive relations. For this latter approach we discuss in detail the issues crucial to ensuring the consistency of the atomistic results and continuum mechanics. A case study of the constitutive‐relation approach is presented for the problem of dislocation nucleation from a crack tip in a crystal under stress; a comparison of the results of atom‐istic simulations to the Peierls–Nabarro continuum model is made.