ATOMISTIC SIMULATIONS OF MATERIALS FRACTURE AND THE LINK BETWEEN ATOMIC AND CONTINUUM LENGTH SCALES

The macroscopic fracture response of real materials originates from th e competition and interplay of several atomic-scale mechanisms of deco hesion and shear, such as interplanar cleavage and dislocation nucleat ion 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 m odeling 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 mechanic s, in a ''top-down'' approach; and (3) by defining a set of variables common to atomistic simulations and continuum mechanics and feeding th e results of atomistic simulations into continuum-mechanics models in the form of constitutive relations, For this latter approach we discus s in detail the issues crucial to ensuring the consistency of the atom istic results and continuum mechanics. A case study of the constitutiv e-relation approach is presented for the problem of dislocation nuclea tion from a crack tip in a crystal under stress; a comparison of the r esults of atomistic simulations to the Peierls-Nabarro continuum model is made.