Effect of atomic crack tip geometry on local stresses

The results of a molecular dynamic investigation, designed to explore the sensitivity of the crack tip stress distribution to changes in crack length and crack tip geometry (shape) on the atomic scale, are described. The simulation was carried out on a two-dimensional sample of 10704 atoms arranged in a triangular lattice and interacting with a Lennard-Jones (6-12) or a Johnson potential. Surprisingly, no significant difference in the stress distribution was observed between narrow (sharp) and wide (blunt) cracks. However, wide cracks with irregularly shaped tips (termed the wide jagged crack) displayed appreciably lower stresses in the near tip region. The magnitude of the maximum stress concentration (at the tip, i.e. at r = 0) was about a factor of ten lower than that predicted by classical continuum treatments of elliptically shaped cracks. For cracks of length 2a at distances r from the crack tip the results of the simulations in the 0.1 < r a < 1.5 range are in good agreement with stresses predicted by the continuum elastic theory of elliptical cracks. The lack of variation in the stress distribution in going from narrow to wide cracks suggests that there is an effective radius of the crack tip controlling the magnitude of the stresses. The simulation results indicate that the discreteness of the lattice limits the degree of geometric blunting-at least within the size scale readily accessible with the present simulations. Conventional continuum analysis was found to account for the functional dependence of stress on crack length but not the magnitude of the stresses, whereas the nonlocal theory of Eringen was found to account for the order of magnitude of the stresses but not the functional dependence.