Continuum mechanics of crack blunting on the atomic scale: elastic solutions

In order to improve upon continuum models for understanding the origins of ductile versus brittle response in materials, an accurate assessment of the stress fields near a crack tip must be developed. Existing continuum models have considered the crack tip to be perfectly sharp in order to use convenient analytical solutions for the stress fields around the crack tip. Numerous experimental observations have indicated that an atomically sharp crack is very rare and that crack tip blunting can precede or accompany crack propagation. A two-dimensional finite element model has been developed to evaluate the stress fields at a blunted crack tip subjected to loading. Stress fields have been calculated for mode I loading as well as for the self-stress due to the presence of a dislocation near a crack tip. These calculated stress fields have been compared with analytical solutions for appropriate limiting cases.