Effect of crack geometry on dislocation nucleation and cleavage thresholds

A continuum model based upon the Peierls-Nabarro description of a dislocation ahead of a crack is used to evaluate the critical mode I loading for dislocation nucleation at the tip of a finite, pre-blunted crack. A similar approach is used to evaluate the critical mode I loading for atomic decohesion. Results are presented for various crack tip root radii (a measure of bluntness), for several crack lengths. It is shown that increasing the crack length increases the critical energy release rate for both material behaviors. Increasing the bluntness of a crack tip always increases the required loading for atomic decohesion but nucleation thresholds are initially decreased by very small increases in crack tip bluntness. Nucleation thresholds are later increased after reaching significant crack tip blunting. Implications for ductile versus brittle competition are discussed by comparing the ongoing competition between these two different material behaviors.