The effects of crack blunting upon the competition between dislocation nucleation and atomic decohesion were examined here by using continuum methods. It was assumed that the crack geometry was elliptical; thus ensuring that the stress fields were available in closed form. These stress field solutions were then used to calculate the thresholds for dislocation nucleation and atomic decohesion. A Peierls-type framework was used to obtain the threshold for dislocation nucleation, where the region of the slip plane ahead of the crack developed a distribution of slip discontinuities before nucleation. This slip distribution increased as the applied load was increased, until an instability condition was reached and the governing integral equation could no longer be solved. The calculations were carried out for various crack-tip geometries in order to determine the effects of crack-tip blunting. The thresholds for atomic decohesion were calculated by using a cohesive zone model, in which the region of the crack front developed a distribution of opening displacements before atomic decohesion. Loading the elliptical crack tip eventually resulted in an instability which marked the onset of crack advance. These calculations were carried out for various crack-tip geometries. The result of these separate calculations were presented as critical energy release rates versus crack tip radius of curvature, for a given crack length. The 2 threshold curves were compared simultaneously in order to determine which failure mode was energetically most likely at various crack-tip curvatures. From these comparisons, 4 possible types of material fracture behavior were identified: intrinsically brittle, quasi-brittle, intrinsically ductile, and quasi-ductile.

The Effect of Crack Blunting on the Competition between Dislocation Nucleation and Cleavage. L.L.Fischer, G.E.Beltz: Journal of the Mechanics and Physics of Solids, 2001, 49[3], 635-54