The e'ect of crack blunting on the competition between dislocation nucleation and cleavage

To better understand the ductile versus brittle fracture behavior of crystalline materials, attention should be directed towards physically realistic crack geometries. Currently, continuum models of ductile versus brittle behavior are typically based on the analysis of a pre-existing sharp crack in order to use analytical solutions for the stress 8elds around the crack tip. This paper examines the e'ects of crack blunting on the competition between dislocation nucleation and atomic decohesion using continuum methods. We accomplish this by assuming that the crack geometry is elliptical, which has the primary advantage that the stress 8elds are available in closed form. These stress 8eld solutions are then used to calculate the thresholds for dislocation nucleation and atomic decohesion. A Peierls-type framework is used to obtain the thresholds for dislocation nucleation, in which the region of the slip plane ahead of the crack develops a distribution of slip discontinuity prior to nucleation. This slip distribution increases as the applied load is increased until an instability is reached and the governing integral equation can no longer be solved. These calculations are carried out for various crack tip geometries to ascertain the e'ects of crack tip blunting. The thresholds for atomic decohesion are calculated using a cohesive zone model, in which the region of the crack front develops a distribution of opening displacement prior to atomic decohesion. Again, loading of the elliptical crack tip eventually results in an instability, which marks the onset of crack advance. These calculations are carried out for various crack tip geometries. The results of these separate calculations are presented as the critical energy release rates versus the crack tip radius of curvature for a given crack length. The two threshold curves are compared simultaneously to determine which failure mode is energetically more likely at various crack tip curvatures. From these comparisons, four possible types of material fracture behavior are identi8ed: intrinsically brittle, quasi-brittle, intrinsically ductile, and quasi-ductile. Finally, real material examples are discussed. c © 2001 Elsevier Science Ltd. All rights reserved.