Abstract
Continuum concepts are used to evaluate the competition between crack advance and dislocation nucleation at the tip of a crack having a finite tip curvature. The analysis reveals that the favorability of crack propagation versus dislocation emission depends upon the bluntness of the crack tip. One implication is that a crack may initially emit dislocations only to reinitiate cleavage upon reaching a sufficiently blunted tip geometry. The present framework is used to classify crystals as intrinsically ductile or brittle in terms of the unstable stacking energy, the surface energy, and the peak cohesive stresses achieved during opening and shear of the atomic planes.
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