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

Abstract

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.

Effect of finite crack length and blunting on dislocation nucleation in mode III

“…Moreover, the geometry under consideration is artificial in that the antiplane deformation associated with prior screw dislocation activity would nor blunt a crack. Work in progress by Fischer and Beltz (1998) confirms that more applicable in-plane models (i.e. for dislocations with edge components in bodies loaded under Mode I) give identical trends, as well as the fact that conditions for cleavage also become less favourable as the crack blunts.…”

“…The mode I11 stress fields were derived using antiplane elasticity. Fischer and Beltz (1997) stress fields of a similar blunt crack tip under mode I loading. In both cases, the stress fields of blunted cracks were shown to deviate moderately from those of sharp cracks, especially at length scales of interest away from the tip.…”

Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel

“…The reduction of sharpness at the crack tip by providing a radius or blunting of crack tip increases the force required to propagate it (Schiøtz et al, 1996(Schiøtz et al, , 1997. Some conditions have been stipulated to predict whether a sharp crack tip will blunt leading to a ductile fracture, or continue to cleave in a brittle fashion (Fischer and Beltz, 1997). Many models for investigating ductile versus brittle response have been based on an analysis of a sharp crack.…”