Effect of Crack Blunting on Subsequent Crack Propagation

Abstract

Theories of toughness of materials depend on an understanding of the characteristic instabilities of the crack tip, and their possible interactions. In this paper we examine the effect of dislocation emission on subsequent cleavage of a crack and on further dislocation emission. The work is an extension of the previously published Lattice Greens Function methodology [1,2,3]. We have developed a Cavity Greens Function describing a blunt crack and used it to study the effect of crack blunting under a range of different force laws. As the crack is blunted, we find a small but noticeable increase in the crack loading needed to propagate the crack. This effect may be of importance in materials where a dislocation source near the crack tip in a brittle material causes the crack to absorb anti-shielding dislocations, and thus cause a blunting of the crack. It is obviously also relevant to cracks in more ductile materials where the crack itself may emit dislocations.

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

“…In most cases sharp crack has been considered to begin with. Schiøtz et al (1996Schiøtz et al ( , 1997 and Fischer and Beltz (2001) have reported the effects of crack tip radius on the brittle and ductile crack growth and extension. Recently, Hampton and Nelson (2003) have characterized the SCG through thin sheets in terms of CTOA and the results have been applied to predict the crack tearing and instability in pressurized cylinder of the same thickness.…”

“…They have used the elasticity solutions to solve for the thresholds to emit a fully formed dislocation on a slip plane intersecting the crack tip. 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).…”

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

“…The physical reality of a blunted crack configuration has motivated limited attempts at evaluating its effect and determining to what extent its stress fields differ from the sharp crack stress fields. Schiøtz [3,4] has tackled this problem using a conformal mapping technique. Using the Schwarz-Christoffel transformation, a simple 60 • blunted crack tip can be mapped to the upper complex half plane with z = x 1 + ix 2 .…”

“…However, this process is extremely calculation intensive and expensive if one wants to study a configuration of reasonable size. Recent work done on atomistic models developed by Schiøtz and co-workers [3,4], Gumbsch and co-workers [6,7], and Thomson [8] have provided partial motivation for the development of the model and specific geometry discussed in this paper.…”

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

“…More compelling support for this idea comes from atomistic studies of dislocation nucleation, which clearly show blunting at the atomic scale. Realistic crack tip geometries have received recent attention in the work of Schi0tz et al (1996Schi0tz et al ( , 1997, in which a blunt crack tip was conformally mapped to the upper half of the complex plane. The mode I11 stress fields were derived using antiplane elasticity.…”