Nonlocal effects of existing dislocations on crack-tip emission and cleavage
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Robb Thomson Laboratory for Materials Science and Engineering, National Institute of Standards and Technology, Building 223, Room B309, Gaithersburg, Maryland 20899 (Received 19 August 1993; accepted 10 November 1993)
This paper investigates the criterion for a ductile-to-brittle transition in materials, due to nonlocal shielding effects at the crack tip when the dislocation free zone (DFZ) size is small. It is found that both cleavage and emission criteria are altered by nonlocal shielding, but that the emission shift is dominant, and is always in the direction to increase the local critical stress intensity for emission, kUe- The nonlocal shift varies with the sum, 2(yust//-)~3/2> over each dislocation (_/), where y us is the unstable stacking fault energy, and dj is the distance from each dislocation to the crack tip. When there is a pileup of many shielding dislocations against a barrier near the crack tip, the total shift for the pileup varies as (yusd)~l. The most likely candidates for a brittle transition induced by the nonlocal shift are materials where barriers to dislocation motion exist within 10-100 nanometers of the crack tip, such as in thin films, multilayers, or ultrafine grain materials.
I. INTRODUCTION The purpose of this paper is to understand how existing dislocations in the vicinity of a crack tip affect cleavage and nucleation of dislocations from that crack tip. This issue is motivated by TEM observations of crack tips that initially emit profuse numbers of dislocations, but with continued loading, eventually begin to propagate through the material.1 Associated with the transition process is a substantial pileup and entanglement of dislocations ahead of the crack tip. Such microscopic observations are qualitatively consistent with the more macroscopic practice of applying a fatigue load in order to work-harden the region in front of a blunt notch and eventually grow a sharp crack through it. Earlier work2 envisaged that macroscopic ductileto-brittle transitions may be controlled by whether dislocation sources other than the crack tip operate and effectively shield the crack. In such cases, an inherently brittle crack may not cleave as long as non-cracktip sources provide sufficient shielding, but may begin to cleave when the external sources are shut down and can no longer provide sufficient shielding. Other work3 considers situations in which shielding produced by continued crack-tip dislocation emission produces changes in local (crack tip) stress intensity factors that favor cleavage. The above approaches are based on a local theory, in which dislocation emission and cleavage occur when a critical combination of local stress intensity factors 812
http://journals.cambridge.org
J. Mater. Res., Vol. 9, No. 3, Mar 1994
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lie outside of emission and cleavage surfaces, respectively. In particular, the local stress intensity factors are defined as: ka=KaKDa, a = l, II, III, (1) where Ka is the remote stress intensity factor, and K% is the shielding stress intensity fac
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