Nonlocal effects of existing dislocations on crack-tip emission and cleavage

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Abstract
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, kIIe. The nonlocal shift varies with the sum, Σ(γusdj)−3/2, over each dislocation (j), where γus 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 (γusd)−1. 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.
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