Dynamic cleavage in ductile materials

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R. M. Thomson Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received 24 September 1985; accepted 11 December 1985) Ductile materials are found to sustain brittle fracture when the crack moves at high speed. This fact poses a paradox under current theories of dislocation emission, because even at high velocities, these theories predict ductile behavior. A theoretical treatment of time-dependent emission and cleavage is given which predicts a critical velocity above which cleavage can occur without emission. Estimates suggest that this velocity is in the neighborhood of the sound velocity. The paper also discusses the cleavage condition under mixed mode loading, and concludes that the cleavage condition involves solely the mode I loading, with possible sonic emission under such loadings.

I. INTRODUCTION There exists an extensive literature discussing the criteria for whether a given material can support an atomically sharp crack.1"5 In addition, there is also substantial evidence that such materials as the soft fee metals are not able to sustain atomically sharp cracks without breaking down by dislocation emission,6"8 while other classes of materials can.9 At the same time there is growing experimental evidence that sharp cleavage cracks do operate in the softest materials when they move dynamically. This evidence is perhaps most sharply exhibited by the stress corrosion experiments in brass and copper single crystals.10-11 In these experiments the corrodent apparently embrittles a small region near the crack tip, where the crack begins to propagate. When this crack meets the ductile medium, it is apparently moving at a very fast speed and progresses dynamically through the ductile medium for typical distances of the order of 10 /xm. Careful exploration of the surface chemistry at the crack tips in these experiments appears to rule out the possibility that more than a few atomic layers at the crack tip are embrittled by the corrodent and confirms that the fast moving cleavage crack indeed traverses the ductile medium. Although the stress corrosion experiments seem to be the most clear-cut evidence for dynamic propagation of brittle cracks in ductile media, there is supporting evidence in thin-film microscopy experiments as well. For example, Wilsdorf7 has published results for a crack progressing through ductile thin films by homogeneous hole initiation and growth. He finds that when a new hole initiates, it does so as a dynamically propagating brittle crack, which grows for a distance of some tens of microns, after which it stops and opens by dislocation

emission and blunting. Similarly, Ohr 6 has observed in his thin-film geometry that when the crack opens by mode I in the thicker portions of the specimen, limited dynamic propagation again takes place as a sharp brittle crack in materials where the same cracks clearly emit dislocations easily when they are static. In addition to these simple experiments, the wellknown ductile/brittle transition in ste