Dislocation emission at ledges on cracks
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I. INTRODUCTION
A number of years ago, one of us coauthored a paper on the emission condition for dislocations from cracks, and suggested that the condition for intrinsic brittleness in a material would be when the criterion for spontaneous emission is more than the criterion for Griffith cleavage.1 When a crack is intrinsically brittle in this sense, i.e., stable against spontaneous emission, then it was proposed that it would still be possible for dislocations to be emitted by thermal fluctuations in a thermally activated manner. At that time, we estimated that such activated events would be difficult in nearly all intrinsically brittle materials because the activation energy was estimated to be too high. We use the term "intrinsic" here to emphasize the fact that we are dealing with an intrinsic homogeneous property of the crack in the given material, and not with dislocation formation at sources outside the core region of the crack. Although the general ideas proposed in that paper have proved useful, there have been extensive reports that emission in a variety of brittle materials is an easy process. Perhaps the earliest observation of dislocations apparently being emitted from cracks in a brittle material were those by Gilman et al.2 for dislocations associated with arrested cracks in LiF. More strikingly, experiments on Si stretching back to the early work of St. John3 and more recent work carried out in a number of laboratories4"7 have shown that dislocations are emitted easily from this very brittle material in spite of our early estimate of 111 ev. for the activation energy. Other observations by Hockey reported in Lawn et al} show numerous events which are probably dislocation
emission from cracks in Si, A12O3, and MgO. In none of the above experiments was the critical stress intensity for emission, ke, measured, however. Chia and Burns9 were apparently the first to call attention to the large discrepancy between the critical stress for emission in Ref. 1 and the observed low measured values which they reported in LiF. Their experimental values for ke are a factor of approximately 5 lower than the theoretical value. Finally, recent experiments by Gerberich et al.10 in NaCl also confirm easy dislocation emission in that system at stress intensity factors considerably lower than those derived from Ref. 1. In sharp contrast to this work, however, is the classic in situ work by Ohr and coworkers11 with thin films oriented in Mode III. In this case, dislocations are emitted at ke values which are consistent with the estimates of Ref. 1. In unpublished work just before his death, Ohr has privately confirmed this result through later, more careful, measurements. The absence of additional reports of actual stress intensity measurements associated with dislocation emission is regrettable, but understandable because of the very considerable experimental difficulties in making such measurements. On the theoretical side, Haasen12 has suggested that one reason why the dislocation activation energy in Si may be low
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