The limiting grain size dependence of the strength of a polycrystalline aggregate

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Abstract
Recent experiments on high strength steel having a very fine microstructure have been interpreted in terms of the Petch relationship with the apparent dislocation pile-up lengths as small as 85 Å. For this reason, the behaviour of such small dislocation pile-ups has been examined theoretically. The results indicate that the Petch relation can be extended in a modified way to these extremely small grain sizes, e.g. < 50 Å. The main point is that for a small number of straight dislocations, the discontinuous nature of the Petch relation is important because each dislocation has a significant influence upon the stress concentrating character of the pile-up.