Crack, Dislocation Free Zone, and Dislocation Pile-Up Model for the Behavior of the Hall-Petch Relation in the Range of Ultrafine Grain Sizes
In order to elucidate the failure of the linear dependence of the yield stress of polycrystalline metals on the grain size in the range of ultrafine grain sizes, we propose the dislocation pile-up model which consists of a crack, a dislocation free zone (DFZ), and the slip band blocked at the grain boundary.
Analyzing the above model by the method of the continuously distributed theory of dislocations, we get the analytical expression which gives the relationship between the macroscopic applied stress and the grain size D. It can be shown that the behavior of the macroscopic yield stress versus D −1/2 explains the experimental result well. Applicability of this model to the grain-size dependence of the fracture stress of engineering ceramics will also be discussed.
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- Armstrong, R. W. (1983), The yield and flow stress dependence on polycrystal grain size, in Yield, Flow and Fracture of Polycrystals, edited by T. N. Baker, Applied Science, London and New York, p. 1.Google Scholar
- Bilby, B. A. and Eshelby, J. D. (1968), Dislocations and the theory of fracture, in Fracture, 1, edited by H. Liebowitz, Academic Press, New York, p. 99.Google Scholar
- Kobayashi, S. and Ohr, S. M. (1980), In situ fracture experiments in B.C.C. metals, Phil. Mag., A42, 763–772.Google Scholar
- Li, J. C. M. (1981), Dislocation sources, in Dislocation Modelling of Physical Systems, edited by M. F. Ashby, R. Bullough, C. S. Hartley, and J. P. Hirth, Pergamon, New York, p. 498.Google Scholar
- Mura, T. (1982), Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague, p. 427.Google Scholar
- Nishida, T. (1988), Ceramics no Zeisei Hakai, Zairyou Kagaku, 24, 165–171 (in Japanese).Google Scholar