Crack, Dislocation Free Zone, and Dislocation Pile-Up Model for the Behavior of the Hall-Petch Relation in the Range of Ultrafine Grain Sizes

  • K. Saito
  • M. Iwamoto
  • Y. Nomura
  • T. Nakamura

Abstract

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.

Keywords

Brittle 

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References

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • K. Saito
    • 1
  • M. Iwamoto
    • 1
  • Y. Nomura
    • 1
  • T. Nakamura
    • 2
  1. 1.Department of Mechanical and System EngineeringKyoto Institute of TechnologySakyo-ku, KyotoJapan
  2. 2.Technical Research LaboratoryToyo Umpanki, Co., Ltd.Ibaraki 301Japan

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