Grain-size dependence of the flow stress of Cu from millimeters to nanometers
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8/11/04
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Grain-Size Dependence of the Flow Stress of Cu from Millimeters to Nanometers HANS CONRAD Data in the literature on the effect of grain size (d) from millimeters to nanometers on the flow stress of Cu are evaluated. Three grain-size regimes are identified: regime I, d 106 m; regime II, d 108 to 106 m; and regime III, d 108 m. Grain-size hardening occurs in regimes I and II; grain-size softening occurs in regime III. The deformation structure in regime I consists of dislocation cells; in regime II, the dislocations are mostly restricted to their slip planes; in regime III, computer simulations indicate that dislocations are absent and that deformation occurs by the shearing of grain-boundary atoms. The transition from regime I to II occurs when the dislocation cell size becomes larger than the grain size, and the transition from regime II to III occurs when the dislocation spacing due to elastic interactions becomes larger than the grain size. The rate-controlling mechanism in regime I is concluded to be the intersection of dislocations; in regime II, it is proposed to be grain-boundary shear promoted by the pileup of dislocations; in regime III, it appears to be grain-boundary shear by the applied stress alone.
I. INTRODUCTION
IT is well known, through the many articles by Armstrong,[1] that the mechanical properties of crystalline materials are dependent on the grain size. In recent years there has developed a renewed interest in this subject, especially regarding the properties of materials with a submicron grain size. Of special interest has been the behavior in the nanocrystalline range where grain-size softening, i.e., a so called inverse Hall–Petch (H–P) effect, has been reported (Reference 2). Since most previous models for the effect of grain size on the flow stress of metals were developed based on behavior in the micron range, it seemed desirable to review the data over the wide range from millimeters to nanometers, with special attention to the governing physical mechanisms. This, then, is the objective of the present article. The material considered here is Cu tested at low homologeous temperatures (T 0.3 TM), relatively small strains ( 20 pct), and conventional strain rates (· 105 to 103 s1). Prior work by the present author on the general subject matter of this article is given in References 2 through 6. The present article draws on, and develops further, the concepts in the earlier study on Cu.[5] II. ANALYSIS A. General The effect of grain size (d) on the flow stress () of metals is generally considered in terms of the H–P equation:[7,8] s si KHP d 1/2
[1]
HANS CONRAD is Professor Emeritus with the Materials Science and Engineering Department, North Carolina State University, Raleigh, NC 27695-7907. Contact e-mail: [email protected] This article is based on a presentation given in the symposium “Dynamic Deformation: Constitutive Modeling, Grain Size, and Other Effects: In Honor of Prof. Ronald W. Armstrong,” March 2–6, 2003, at the 20
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