Strength softening and stress relaxation of nanostructured materials
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NTRODUCTION
IT has long been accepted that dislocations emitted from Frank–Read sources and/or grain boundaries are the carriers for the plastic deformation of coarse-grained polycrystalline materials.[1,2] When a dislocation slips from the grain interior to the grain boundaries, the grain boundaries with a high-angle orientation will stop the dislocation from traveling across them, since crystallographic factors will not allow the dislocation transmission from one grain to an adjacent one through the grain boundary. This process will lead to dislocation pileups at grain boundaries, which embodies the well-known pileup mechanism for the plastic deformation of polycrystalline materials. In this framework, the presence of grain boundaries can effectively strengthen a material by hindering the dislocation motion, and the grain boundary itself is the source for the dislocation nucleation. On the basis of this dislocation pileup mechanism, the flow strength () of a material is inversely proportional to the square root of the grain size (d), i.e., s s0 kd 1/2
[1]
where 0 and k are material constants. Equation [1] is the well-known Hall–Petch relation,[3,4] which was found to hold for a wide range of polycrystalline materials with grain sizes ranging from a millimeter down to the submicrometer range. Recently, the applicability of Eq. [1] in the case of nanocrystalline (NC) materials (e.g., grain sizes typically less than 100 nm) has raised some interesting questions, given the fact that in this regime, the grain size is comparable to the grain-boundary width (w).[5,6] There are several reasons that may be used to argue that Eq. [1] may not be valid in the case of NC materials. First, the size of a Frank–Read source for the dislocation nucleation would become larger than the grain size, when the grain size is reduced to a nanometer scale, implying that the accumulation of dislocations would become difficult for NC materials.[7]
G.J. FAN, Researcher, H. CHOO, Assistant Professor, and P.K. LIAW, Professor, are with the Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37516. Contact e-mail: [email protected] E.J. LAVERNIA, Professor, is with the University of California, Davis, CA 95616. Manuscript submitted January 27, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
In contrast to coarse-grained polycrystals, dislocations are, therefore, source-limited for NC materials, implying that dislocation pileups at grain boundaries are unlikely in the case of NC materials. Published experimental results have already indicated a deviation from the Hall–Petch relation with a relatively lower k value in Eq. [1], when the grain sizes are reduced from the micrometer to nanometer range.[8,9,10] Second, when the grain size is comparable to the grain-boundary width, the grain-boundary contribution to the overall plasticity needs to be taken into account, which is typically safely neglected in the case of coarse-grained polycrystals. Finally, the obvious limitation of Eq. [1] stems from the obviou
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