Correlation between the Deformation of Nanostructured Materials and the Model of Dislocation Accommodated Boundary Slidi
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Very recently, a new model for deformation in nanocrystalline (nc) materials has been developed.[1] The development of the model was based on the concept that plasticity in nc materials is the result of grain boundary sliding accommodated by the generation and motion of dislocations under local stresses,[1,2] which are higher than applied stresses due to the development of stress concentrations.* Specifically, it has been assumed *A large-scale application of Molecular Dynamics and finite simulation modeling has shown[2] that the occurrence of boundary sliding leads to redistributing applied stresses and that this distribution can produce local stresses several times higher than applied stresses.
that as a result of sliding of a group of grains, the shear stress becomes concentrated at any grain, triple point, or protrusion that obstructs motion of this group; that this local high stress can then generate dislocations in the blocking grain (or initiate voids); and that the generated dislocations move one by one to the opposite boundary where they climb to their annihilation sites (no dislocation-ups). By postulating that the creep rate, c_ , is governed by the time for the climb of a dislocation along the boundary until annihilation occurs, the following rate-controlling equation was derived:[1]
FARGHALLI A. MOHAMED, Professor, is with the Department of Chemical Engineering and Materials Science, University of California, Irvine, CA 92697-2575, USA. Contact e-mail: famohame@ uci.edu Manuscript submitted April 12, 2007. Article published online December 21, 2007 470—VOLUME 39A, FEBRUARY 2008
c_ ¼ 9
3 b Dgbo Qgb 2Ms b3 exp exp 1 d RT kT b2 ½1a
where b is the Burgers vector, d is the grain size, Dgbo is the frequency factor for grain boundary diffusion, R is the gas constant, Qgb is the activation energy for grain boundary diffusion, M is a stress concentration factor, which may depend on variables such as temperature, s is the applied shear stress, T is the absolute temperature, and k is Boltzmanns constant. The definition of the apparent activation volume, m, is given by @ ln c_ ½1b v ¼ kT @s Applying the previous definition of the apparent to Eq. [1a] leads to the following: m = 2Mb3. On this basis, Eq. [1a] can be written as 3 s v i b Dgbo Qgb h 1 ½1c exp exp c_ ¼ 9 d kT RT b2 The predictions of the model, as represented by Eqs. [1a] and [1c], were found to be consistent with the characteristics of deformation behavior in electrodeposited nc-Ni that was studied[1] over more than five orders of magnitude of strain rate (10-9 s-1 to 2 · 10-4 s-1) at 393 K. In particular, there was agreement between predictions and experimental data on nc-Ni with regard to the magnitudes of creep rates, the variation of the stress exponent with applied stress, the decrease in the apparent activation energy with applied stress, the apparent activation volume, and the grain size sensitivity. The present investigation was undertaken to examine whether Eq. [1c] can describe the deformation behav
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