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Research Papers

# Shear Deformation Behavior of Copper Nanocrystals Under Imposed Hydrostatic Stress

[+] Author and Article Information
Shreevant Tiwari

School of Materials Science and Engineering,
Georgia Institute of Technology,
771 Ferst Drive NW,
Atlanta, GA 30332
e-mail: stiwari3@gatech.edu

David L. McDowell

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
801 Ferst Drive NW,
Atlanta, GA 30332
School of Materials Science and Engineering,
Georgia Institute of Technology,
771 Ferst Drive NW,
Atlanta, GA 30332

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 18, 2015; final manuscript received June 13, 2015; published online June 30, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(9), 091011 (Sep 01, 2015) (11 pages) Paper No: JAM-15-1261; doi: 10.1115/1.4030853 History: Received May 18, 2015; Revised June 13, 2015; Online June 30, 2015

## Abstract

In this research, we have employed molecular dynamics (MD) simulations to computationally explore the effects of hydrostatic stress on the shear deformation behavior of nanocrystalline (NC) Cu, over a range of grain size (5–20 nm) and temperature (10–500 K). Simulated nanocrystals were deformed under shear with superimposed isotropic tensile/compressive hydrostatic stress $σ∧$ of magnitude up to 5 GPa. The results suggest that the shear strength increases under imposed compressive $σ∧$, and decreases under imposed tensile $σ∧$, by around 0.05–0.09 GPa for every GPa of imposed hydrostatic pressure. At 300 K, we computed activation volumes (3.5–9 b3) and activation energies (0.2–0.3 eV), with values agreeing with those reported in previous experimental and theoretical work, notwithstanding the extreme deformation rates imposed in MD simulations. Additionally, we observed that shear deformation under an imposed compressive hydrostatic stress tends to slightly increase both the activation volumes and the energy activation barrier. Finally, no discernible pressure effect could be observed on the distribution of inelastic shear strain.

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## Figures

Fig. 1

(a) Snapshot of g = 10 nm NC Cu microstructure, prior to any deformation. The GBAZ is shown in dark blue, and the numbered regions denote grain interiors. (b) A snapshot of atoms that constitute the GB separating grains 1 and 5 in the g = 10 nm structure, with non-12 coordinated interface atoms shown in blue, and atoms with fcc coordination shown in red (see online version for color).

Fig. 2

Effect of imposed hydrostatic pressure (GPa) on the GSFE curve for slip along the {111}〈112〉 slip system in Cu

Fig. 3

A deformed configuration (γyz = 0.04) of the g = 20 nm structure, showing GB-mediated dislocation nucleation with no imposed hydrostatic pressure. To reveal individual dislocation loops, a cross section has been taken normal to the z-direction, and all locally fcc atoms have been hidden from view. Three to four leading partial dislocation loops (white arrows) are seen to nucleate from GB sources in grain #3 (dashed line).

Fig. 6

Evolution of σ¯, computed over the entire g = 5 nm structure, with global shear strain (γyz). Each plot in (a)–(c) corresponds to a different deformation temperature (T). The legend in plots (a)–(c) denotes imposed hydrostatic pressure (σ∧) in GPa. In (d), the yield stresses σ¯Y (the peak stresses in plots (a)–(c)) are plotted for different temperatures with respect to σ∧.

Fig. 4

Evolution of σ¯ in the interior of grain 3, plotted with respect to the global shear strain γyz. Each plot corresponds to a different grain size (g) and deformation temperature (T). The legend in each plot denotes imposed hydrostatic pressure in GPa.

Fig. 5

Evolution of σ¯, computed over the region GB{1/5} (see Fig. 1(b)), with global shear strain. Each plot corresponds to a different grain size (g) and deformation temperature (T). The legend in each plot denotes imposed hydrostatic pressure in GPa.

Fig. 8

Activation volume (Ω), athermal activation energy barrier (Q*), and activation energy (Q) of shear deformation as a function of imposed hydrostatic stress σ∧. Results have been shown for two grain sizes: (a) g = 5 nm and (b) g = 20 nm.

Fig. 7

Evolution of σ¯, computed over the entire g = 20 nm structure, with global shear strain (γyz). Each plot in (a)–(c) corresponds to a different deformation temperature (T). The legend in plots (a)–(c) denotes imposed hydrostatic pressure (σ∧) in GPa. In (d), the yield stresses σ¯Y (the peak stresses in plots (a)–(c)) are plotted for different temperatures with respect to σ∧.

Fig. 9

The distribution of per-atom total ((a)–(c)) and inelastic von Mises strains (ɛ¯in/atom) ((d)–(f)) in microstructures that were deformed at a temperature of 10 K under different imposed hydrostatic pressures, to a total shear strain of γyz = 0.1. The imposed hydrostatic pressure (in GPa) is shown in the legend of each plot. Note that plots (c) and (f) compare hydrostatic pressures of 0 and 5 GPa, since the g = 20 nm microstructure developed a void before the shear strain reached the value of 0.1 under an imposed hydrostatic stress of −5 GPa.

Fig. 10

The distribution of per-atom total ((a)–(c)) and inelastic von Mises strains (ɛ¯in/atom) ((d)–(f)) in microstructures that were deformed at a temperature of 500 K under different imposed hydrostatic pressures, to a total shear strain of γyz=0.1. The imposed hydrostatic pressure (in GPa) is shown in the legend of each plot.

Fig. 11

Evidence of the dislocation nucleation mechanism proposed by Asaro and Suresh [36], where a shear stress τ in the plane of a GB initiates sliding, leading to the formation of stacking fault in an adjacent grain. A section of the g = 10 nm microstructure, at global strain γyz = 0.045, showing a concentration in the atomic strain field inside grain 3 (dashed circle), arising from the GB sliding event between grains 5 and 7.

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