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Journal of Applied Mechanics | Volume 82 | Issue 12 | research-article
Research Papers

A Simple Physically Based Phenomenological Model for the Strengthening/Softening Behavior of Nanotwinned Copper

[+] Author and Article Information
X. Zhang

School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: xuzhang85@126.com

A. E. Romanov

International Laboratory of Modern
Functional Materials,
ITMO University,
St. Petersburg 199034, Russia
e-mail: alexey.romanov@niuitmo.ru

E. C. Aifantis

School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, China;International Laboratory of Modern
Functional Materials,
ITMO University,
St. Petersburg 199034, Russia;Michigan Technological University,
Houghton, MI 49931;Laboratory of Mechanics and Materials,
Aristotle University,
Thessaloniki 54124, Greece
e-mail: mom@mom.gen.auth.gr

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 21, 2015; final manuscript received August 11, 2015; published online September 10, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(12), 121005 (Sep 10, 2015) (8 pages) Paper No: JAM-15-1377; doi: 10.1115/1.4031291 History: Received July 21, 2015; Revised August 11, 2015
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A robust phenomenological model based on a modified size-dependent Voce-type constitutive equation is proposed to describe the dependence of strength on twin thickness, for nanotwinned copper (nt-Cu) polycrystals, in agreement with experiments and related atomistic simulations. A gradient plasticity argument is employed to determine the critical nanotwin thickness where the transition from Hall–Petch (HP) hardening to inverse Hall–Petch (IHP) softening occurs. Strain rate and temperature effects are also discussed. The proposed constitutive equation may be used for engineering design purposes by controlling the interplay between grain size and twin thickness.
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References

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Figures

Grahic Jump Location
Fig. 1

The fit of the various size-dependent true stress–strain curves for nt-Cu specimens with varying twin thicknesses. The modified size-dependent Voce model employed was based on Eqs. (7) and (8) with the unique set of the parameter values used for all curves given in Table 1: (a) twin thickness is the same as that reported in Ref. [1] and (b) slightly modified twin thickness.

+The fit of the various size-dependent true stress–strain curves for nt-Cu specimens with varying twin thicknesses. The modified size-dependent Voce model employed was based on Eqs. (7) and (8) with the unique set of the parameter values used for all curves given in Table 1: (a) twin thickness is the same as that reported in Ref. [1] and (b) slightly modified twin thickness.
View Large  |  Save Figure  |  Download Slide (.ppt)
The fit of the various size-dependent true stress–strain curves for nt-Cu specimens with varying twin thicknesses. The modified size-dependent Voce model employed was based on Eqs. (7) and (8) with the unique set of the parameter values used for all curves given in Table 1: (a) twin thickness is the same as that reported in Ref. [1] and (b) slightly modified twin thickness.
Grahic Jump Location
Fig. 2

Schematic illustration of the different deformed zones of a representative twin lamella comprised of a TBAZ, a PTL, and an EC

+Schematic illustration of the different deformed zones of a representative twin lamella comprised of a TBAZ, a PTL, and an EC
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic illustration of the different deformed zones of a representative twin lamella comprised of a TBAZ, a PTL, and an EC
Grahic Jump Location
Fig. 3

Comparison between the theoretical predictions and experimental measurements for the size-dependent initial yield stress of nt-Cu specimens with varying twin thicknesses

+Comparison between the theoretical predictions and experimental measurements for the size-dependent initial yield stress of nt-Cu specimens with varying twin thicknesses
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison between the theoretical predictions and experimental measurements for the size-dependent initial yield stress of nt-Cu specimens with varying twin thicknesses
Grahic Jump Location
Fig. 4

Comparison between the theoretical predictions and results obtained from the experiments (d = 500 nm) and molecular dynamic simulations (d = 10 nm, 20 nm, and 70 nm) for the twin thickness-dependent yield strength of nt-Cu specimens

+Comparison between the theoretical predictions and results obtained from the experiments (d = 500 nm) and molecular dynamic simulations (d = 10 nm, 20 nm, and 70 nm) for the twin thickness-dependent yield strength of nt-Cu specimens
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison between the theoretical predictions and results obtained from the experiments (d = 500 nm) and molecular dynamic simulations (d = 10 nm, 20 nm, and 70 nm) for the twin thickness-dependent yield strength of nt-Cu specimens

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