Geometrically necessary dislocations induced size effect in the torsional stress relaxation behavior of thin metallic wires

doi:10.1016/j.scriptamat.2019.08.002

Scripta Materialia

Volume 173, December 2019, Pages 129-133

https://doi.org/10.1016/j.scriptamat.2019.08.002 Get rights and content

Abstract

Torsional stress relaxation experiments on thin copper wires are performed. A size effect is observed. That is a faster relaxation deformation arises in a thinner wire. As the wire diameter increases, the activation volume increases but the strain rate sensitivity decreases. A greater effect of geometrically necessary dislocations on the relaxation deformation accounts for the size effect. In a thinner wire, geometrically necessary dislocations undergo fewer obstacles to reach the wire center and then neutralize, causing a more rapid evolution of mobile dislocations.

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Acknowledgement

This work is financially supported by the National Natural Science Foundation of China (Nos. 11772138, 11702103 and 11472114). We thank School of Mechanical Science and Engineering of HUST for performing the FIB measurement, and Analytical and Testing Center of HUST for performing the EBSD measurement.

References (36)

L. Lu et al.
Acta Mater.
(2009)
X.S. Yang et al.
Acta Mater.
(2016)
X.S. Yang et al.
J. Mech. Phys. Solids
(2016)
H. Hirakata et al.
Acta Mater.
(2012)
I.C. Choi et al.
Int. J. Plast.
(2013)
R. Gu et al.
Int. J. Plast.
(2014)
S. Guo et al.
Int. J. Plast.
(2019)
S. Guo et al.
Mater. Sci. Eng. A
(2017)
D. Liu et al.
Scr. Mater.
(2012)
S. Guo et al.
Scr. Mater.
(2017)

N. Fleck et al.

Acta Metall. Mater.

(1994)

J.S. Stölken et al.

Acta Mater.

(1998)

D. Liu et al.

Int. J. Plast.

(2013)

D. Liu et al.

Int. J. Plast.

(2017)

G. Saada et al.

Mater. Sci. Eng. A

(1997)

E.W. Hart

Acta Metall.

(1970)

M. Haque et al.

Acta Mater.

(2003)

I. Hayashi et al.

J. Mech. Phys. Solids

(2011)

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Dislocations can be classified as geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) [1]. During plastic deformation, GNDs are formed and act as barriers to mobile dislocations, i.e. strain hardening of metals [2]. To understand the behavior of dislocations, different methods such as transmission electron microscopy (TEM), X-ray diffraction (XRD), and electron backscattering diffraction (EBSD) have been used [3,4].
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Torsion of thin metallic wires has been one of the most fundamental approaches to characterizing the mechanical behavior of small volumes since the pioneering work by Fleck and co-authors [8]. On the basis of this, the torsional behavior of thin wire has attracted more and more attention, including size effect [6–8,19], Bauschinger effect [5,20], torsional stress relaxation [21–23]. However, the torsional cyclic hardening/softening and mean stress relaxation behaviors of thin wire have not been studied yet.
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Geometrically necessary dislocations induced size effect in the torsional stress relaxation behavior of thin metallic wires

Abstract

Graphical abstract

Section snippets

Acknowledgement

Acta Mater.

Acta Mater.

J. Mech. Phys. Solids

Acta Mater.

Int. J. Plast.

Int. J. Plast.

Int. J. Plast.

Mater. Sci. Eng. A

Scr. Mater.

Scr. Mater.

Acta Metall. Mater.

Acta Mater.

Int. J. Plast.

Int. J. Plast.

Mater. Sci. Eng. A

Acta Metall.

Acta Mater.

J. Mech. Phys. Solids