Modern techniques of severe plastic deformation (SPD) used as a means for grain refinement in metallic materials rely on simple shear as the main deformation mode. Prediction of the mechanical properties of the processed materials under tensile loading is a formidable task as commonly no universal, strain path independent constitutive laws are available. In this paper, we derive an analytical relation that makes it possible to predict the mechanical response to uniaxial tensile loading for a material that has been preprocessed by simple shear and, as a result, has developed a linear strain gradient. A facile recipe for mechanical tests on solid bars required for this prediction to be made is proposed. As a trial, it has been exercised for the case of commercial purity copper rods. The method proposed is recommended for design with metallic materials that underwent preprocessing by simple shear.

References

1.
Valiev
,
R. Z.
, and
Langdon
,
T. G.
,
2010
, “
The Art and Science of Tailoring Materials by Nanostructuring for Advanced Properties Using SPD Techniques
,”
Adv. Eng. Mater.
,
12
(
8
), pp.
677
691
.
2.
Estrin
,
Y.
, and
Vinogradov
,
A. V.
,
2013
, “
Extreme Grain Refinement by Severe Plastic Deformation: A Wealth of Challenging Science
,”
Acta Mater.
,
61
(
3
), pp.
782
817
.
3.
Tome
,
C.
,
Canova
,
G. R.
,
Kocks
,
U. F.
,
Christodoulou
,
N.
, and
Jonas
,
J. J.
,
1984
, “
The Relation Between Macroscopic and Microscopic Strain Hardening in F.C.C. Polycrystals
,”
Acta Metall.
,
32
(
10
), pp.
1637
1653
.
4.
Ungar
,
T.
,
Toth
,
L. S.
,
Illy
,
J.
, and
Kovacs
,
I.
,
1986
, “
Dislocation-Structure and Work Hardening in Polycrystalline OFHC Copper Rods Deformed by Torsion and Extension
,”
Acta Metall.
,
34
(
7
), pp.
1257
1267
.
5.
Fields
,
D. S.
, Jr.
, and
Backofen
,
W. A.
,
1957
, “
Determination of Strain Hardening Characteristics by Torsion Testing
,”
Proc. ASTM
,
57
, pp.
1259
1272
.
6.
Ilyushin
,
A. A.
, and
Lensky
,
V. S.
,
1967
,
Strength of Materials
,
Pergamon Press
,
Oxford
, UK.
7.
Bell
,
J.
, and
Khan
,
A. S.
,
1980
, “
Finite Plastic Strain in Annealed Copper During Non-Proportional Loading
,”
Int. J. Solids Struct.
,
16
(
8
), pp.
683
693
.
8.
Delobelle
,
P.
,
Robinet
,
P.
,
Geyer
,
P.
, and
Bouffioux
,
P.
,
1996
, “
A Model to Describe the Anisotropic Viscoplastic Behaviour of Zircaloy-4 Tubes
,”
J. Nucl. Mater.
,
238
(
2–3
), pp.
135
162
.
9.
Takahashi
,
H.
,
Fujiwara
,
K.
, and
Nakagawa
,
T.
,
1998
, “
Multiple-Slip Work-Hardening Model in Crystals With Application to Torsion-Tension Behaviors of Aluminium Tubes
,”
Int. J. Plast.
,
14
(
6
), pp.
489
509
.
10.
Khan
,
A. S.
, and
Liang
,
R.
,
2000
, “
Behaviors of Three BCC Metals During Non-Proportional Multi-Axial Loadings: Experiments and Modeling
,”
Int. J. Plast.
,
16
(
12
), pp.
1443
1458
.
11.
Faleskog
,
J.
, and
Barsoum
,
I.
,
2013
, “
Tension-Torsion Fracture Experiments—Part I: Experiments and a Procedure to Evaluate the Equivalent Plastic Strain
,”
Int. J. Solids Struct.
,
50
(
25–26
), pp.
4241
4257
.
12.
Mehrabi
,
R.
,
Andani
,
M. T.
,
Kadkhodaei
,
M.
, and
Elahinia
,
M.
,
2015
, “
Experimental Study of NiTi Thin-Walled Tubes Under Uniaxial Tension, Torsion, Proportional and Non-Proportional Loadings
,”
Exp. Mech.
,
55
(
6
), pp.
1151
1164
.
13.
Kachanov
,
L. M.
,
1971
,
Foundations of the Theory of Plasticity
,
North-Holland Publishing Co., Amsterdam
,
The Netherlands
, pp.
123
144
.
14.
Jonas
,
J. J.
,
Montheillet
,
F.
, and
Shrivastava
,
S.
,
1985
, “
The Elastic Unloading of Torsion Bars Subjected to Prior Plastic Deformation
,”
Scr. Metall.
,
19
(
2
), pp.
235
240
.
15.
Valiev
,
R. Z.
,
Estrin
,
Y.
,
Horita
,
Z.
,
Langdon
,
T. G.
,
Zehetbauer
,
M. J.
, and
Zhu
,
Y. T.
,
2006
, “
Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation
,”
JOM
,
58
(
4
), pp.
33
39
.
16.
Montheillet
,
F.
,
Cohen
,
M.
, and
Jonas
,
J. J.
,
1984
, “
Axial Stresses and Texture Development During the Torsion Testing of Al, Cu and Alpha-Fe
,”
Acta Metall.
,
32
(
11
), pp.
2077
2089
.
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