A new multiscale modeling approach is proposed to predict the contributions of dynamic strain aging (DSA) and the resulting negative strain rate sensitivity (NSRS) on the unusual strain-hardening response of Hadfield steel (HS). Mechanical response of HS was obtained from monotonic and strain rate jump experiments under uniaxial tensile loading within the 10−4 to 10−1 s−1 strain rate range. Specifically, a unique strain-hardening model was proposed that incorporates the atomic-level local instabilities imposed upon by the pinning of dislocations by diffusing carbon atoms to the classical Voce hardening. The novelty of the current approach is the computation of the shear stress contribution imposed on arrested dislocations leading to DSA at the atomic level, which is then implemented to the overall strain-hardening rule at the microscopic level. The new model not only successfully predicts the role of DSA and the resulting NSRS on the macroscopic deformation response of HS but also opens the venue for accurately predicting the deformation response of rate-sensitive metallic materials under any given loading condition.

References

References
1.
Dastur
,
Y. N.
, and
Leslie
,
W. C.
,
1981
, “
Mechanism of Work Hardening in Hadfield Manganese Steel
,”
Metall. Trans. A
,
12
(
5
), pp.
749
759
.
2.
Adler
,
P. H.
,
Olson
,
G. B.
, and
Owen
,
W. S.
,
1986
, “
Strain Hardening of Hadfield Manganese Steel
,”
Metall. Trans. A
,
17
(
10
), pp.
1725
1737
.
3.
Efstathiou
,
C.
, and
Sehitoglu
,
H.
,
2010
, “
Strain Hardening and Heterogeneous Deformation During Twinning in Hadfield Steel
,”
Acta Mater.
,
58
(
5
), pp.
1479
1488
.
4.
Karaman
,
I.
,
Sehitoglu
,
H.
,
Gall
,
K.
,
Chumlyakov
,
Y. I.
, and
Maier
,
H. J.
,
2000
, “
Deformation of Single Crystal Hadfield Steel by Twinning and Slip
,”
Acta Mater.
,
48
(
6
), pp.
1345
1359
.
5.
Canadinc
,
D.
,
Sehitoglu
,
H.
,
Maier
,
H. J.
, and
Chumlyakov
,
Y. I.
,
2005
, “
Strain Hardening Behavior of Aluminum Alloyed Hadfield Steel Single Crystals
,”
Acta Mater.
,
53
(
6
), pp.
1831
1842
.
6.
Feng
,
X. Y.
,
Zhang
,
F. C.
,
Yang
,
Z. N.
, and
Zhang
,
M.
,
2013
, “
Wear Behaviour of Nanocrystallised Hadfield Steel
,”
Wear
,
305
(
1–2
), pp.
299
304
.
7.
Atabaki
,
M. M.
,
Jafari
,
S.
, and
Abdollah-Pour
,
H.
,
2012
, “
Abrasive Wear Behavior of High Chromium Cast Iron and Hadfield Steel—A Comparison
,”
J. Iron Steel Res. Int.
,
19
(
4
), pp.
43
50
.
8.
Kang
,
J.
,
Zhang
,
F. C.
,
Long
,
X. Y.
, and
Lv
,
B.
,
2014
, “
Cyclic Deformation and Fatigue Behaviors of Hadfield Manganese Steel
,”
Mater. Sci. Eng. A
,
591
, pp.
59
68
.
9.
Petrov
,
Y. N.
,
Gavriljuk
,
V. G.
,
Berns
,
H.
, and
Schmalt
,
F.
,
2006
, “
Surface Structure of Stainless and Hadfield Steel After Impact Wear
,”
Wear
,
260
(
6
), pp.
687
691
.
10.
Efstathiou
,
C.
, and
Sehitoglu
,
H.
,
2009
, “
Strengthening Hadfield Steel Welds by Nitrogen Alloying
,”
Mater. Sci. Eng. A
,
506
(
1–2
), pp.
174
179
.
11.
Canadinc
,
D.
,
2005
, “
A Detailed Investigation of the Strain Hardening Response of Aluminum Alloyed Hadfield Steel
,” Ph.D. thesis, University of Illinois at Urbana-Champaign, Champaign, IL.
12.
Owen
,
W. S.
, and
Grujicic
,
M.
,
1999
, “
Strain Aging of Austenitic Hadfield Manganese Steel
,”
Acta Mater.
,
47
(
1
), pp.
111
126
.
13.
Raghavan
,
K. S.
,
Sastri
,
A. S.
, and
Marcinkowski
,
M. J.
,
1969
, “
Nature of the Work-Hardening Behavior in Hadfield's Manganese Steel
,”
Trans Metall. Soc. AIME
,
245
, pp.
1569
1575
.
14.
Karaman
,
I.
,
Sehitoglu
,
H.
,
Beaudoin
,
A. J.
,
Chumlyakov
,
Y. I.
,
Maier
,
H. J.
, and
Tome
,
C. N.
,
2000
, “
Modeling the Deformation Behavior of Hadfield Steel Single and Polycrystals Due to Twinning and Slip
,”
Acta Mater.
,
48
(
9
), pp.
2031
2047
.
15.
Karaman
,
I.
,
Sehitoglu
,
H.
,
Chumlyakov
,
Y. I.
,
Maier
,
H. J.
, and
Kireeva
,
I. V.
,
2001
, “
The Effect of Twinning and Slip on the Bauschinger Effect of Hadfield Steel Single Crystals
,”
Metall. Mater. Trans. A
,
32
(
13
), pp.
695
706
.
16.
Karaman
,
I.
,
Sehitoglu
,
H.
,
Chumlyakov
,
Y.
,
Maier
,
H.
, and
Kireeva
,
I.
,
2001
, “
Extrinsic Stacking Faults and Twinning in Hadfield Manganese Steel Single Crystals
,”
Scr. Mater.
,
44
(
2
), pp.
337
343
.
17.
Shtremel
,
M. A.
, and
Kovalenko
,
I. A.
,
1987
, “
On the Work Hardening Mechanism of Hadfield Steel
,”
Phys. Met. Metall.
,
63
, pp.
158
166
.
18.
Canadinc
,
D.
,
Sehitoglu
,
H.
, and
Maier
,
H. J.
,
2007
, “
The Role of Dense Dislocation Walls on the Deformation Response of Aluminum Alloyed Hadfield Steel Polycrystals
,”
Mater. Sci. Eng. A
,
454–455
, pp.
662
666
.
19.
Canadinc
,
D.
,
Efstathiou
,
C.
, and
Sehitoglu
,
H.
,
2008
, “
On the Negative Strain Rate Sensitivity of Hadfield Steel
,”
Scr. Mater.
,
59
(
10
), pp.
1103
1106
.
20.
Cottrell
,
A. H.
, and
Bilby
,
B. A.
,
1948
, “
Dislocation Theory of Yielding and Strain Ageing of Iron
,”
Proc. Phys. Soc. Lond. A
,
49
(
62
), pp.
49
62
.
21.
Cottrell
,
A. H.
, and
Jaswon
,
M. A.
,
1949
, “
Distribution of Solute Atoms Round a Slow Dislocation
,”
Proc. R. Soc. A
,
199
(
1056
), pp.
104
114
.
22.
Huang
,
Z. Y.
,
Chaboche
,
J.-L.
,
Wang
,
Q. Y.
,
Wagner
,
D.
, and
Bathias
,
C.
,
2014
, “
Effect of Dynamic Strain Aging on Isotropic Hardening in Low Cycle Fatigue for Carbon Manganese Steel
,”
Mater. Sci. Eng. A
,
589
, pp.
34
40
.
23.
van Den Brink
,
S. H.
,
Van Den Beukel
,
A.
, and
McCormick
,
P. G.
,
1975
, “
Strain Rate Sensitivity and the Portevin-Le Chatelier Effect in Au–Cu Alloys
,”
Phys. Status Solidi
,
30
(
2
), pp.
469
477
.
24.
Louat
,
N.
,
1981
, “
On the Theory of the Portevin-Le Châtelier Effect
,”
Scr. Metall.
,
15
(
11
), pp.
1167
1170
.
25.
McCormick
,
P. G.
,
1988
, “
Theory of Flow Localisation Due to Dynamic Strain Ageing
,”
Acta Metall.
,
36
(
12
), pp.
3061
3067
.
26.
Estrin
,
Y.
, and
McCormick
,
P. G.
,
1991
, “
Modelling the Transient Flow Behaviour of Dynamic Strain Ageing Materials
,”
Acta Metall. Mater.
,
39
(
12
), pp.
2977
2983
.
27.
McCormick
,
P. G.
, and
Ling
,
C. P.
,
1995
, “
Numerical Modelling of the Portevin-Le Chatelier Effect
,”
Acta Metall. Mater.
,
43
(
5
), pp.
1969
1977
.
28.
Wang
,
C.
,
Li
,
Z.
,
Xu
,
Y.
, and
Han
,
E.
,
2007
, “
Acoustic Emission Inspection of Portevin-Le Chatelier Effect and Deformation Mechanisms of Two Mg-Li-Al Alloys
,”
J. Mater. Sci.
,
42
(
10
), pp.
3573
3579
.
29.
Renard
,
K.
,
Ryelandt
,
S.
, and
Jacques
,
P. J.
,
2010
, “
Characterisation of the Portevin-Le Châtelier Effect Affecting an Austenitic TWIP Steel Based on Digital Image Correlation
,”
Mater. Sci. Eng. A
,
527
(
12
), pp.
2969
2977
.
30.
Chmelík
,
F.
,
Klose
,
F. B.
,
Dierke
,
H.
,
Šachl
,
J.
,
Neuhäuser
,
H.
, and
Lukáč
,
P.
,
2007
, “
Investigating the Portevin-Le Châtelier Effect in Strain Rate and Stress Rate Controlled Tests by the Acoustic Emission and Laser Extensometry Techniques
,”
Mater. Sci. Eng. A
,
462
(1–2), pp.
53
60
.
31.
Yilmaz
,
A.
,
2011
, “
The Portevin–Le Chatelier Effect: A Review of Experimental Findings
,”
Sci. Technol. Adv. Mater.
,
12
(
6
), p.
063001
.
32.
van den Beukel
,
A.
,
1975
, “
Theory of the Effect of Dynamic Strain Aging on Mechanical Properties
,”
Phys. Status Solidi
,
30
(
1
), pp.
197
206
.
33.
Canadinc
,
D.
,
2001
, “
The Effect of Nitrogen and Aluminum on the Deformation Behavior of Hadfield Manganese Steel Single Crystals
,” M.S. thesis, University of Illinois at Urbana-Champaign, Champaign, IL.
34.
Kubin
,
L. P.
,
Estrin
,
Y.
, and
Perrier
,
C.
,
1992
, “
On Static Strain Ageing
,”
Acta Metall. Mater.
,
40
(
5
), pp.
1037
1044
.
35.
Ling
,
C. P.
, and
McCormick
,
P. G.
,
1990
, “
Strain Rate Sensitivity and Transient Behaviour in an Al Mg Si Alloy
,”
Acta Metall. Mater.
,
38
(
12
), pp.
2631
2635
.
36.
Soare
,
M. A.
, and
Curtin
,
W. A.
,
2008
, “
Single-Mechanism Rate Theory for Dynamic Strain Aging in fcc Metals
,”
Acta Mater.
,
56
(
15
), pp.
4091
4101
.
37.
Soare
,
M. A.
, and
Curtin
,
W. A.
,
2008
, “
Solute Strengthening of Both Mobile and Forest Dislocations: The Origin of Dynamic Strain Aging in fcc Metals
,”
Acta Mater.
,
56
(
15
), pp.
4046
4061
.
38.
Anjabin
,
N.
,
Taheri
,
A. K.
, and
Kim
,
H. S.
,
2013
, “
Simulation and Experimental Analyses of Dynamic Strain Aging of a Supersaturated Age Hardenable Aluminum Alloy
,”
Mater. Sci. Eng. A
,
585
, pp.
165
173
.
39.
Narayanan
,
S.
,
McDowell
,
D. L.
, and
Zhu
,
T.
,
2014
, “
Crystal Plasticity Model for BCC Iron Atomistically Informed by Kinetics of Correlated Kinkpair Nucleation on Screw Dislocation
,”
J. Mech. Phys. Solids
,
65
, pp.
54
68
.
40.
Friedel
,
J.
,
1964
,
Dislocations
,
Pergamon Press
,
Oxford, UK
.
41.
Kang
,
K.
,
Yin
,
J.
, and
Cai
,
W.
,
2014
, “
Journal of the Mechanics and Physics of Solids Stress Dependence of Cross Slip Energy Barrier for Face-Centered Cubic Nickel
,”
J. Mech. Phys. Solids
,
62
, pp.
181
193
.
42.
Springer
,
F.
,
Nortmann
,
A.
, and
Schwink
,
C.
,
1998
, “
A Study of Basic Processes Characterizing Dynamic Strain Ageing
,”
Phys. Status Solidi A
,
170
(
1
), pp.
63
81
.
43.
Ono
,
K.
,
1968
, “
Temperature Dependence of Dispersed Barrier Hardening
,”
J. Appl. Phys.
,
39
(
3
), pp.
1803
1806
.
44.
Peter
,
H.
,
1996
, “
On the Physics of the Portevin-Le Châtelier Effect—Part 1: The Statistics of Dynamic Strain Ageing
,”
Mater. Sci. Eng. A
,
207
(2), pp.
208
215
.
45.
Bayley
,
C. J.
,
Brekelmans
,
W. A. M.
, and
Geers
,
M. G. D.
,
2006
, “
A Comparison of Dislocation Induced Back Stress Formulations in Strain Gradient Crystal Plasticity
,”
Int. J. Solids Struct.
,
43
(
24
), pp.
7268
7286
.
46.
Vallée
,
C.
,
Fortuné
,
D.
, and
Lerintiu
,
C.
,
2008
, “
On the Dual Variable of the Cauchy Stress Tensor in Isotropic Finite Hyperelasticity
,”
C. R. Méc.
,
336
(
11–12
), pp.
851
855
.
47.
Bell
,
J. F.
,
1995
, “
Laboratory Experiments on Thin-Walled Tubes at Large Finite Strain: Symmetry, Coaxiality, Rigid Body Rotation, and the Role of Invariants, for the Applied Stress σ = RTRT, the Cauchy Stress σ* = [IIIV]−1FRT, and the Left Cauchy-Green Stretch Tensor
,”
Int. J. Plast.
,
11
(
1
), pp.
119
144
.
48.
Kalidindi
,
S. R.
,
Bronkhorst
,
C. A.
, and
Anand
,
L.
,
1992
, “
Crystallographic Texture Evolution in Bulk Deformation Processing of FCC Metals
,”
J. Mech. Phys. Solids
,
40
(
3
), pp.
537
569
.
49.
Patra
,
A.
,
Zhu
,
T.
, and
McDowell
,
D. L.
,
2014
, “
Constitutive Equations for Modeling Non-Schmid Effects in Single Crystal bcc-Fe at Low and Ambient Temperatures
,”
Int. J. Plast.
,
59
, pp.
1
14
.
50.
Jörn
,
H.
,
1999
, “
A Crystallographic Model for the Study of Local Deformation Processes in Polycrystals
,”
Int. J. Plast.
,
15
(6), pp.
605
624
.
51.
Evers
,
L. P.
,
Brekelmans
,
W. A. M.
, and
Geers
,
M. G. D.
,
2004
, “
Scale Dependent Crystal Plasticity Framework With Dislocation Density and Grain Boundary Effects
,”
Int. J. Solids Struct.
,
41
(
18–19
), pp.
5209
5230
.
52.
Sofronis
,
P.
, and
Birnbaum
,
H. K.
,
1995
, “
Mechanics of the Hydrogen-Dislocation-Impurity Interactions—Part I: Increasing Shear Modulus
,”
J. Mech. Phys. Solids
,
43
(
1
), pp.
49
90
.
53.
Voce
,
E.
,
1948
, “
The Relationship Between Stress and Strain for Homogeneous Deformation
,”
J. Inst. Met.
,
74
, pp.
537
562
.
54.
Canadinc
,
D.
,
Biyikli
,
E.
,
Niendorf
,
T.
, and
Maier
,
H. J.
,
2011
, “
Experimental and Numerical Investigation of the Role of Grain Boundary Misorientation Angle on the Dislocation–Grain Boundary Interactions
,”
Adv. Eng. Mater.
,
13
(
4
), pp.
281
287
.
55.
Onal
,
O.
,
Ozmenci
,
C.
, and
Canadinc
,
D.
,
2014
, “
Multi-Scale Modeling of the Impact Response of a Strain-Rate Sensitive High-Manganese Austenitic Steel
,”
Front. Mater.
,
1
, p.
16
.
56.
Canadinc
,
D.
,
Karaman
,
I.
,
Sehitoglu
,
H.
,
Chumlyakov
,
Y. I.
, and
Maier
,
H. J.
,
2003
, “
The Role of Nitrogen on the Deformation Response of Hadfield Steel Single Crystals
,”
Metall. Mater. Trans. A
,
34
(
9
), pp.
1821
1831
.
57.
Onal
,
O.
,
Bal
,
B.
,
Toker
,
S. M.
,
Mirzajanzadeh
,
M.
,
Canadinc
,
D.
, and
Maier
,
H. J.
,
2014
, “
Microstructure-Based Modeling of the Impact Response of a Biomedical Niobium–Zirconium Alloy
,”
J. Mater. Res.
,
29
(
10
), pp.
1123
1134
.
58.
Lebensohn
,
R. A.
, and
Tomé
,
C. N.
,
1993
, “
A Self-Consistent Anisotropic Approach for the Simulation of Plastic Deformation and Texture Development of Polycrystals: Application to Zirconium Alloys
,”
Acta Metall. Mater.
,
41
(
9
), p.
2611
.
59.
Canadinc
,
D.
,
Sehitoglu
,
H.
,
Maier
,
H. J.
, and
Kurath
,
P.
,
2008
, “
On the Incorporation of Length Scales Associated With Pearlitic and Bainitic Microstructures Into a Visco-Plastic Self-Consistent Model
,”
Mater. Sci. Eng. A
,
485
(1–2), p.
258
.
60.
Bishop
,
J. F. W.
, and
Hill
,
R.
,
1951
, “
XLVI. A Theory of the Plastic Distortion of a Polycrystalline Aggregate Under Combined Stresses
,”
Phil. Mag.
,
42
(
327
), pp.
414
427
.
You do not currently have access to this content.