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.
Issue Section:
Research Papers
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
.Copyright © 2016 by ASME
You do not currently have access to this content.
