This paper presents a double-slip/double-twin polycrystal plasticity model using finite element solution to investigate the kinetics of deformation twinning of medium manganese (Mn) twinning-induced plasticity (TWIP) steels. Empirical equations are employed to estimate the stacking fault energy (SFE) of TWIP steels and the critical resolved shear stress (CRSS) for dislocation slip and deformation twinning, respectively. The results suggest that the evolution of twinning in Fe–xMn–1.4Al–0.6 C (x = 11.5, 13.5, 15.5, 17.5, and 19.5 mass%) TWIP steels, and its relation to the Mn content, can explain the effect of Mn on mechanical properties. By comparing the double-slip/double-twin model to a double-slip model, the predicted results essentially reveal that the interaction behavior between dislocation slip and deformation twinning can lead to an additional work hardening. Also, numerical simulations are carried out to study the influence of boundary conditions on deformation behavior and twin formation. The nucleation and growth of twinning are found to depend on internal properties (e.g., mismatch orientation of grains and stress redistribution) as well as on external constraints (e.g., the applied boundary conditions) of the material.
Issue Section:
Research Papers
Keywords:
Constitutive relations,
Mechanical behavior,
Metals,
Microstructure property relationships,
Plastic behavior,
Polymers,
Ceramics,
Intermetallics,
Composites
Topics:
Deformation,
Steel,
Stress,
Twinning,
Boundary-value problems,
Shear (Mechanics),
Plasticity
References
1.
Shen
, F.
, Zhou
, J.
, Liu
, Y.
, Zhu
, R.
, Zhang
, S.
, and Wang
, Y.
, 2010
, “Deformation Twinning Mechanism and Its Effects on the Mechanical Behaviors of Ultra-fine Grained and Nanocrystalline Copper
,” Comput. Mater. Sci.
, 49
(2
), pp. 226
–235
.10.1016/j.commatsci.2010.04.0442.
Meyers
, M. A.
, Vöhringer
, O.
, and Lubarda
, V. A.
, 2001
, “The Onset of Twinning in Metals: A Constitutive Description
,” Acta Mater.
, 49
(19
), pp. 4025
–4039
.10.1016/S1359-6454(01)00300-73.
Kim
, J.
, Lee
, S.-J.
, and De Cooman
, B. C.
, 2011
, “Effect of Al on the Stacking Fault Energy of Fe-18Mn-0.6C Twinning-Induced Plasticity
,” Scr. Mater.
, 65
(4
), pp. 363
–366
.10.1016/j.scriptamat.2011.05.0144.
Van Houtte
, P
., 1978
, “Simulation of the Rolling and Shear Texture of Brass by the Taylor Theory Adapted for Mechanical Twinning
,” Acta Metall.
, 26
(4
), pp. 591
–604
.10.1016/0001-6160(78)90111-65.
Choi
, S. H.
, Kim
, D. W.
, Seong
, B. S.
, and Rollett
, A. D.
, 2011
, “3-D Simulation of Spatial Stress Distribution in an AZ31 Mg Alloy Sheet Under In-Plane Compression
,” Int. J. Plast.
, 27
(10
), pp. 1702
–1720
.10.1016/j.ijplas.2011.05.0146.
Thamburaja
, P.
, Pan
, H.
, and Chau
, F. S.
, 2009
, “The Evolution of Microstructure During Twinning: Constitutive Equations, Finite-Element Simulations and Experimental Verification
,” Int. J. Plast.
, 25
(11
), pp. 2141
–2168
.10.1016/j.ijplas.2009.02.0047.
Wang
, H.
, Wu
, P. D.
, Wang
, J.
, and Tomé
, C. N.
, 2013
, “A Crystal Plasticity Model for Hexagonal Close Packed (HCP) Crystals Including Twinning and De-Twinning Mechanisms
,” Int. J. Plast.
, 49
, pp. 36
–52
.10.1016/j.ijplas.2013.02.0168.
Prakash
, A.
, Weygand
, S. M.
, and Riedel
, H.
, 2009
, “Modeling the Evolution of Texture and Grain Shape in Mg Alloy AZ31 Using the Crystal Plasticity Finite Element Method
,” Comput. Mater. Sci.
, 45
(3
), pp. 744
–750
.10.1016/j.commatsci.2008.06.0159.
Clayton
, J. D.
, 2011
, Nonlinear Mechanics of Crystals
, Springer, Dordrecht
, The Netherlands
, pp. 379
–421
.10.
Wang
, J.
, Beyerlein
, I. J.
, Hirth
, J. P.
, and Tomé
, C. N.
, 2011
, “Twinning Dislocations on and Planes in Hexagonal Close-Packed Crystals
,” Acta Mater.
, 59
(10
), pp. 3990
–4001
.10.1016/j.actamat.2011.03.02411.
Yan
, K.
, Carr
, D. G.
, Callaghan
, M. D.
, Liss
, K.-D.
, and Li
, H.
, 2010
, “Deformation Mechanisms of Twinning-Induced Plasticity Steels: In Situ Synchrotron Characterization and Modeling
,” Scr. Mater.
, 62
(5
), pp. 246
–249
.10.1016/j.scriptamat.2009.11.00812.
Wang
, Y. Y.
, Sun
, X.
, Wang
, Y. D.
, Hu
, X. H.
, and Zbib
, H. M.
, 2014
, “A Mechanism-Based Model for Deformation Twinning in Polycrystalline FCC Steel
,” Mater. Sci. Eng. A
, 607
, pp. 206
–218
.10.1016/j.msea.2014.04.01013.
Suzuki
, H.
, and Barrett
, C. S.
, 1958
, “Deformation Twinning in Silver-Gold Alloys
,” Acta Metall.
, 6
(3
), pp. 156
–165
.10.1016/0001-6160(58)90002-614.
Salem
, A. A.
, Kalidindi
, S. R.
, and Semiatin
, S. L.
, 2005
, “Strain Hardening Due to Deformation Twinning in Alpha-Titanium: Constitutive Relations and Crystal-Plasticity Modeling
,” Acta Mater.
, 53
(12
), pp. 3495
–3502
.10.1016/j.actamat.2005.04.01415.
Saeed-Akbari
, A.
, Imlau
, J.
, Prahl
, U.
, and Bleck
, W.
, 2009
, “Derivation and Variation in Composition-Dependent Stacking Fault Energy Maps Based on Subregular Solution Model in High-Manganese Steels
,” Metall. Mater. Trans. A
, 40
(13
), pp. 3076
–3090
.10.1007/s11661-009-0050-816.
Soulami
, A.
, Choi
, K. S.
, Shen
, Y. F.
, Liu
, W. N.
, Sun
, X.
, and Khaleel
, M. A.
, 2011
, “On Deformation Twinning in a 17.5%Mn–TWIP Steel: A Physically Based Phenomenological Model
,” Mater. Sci. Eng. A
, 528
(3
), pp. 1402
–1408
.10.1016/j.msea.2010.10.03117.
Gutierrez-Urrutia
, I.
, Zaefferer
, S.
, and Raabe
, D.
, 2010
, “The Effect of Grain Size and Grain Orientation on Deformation Twinning in a Fe-22wt.%Mn-0.6wt.%C TWIP Steel
,” Mater. Sci. Eng. A
, 527
(15
), pp. 3552
–3560
.10.1016/j.msea.2010.02.04118.
Wei
, Y
., 2011
, “Scaling of Maximum Strength With Grain Size in Nanotwinned FCC Metals
,” Phys. Rev. B
, 83
(13
), p. 132104
.10.1103/PhysRevB.83.13210419.
de las Cuevas
, F.
, Reis
, M.
, Ferraiuolo
, A.
, Pratolongo
, G.
, Karjalainen
, L. P.
, Alkorta
, J.
, and Gil Sevillano
, J.
, 2010
, “Hall-Petch Relationship of a TWIP Steel
,” Key Eng. Mater.
, 423
, pp. 147
–152
.10.4028/www.scientific.net/KEM.423.14720.
Babu
, S. S.
, Specht
, E. D.
, David
, S. A.
, Karapetrova
, E.
, Zschack
, P.
, Peet
, M.
, and Bhadeshia
, H. K. D. H.
, 2005
, “In-Situ Observations of Lattice Parameter Fluctuations in Austenite and Transformation to Bainite
,” Metall. Mater. Trans. A
, 36
(12
), pp. 3281
–3289
.10.1007/s11661-005-0002-x21.
Allain
, S.
, Chateau
, J. P.
, Bouaziz
, O.
, Migot
, S.
, and Guelton
, N.
, 2004
, “Correlations Between the Calculated Stacking Fault Energy and the Plasticity Mechanisms in Fe-Mn-C Alloys
,” Mater. Sci. Eng. A
, 387–389
, pp. 158
–162
.10.1016/j.msea.2004.01.05922.
Mayama
, T.
, Aizawa
, K.
, Tadano
, Y.
, and Kuroda
, M.
, 2009
, “Influence of Twinning Deformation and Lattice Rotation on Strength Differential Effect in Polycrystalline Pure Magnesium With Rolling Texture
,” Comput. Mater. Sci.
, 47
(2
), pp. 448
–455
.10.1016/j.commatsci.2009.09.00923.
Peirce
, D.
, Asaro
, R. J.
, and Needleman
, A.
, 1983
, “Material Rate Dependence and Localized Deformation in Crystalline Solids
,” Acta Metall.
, 31
(12
), pp. 1951
–1976
.10.1016/0001-6160(83)90014-724.
Walde
, T.
, and Riedel
, H.
, 2007
, “Modeling Texture Evolution During Hot Rolling of Magnesium Alloy AZ31
,” Mater. Sci. Eng. A
, 443
(1–2
), pp. 277
–284
.10.1016/j.msea.2006.09.02825.
Jin
, Z. H.
, Gumbsch
, P.
, Ma
, E.
, Albe
, K.
, Lu
, K.
, Hahn
, H.
, and Gleiter
, H.
, 2006
, “The Interaction Mechanism of Screw Dislocations With Coherent Twin Boundaries in Different Face-Centred Cubic Metals
,” Scr. Mater.
, 54
(6
), pp. 1163
–1168
.10.1016/j.scriptamat.2005.11.07226.
Sleeswyk
, A. W.
, and Helle
, J. N.
, 1963
, “Ductile Cleavage Fracture, Yielding and Twinning in Alpha-Iron
,” Acta Metall.
, 11
(3
), pp. 187
–194
.10.1016/0001-6160(63)90211-627.
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
.10.1016/S1359-6454(99)00383-328.
Curtze
, S.
, and Kuokkala
, V. T.
, 2010
, “Dependence of Tensile Deformation Behavior of TWIP Steels on Stacking Fault Energy, Temperature and Strain Rate
,” Acta Mater.
, 58
(15
), pp. 5129
–5141
.10.1016/j.actamat.2010.05.04929.
Kibey
, S.
, Liu
, J. B.
, Johnson
, D. D.
, and Sehitoglu
, H.
, 2007
, “Predicting Twinning Stress in FCC Metals: Linking Twin-Energy Pathways to Twin Nucleation
,” Acta Mater.
, 55
(20
), pp. 6843
–6851
.10.1016/j.actamat.2007.08.04230.
Kim
, J.
, Estrin
, Y.
, and Cooman
, B.
, 2013
, “Application of a Dislocation Density-Based Constitutive Model to Al-Alloyed TWIP Steel
,” Metall. Mater. Trans. A
, 44
(9
), pp. 4168
–4182
.10.1007/s11661-013-1771-231.
Sun
, X.
, Choi
, K. S.
, Liu
, W. N.
, and Khaleel
, M. A.
, 2009
, “Predicting Failure Modes and Ductility of Dual Phase Steels Using Plastic Strain Localization
,” Int. J. Plast.
, 25
(10
), pp. 1888
–1909
.10.1016/j.ijplas.2008.12.01232.
Choi
, K. S.
, Liu
, W. N.
, Sun
, X.
, and Khaleel
, M. A.
, 2009
, “Microstructure-Based Constitutive Modeling of TRIP Steel: Prediction of Ductility and Failure Modes Under Different Loading Conditions
,” Acta Mater.
, 57
(8
), pp. 2592
–2604
.10.1016/j.actamat.2009.02.02033.
Xia
, Z.
, Zhang
, Y.
, and Ellyin
, F.
, 2003
, “A Unified Periodical Boundary Conditions for Representative Volume Elements of Composites and Applications
,” Int. J. Solids Struct.
, 40
(8
), pp. 1907
–1921
.10.1016/S0020-7683(03)00024-634.
Kouznetsova
, V.
, Brekelmans
, W. A. M.
, and Baaijens
, F. P. T.
, 2001
, “An Approach to Micro-Macro Modeling of Heterogeneous Materials
,” Comput. Mech.
, 27
(1
), pp. 37
–48
.10.1007/s004660000212Copyright © 2015 by ASME
You do not currently have access to this content.
