This paper focuses on micromechanical finite element (FE) modeling of the effects of size and morphology (particularly elongation or aspect ratio (AR) along the loading direction) of martensite particles and the ferrite grains on the overall mechanical behavior of dual-phase (DP) steels. To capture the size-effect of the martensite particles and ferrite grains, the core and mantle approach is adapted in which a thin interphase of geometrically necessary dislocations (GNDs) is embedded at the martensite–ferrite boundaries. It is shown that as the martensite particles size decreases or their aspect ratio increases, both the strength and ductility of DP steel increase simultaneously. On the other hand, as the ferrite grain size decreases or its aspect ratio increases, the overall strength increases on the expense of the ductility. The conclusions from this study can be used in guiding the microstructural design of DP steels.

References

References
1.
Rashid
,
M.
,
1981
, “
Dual Phase Steels
,”
Annu. Rev. Mater. Sci.
,
11
(
1
), pp.
245
266
.
2.
Pierman
,
A. P.
,
Bouaziz
,
O.
,
Pardoen
,
T.
,
Jacques
,
P. J.
, and
Brassart
,
L.
,
2014
, “
The Influence of Microstructure and Composition on the Plastic Behaviour of Dual-Phase Steels
,”
Acta Mater.
,
73
, pp.
298
311
.
3.
Davies
,
R. G.
,
1978
, “
Influence of Martensite Composition and Content on the Properties of Dual Phase Steels
,”
Metall. Trans. A
,
9
(
5
), pp.
671
679
.
4.
Kim
,
N. J.
, and
Thomas
,
G.
,
1981
, “
Effects of Morphology on the Mechanical Behavior of a Dual Phase Fe/2Si/0.1C Steel
,”
Metall. Trans. A
,
12
(
3
), pp.
483
489
.
5.
Park
,
K.
,
Nishiyama
,
M.
,
Nakada
,
N.
,
Tsuchiyama
,
T.
, and
Takaki
,
S.
,
2014
, “
Effect of the Martensite Distribution on the Strain Hardening and Ductile Fracture Behaviors in Dual-Phase Steel
,”
Mater. Sci. Eng. A
,
604
, pp.
135
141
.
6.
Kim
,
N. J.
,
Nakagawa
,
A. H.
, and
Nakagawa
,
A. H.
,
1986
, “
Effective Grain Size of Dual-Phase Steel
,”
Mater. Sci. Eng.
,
83
(
1
), pp.
145
149
.
7.
Erdogan
,
M.
,
2002
, “
The Effect of New Ferrite Content on the Tensile Fracture Behaviour of Dual Phase Steels
,”
J. Mater. Sci.
,
37
(
17
), pp.
3623
3630
.
8.
Erdogan
,
M.
, and
Priestner
,
R.
,
2002
, “
Effect of Martensite Content, Its Dispersion, and Epitaxial Ferrite Content on Bauschinger Behaviour of Dual Phase Steel
,”
Mater. Sci. Technol.
,
18
(
4
), pp.
369
376
.
9.
Al-Abbasi
,
F. M.
, and
Nemes
,
J. A.
,
2003
, “
Micromechanical Modeling of Dual Phase Steels
,”
Int. J. Mech. Sci.
,
45
(
9
), pp.
1449
1465
.
10.
Al-Abbasi
,
F. M.
, and
Nemes
,
J. A.
,
2003
, “
Micromechanical Modeling of the Effect of Particle Size Difference in Dual Phase Steels
,”
Int. J. Solids Struct.
,
40
(
13–14
), pp.
3379
3391
.
11.
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
.
12.
Sun
,
X.
,
Choi
,
K. S.
,
Soulami
,
A.
,
Liu
,
W. N.
, and
Khaleel
,
M. A.
,
2009
, “
On Key Factors Influencing Ductile Fractures of Dual Phase (DP) Steels
,”
Mater. Sci. Eng. A
,
526
(1–2), pp.
140
149
.
13.
Choi
,
K. S.
,
Liu
,
W. N.
,
Sun
,
X.
,
Khaleel
,
M. A.
, and
Fekete
,
J. R.
,
2009
, “
Influence of Manufacturing Processes and Microstructures on the Performance and Manufacturability of Advanced High Strength Steels
,”
ASME J. Eng. Mater. Technol.
,
131
(
4
), p.
041205
.
14.
Choi
,
K. S.
,
Liu
,
W. N.
,
Sun
,
X.
, and
Khaleel
,
M. A.
,
2009
, “
Influence of Martensite Mechanical Properties on Failure Mode and Ductility of Dual-Phase Steels
,”
Metall. Mater. Trans. A
,
40
(
4
), pp.
796
809
.
15.
Katani
,
S.
,
Ziaei-Rad
,
S.
,
Nouri
,
N.
,
Saeidi
,
N.
,
Kadkhodapour
,
J.
,
Torabian
,
N.
, and
Schmauder
,
S.
,
2013
, “
Microstructure Modelling of Dual-Phase Steel Using SEM Micrographs and Voronoi Polycrystal Models
,”
Metallogr. Microstruct. Anal.
,
2
(
3
), pp.
156
169
.
16.
Kim
,
J. H.
,
Lee
,
M. G.
,
Kim
,
D.
,
Matlock
,
D. K.
, and
Wagoner
,
R. H.
,
2010
, “
Hole-Expansion Formability of Dual-Phase Steels Using Representative Volume Element Approach With Boundary-Smoothing Technique
,”
Mater. Sci. Eng. A
,
527
(27–28), pp.
7353
7363
.
17.
Marvi-Mashhadi
,
M.
,
Mazinani
,
M.
, and
Rezaee-Bazzaz
,
A.
,
2012
, “
FEM Modeling of the Flow Curves and Failure Modes of Dual Phase Steels With Different Martensite Volume Fractions Using Actual Microstructure as the Representative Volume
,”
Comput. Mater. Sci.
,
65
, pp.
197
202
.
18.
Paul
,
S. K.
,
2013
, “
Real Microstructure Based Micromechanical Model to Simulate Microstructural Level Deformation Behavior and Failure Initiation in DP 590 Steel
,”
Mater. Des.
,
44
, pp.
397
406
.
19.
Paul
,
S. K.
, and
Kumar
,
A.
,
2012
, “
Micromechanics Based Modeling to Predict Flow Behavior and Plastic Strain Localization of Dual Phase Steels
,”
Comput. Mater. Sci.
,
63
, pp.
66
74
.
20.
Sodjit
,
S.
, and
Uthaisangsuk
,
V.
,
2012
, “
Microstructure Based Prediction of Strain Hardening Behavior of Dual Phase Steels
,”
Mater. Des.
,
41
, pp.
370
379
.
21.
Vajragupta
,
N.
,
Uthaisangsuk
,
V.
,
Schmaling
,
B.
,
Münstermann
,
S.
,
Hartmaier
,
A.
, and
Bleck
,
W.
,
2012
, “
A Micromechanical Damage Simulation of Dual Phase Steels Using XFEM
,”
Comput. Mater. Sci.
,
54
, pp.
271
279
.
22.
Chen
,
P.
,
Ghassemi-Armaki
,
H.
,
Kumar
,
S.
,
Bower
,
A.
,
Bhat
,
S.
, and
Sadagopan
,
S.
,
2014
, “
Microscale-Calibrated Modeling of the Deformation Response of Dual-Phase Steels
,”
Acta Mater.
,
65
, pp.
133
149
.
23.
Ramazani
,
A.
,
Abbasi
,
M.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2012
, “
Failure Analysis of DP600 Steel During the Cross-Die Test
,”
Comput. Mater. Sci.
,
64
, pp.
101
105
.
24.
Ramazani
,
A.
,
Mukherjee
,
K.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2012
, “
Modelling the Effect of Microstructural Banding on the Flow Curve Behaviour of Dual-Phase (DP) Steels
,”
Comput. Mater. Sci.
,
52
(
1
), pp.
46
54
.
25.
Ramazani
,
A.
,
Mukherjee
,
K.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2012
, “
Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of Grain Size
,”
Metall. Mater. Trans. A
,
43
(
10
), pp.
3850
3869
.
26.
Ramazani
,
A.
,
Mukherjee
,
K.
,
Quade
,
H.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2013
, “
Correlation Between 2D and 3D Flow Curve Modelling of DP Steels Using a Microstructure-Based RVE Approach
,”
Mater. Sci. Eng. A
,
560
, pp.
129
139
.
27.
Ramazani
,
A.
,
Mukherjee
,
K.
,
Schwedt
,
A.
,
Goravanchi
,
P.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2013
, “
Quantification of the Effect of Transformation-Induced Geometrically Necessary Dislocations on the Flow-Curve Modelling of Dual-Phase Steels
,”
Int. J. Plast.
,
43
, pp.
128
152
.
28.
Ramazani
,
A.
,
Pinard
,
P. T.
,
Richter
,
S.
,
Schwedt
,
A.
, and
Prahl
,
U.
,
2013
, “
Characterisation of Microstructure and Modelling of Flow Behaviour of Bainite-Aided Dual-Phase Steel
,”
Comput. Mater. Sci.
,
80
, pp.
134
141
.
29.
Ramazani
,
A.
,
Schwedt
,
A.
,
Aretz
,
A.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2013
, “
Characterization and Modelling of Failure Initiation in DP Steel
,”
Comput. Mater. Sci.
,
75
, pp.
35
44
.
30.
Ramazani
,
A.
,
Ebrahimi
,
Z.
, and
Prahl
,
U.
,
2014
, “
Study the Effect of Martensite Banding on the Failure Initiation in Dual-Phase Steel
,”
Comput. Mater. Sci.
,
87
, pp.
241
247
.
31.
Abid
,
N. H.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
,
2015
, “
Computational Modeling of the Effect of Equiaxed Heterogeneous Microstructures on Strength and Ductility of Dual Phase Steels
,”
Comput. Mater. Sci.
,
103
, pp.
20
37
.
32.
Asgari
,
S. A.
,
Hodgson
,
P. D.
,
Yang
,
C.
, and
Rolfe
,
B. F.
,
2009
, “
Modeling of Advanced High Strength Steels With the Realistic Microstructure–Strength Relationships
,”
Comput. Mater. Sci.
,
45
(
4
), pp.
860
866
.
33.
Nygårds
,
M.
, and
Gudmundson
,
P.
,
2002
, “
Three-Dimensional Periodic Voronoi Grain Models and Micromechanical FE-Simulations of a Two-Phase Steel
,”
Comput. Mater. Sci.
,
24
(
4
), pp.
513
519
.
34.
Ghosh
,
S.
,
Nowak
,
Z.
, and
Lee
,
K.
,
1997
, “
Quantitative Characterization and Modeling of Composite Microstructures by Voronoi Cells
,”
Acta Mater.
,
45
(
6
), pp.
2215
2234
.
35.
Kadkhodapour
,
J.
,
Schmauder
,
S.
,
Raabe
,
D.
,
Ziaei-Rad
,
S.
,
Weber
,
U.
, and
Calcagnotto
,
M.
,
2011
, “
Experimental and Numerical Study on Geometrically Necessary Dislocations and Non-Homogeneous Mechanical Properties of the Ferrite Phase in Dual Phase Steels
,”
Acta Mater.
,
59
(
11
), pp.
4387
4394
.
36.
Ghassemi-Armaki
,
H.
,
Maaß
,
R.
,
Bhat
,
S. P.
,
Sriram
,
S.
,
Greer
,
J. R.
, and
Kumar
,
K. S.
,
2014
, “
Deformation Response of Ferrite and Martensite in a Dual-Phase Steel
,”
Acta Mater.
,
62
, pp.
197
211
.
37.
Peng-Heng
,
C.
, and
Preban
,
A.
,
1985
, “
The Effect of Ferrite Grain Size and Martensite Volume Fraction on the Tensile Properties of Dual Phase Steel
,”
Acta Metall.
,
33
(
5
), pp.
897
903
.
38.
Calcagnotto
,
M.
,
Adachi
,
Y.
,
Ponge
,
D.
, and
Raabe
,
D.
,
2011
, “
Deformation and Fracture Mechanisms in Fine-and Ultrafine-Grained Ferrite/Martensite Dual-Phase Steels and the Effect of Aging
,”
Acta Mater.
,
59
(
2
), pp.
658
670
.
39.
Jiang
,
Z.
,
Guan
,
Z.
, and
Lian
,
J.
,
1995
, “
Effects of Microstructural Variables on the Deformation Behaviour of Dual-Phase Steel
,”
Mater. Sci. Eng. A
,
190
(
1
), pp.
55
64
.
40.
Petch
,
N. J.
,
1953
, “
The Cleavage Strength of Polycrystals
,”
J. Iron Steel Inst.
,
174
, pp.
25
28
.
41.
Fu
,
H. H.
,
Benson
,
D. J.
, and
Meyers
,
M. A.
,
2001
, “
Analytical and Computational Description of Effect of Grain Size on Yield Stress of Metals
,”
Acta Mater.
,
49
(
13
), pp.
2567
2582
.
42.
Fu
,
H. H.
,
Benson
,
D. J.
, and
Meyers
,
M. A.
,
2004
, “
Computational Description of Nanocrystalline Deformation Based on Crystal Plasticity
,”
Acta Mater.
,
52
(
15
), pp.
4413
4425
.
43.
Abu Al-Rub
,
R. K.
,
2008
, “
Interfacial Gradient Plasticity Governs Scale-Dependent Yield Strength and Strain Hardening Rates in Micro/Nano Structured Metals
,”
Int. J. Plast.
,
24
(
8
), pp.
1277
1306
.
44.
Ohno
,
N.
, and
Okumura
,
D.
,
2007
, “
Higher-Order Stress and Grain Size Effects Due to Self-Energy of Geometrically Necessary Dislocations
,”
J. Mech. Phys. Solids
,
55
(
9
), pp.
1879
1898
.
45.
Voyiadjis
,
G. Z.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
,
2006
, “
On the Small and Finite Deformation Thermo-Elasto-Viscoplasticity Theory for Strain: Algorithmic and Computational Aspects
,”
Eur. J. Comput. Mech.
,
15
(
7–8
), pp.
945
987
.
46.
Hibbitt, D., Karlsson, B., and Sorensen, P.,
2013
, “
Abaqus, Version 6.13-2
,” Dassault Systémes Simulia Corporation, Johnston, RI.
47.
Reddy
,
J. N.
,
2004
,
An Introduction to Nonlinear Finite Element Analysis
,
Oxford University Press
,
Oxford, UK
.
48.
Clayton
,
J. D.
,
2011
,
Nonlinear Mechanics of Crystals
,
Springer
,
Dordrecht, The Netherlands
.
49.
Choi
,
S. H.
,
Kim
,
E. Y.
,
Woo
,
W.
,
Han
,
S. H.
, and
Kwak
,
J. H.
,
2013
, “
The Effect of Crystallographic Orientation on the Micromechanical Deformation and Failure Behaviors of DP980 Steel During Uniaxial Tension
,”
Int. J. Plast.
,
45
, pp.
85
102
.
50.
Rodriguez
,
R. M.
, and
Gutierrez
,
I.
,
2003
, “
A Unified Formulation to Predict the Tensile Curves of Steels With Different Microstructures
,”
Mater. Sci. Forum
,
426–432
, pp.
4525
4530
.
51.
Saeidi
,
N.
,
Ashrafizadeh
,
F.
, and
Niroumand
,
B.
,
2014
, “
Development of a New Ultrafine Grained Dual Phase Steel and Examination of the Effect of Grain Size on Tensile Deformation Behavior
,”
Mater. Sci. Eng. A
,
599
, pp.
145
149
.
52.
Anand
,
L.
,
Gurtin
,
M. E.
,
Lele
,
S. P.
, and
Gething
,
C.
,
2005
, “
A One-Dimensional Theory of Strain-Gradient Plasticity: Formulation, Analysis, Numerical Results
,”
J. Mech. Phys. Solids
,
53
(
8
), pp.
1789
1826
.
53.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
1997
, “
Strain Gradient Plasticity
,”
Adv. Appl. Mech.
,
33
, pp.
295
361
.
54.
Marketz
,
F.
, and
Fischer
,
F. D.
,
1994
, “
A Micromechanical Study on the Coupling Effect Between Microplastic Deformation and Martensitic Transformation
,”
Comput. Mater. Sci.
,
3
(
2
), pp.
307
325
.
55.
Tjahjanto
,
D.
,
Turteltaub
,
S.
,
Suiker
,
A.
, and
Van der Zwaag
,
S.
,
2006
, “
Modelling of the Effects of Grain Orientation on Transformation-Induced Plasticity in Multiphase Carbon Steels
,”
Model. Simul. Mater. Sci. Eng.
,
14
(
4
), pp.
617
636
.
56.
Jia
,
N.
,
Cong
,
Z. H.
,
Sun
,
X.
,
Cheng
,
S.
,
Nie
,
Z. H.
,
Ren
,
Y.
,
Liaw
,
P. K.
, and
Wang
,
Y. D.
,
2009
, “
An In Situ High-Energy X-Ray Diffraction Study of Micromechanical Behavior of Multiple Phases in Advanced High-Strength Steels
,”
Acta Mater.
,
57
(
13
), pp.
3965
3977
.
57.
Xiao
,
L.
,
Fan
,
Z.
,
Jinxiu
,
Z.
,
Mingxing
,
Z.
,
Mokuang
,
K.
, and
Zhenqi
,
G.
,
1995
, “
Lattice-Parameter Variation With Carbon Content of Martensite—I: X-Ray-Diffraction Experimental Study
,”
Phys. Rev. B
,
52
(
14
), pp.
9970
9978
.
58.
Radu
,
M.
,
Valy
,
J.
,
Gourgues
,
A. F.
,
Strat
,
F. L.
, and
Pineau
,
A.
,
2005
, “
Continuous Magnetic Method for Quantitative Monitoring of Martensitic Transformation in Steels Containing Metastable Austenite
,”
Scr. Mater.
,
52
(
6
), pp.
525
530
.
59.
Ekrami
,
A.
,
2005
, “
High Temperature Mechanical Properties of Dual Phase Steels
,”
Mater. Lett.
,
59
(
16
), pp.
2070
2074
.
60.
Sarwar
,
M.
,
Manzoor
,
T.
,
Ahmad
,
E.
, and
Hussain
,
N.
,
2007
, “
The Role of Connectivity of Martensite on the Tensile Properties of a Low Alloy Steel
,”
Mater. Des.
,
28
(
6
), pp.
1928
1933
.
61.
Ahmad
,
E.
,
Manzoor
,
T.
,
Ziai
,
M. M. A.
, and
Hussain
,
N.
,
2012
, “
Effect of Martensite Morphology on Tensile Deformation of Dual-Phase Steel
,”
J. Mater. Eng. Perform.
,
21
(
3
), pp.
382
387
.
62.
Voyiadjis
,
G. Z.
, and
Abu Al-Rub
,
R. K.
,
2005
, “
Gradient Plasticity Theory With a Variable Length Scale Parameter
,”
Int. J. Solids Struct.
,
42
(
14
), pp.
3998
4029
.
63.
Aifantis
,
K. E.
, and
Willis
,
J. R.
,
2005
, “
The Role of Interfaces in Enhancing the Yield Strength of Composites and Polycrystals
,”
J. Mech. Phys. Solids
,
53
(
5
), pp.
1047
1070
.
64.
Abu Al-Rub
,
R. K.
,
2007
, “
Prediction of Micro and Nanoindentation Size Effect From Conical or Pyramidal Indentation
,”
Mech. Mater.
,
39
(
8
), pp.
787
802
.
65.
Abu Al-Rub
,
R. K.
,
Ettehad
,
M.
, and
Palazotto
,
A. N.
,
2015
, “
Microstructural Modeling of Dual Phase Steel Using a Higher-Order Gradient Plasticity–Damage Model
,”
Int. J. Solids Struct.
,
58
, pp.
178
189
.
66.
Erdogan
,
M.
, and
Tekeli
,
S.
,
2003
, “
The Effect of Martensite Volume Fraction and Particle Size on the Tensile Properties of a Surface-Carburized AISI 8620 Steel With a Dual-Phase Core Microstructure
,”
Mater. Charact.
,
49
(5), pp.
445
454
.
67.
Balint
,
D.
,
Deshpande
,
V.
,
Needleman
,
A.
, and
van der Giessen
,
E.
,
2005
, “
A Discrete Dislocation Plasticity Analysis of Grain-Size Strengthening
,”
Mater. Sci. Eng. A
,
400–401
, pp.
186
190
.
68.
Calcagnotto
,
M.
,
Ponge
,
D.
, and
Raabe
,
D.
,
2010
, “
Effect of Grain Refinement to 1 μm on Strength and Toughness of Dual-Phase Steels
,”
Mater. Sci. Eng. A
,
527
(
29
), pp.
7832
7840
.
69.
Wu
,
Q.
, and
Zikry
,
M. A.
,
2014
, “
Microstructural Modeling of Crack Nucleation and Propagation in High Strength Martensitic Steels
,”
Int. J. Solids Struct.
,
51
, pp.
4345
4356
.
You do not currently have access to this content.