Recent studies on developing dual phase (DP) steels showed that the combination of strength/ductility could be significantly improved when changing the volume fraction and grain size of phases in the microstructure depending on microstructure properties. Consequently, DP steel manufacturers are interested in predicting microstructure properties as well as optimizing microstructure design at different strain rate conditions. In this work, a microstructure-based approach using a multiscale material and structure model was developed. The approach examined the mechanical behavior of DP steels using virtual tensile tests with a full micro-macro multiscale material model to identify specific mechanical properties. Microstructures with varied ferrite grain sizes, martensite volume fractions, and carbon content in DP steels were also studied. The influence of these microscopic parameters at different strain rates on the mechanical properties of DP steels was examined numerically using a full micro-macro multiscale finite element method. An elasto-viscoplastic constitutive model and a response surface methodology (RSM) were used to determine the optimum microstructure parameters for a required combination of strength/ductility at different strain rates. The results from the numerical simulations were compared with experimental results found in the literature. The developed methodology proved to be a powerful tool for studying the effect and interaction of key strain rate sensitivity and microstructure parameters on mechanical behavior and thus can be used to identify optimum microstructural conditions at different strain rates.

References

References
1.
Alturk
,
R.
,
Mates
,
S.
,
Xu
,
Z.
, and
Abu-Farha
,
F.
,
2017
, “
Effects of Microstructure on the Strain Rate Sensitivity of Advanced Steels
,”
146th Annual Meeting and Exhibition Supplemental Proceedings
(TMS 2017), Pittsburgh, PA, Feb. 26–Mar. 2, pp.
243
254
.
2.
Wang
,
W.
,
Li
,
M.
,
He
,
C.
,
Wei
,
X.
,
Wang
,
D.
, and
Du
,
H.
,
2013
, “
Experimental Study on High Strain Rate Behavior of High Strength 600–1000 MPa Dual Phase Steels and 1200 MPa Fully Martensitic Steels
,”
Mater. Des.
,
47
, pp.
510
521
.
3.
Baltazar Hernandez
,
V. H.
,
Nayak
,
S. S.
, and
Zhou
,
Y.
,
2011
, “
Tempering of Martensite in Dual-Phase Steels and Its Effects on Softening Behavior
,”
Metall. Mater. Trans. A
,
42
(
10
), pp.
3115
3129
.
4.
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
.
5.
Qin
,
J.
,
Chen
,
R.
,
Wen
,
X.
,
Lin
,
Y.
,
Liang
,
M.
, and
Lu
,
F.
,
2013
, “
Mechanical Behaviour of Dual-Phase High-Strength Steel Under High Strain Rate Tensile Loading
,”
Mater. Sci. Eng. A
,
586
, pp.
62
70
.
6.
Kumar
,
S.
,
Singhai
,
M.
,
Desai
,
R.
,
Sam
,
S.
, and
Patra
,
P. K.
,
2016
, “
Development of Advanced High Strength Steel for Improved Vehicle Safety, Fuel Efficiency and CO2 Emission
,”
J. Inst. Eng., Ser. D
,
97
(
2
), pp.
153
158
.
7.
Tasan
,
C. C.
,
Diehl
,
M.
,
Yan
,
D.
,
Bechtold
,
M.
,
Roters
,
F.
,
Schemmann
,
L.
,
Zheng
,
C.
,
Peranio
,
N.
,
Ponge
,
D.
,
Koyama
,
M.
,
Tsuzaki
,
K.
, and
Raabe
,
D.
,
2015
, “
An Overview of Dual-Phase Steels: Advances in Microstructure-Oriented Processing and Micromechanically Guided Design
,”
Annu. Rev. Mater. Res.
,
45
(
1
), pp.
391
431
.
8.
Yu
,
H.
,
Guo
,
Y.
,
Zhang
,
K.
, and
Lai
,
X.
,
2009
, “
Constitutive Model on the Description of Plastic Behavior of DP600 Steel at Strain Rate From 10-4 to 103 S-1
,”
Comput. Mater. Sci.
,
46
(
1
), pp.
36
41
.
9.
Singh
,
N. K.
,
Cadoni
,
E.
,
Singha
,
M. K.
, and
Gupta
,
N. K.
,
2011
, “
Dynamic Tensile Behavior of Multi Phase High Yield Strength Steel
,”
Mater. Des.
,
32
(
10
), pp.
5091
5098
.
10.
Kim
,
J.-H.
,
Kim
,
D.
,
Han
,
H. N.
,
Barlat
,
F.
, and
Lee
,
M.-G.
,
2013
, “
Strain Rate Dependent Tensile Behavior of Advanced High Strength Steels: Experiment and Constitutive Modeling
,”
Mater. Sci. Eng. A
,
559
, pp.
222
231
.
11.
Kim
,
S.
, and
Lee
,
S.
,
2000
, “
Effects of Martensite Morphology and Volume Fraction on Quasi-Static and Dynamic Deformation Behavior of Dual-Phase Steels
,”
Metall. Mater. Trans. A
,
31
(
7
), pp.
1753
1760
.
12.
Cao
,
Y.
,
Karlsson
,
B.
, and
Ahlström
,
J.
,
2015
, “
The Influence of Temperatures and Strain Rate Effects on the Mechanical Behavior of Dual Phase Steel in Different Conditions
,”
Mater. Sci. Eng. A
,
636
(
1
), pp.
124
132
.
13.
Hwang
,
B.
,
Cao
,
T. Y.
,
Shin
,
S. Y.
,
Kim
,
S. H.
,
Lee
,
S. H.
, and
Kim
,
S. J.
,
2005
, “
Effects of Ferrite Grain Size and Martensite Volume Fraction on Dynamic Deformation Behaviour of 0.15C–2.0Mn–0.2Si Dual Phase Steels
,”
Mater. Sci. Technol.
,
21
(
8
), pp.
967
975
.
14.
Zare
,
A.
, and
Ekrami
,
A.
,
2013
, “
Influence of Martensite Volume Fraction on Impact Properties of Triple Phase (TP) Steels
,”
J. Mater. Eng. Perform.
,
22
(
3
), pp.
823
829
.
15.
Oscar
,
P.
, and
Eduardo
,
R. L.
,
2008
, “
Impact Performance of Advanced High Strength Steel Thin-Walled Columns
,”
World Congress on Engineering
, London, July 2–4.
16.
Cadoni
,
E.
,
Singh
,
N. K.
,
Forni
,
D.
,
Singha
,
M. K.
, and
Gupta
,
N. K.
,
2016
, “
Strain Rate Effects on the Mechanical Behavior of Two Dual Phase Steels in Tension
,”
Eur. Phys. J. Spec. Top.
,
225
(
2
), pp.
409
421
.
17.
Rahmaan
,
T.
,
Butcher
,
C.
,
Abedini
,
A.
, and
Worswick
,
M.
,
2015
, “
Effect of Strain Rate on Shear Properties and Fracture Characteristics of DP600 and AA5182-O Sheet Metal Alloys
,”
11th International DYMAT Conference
, Lugano, Switzerland, Sept. 7–11, p.
1033
.
18.
Jiang
,
Z. H.
,
Guan
,
Z. Z.
, and
Lian
,
J. S.
,
1995
, “
Effects of Microstructural Variables on the Deformation-Behavior of Dual-Phase Steel
,”
Mater. Sci. Eng.
,
190
(
1–2
), pp.
55
64
.
19.
Delincé
,
M.
,
Bréchet
,
Y.
,
Embury
,
J. D.
,
Geers
,
M. G. D.
,
Jacques
,
P. J.
, and
Pardoen
,
T.
,
2007
, “
Structure-Property Optimization of Ultrafine-Grained Dual-Phase Steels Using a Microstructure-Based Strain Hardening Model
,”
Acta Mater.
,
55
(
7
), pp.
2337
2350
.
20.
Amirmaleki
,
M.
,
Samei
,
J.
,
Green
,
D. E.
,
van Riemsdijk
,
I.
, and
Stewart
,
L.
,
2016
, “
3D Micromechanical Modeling of Dual Phase Steels Using the Representative Volume Element Method
,”
Mech. Mater.
,
101
, pp.
27
39
.
21.
Khan
,
A. S.
,
Baig
,
M.
,
Choi
,
S.-H.
,
Yang
,
H.-S.
, and
Sun
,
X.
,
2012
, “
Quasi-Static and Dynamic Responses of Advanced High Strength Steels: Experiments and Modeling
,”
Int. J. Plast.
,
30–31
, pp.
1
17
.
22.
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
.
23.
Sodjit
,
S.
, and
Uthaisangsuk
,
V.
,
2012
, “
Microstructure Based Prediction of Strain Hardening Behavior of Dual Phase Steels
,”
Mater. Des.
,
41
, pp.
370
379
.
24.
Belgasam, T. M.
, and
Zbib, H. M.
, 2017, “
Microstructure Optimization of Dual-Phase Steels Using a Representative Volume Element and a Response Surface Method: Parametric Study
,”
Metall. Mater. Trans. A
,
48
(12), pp. 6153–6177.
25.
Sodjit
,
S.
, and
Uthaisangsuk
,
V.
,
2012
, “
A Micromechanical Flow Curve Model for Dual Phase Steels
,”
J. Met. Mater. Miner.
,
22
(
1
), pp.
87
97
.
26.
Ramazani
,
A.
,
Mukherjee
,
K.
,
Abdurakhmanov
,
A.
,
Prahl
,
U.
,
Schleser
,
M.
,
Reisgen
,
U.
, and
Bleck
,
W.
,
2014
, “
Micro-Macro-Characterisation and Modelling of Mechanical Properties of Gas Metal Arc Welded (GMAW) DP600 Steel
,”
Mater. Sci. Eng. A
,
589
, pp.
1
14
.
27.
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
.
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.
Thomser
,
C.
,
Uthaisangsuk
,
V.
, and
Bleck
,
W.
,
2009
, “
Influence of Martensite Distribution on the Mechanical Properties of Dual Phase Steels: Experiments and Simulation
,”
Steel Res. Int.
,
80
(
8
), pp.
582
587
.
30.
Paul
,
S. K.
,
2013
, “
Effect of Material Inhomogeneity on the Cyclic Plastic Deformation Behavior at the Microstructural Level: Micromechanics-Based Modeling of Dual-Phase Steel
,”
Model. Simul. Mater. Sci. Eng.
,
21
(
5
), p. 055001.
31.
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
.
32.
Uthaisangsuk
,
V.
,
Prahl
,
U.
, and
Bleck
,
W.
,
2011
, “
Modelling of Damage and Failure in Multiphase High Strength DP and TRIP Steels
,”
Eng. Fract. Mech.
,
78
(
3
), pp.
469
486
.
33.
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
.
34.
Bergström
,
Y.
,
Granbom
,
Y.
, and
Sterkenburg
,
D.
,
2010
, “
A Dislocation-Based Theory for the Deformation Hardening Behavior of DP Steels: Impact of Martensite Content and Ferrite Grain Size
,”
J. Metall.
,
2010
, pp.
1
16
.
35.
Krauss
,
G.
,
2001
, “
Deformation and Fracture in Martensitic Carbon Steels Tempered at Low Temperatures
,”
Metall. Mater. Trans. B
,
32
(
4
), pp.
205
221
.
36.
Byun
,
T. S.
, and
Kim
,
I. S.
,
1993
, “
Tensile Properties and Inhomogeneous Deformation of Ferrite-Martensite Dual-Phase Steels
,”
J. Mater. Sci.
,
28
(
11
), pp.
2923
2932
.
37.
Sudersanan
,
P. D.
,
Kori
,
N.
,
Aprameyan
,
S.
, and
Kempaiah
,
U. N.
,
2012
, “The Effect of Carbon Content in Martensite on the Strength of Dual Phase Steel,” Bonfring Int. J. Ind. Eng. Manage. Sci., 2(2), pp.
1
4
.
38.
Movahed
,
P.
,
Kolahgar
,
S.
,
Marashi
,
S. P. H.
,
Pouranvari
,
M.
, and
Parvin
,
N.
,
2009
, “
The Effect of Intercritical Heat Treatment Temperature on the Tensile Properties and Work Hardening Behavior of Ferrite-Martensite Dual Phase Steel Sheets
,”
Mater. Sci. Eng. A
,
518
(
1–2
), pp.
1
6
.
39.
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.
40.
Rodriguez
,
R.-M.
, and
Gutiérrez
,
I.
,
2003
, “
Unified Formulation to Predict the Tensile Curves of Steels With Different Microstructures
,”
Mater. Sci. Forum
,
426–432
, pp.
4525
4530
.
41.
Abid
,
N. H.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
,
2017
, “
Micromechanical Finite Element Analysis of the Effects of Martensite Morphology on the Overall Mechanical Behavior of Dual Phase Steel
,”
Int. J. Solids Struct.
,
104–105
, pp.
8
24
.
42.
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
.
43.
Tarigopula
,
V.
,
Hopperstad
,
O. S.
,
Langseth
,
M.
,
Clausen
,
A. H.
, and
Hild
,
F.
,
2008
, “
A Study of Localisation in Dual-Phase High-Strength Steels Under Dynamic Loading Using Digital Image Correlation and FE Analysis
,”
Int. J. Solids Struct.
,
45
(
2
), pp.
601
619
.
44.
Gutierrez
,
I.
,
2012
, “
AME Modeling the Mechanical Behavior of Steels With Mixed Microstructures
,”
Metalurgija
,
11
(
3
), pp.
201
214
.
45.
Perdahcıoğlu
,
E. S.
, and
Geijselaers
,
H. J. M.
,
2011
, “
Constitutive Modeling of Two Phase Materials Using the Mean Field Method for Homogenization
,”
Int. J. Mater. Form.
,
4
(
2
), pp.
93
102
.
46.
Adam
,
L.
,
Depouhon
,
A.
, and
Assaker
,
R.
,
2009
, “
Multi-Scale Modeling of Crash & Failure of Reinforced Plastics Parts With DIGIMAT to LS-DYNA Interface
,”
Seventh European LS-DYNA Conference
, Salzburg, Austria, May 14–15, pp.
1
9
.
47.
Klusemann
,
B.
, and
Svendsen
,
B.
,
2010
, “
Homogenization Methods for Multi-Phase Elastic Composites: Comparisons and Benchmarks
,”
Tech. Mech.
,
30
(
4
), pp.
374
386
.
48.
Mori
,
T.
, and
Tanaka
,
K.
,
1973
, “
Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,”
Acta Metall.
,
21
(
5
), pp.
571
574
.
49.
Makadia
,
A. J.
, and
Nanavati
,
J. I.
,
2013
, “
Optimisation of Machining Parameters for Turning Operations Based on Response Surface Methodology
,”
Measurement
,
46
(
4
), pp.
1521
1529
.
50.
Öktem
,
H.
,
Erzurumlu
,
T.
, and
Kurtaran
,
H.
,
2005
, “
Application of Response Surface Methodology in the Optimization of Cutting Conditions for Surface Roughness
,”
J. Mater. Process. Technol.
,
170
(
1–2
), pp.
11
16
.
51.
Oehlert
,
G. W.
,
2000
,
A First Course in Design and Analysis of Experiments
,
W.H. Freeman
,
Gordonsville, VA
.
52.
Montgomery
,
D. C.
,
2012
,
Design and Analysis of Experiments
,
Wiley
,
Hoboken, NJ
.
53.
Khuri
,
A. I.
, and
Mukhopadhyay
,
S.
,
2010
, “
Response Surface Methodology
,”
Wiley Interdiscip. Rev. Comput. Stat.
,
2
(
2
), pp.
128
149
.
54.
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
.
55.
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
(
29–30
), pp.
7832
7840
.
56.
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
.
57.
Calcagnotto
,
M.
,
Ponge
,
D.
,
Demir
,
E.
, and
Raabe
,
D.
,
2010
, “
Orientation Gradients and Geometrically Necessary Dislocations in Ultrafine Grained Dual-Phase Steels Studied by 2D and 3D EBSD
,”
Mater. Sci. Eng. A
,
527
(
10–11
), pp.
2738
2746
.
58.
Paul
,
S. K.
,
2013
, “
Effect of Martensite Volume Fraction on Stress Triaxiality and Deformation Behavior of Dual Phase Steel
,”
Mater. Des.
,
50
, pp.
782
789
.
59.
Chen
,
H. C.
, and
Cheng
,
G. H.
,
1989
, “
Effect of Martensite Strength on the Tensile Strength of Dual Phase Steels
,”
J. Mater. Sci.
,
24
(
6
), pp.
1991
1994
.
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