DP-Triaxiality.pdf

Contents lists available at ScienceDirect
Mechanics of Materials
journal homepage: www.elsevier.com/locate/mechmat
A comparative study on mechanical behavior and damage scenario of DP600
and DP980 steels
Ali Cheloee Darabia,b
, Vinzenz Guskia
, Alexander Butzc
, Javad Kadkhodapoura,b,⁎
,
Siegfried Schmaudera
a
Institute for Materials Testing, Materials Science and Strength of Materials, University of Stuttgart, Pfaffenwaldring 32, 70569, Stuttgart, Germany
b
Shahid Rajaee Teacher Training University, Lavizan, Teheran, Iran
c
Fraunhofer Institute for Mechanics of Materials IWM, 79108 Freiburg, Germany
A R T I C L E I N F O
Keywords:
Dual phase steel
Stress state
Mechanical behavior
Damage scenario
In-situ tensile test
A B S T R A C T
In this study, the mechanical behavior of two cold rolled commercial dual phase steels (DP) were analyzed on
micro and macro scales. First, the anisotropic behavior of these steels were investigated by standard tensile tests
in three directions. The results showed that the anisotropy behavior of the fracture strain of DP980 is more
pronounced than of DP600. Then, in order to assess the influence on the stress state on the mechanical behavior,
four specimens with different stress states were analyzed by ARAMIS approach which is based on digital image
correlation (DIC). The ARAMIS results were compared with 3D numerical simulations using the Abaqus/Explicit
solver. In this part, the effect of stress state on flow curve and strain distribution in the specimens (i.e. tensile,
notched-tensile, shear and bulge specimens) were investigated. To predict the fracture behavior of DP600 and
DP980 steels under various loading conditions, the Modified Mohr-Coulomb (MMC) damage model was utilized.
A VUMAT subroutine was developed to include a MMC damage model in the 3D models, and good agreement
between the numerical and experimental results was observed. Finally, the microstructure failure mechanisms at
three different stages (i.e. strain localization, micro-crack initiation and micro-crack coalescence) during uni-
axial tensile loading were investigated inside the microstructure of DP600 and DP980 steels using an interrupted
in-situ setup. In the results three different damage localizations were observed in both materials, and strain
localization in the center of large ferrite phases and at the boundary of ferrite and martensite phases were
dominant in DP600 and DP980, respectively. Two different micro-crack initiation mechanisms were observed
that were similar in both materials.
1. Introduction
Different grades of dual phase (DP) belong to the most important
steels used in the automotive industry because of their excellent me-
chanical properties. The microstructure of these steels consists of a
ferrite phase with a high ductility and a martensite phase with a high
strength. The existence of these phases in DP steels leads to parts with
high strength and good formability. In these materials, parameters such
as grain size, grain orientations, martensite volume fraction and mor-
phology of martensite islands have an important effect on mechanical
properties (Furukawa et al., 1984; Bleck et al., 2016).
Martensite phase distribution is one of the most important para-
meters which can influence the anisotropic deformation behavior of DP
steels. In the manufacturing process of commercial DP steels, the cold-
rolling step leads to creation of martensite bands in the microstructure.
Some researchers (Bandyopadhyay et al., 2017; Deng and
Korkolis, 2018; Ennis et al., 2018) have reported that anisotropic be-
havior in dual phase steels is very critical and should be considered.
However, others (Santos et al., 2019; Bai and Wierzbicki, 2010) have
shown that the effect of martensite bands on the anisotropy of the
mechanical behavior is negligible and DP steels can be considered as
isotropic materials.
Nakada et al. (2012) showed that with the cold-rolling process, the
chain-networked martensite grains are formed in grain boundaries of
ferrite islands. Nourozi et al. (2018) conducted an intercritical an-
nealing on a cold-rolled martensite phase and illustrated that DP steel
with fine grains and the chain-network martensite has high tensile
toughness and work-hardening behavior with low yield ratio. Kamakar
et al. (2016) showed a cold-rolled DP steel with fine grain size and
uniform distribution of the martensite phase causes the combination of
https://doi.org/10.1016/j.mechmat.2020.103339
Received 22 September 2019; Received in revised form 17 December 2019; Accepted 17 January 2020
⁎
Corresponding author.
E-mail address: J.kad@srttu.edu (J. Kadkhodapour).
Mechanics of Materials 143 (2020) 103339
Available online 21 January 2020
0167-6636/ © 2020 Elsevier Ltd. All rights reserved.
T

good strength and ductility.
Bridgman (1952) tested axisymmetric specimens with various im-
posed hydrostatic pressure and showed the effect of pressure on frac-
ture strain. Other researchers e.g., (Lewandowski and Lowhaphandu
1988) confirmed Bridgman's results. Bai et al. (2009) studied the effect
of different notches on axisymmetric specimens and different groove
radii on grooved flat specimens on fracture locus for DH36 and 1045
steels. They assess the influence of Lode angle parameter on fracture
strain at DH36 and 1045 steels. Al-Abbasi et al. (2003) showed the local
failure mode in dual phase steel is accurately dependent on stress state.
Ductile fracture is a local phenomenon and to simulate it the value
of local strain in potential fracture locations should be calculated.
Therefore, the calculation of local plastic strain is vital for the de-
termination of the fracture initiation point under different stress states.
The relationships between the local plastic strain and the stress state
have been successfully investigated numerically for DP steels by several
researchers (Bao and Wierzbicki, 2004; Bai and Wierzbicki, 2010). The
researchers investigated the deformation history in a wide range of
stress state specimens and proposed a hybrid methodology for the
calculation of local equivalent plastic strains at the fracture point,
which combines numerical simulations and experimental results.
DIC is an experimental method used for examination of strain his-
tory in 2D or 3D coordinate systems. The mathematical description at
this contactless approach is based on continuum mechanics
(Fung, 1965; Novozhilov, 1861). Tarigopula et al. (2008) studied large
plastic deformation in DP800 using digital image correlation and
compared experimentally obtained local strains with Finite Element
(FE) simulation results. (Roth and Mohr 2016) determined effective
strain by DIC method in punch, V-bending, shear and combined shear-
tensile specimens for DP780 steel.
To predict fracture behavior of a ductile material under complex
loading, various damage models have been suggested in literature. The
classical damage models e.g., by Rice and Tracey (1969) and Johnson
and Cook (1985) are based on triaxiality. Recently, different studies
have been performed on the influence of Lode-angle parameter on da-
mage evolution (Bai and Wierzbicki, 2008; Bao and Wierzbicki, 2005;
Wierzbicki and Xue, 2005). Wierzbicki and Xue (2005) generated a
symmetric fracture locus based on Lode angle parameter and stress
triaxiality utilizing Wilkins and Rice and Tracey damage models. Bai
and Wierzbicki (2008) used a parabolic function in order to consider
the effect of Lode-angle on fracture locus. Then, they proposed a da-
mage model based on triaxiality and Lode angle by combining Lode
angle function and the Rice and Tracey damage model. Bai and
Wierzbicki (2010) extended the Mohr-Coulomb (MC) damage model for
ductile metals. They reformulated the MC damage model in the sphe-
rical coordinated system and used triaxiality, Lode angle and local
fracture strain as coordinate axes. This is the so called modified Mohr-
Coulomb (MMC) damage model.
In recent years, several studies have been conducted on plastic
strain partitioning between ferrite and martensite phases during de-
formation (Choi et al., 2013; Frechard et al., 2006; Han et al., 2013;
Joo et al., 2013; Woo et al., 2012). Guo et al. (2013) investigated the
plastic deformation in an austenitic-ferritic cast duplex stainless steel
(CDSS) by in-situ tensile tests at different temperatures. Kang et al.
(2007) investigated damage initiation in dual phase steels with DIC
method in different microstructures. They compared damage initiation
mechanism for two different heat treatment processes (i.e., annealed-
quenched and tempered heat treatment processes) on DP600. In both
obtained materials, damage initiation increased and this effect was
more pronounced in tempered specimens than in annealed-quenched
materials. Ososkov et al. (2007) studied local strain distribution values
in ferrite phase and within martensite phases using DIC. Ghadbeigi
et al. (2010) analyzed the local plastic strain evolution in martensite
and ferrite phases in tensile specimens during deformation using an in-
situ setup inside a scanning electron microscope (SEM). They also ob-
served two different damage initiation mechanisms. They reported that
the most common damage initiation happens at the interface of mar-
tensite and ferrite phases. Kadkhodapour et al. (2011) presented a
quantitative description of deformation localization in the ferrite phase
that was located between two martensite phases. Several researchers
reported three different strain localizations in the ferrite phase that
were observed using in-situ tests for DP600 (Alaie et al., 2015a;
Darabi et al., 2017; Kadkhodapour et al., 2011). The first one is in the
middle of large ferrite phases, the second in ferrite phases surrounding
martensite phases, and the third one at the interface between ferrite and
martensite phases.
Several studies have been performed on micro crack initiation in the
microstructure. He et al. (1984) compared fracture mechanisms in
coarse and fine martensite dual phase steels with constant value of
martensite volume fraction. Micro crack initiation in the martensite
phases happens at low strain and crack propagation at the interface of
ferrite and martensite phases at higher strain levels. Whereas in fine
martensite grains, the most common micro crack initiation happens
between two phases. Alaie et al. (2015a) assessed micro crack initiation
and propagation in martensite phases. They showed that propagation of
localized shear bands lead to micro crack initiation in low thickness
martensite phases. Alharbi et al. (2015) utilized the in-situ test and DIC
method, in order to examine failure mechanisms in microstructure of
DP1000 steels. Kahziz et al. (2013) investigated damage propagation
during bending of DP600 steel using laminography. Zhang et al. (2015)
evaluated the fracture mechanisms in two different morphologies of the
martensite phase. Here, two different damage mechanisms were ob-
served. The first mechanism happens in the interface of martensite-
ferrite phases and the second one is martensite cracking. They showed
for DP steel with fibrous martensite, martensite cracking is more
dominant. Whereas, for DP steel with high martensite fraction, the
value of strain localization is very low and the micro void nucleation is
more dominant. Due to the problems in-situ test setup, only a small
number of studies have been conducted up to final failure.
In this paper a comparative study was conducted on mechanical
behavior of DP600 and DP980 steels. This paper follows three different
targets. First, anisotropic behavior in both materials were assessed
using standard tensile tests in three different directions and the effect of
grain orientation on the anisotropic behavior was seen using electron
backscatter diffraction in the micro-scale. In second step, four different
specimens with different stress states (i.e., tensile, notched tensile,
shear, and bulge specimens) were tested for investigation of the effect
of stress state on stress-strain curve and local fracture strain in both
materials. Local plastic strains in the specimens were determined ex-
perimentally by DIC (using ARAMIS) and numerically by the Abaqus/
Explicit solver. In order to predict the fracture behavior under complex
loading, A VUMAT subroutine was developed to include the MMC da-
mage model in a 3D macro-mechanical model in Abaqus software and
the results were compared with experimental data. Furthermore, the
effect of strain rate was examined for both materials on notched-tensile
tests. Finally, the in-situ test setup was used to compare the damage
scenario (i.e., strain localization, micro-crack initiation, and coales-
cence and failure) in both materials.
2. Experimental procedure
2.1. Macro-scale testing
2.1.1. Standard material characterization
Two commercial high-strength dual-phase steels of DP600 and
DP980 grades were studied in the present work. The steels were re-
ceived in the form of 1.5 mm thick sheets. Their chemical composition
was measured by using glow-discharge optical emission spectroscopy
(GDOES) and is shown in Table 1.
Tensile test specimens were prepared from both steel sheets based
on the standard DIN EN ISO 6892-1 (Fig. 1). In order to account for
anisotropic behavior of the steels, tensile tests were performed in three
A. Cheloee Darabi, et al. Mechanics of Materials 143 (2020) 103339
2

different orientations (parallel to rolling, normal to loading, and 45° to
rolling direction) and sheet metal forming parameters, i.e. yield
strength, hardening behavior, and r-values were extracted based on DIN
ISO 10113 and DIN ISO 10275 standards. A MTS Sintech 65/G machine
was used to carry out the tensile tests in displacement control mode and
displacements were recorded using an extensometer. Each test was re-
peated three times.
2.1.2. Mechanical behavior under different stress states
In order to analyze the effect of stress state on fracture strain, four
different tests were performed. Tensile, notched tensile, shear, and
biaxial using bulge test specimens were prepared based on DIN EN ISO
6892-1, which is shown in Fig. 2. All the tests were conducted at the
strain rate of 0.01 −
s 1.
In order to investigate the effect of strain rate on mechanical
properties of the DP600 and DP980 steels, notched tensile specimens
were tested under three different strain rates (0.002, 0.01 and 0.02 −
s 1).
Also, ARAMIS measurements were utilized to analyze the deformation
history and strain localization pattern during loading. Fig. 3 shows the
Table 1
Chemical composition of steels used in this study.
Material Element (Mass contents%)
C Mn Si P S Cr Ni Al Mo V Cu Co
DP600 0.086 1.82 0.21 0.011 0.002 0.3 0.03 0.04 0.001 0.008 0.016 0.002
DP980 0.142 1.81 0.29 0.011 0.002 0.38 0.04 0.05 0.05 0.01 0.022 0.003
Fig. 1. Standard tensile specimen prepared from DP steels after DIN EN ISO 6892-1.
Fig. 2. Experimental specimens prepared from DP steels: (a) tensile, (b) Notched tensile, (c) shear, and (d) bulge specimens.
Fig. 3. ARAMIS Testing Setup (a) ARAMIS system, (b) prepared specimen
during ARAMIS testing.
3

experimental setup and a tensile specimen prepared with a speckle
pattern for capturing the deformation on the surface during the test.
2.2. Micro-scale testing
2.2.1. Microstructure analysis
To obtain information about microstructural features of the DP
steels used in this study, multiple microstructure analysis methods were
employed. The initial state of both DP steel grades was analyzed using
light optical (LOM) and scanning electron microscopy (SEM). Phase
size, volume fraction and size distribution of martensite were calculated
according to ASTM E562 (2008). Also, electron backscatter diffraction
(EBSD) measurements were used to study crystallographic orientation
(texture) of ferrite grains in both steels.
2.2.2. Micro in-situ test
A better understanding of the fracture process and failure micro-
mechanisms could be gained through SEM analysis. In this paper, a
uniaxial in-situ test setup was utilized in order to compare the failure
scenario in DP600 and DP980 steels. This setup was designed according
to the required deformational load before failure of the specimens, and
consists of two components. The first component is a screw-driven
Fig. 4. (a) Portable fixture located inside the SEM chamber, (b) Loading setup, (c) DP600 tensile specimen close to failure (d) DP980 tensile specimen close to failure.
Table 2
Summary of 3D simulations carried out to calibrate the MMC model for DP600
and DP980 steels.
No Specimen ηav θ̄av ε̄f
DP600 DP980
1 Tensile 0.34 0.995 1.398 0.552
2 Simple shear 0.015 0.02 1.048 0.868
3 Notched-tensile 0.57 0.15 0.542 0.342
4 Bulge 0.658 −0.994 0.66 0.496
Table 3
Tensile test data for DP600 and DP980 steels.
Material UTS0 (MPa) UTS45 (MPa) UTS90 (MPa) σy/0 (MPa) σy/45 (MPa) σy/90 (MPa) r0 (-) r45 (-) r90 (-)
DP600 644 649 648 357 372 365.5 0.9 0.809 1.034
DP980 1009 1026 1044.5 665.5 667 681.5 0.635 0.927 0.724
Table 4
The values of the fracture strain in three different directions.
Material ɛf, 0 (-) ɛf, 45 (-) ɛf, 90 (-)
DP600 0.288 0.273 0.2696
DP980 0.128 0.132 0.094
4

Fig. 5. Experimental stress-strain curves obtained from (a) tensile, (b) notched tensile, (c) shear, and (d) bulge tests.
Fig. 6. Calculation of local plastic strain in X-direction using ARAMIS analysis for tensile loading before fracture; (a) the diﬀerent selected regions, (b) local plastic
strain values in X-direction for each region.
Fig. 7. Comparison of local strain in loading direction resulting from ARAMIS measurements and numerical modeling for DP600 steel for diﬀerent load cases before
fracture: (a) tensile, (b) notched tensile, and (c) shear.
5

fixture used for drawing and holding the sample during the experiment
and is installed inside the chamber of the SEM. The second component
applies enough load to deform the sub-sized tensile sample in the fol-
lowing deformation step. The test is divided into multiple loading steps.
During the test, after collecting the images for each step, the first
component is removed from the SEM chamber and, using the second
component the sample is stretched to the next deformation level.
Although this technique takes more time than conventional in-situ
methods, it allows using small or medium SEM chamber sizes.
The tensile and notched-tensile in-situ tests were performed using
the described setup inside an SEM. The specimens were clamped at both
ends and displacement was applied gradually (Fig. 4(a) and (b)). The
changes in the macroscopic dimensions were measured at each de-
formation level. At the start of each test step, an algorithm was used to
find the location of previous points and to take images from the new
deformational state. The tests were continued until the tensile specimen
was very close to final failure because otherwise there was a risk of
specimen fracture under the SEM lens. This procedure enabled ob-
servation of deformational behavior of microstructure at the last steps
before the failure of the specimen (Fig. 4(c) and (d)). Finally, image
processing techniques were applied for local plastic deformation ana-
lysis.
3. Numerical simulation
3.1. Macromechanical modeling
In this study, the modified Mohr-Coulomb (MMC) damage model
has been used to investigate ductile fracture in different specimens
made of DP600 and DP980 and the results were compared with the
experimental results. The MMC damage model is defined as follows
(Bai and Wierzbicki, 2010):
Fig. 8. Comparison of local strain in loading direction resulting from ARAMIS measurements and numerical modeling for DP980 steel for different load cases before
fracture: (a) tensile, (b) notched tensile, and (c) shear.
Fig. 9. Major principal strain values obtained using ARAMIS for DP600 steel in the bulge specimen (a) along section I before fracture, (b) maximum strain during
loading, and (c) Equivalent strain distribution before fracture.
6

⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟ ⎜ ⎟
=
⎧
⎨
⎩
⎡
⎣
⎢ +
−
− ⎛
⎝
⎛
⎝
⎞
⎠
− ⎞
⎠
⎤
⎦
⎥
⎡
⎣
⎢
+ ⎛
⎝
⎞
⎠
+ ⎛
⎝
+ ⎛
⎝
⎞
⎠
⎞
⎠
⎤
⎦
⎥
⎫
⎬
⎭
−
ε
A
c
c c c sec
θπ
c
cos
θπ
c η sin
θπ
¯
3
2 3
( )
¯
6
1
1
3
¯
6
1
3
¯
6
f θ
s
θ
ax
θ
s
n
2
1
2
1
1
(1)
= ⎡
⎣
⎢
≥
≤
c
for θ
c for θ
1 ¯ 1
¯ 1
θ
ax
θ
c
(2)
where η and θ̄ are triaxiality and Lode angle parameters, respectively. A
total of six parameters (A, n, c1, c2, cθ
s
, cθ
ax
) need to be defined. The
parameters A and n are material strain hardening parameters and are
determined using curve fitting for the stress-strain curve by a power
function. c1 and c2 are two basic Mohr–Coulomb parameters and are
calibrated using material tests carried up to fracture. The parameter cθ
s
controls dependence on the Lode angle, and the parameter cθ
ax
controls
the asymmetry of fracture locus. Their default value is 1.0 if no addi-
tional test data are available, which is the case in this paper. A VUMAT
subroutine was developed to include the MMC damage model in the
analysis with the Abaqus/Explicit solver.
Before using the MMC damage model, it is necessary to find local
Fig. 10. Major principal strain values obtained using ARAMIS for DP980 steel in the bulge specimen (a) along section I before fracture, (b) maximum strain during
loading, and (c) Equivalent strain distribution before fracture.
Table 5
Calibrated MMC damage parameters.
Material A (MPa) n (-) cθ
s (-) cθ
ax (-) c1 (-) c2 (MPa)
DP600 1105 0.2079 1.048 1 0.15 685
DP980 1695.12 0.153 0.925 1 0.15 900
Fig. 11. Numerical fracture loci of DP600 (a) and DP980 (b).
7

equivalent fracture strain in different loading conditions. This was done
through 3D numerical simulations of flat test specimens using C3D8
elements in the Abaqus/Explicit solver. Material behavior for all si-
mulations were extracted from uniaxial experiments performed in the
Section 2 (Fig. 2) and material damage was not considered. The local
fracture strain (ε̄f ) and two stress state parameters, stress triaxiality (η)
and Lode angle (θ̄) parameters were determined at the location of
fracture initiation. Since the stress states parameters (triaxiality and
Lode angle) are variable during the loading test, (Bao and Wierzbicki
2004) and (Bai ad Wierzbicki 2010) calculated the average histories of
stress triaxiality and Lode angle parameters using numerical simula-
tions. They utilized a concept of average stress triaxiality and Lode
angle parameters which are defined by Eqs. (3) and (4), respectively. In
this paper, the proposed approach was applied to calculate the average
values of stress states parameters. A detailed description of the simu-
lation approach can be found in Refs. (Bao and Wierzbicki, 2004;
Basaran, 2011; Bai and Wierzbicki, 2010). A summary of stress state
parameters, ηav and θ̄av, and the equivalent strain to fracture ε̄f for
DP600 and DP980 are shown in Table 2.
∫
=
η
ε
η ε dε
1
¯
(¯ ) ¯
av
f
ε
p p
0
¯f
(3)
∫
=
θ
ε
θ ε dε
¯ 1
¯
¯(¯ ) ¯
av
f
ε
p p
0
¯f
(4)
where ε ̅_p is the calculated equivalent local plastic strain in each in-
crement and η ε
(¯ )
p and θ ε
¯(¯ )
p are unique functions of equivalent plastic
strain.
In order to model damage evolution, as suggested in Ref. (Bai and
Wierzbicki, 2010) a linear incremental relationship based on the da-
mage indicator, D, and local equivalent plastic strain under monotonic
loading conditions was assumed:
∫
=
D ε
dε
f η θ
(¯ )
¯
( , ¯)
p
ε
p
0
¯p
(5)
where f η θ
( , ¯) or ε̄f is the MMC function from Eq. (1) which should be
calculated in each increment based on triaxiality and Lode parameters.
The final failure based on Eq. (3) happens when D = 1, so that =
ε ε
¯ ¯
p f .
4. Results and discussion
4.1. Macroscopic analysis
4.1.1. Anisotropic behavior
In this study, standard tensile tests were carried out in order to
study the isotropic and anisotropic behavior of the DP600 and DP980
steels. Table 3 summarizes results of standard tensile tests for DP600
and DP980 in terms of ultimate tensile strength (UTS), yield strength
(σy) and, r-ratio in three directions (rolling direction, transverse direc-
tion, and 45° to rolling direction). Difference in yield strength in the
three directions is negligible for both steels. Consequently, the r-ratio is
very similar in the three directions. Average values of r-ratio were
calculated using Eq. (6). The average r-ratio for DP600 and DP980
steels was 0.88 and 0.8, respectively, showing a small amount of ani-
sotropic behavior in the flow curve.
=
+ +
r
r r r
2
4
0 45 90
(6)
Fig. 12. Comparison of experimental stress-strain curves and the results of macromechanical simulations incorporating the MMC damage model for DP600 (a) and
DP980 (b).
Fig. 13. Experimental engineering stress–strain curves of notched tensile specimens of (a) DP600 and (b) DP980 steels.
8

In order to investigate fracture behavior, tensile tests were per-
formed until final fracture. The fracture strain for both materials and in
three directions are listed in Table 4. The results show some
discrepancies in fracture strain at different directions, with the differ-
ences being greater in DP980 than DP600. It can be concluded that at
higher martensite volume fractions, the rolling process results in more
Fig. 14. Optical light microscopy and scanning electron microscopy images of DP steels.
Fig. 15. EBSD grain orientation maps method for (a) DP600, and (b) DP980 steels.
9

anisotropic material behavior. Fracture behavior of DP600 steel could
be assumed as isotropic, but for DP980 steel this assumption is in-
accurate.
4.1.2. Mechanical behavior under different stress-states
Average engineering stress-strain curves from the tensile, notched
tensile, shear and bulge tests on DP600 and DP980 are illustrated in
Fig. 5. It is evident that in all stress states, DP600 has a higher fracture
strain than DP980, owing to its higher ferrite phase fraction which
increases formability, whereas DP980 shows a higher strength.
4.1.3. Calculation of local strain distribution
ARAMIS analysis was used to investigate local plastic strain in the
specimens. In order to compare local plastic strain in the last step of
loading before fracture, it is necessary to choose one region of the
specimen as reference. Therefore, five parallel lines with several points
were considered and strain in the X-direction was calculated for each
line (Fig. 6a). The results show that the strain increases in the middle of
the specimen, and reaches the maximum in section-2 (Fig. 6b). This
region was chosen for future calculations.
Figs. 7 and 8 show local plastic strain in loading direction obtained
using ARAMIS in tensile, notched tensile, and shear specimens com-
pared to simulation results. It can be seen in Fig. 7 that in DP600 steels,
the maximum local strain in loading direction occurs in the tensile
specimen and the minimum value is observed in notched-tensile spe-
cimens, whereas in DP980 (Fig. 8), the maximum local strain in loading
direction occurs in tensile and notched-tensile specimens and the
minimum value is in the shear specimen. A good agreement between
ARAMIS and 3D simulations for DP600 and DP980 steels can be ob-
served in Figs. 7 and 8. It should be noted that the results of ARAMIS
data obtained from the surface of specimens and that strain in the out of
plane direction (z-direction) cannot be calculated from these experi-
ments. Consequently, the numerical approach could be used to calcu-
late the value of the equivalent plastic strain during different loading
conditions.
Results of ARAMIS analysis for bulge tests in DP600 and DP980
steels are illustrated in Figs. 9 and 10, respectively. Figs. 9(a) and 10(a)
show that the maximum value of local major principal strain occurs in
the middle of the bulge specimens. It is evident from Figs. 9(b) and
10(b) that the local strain increases with loading, and the maximum
value of local strain happens in the final loading stage before fracture.
Local major principal strain distributions are shown in Figs. 9(c) and
10(c) for DP600 and DP980, respectively. In DP600, the maximum local
strain occurs in a point in the middle of the specimen, showing that in
DP600 strain localization is very important and damage begins with
localization in a very small area. However, in DP980 the maximum
local strain value is smaller and the localization region is larger.
4.1.4. Damage calibration
To predict the fracture behavior under different loading conditions,
the MMC damage model was applied to 3D macro-mechanical models.
Calibrated MMC damage parameters for DP600 and DP980 are given in
Table 5. The resulting fracture loci are plotted in Fig. 11. Stress-Strain
curve of 3D numerical simulations with MMC damage model are
compared with the experiments in Fig. 12. It can be observed that the
3D models with the MMC damage model provide very good estimates
for the experimental results under different loading conditions. There-
fore, this 3D macro-mechanical model with MMC damage model could
be used for the prediction of the damage behavior under different stress
states for both materials.
Fig. 16. Pole EBSD texture plot in (100), (110), and (111) orientations for DP600 (top) and DP980 (bottom).
10

4.1.5. Effect of strain rate
Engineering stress-strain curves for notched tensile tests of DP600
and DP980 under different strain rates are displayed in Fig. 13. In both
steels, Young's modulus and yield strength are the same at various
strain rates, but elongation increases with increasing strain rate, and
this phenomenon is more pronounced in DP600 than in DP980. Ac-
cording to Huh et al. (2008), positive strain rate sensitivity may be
present a higher strain rate decelerates annihilation of dislocations and
increases the barriers of dislocation motion for thermal and mechani-
cally activated plastic deformations.
4.2. Microscopic analysis
Fig. 14 shows microstructures of DP600 and DP980 steels obtained
using optical light microscopy (OLM) and scanning electron microscopy
(SEM). In all images, light regions are ferrite phase and dark zones are
martensite phase. Volume fraction of martensite phase (Vm) was cal-
culated according to ASTM E562-08 (2008) using mean linear intercept
method to be approximately 33% and 52% for DP600 and DP9800,
respectively. In the OLMs, phase orientation due to the rolling process is
observed which explains small discrepancies in the fracture strain in
different directions for the two steels reported in Table. 4. This is
especially pronounced for the DP980 specimen.
4.2.1. Comparison of grain distribution using EBSD
Fig. 15 illustrates grain orientation maps for DP600 and DP980
steels obtained using SEM-EBSD. The image size is 50 μm x 50 μm. It is
clear that the grain size of DP600 is larger than for DP980. Despite the
cold rolling operation on the steels, grains are not very oriented in the
rolling direction. Therefore, both materials have a rather isotropic
hardening behavior. Fig. 16 shows pole EBSD texture plots in three
different grain orientations ((100), (110) and (111)) for DP600 and
DP980 steels. Grain distributions in both steels are roughly the same,
but the density of these orientations in DP980 is higher than in DP600
which is in agreement with the small anisotropy of UTS reported in
Table 3.
4.2.2. Comparison of damage initiation and propagation by in-situ tensile
test
In this study, an in-situ analysis was used in order to investigate the
failure scenario inside the microstructure of DP steels with low (DP600)
and high (DP980) martensite volume fractions.
Fig. 17 shows results of in-situ tensile tests from low macroscopic
applied strains to final loading stage before fracture in DP600 steel
specimens. Fig. 17(a) shows damage initiation mechanisms at low ap-
plied strains in tensile specimens. As reported in previous studies
(Alaie et al., 2015a,b), the thickness of the geometrically necessary
dislocation (GND) layer is 25% of the size of the martensite phases. In
DP600, there are many large ferrite phases and centers of these phases
are less affected by the martensite volume changes. Consequently, shear
bands can be observed as first candidates for the formation of damage
initiation (Fig. 17(a), regions A and B).
As strain increases, the difference in deformation behavior of soft
phase (ferrite) and hard phase (martensite) causes two types of strain
localizations. The first is at the boundary between ferrite and marten-
site phases (Fig. 17(b), regions C and D). Ferrite undergoes much more
deformation than martensite and this mismatch causes the formation of
localized strain in ferrite within the neighborhood of martensite phases.
Fig. 17. Damage initiation and propagation in DP600 after (a) 7%, (b) 14%, (c) 21%, and (d) 28% strain. Loading direction is vertical.
11

The second type of strain localization happens in ferrite phases trapped
in the martensite (Fig. 17(b), regions E-G). The existence of martensite
phases close to each other results in void initiation in ferrite due to high
stress triaxiality. In DP600 steel, strain localization in the center of the
ferrite phase is more dominant than other types of localizations.
At higher strains, three types of micro-cracks are formed in the
microstructure: (1) strain bands propagate, and become longer and
thicker. Fig. 17(c) illustrates the deformation and the propagation of
strain bands. The martensite phases usually alter the path of strain
bands, but some thin martensite phases (e.g. regions H and J) cannot
change the path of strain bands and are consequently subjected to
failure due to the high strain field inside the strain bands. Separated
pieces of the phase move apart in the loading direction. Therefore, the
ferrite grains within the neighborhood of the separated pieces can be
considered as a high potential site for micro-crack initiation. (2) The
voids in the boundary of ferrite and martensite phases propagate in a
crack type manner and formed a micro-crack at the interphases (regions
K-M in Fig. 17(c)). Finally, applied deformation was increased until the
specimen was near failure (Fig. 17(d)). Here micro-cracks propagate
and form the cracks through the strain bands, leading to final fracture
of the low martensite volume fraction steel.
Evolution of microscopic damage in the high martensite volume
fraction steel (DP980) is shown in Fig. 18. The size of ferrite phases is
small and dislocation density is roughly the same in different regions of
ferrite phases (Ramazani et al., 2013). Therefore the localization in the
middle of DP980’s ferrite phase is lower than in the DP600 steel under
low macroscopic applied strain (Fig. 18(a)). The first candidate for
damage initiation in DP980 is in the ferrite phase neighboring mar-
tensite phases, because of the difference between the deformation of the
ferrite and martensite phases (see region A in Fig. 18(a)). According
Fig. 18(b), as the loading increases, the number of damage sites at
phase boundaries increases, and another type of strain localization and
void nucleation occurs in ferrite phases between closely spaced mar-
tensite phases, because of high stress triaxiality (see regions B and C in
Fig. 18(b)). In DP980 steel, the strain localization at the boundary of
ferrite and martensite phases is more dominant than other types of
localizations due to the higher amount of interfaces.
In Fig. 18(c), the propagation of localized shear bands and voids are
shown. In Fig. 18(d), the shear bands propagated and joined each other
which causes martensite cracking (regions D-F in Fig. 18). Also, it can
be observed that the voids propagated and formed a micro-crack at the
boundary of ferrite and martensite phases (region G and H). In the end,
final failure is caused by coalescence of micro-cracks in shear bands and
at the boundary of ferrite and martensite phases.
5. Conclusion
In this paper, the mechanical behavior and damage evolution of
commercial DP600 and DP980 dual-phase steel were investigated using
experimental methods. The mechanical behavior were analyzed in
three parts.
At first, as shown by standard tensile and EBSD results, both ma-
terials demonstrated isotropic hardening behavior. DP600 had roughly
isotropic behavior at fracture point whereas fracture behavior of DP980
Fig. 18. Damage initiation and propagation in DP980 after (a) 6%, (b) 9%, (c) 11%, and (d) 12.5% strain. Loading direction is vertical.
12

showed a small amount of anisotropy.
Second, the effect of stress state on flow curve and local strain were
examined. The results showed that the maximum value of local strain
occurs roughly in the middle of critical region in all four specimens. The
local strain in DP600 was more than in DP980 and the maximum dis-
crepancy occurred for tensile and shear specimens. Also the difference
between the maximum local strain in tensile specimen (at maximum
Lode angle) to minimum local strain in bulge specimen (at minimum
Lode angle) is high, whereas for DP980 steel, this difference is lower.
In the third part, the effect of strain rate in notched-tensile speci-
mens were studied. The results showed that strain rate doesn't have any
influence on Young's modulus and yield strength for both materials. It is
observed that the elongation increases with increasing strain rate and
this discrepancy in DP600 is higher than in DP980, due to the higher
amount of the ductile ferrite phase in DP600.
Finally, the damage evolution was assessed under tensile loading
conditions in both materials in three stages (i.e., damage initiation,
damage growth and damage coalescence) by in-situ testing. At low level
of applied loading, three different types of damage initiation mechan-
isms were observed in both materials, (a) in the middle of large ferrite
phase, (b) at the interface of ferrite and martensite phase, and (c) at the
trapped ferrite phase surrounded by martensite phases. The most im-
portant damage initiation mechanisms in DP600 and DP980 were (a)
and (b), respectively. At high strains, two effective micro-crack initia-
tion mechanisms were reported during in-situ test: (i) at thin martensite
phase, due to strain or shear band growth, (ii) at boundary between
ferrite and martensite phases. DP600 and DP980 steels have the same
behavior in the micro-crack initiation stage. With applying more strain,
the micro-cracks propagate through the strain bands and then it leads to
final fracture in both grades of steel.
CRediT authorship contribution statement
Ali Cheloee Darabi: Methodology, Software, Validation, Writing -
original draft, Visualization. Vinzenz Guski: Formal analysis,
Investigation, Data curation, Visualization. Alexander Butz: Formal
analysis, Investigation, Resources, Data curation. Javad
Kadkhodapour: Conceptualization, Investigation, Resources,
Supervision. Siegfried Schmauder: Writing - review & editing,
Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Acknowledgments
The authors would like to thank the German Research Foundation
(DFG) for financial support of the project at the University of Stuttgart
(SCHM 746/166-1) and Fraunhofer Institute for Mechanics of
MaterialsIWM (BU 3184/2-1), in title: micro-mechanical investigation
of deformation and failure scenario in dual phase steel using experi-
mental and numerical methods.
References
Al-Abbasi, F.M., Nemes, J.A., 2003. Micromechanical modeling of the effect of particle
size difference in dual phase steels. Int. J. Solid. Struct. 40, 3379–3391.
Alaie, A., Kadkhodapour, J., Rad, S.Z., Asadabad, M.A., Schmauder, S., 2015b. Formation
and coalescence of strain localized regions in ferrite phase of DP600 steels under
uniaxial tensile deformation. Mater. Sci. Eng. 623, 133–144.
Alaie, A., Rad, S.Z., Kadkhodapour, J., Jafari, M., Asadabad, M.A., Schmauder, S., 2015a.
Effect of microstructure pattern on the strain localization in DP600 steels analyzed
using combined in-situ experimental test and numerical simulation. Mater. Sci. Eng.
638, 251–261.
Alharbi, K., Ghadbeigi, H., Efthymiadis, P., Zanganeh, M., Celotto, S., Dashwood, R.,
Pinna, C., 2015. Damage in dual phase steel DP1000 investigated using digital image
correlation and microstructure simulation. Model. Simul. Mater. Sci. Eng. 23.
ASTM E562-08, Standard test method for determining volume fraction by systematic
manual point count (2008). https://www.astm.org/DATABASE.CART/HISTORICAL/
E562-08.htm.
Bai, Y., Teng, X., Wierzbicki, T., 2009. On the application of stress triaxiality formula for
plane strain fracture testing. J. Eng. Mater. Technol. 131.
Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure
and Lode dependence. Int. J. Plasticity 24, 1071–1096.
Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr–Coulomb criterion to ductile
fracture. Int. J. Fract. 161, 1–20.
Bandyopadhyay, K., Lee, M.G., Panda, S.K., Saha, P., Lee, J.H., 2017. Formability as-
sessment and failure prediction of laser welded dual phase steel blanks using aniso-
tropic plastic properties. Int. J. Mech. Sci. 126, 203–221.
Bao, Y., Wierzbicki, T., 2004. On fracture locus in the equivalent strain and stress
triaxiality space. Int. J. Mech. Sci. 46, 81–98.
Bao, Y., Wierzbicki, T., 2005. On the cut‐off value of negative triaxiality for fracture. Eng.
Fract. Mech. 72, 1049–1069.
Basaran, M., 2011. Stress state dependent damage modeling with a focus on the lode
angle influence. Ph.D. thesis. Aachen, Shaker.
Bleck, W., Papaefthymiou, S., Frehn, A., 2016. Microstructure and Tensile Properties in
Dual Phase and Trip Steels. steel research int. 75, 704–710.
Bridgman, P.W., 1952. Studies in Large Plastic Flow and Fracture. McGrraw-Hill, New
York.
Choi, S.H., Kim, E.Y., Woo, W., Han, S., Kwak, J., 2013. The effect of crystallographic
orientation on the micromechanical deformation and failure behaviors of DP980 steel
during uniaxial tension. Int. J. Plast. 45, 85–102.
Darabi, A.C., Chamani, H.R., Kadkhodapour, J., Anaraki, A.P., Alaie, A., Ayatollahi, M.R.,
2017. Micromechanical analysis of two heat-treated dual phase steels: DP800 and
DP980. Mech. Mater. 110, 68–83.
Deng, N., Korkolis, Y.P., 2018. Elastic anisotropy of dual-phase steels with varying
martensite content. Int. J. Solid. Struct. 141–142, 264–278.
Ennis, B.L., Bos, C., Aarnts, M.P., Lee, P.D., Jimenez-Melero, E., 2018. Work hardening
behaviour in banded dual phase steel structures with improved formability. Mater.
Sci. Eng. 713, 278–286.
Frechard, S., Martin, F., Clement, C., Cousty, J., 2006. AFM and EBSD combined studies of
plastic deformation in a duplex stainless steel. Mater. Sci. Eng. 418, 312–319.
Fung, Y.C., 1965. Foundations of Solid Mechanics. Prentice Hall Inc, Englewood
Cliffs, NJ.
Furukawa, T., Tanino, M., Morikawa, H., ENDO, M., 1984. Effects of composition and
processing factors on the mechanical properties of as-hot-rolled dual-phase steels.
Trans. Iron Steel Inst. Jpn. 24, 113–121.
Ghadbeigi, H., Pinna, C., Celotto, S., Yates, J.R., 2010. Local plastic strain evolution in a
high strength dual-phase steel. Mater. Sci. Eng. A 527, 5026–5032.
Guo, E., Wang, M., Jing, T., Chawla, N., 2013. Temperature-dependent mechanical
properties of an austenitic–ferritic stainless steel studied by in situ tensile loading in a
scanning electron microscope (SEM). Mater. Sci. Eng. 580, 159–168.
Han, Q., Kang, Y., Hodgson, P., Stanford, N., 2013. Quantitative measurement of strain
partitioning and slip systems in a dual-phase steel. Scr. Mater. 69, 13–16.
He, X.J., Terao, N., Berghezan, A., 1984. Influence of martensite morphology and its
dispersion on mechanical properties and fracture mechanisms of Fe-Mn-C dual phase
steels. Met. Sci. 18, 367–373.
Huh, H., Kim, S.B., Song, J.H., Lim, J.H., 2008. Dynamic tensile characteristics of TRIP-
type and DP-type steel sheets for an auto-body. Int. J. Mech. Sci. 50, 918–931.
Johnson, G.R., Cook, W.H., 1985. Fracture characteristics of three metals subjected to
various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21, 31–48.
Joo, S., Lee, J.K., Koo, J., Lee, S., Suh, D., Kim, H.S., 2013. Method for measuring na-
noscale local strain in a dual phase steel using digital image correlation with nanodot
patterns. Scr. Mater. 68, 245–248.
Kadkhodapour, J., Butz, A., Ziaei-Rad, S., 2011. Mechanisms of void formation during
tensile testing in a commercial, dual-phase steel. Acta Mater. 59, 2575–2588.
Kahziz, M., Morgeneyer, T., Maziere, M., Maire, E., Bouaziz, O., 2013. 3D Synchrotron
laminography assessment of damage evolution in blanked dual phase steels. In:
Proceedings of 13th International Conference on Fracture. Beijing, China. 16 June.
Kang, J.D., Ososkov, Y., Embury, J.D., Wilkinson, D.S., 2007. Digital image correlation
studies for microscopic strain distribution and damage in dual phase steels. Scr.
Mater. 56, 999–1002.
Karmakar, A., Mandal, M., Mandal, A., B.Sk, M.D., Mukherjee, S., Chakrabarti, D., 2016.
Effect of starting microstructure on the grain refinement in cold-rolled low-carbon
steel during annealing at two different heating rates. Metall. Mater. Trans. 47,
268–281.
Lewandowski, J.J., Lowhaphandu, P., 1988. Effects of hydrostatic pressure on mechanical
behaviour and deformation processing of materials. Int. Mater. Rev. 43, 145–187.
Nakadaa, N., Arakawab, Y., Parkb, K.S., Tsuchiyamaa, T., Takakia, S., 2012. Dual phase
structure formed by partial reversion of cold-deformed martensite. Mater. Sci. Eng. A
553, 128–133.
Nouroozi, M., Mirzadeh, H., Zamani, M., 2018. Effect of microstructural refinement and
intercritical annealing time on mechanical properties of high-formability dual phase
steel. Mater. Sci. Eng. A 736, 22–26.
V.V. Novozhilov, Theory of elasticity, U.S. department of commerce translation (1861).
https://www.cambridge.org/core/journals/aeronautical-journal/article/theory-of-
elasticityv-v-novozhilov-pergamon-press-london-1961-448-pp-4/
BFCD97238703749FE0831CA351ABD2BB.
Ososkov, Y., Wilkinson, D.S., Jain, M., Simpson, T., 2007. In situ measurement of local
strain partitioning in a commercial dual-phase steel. Int. J. Mater Res. 98, 664–673.
Ramazani, A., Mukherjee, K., Schwedt, A., Goravanchi, P., Prahl, U., Bleck, W., 2013.
13

Quantification of the effect of transformation-induced geometrically necessary dis-
locations on the flow-curve modelling of dual-phase steels. Int. J. Plast. 43, 128–152.
Rice, J.R., Tracey, D.M., 1969. On the ductile enlargement of voids in triaxial stress fields.
J. Mech. Phys. Solids 17, 201–217.
Roth, C.C., Mohr, D., 2016. Ductile fracture experiments with locally proportional loading
histories. Int. J. Plast. 79, 328–354.
Santos, R.O., da Silveira, L.B., Moreiraa, L.P., Cardosoc, M.C., da Silvaa, F.R., Paulad,
A.S., Albertacci, D.A., 2019. Damage identification parameters of dual-phase
600–800 steels based on experimental void analysis and finite element simulations. J.
Mater. Res. Technol. 8, 644–659.
Tarigopula, V., Hopperstad, O.S., Langseth, M., Clausen, A.H., Hild, F., Lademo, O.G.,
Eriksson, M., 2008. A study of large plastic deformations in dual phase steel using
digital image correlation and Fe analysis. Exp. Mech. 48, 181–196.
Wierzbicki, T., Xue, L., 2005. On the effect of the third invariant of the stress deviator on
ductile fracture. In: Technical report, Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology. Cambridge, MA (USA).
Woo, W., Em, V., Kim, E., Han, S., Han, Y., Choi, S., 2012. Stress–strain relationship
between ferrite and martensite in a dual-phase steel studied by in situ neutron dif-
fraction and crystal plasticity theories. Acta Mater. 60, 6972–6981.
Zhang, J., Di, H., Deng, Y., Misra, R.D.K., 2015. Effect of martensite morphology and
volume fraction on strain hardening and fracture behavior of martensite–ferrite dual
phase steel. Mater. Sci. Eng. A 627, 230–240.
14

DP-Triaxiality.pdf

Recommended

Recommended

More Related Content

Similar to DP-Triaxiality.pdf

Similar to DP-Triaxiality.pdf (20)

More from Javad Kadkhodapour

More from Javad Kadkhodapour (7)

Recently uploaded

Recently uploaded (20)

DP-Triaxiality.pdf