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A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels
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A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels Ali Cheloee Darabi , Vinzenz Guski , Alexander Butz , Javad. Kadkhodapour , Siegfried Schmauder PII: DOI: Reference:
S0167-6636(19)30811-7 https://doi.org/10.1016/j.mechmat.2020.103339 MECMAT 103339
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Mechanics of Materials
Received date: Revised date: Accepted date:
22 September 2019 17 December 2019 17 January 2020
Please cite this article as: Ali Cheloee Darabi , Vinzenz Guski , Alexander Butz , Javad. Kadkhodapour , Siegfried Schmauder , A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels, Mechanics of Materials (2020), doi: https://doi.org/10.1016/j.mechmat.2020.103339
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Highlights
The influence on the stress state on the mechanical behavior was analyzed by ARAMIS approach which is based on DIC. The MMC damage model could be used for the prediction of the damage behavior under different stress states for DP steel material. Three different types of damage initiation mechanisms were observed in DP600 and DP980 steels. The most important damage initiation mechanisms in DP600 and DP980 were in the middle of large ferrite phase and at the interface of ferrite and martensite phase, respectively. Two effective micro-crack initiation mechanisms were observed during in-situ test and DP600 and DP980 steels have the same behavior in the micro-crack initiation stage.
A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels Ali Cheloee Darabi1,2, Vinzenz Guski1, Alexander Butz3, Javad. Kadkhodapour1,2* , Siegfried Schmauder1 1
Institute for Materials Testing, Materials Science and Strength of Materials, University of Stuttgart, Pfaffenwaldring 32, 70569, Stuttgart, Germany 2 3
Shahid Rajaee Teacher Training University, Lavizan, Teheran, Iran
Fraunhofer Institute for Mechanics of Materials IWM, 79108 Freiburg, Germany
Abstract 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 uniaxial 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. Keywords: Dual phase steel, stress state, mechanical behavior, damage scenario, in-situ tensile test.
1. Introduction Different grades of dual phase (DP) belong to the most important steels used in the automotive industry because of their excellent mechanical 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 morphology of martensite islands have an important effect on mechanical properties [1-2]. Martensite phase distribution is one of the most important parameters which can influence the anisotropic deformation behavior of DP steels. In the manufacturing process of commercial DP steels, the cold*
Corresponding author. E-mail address: [email protected] (J. Kadkhodapour)
rolling step leads to creation of martensite bands in the microstructure. Some researchers [3-5] have reported that anisotropic behavior in dual phase steels is very critical and should be considered. However, others [6-7] 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. [8] showed that with the cold-rolling process, the chain-networked martensite grains are formed in grain boundaries of ferrite islands. Nourozi et al. [9] conducted an intercritical annealing 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. [10] showed a cold-rolled DP steel with fine grain size and uniform distribution of the martensite phase causes the combination of good strength and ductility. Bridgman [11] tested axisymmetric specimens with various imposed hydrostatic pressure and showed the effect of pressure on fracture strain. Other researchers e.g., Lewandowski and Lowhaphandu [12] confirmed Bridgman’s results. Bai et al. [13] 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. AlAbbasi et al. [14] 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 determination 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 [15-16]. 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 history in 2D or 3D coordinate systems. The mathematical description at this contactless approach is based on continuum mechanics [17-18]. Tarigopula et al. [19] studied large plastic deformation in DP800 using digital image correlation and compared experimentally obtained local strains with Finite Element (FE) simulation results. Roth et al. [20] 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-Tracy [21] and Johnson-Cook (JC) [22] are based on triaxiality. Recently, different studies have been performed on the influence of Lode-angle parameter on damage evolution [23-25]. Wierzbicki et al. [23] generated a symmetric fracture locus based on Lode angle parameter and stress triaxiality utilizing Wilkins and Rice-Tracy damage models. Bai et al. [24] used a parabolic function in order to consider the effect of Lode-angle on fracture locus. Then, they proposed a damage model based on triaxiality and Lode angle by combining Lode angle function and the Rice-Tracy damage model. Bai et al. [16] extended the Mohr-Coulomb (MC) damage model for ductile metals. They reformulated the MC damage model in the spherical 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 deformation [26-30]. Guo et al. [31] investigated the plastic deformation in an austenitic-ferritic cast duplex stainless steel (CDSS) by in-situ tensile tests at different temperatures. Kang et al. [32] 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 annealedquenched materials. Ososkov et al. [33] studied local strain distribution values in ferrite phase and within martensite phases using DIC. Ghadbeigi et al. [34] 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 observed two different damage initiation mechanisms. They reported that the most common damage initiation happens at the interface of martensite and ferrite phases. Kadkhodapour et al. [35] 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 [35-37]. 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. [38] 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. [37] 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. [39] utilized the in-situ test and DIC method, in order to examine failure mechanisms in microstructure of DP1000 steels. Kahziz et al. [40] investigated damage propagation during bending of DP600 steel using laminography. Zhang et al. [41] evaluated the fracture mechanisms in two different morphologies of the martensite phase. Here, two different damage mechanisms were observed. 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 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 experimentally 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 damage 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 notchedtensile tests. Finally, the in-situ test setup was used to compare the damage scenario (i.e., strain localization, micro-crack initiation, and coalescence 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 received 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 different orientations (parallel to rolling, normal to loading, and 45 degree 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 repeated three times.
Material
Table 1. Chemical composition of steels used in this study. Element (Mass contents %) Al
Mo
Mn
Si
P
S
Cr
Ni
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
V 0.01
Cu
Co
C
DP600
0.022 0.003
Fig. 1. Standard tensile specimen prepared from DP steels after DIN EN ISO 6892-1.
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 68921, which is shown in Fig. 2. All the tests were conducted at the strain rate of 0.01 .
(a) (b) (c) (d) Fig. 2. Experimental specimens prepared from DP steels: (a) tensile, (b) Notched tensile, (c) shear, and (d) bulge specimens.
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 ). Also, ARAMIS measurements were utilized to analyze the deformation history and strain localization pattern during loading. Fig. 3 shows the experimental setup and a tensile specimen prepared with a speckle pattern for capturing the deformation on the surface during the test.
(a)
(b)
Fig. 3. ARAMIS Testing Setup (a) ARAMIS system, (b) prepared specimen during ARAMIS testing.
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 [42]. 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 screwdriven 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 following 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 (Error! Reference source not found.(a) and 4(b)). The changes in the macroscopic dimensions were measured at each deformation 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 observation of deformational behavior of microstructure at the last steps before the failure of the specimen (Error! Reference source not found.(c) and 4(d)). Finally, image processing techniques were applied for local plastic deformation analysis.
(a)
(b)
(c)
(d)
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.
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 [16]:
̅
{
√
*
(
√
̅
*
(
̅
)
)+ [√
(
̅
)
(
(
̅
))]}
Eq.1
Eq.2 ̅
where η and ̅ are triaxiality and Lode angle parameters, respectively. A total of six parameters ( , , , , , ) need to be defined. The parameters and are material strain hardening parameters and are determined using curve fitting for the stress-strain curve by a power function. and are two basic Mohr–Coulomb parameters and are calibrated using material tests carried up to fracture. The parameter controls dependence on the Lode angle, and the parameter controls the asymmetry of fracture locus. Their default value is 1.0 if no additional 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 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 simulations were extracted from uniaxial experiments performed in the section 2 (Fig.2) and material damage was not considered. The local fracture strain ( ̅ ) and two stress state parameters, stress triaxiality (η) and Lode angle ( ̅ ) 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 [15] and Bai ad Wierzbicki [16] calculated the average histories of stress triaxiality and Lode angle parameters using numerical simulations. They utilized a concept of average stress triaxiality and Lode angle parameters which are defined by Eq. 3 and Eq. 4, respectively. In this paper, the proposed approach was applied to calculate the average values of stress states parameters. A detailed description of the simulation approach can be found in Refs. [15-16, 43]. A summary of stress state parameters, and ̅ , and the equivalent strain to fracture ̅ for DP600 and DP980 are shown in Table 2. ̅
∫ ( ̅ ) ̅
Eq. 3 ̅
̅
̅ ̅
∫ ̅( ̅ ) ̅
Eq. 4
where ε ̅_p is the calculated equivalent local plastic strain in each increment and (̅ ) and ̅ ( ̅ ) are unique functions of equivalent plastic strain.
Table 2. Summary of 3D simulations carried out to calibrate the MMC model for DP600 and DP980 steels.
No
Specimen
1 2 3 4
Tensile Simple shear Notched-tensile Bulge
̅ 0.34 0.015 0.57 0.658
0.995 0.02 0.15 -0.994
̅ DP600 1.398 1.048 0.542 0.66
DP980 0.552 0.868 0.342 0.496
In order to model damage evolution, as suggested in Ref. [16] a linear incremental relationship based on the damage indicator, D, and local equivalent plastic strain under monotonic loading conditions was assumed: ̅
( ̅ )
∫
̅ ̅
Eq. 5
̅ or ̅ is the MMC function from Eq. 1 which should be calculated in each increment based where on triaxiality and Lode parameters. The final failure based on Eq. 3 happens when D=1, so that ̅ ̅.
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 ( ) and, r-ratio in three directions (rolling direction, transverse direction, and 45 degree 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 anisotropic behavior in the flow curve. Eq. 6 In order to investigate fracture behavior, tensile tests were performed 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 differences being greater in DP980 than DP600. It can be concluded that at higher martensite volume fractions, the rolling process results in more anisotropic material behavior. Fracture behavior of DP600 steel could be assumed as isotropic, but for DP980 steel this assumption is inaccurate.
Table 3. Tensile test data for DP600 and DP980 steels. Material
(-)
(-)
(-)
365.5
0.9
0.809
1.034
681.5
0.635
0.927
0.724
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
DP600
644
649
648
357
372
DP980
1009
1026
1044.5
665.5
667
Table 4. The values of the fracture strain in three different directions. Material
(-)
(-)
(-)
DP600
0.288
0.273
0.2696
DP980
0.128
0.132
0.094
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.
(a)
(b)
(c)
(d)
Fig. 5. Experimental stress-strain curves obtained from (a) tensile, (b) notched tensile, (c) shear, and (d) bulge tests.
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 compared 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 specimens, 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 observed 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 experiments. Consequently, the numerical approach could be used to calculate the value of the equivalent plastic strain during different loading conditions.
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.
(a)
(b)
(c)
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.
(a)
(b)
(c)
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.
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.
(a)
(b)
(c)
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.
(a)
(b)
(c)
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.
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. Therefore, 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. Table 5. Calibrated MMC damage parameters. Material DP600 DP980
A (MPa) 1105 1695.12
n (-) 0.2079 0.153
(-) 1.048 0.925
(-) 1 1
(-) 0.15 0.15
(a) (b) Fig. 11: Numerical fracture loci of DP600 (a) and DP980 (b).
(MPa) 685 900
(a) (b) 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).
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. According to [44], 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 mechanically activated plastic deformations.
(a)
(b)
Fig. 13. Experimental engineering stress–strain curves of notched tensile specimens of (a) DP600 and (b) DP980 steels.
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 ( ) was calculated according to ASTM E562-08 [45] 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.
OLM SEM
DP600 (
)
DP980 (
)
Fig. 14. Optical light microscopy and scanning electron microscopy images of DP steels.
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 x 50 . 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.
(a)
(b)
Fig. 15. EBSD grain orientation maps method for (a) DP600, and (b) DP980 steels.
Fig. 16. Pole EBSD texture plot in (100), (110), and (111) orientations for DP600 (top) and DP980 (bottom).
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 applied strains in tensile specimens. As reported in previous studies [37, 46], 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 martensite 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. 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.
(a)
(b)
(c)
(d)
Fig. 17. Damage initiation and propagation in DP600 after (a) 7%, (b) 14%, (c) 21%, and (d) 28% strain. Loading direction is vertical.
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 [47]. 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 martensite 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 martensite 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.
(a)
(b)
c)
(d)
Fig. 18. Damage initiation and propagation in DP980 after (a) 6%, (b) 9%, (c) 11%, and (d) 12.5% strain. Loading direction is vertical.
5. Conclusion In this paper, the mechanical behavior and damage evolution of commercial DP600 and DP980 dualphase 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 materials demonstrated isotropic hardening behavior. DP600 had roughly isotropic behavior at fracture point whereas fracture behavior of DP980 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 discrepancy 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 specimens 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 mechanisms 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 important damage initiation mechanisms in DP600 and DP980 were (a) and (b), respectively. At high strains, two effective micro-crack initiation 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.
Author 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.
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 Materials IWM (BU 3184/2-1), in title: micro-mechanical investigation of deformation and failure scenario in dual phase steel using experimental and numerical methods.
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Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels Ali Cheloee Darabi , Vinzenz Guski , Alexander Butz , Javad. Kadkhodapour , Siegfried Schmauder PII: DOI: Reference:
S0167-6636(19)30811-7 https://doi.org/10.1016/j.mechmat.2020.103339 MECMAT 103339
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Mechanics of Materials
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Please cite this article as: Ali Cheloee Darabi , Vinzenz Guski , Alexander Butz , Javad. Kadkhodapour , Siegfried Schmauder , A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels, Mechanics of Materials (2020), doi: https://doi.org/10.1016/j.mechmat.2020.103339
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Highlights
The influence on the stress state on the mechanical behavior was analyzed by ARAMIS approach which is based on DIC. The MMC damage model could be used for the prediction of the damage behavior under different stress states for DP steel material. Three different types of damage initiation mechanisms were observed in DP600 and DP980 steels. The most important damage initiation mechanisms in DP600 and DP980 were in the middle of large ferrite phase and at the interface of ferrite and martensite phase, respectively. Two effective micro-crack initiation mechanisms were observed during in-situ test and DP600 and DP980 steels have the same behavior in the micro-crack initiation stage.
A comparative study on mechanical behavior and damage scenario of DP600 and DP980 steels Ali Cheloee Darabi1,2, Vinzenz Guski1, Alexander Butz3, Javad. Kadkhodapour1,2* , Siegfried Schmauder1 1
Institute for Materials Testing, Materials Science and Strength of Materials, University of Stuttgart, Pfaffenwaldring 32, 70569, Stuttgart, Germany 2 3
Shahid Rajaee Teacher Training University, Lavizan, Teheran, Iran
Fraunhofer Institute for Mechanics of Materials IWM, 79108 Freiburg, Germany
Abstract 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 uniaxial 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. Keywords: Dual phase steel, stress state, mechanical behavior, damage scenario, in-situ tensile test.
1. Introduction Different grades of dual phase (DP) belong to the most important steels used in the automotive industry because of their excellent mechanical 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 morphology of martensite islands have an important effect on mechanical properties [1-2]. Martensite phase distribution is one of the most important parameters which can influence the anisotropic deformation behavior of DP steels. In the manufacturing process of commercial DP steels, the cold*
Corresponding author. E-mail address: [email protected] (J. Kadkhodapour)
rolling step leads to creation of martensite bands in the microstructure. Some researchers [3-5] have reported that anisotropic behavior in dual phase steels is very critical and should be considered. However, others [6-7] 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. [8] showed that with the cold-rolling process, the chain-networked martensite grains are formed in grain boundaries of ferrite islands. Nourozi et al. [9] conducted an intercritical annealing 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. [10] showed a cold-rolled DP steel with fine grain size and uniform distribution of the martensite phase causes the combination of good strength and ductility. Bridgman [11] tested axisymmetric specimens with various imposed hydrostatic pressure and showed the effect of pressure on fracture strain. Other researchers e.g., Lewandowski and Lowhaphandu [12] confirmed Bridgman’s results. Bai et al. [13] 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. AlAbbasi et al. [14] 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 determination 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 [15-16]. 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 history in 2D or 3D coordinate systems. The mathematical description at this contactless approach is based on continuum mechanics [17-18]. Tarigopula et al. [19] studied large plastic deformation in DP800 using digital image correlation and compared experimentally obtained local strains with Finite Element (FE) simulation results. Roth et al. [20] 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-Tracy [21] and Johnson-Cook (JC) [22] are based on triaxiality. Recently, different studies have been performed on the influence of Lode-angle parameter on damage evolution [23-25]. Wierzbicki et al. [23] generated a symmetric fracture locus based on Lode angle parameter and stress triaxiality utilizing Wilkins and Rice-Tracy damage models. Bai et al. [24] used a parabolic function in order to consider the effect of Lode-angle on fracture locus. Then, they proposed a damage model based on triaxiality and Lode angle by combining Lode angle function and the Rice-Tracy damage model. Bai et al. [16] extended the Mohr-Coulomb (MC) damage model for ductile metals. They reformulated the MC damage model in the spherical 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 deformation [26-30]. Guo et al. [31] investigated the plastic deformation in an austenitic-ferritic cast duplex stainless steel (CDSS) by in-situ tensile tests at different temperatures. Kang et al. [32] 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 annealedquenched materials. Ososkov et al. [33] studied local strain distribution values in ferrite phase and within martensite phases using DIC. Ghadbeigi et al. [34] 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 observed two different damage initiation mechanisms. They reported that the most common damage initiation happens at the interface of martensite and ferrite phases. Kadkhodapour et al. [35] 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 [35-37]. 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. [38] 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. [37] 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. [39] utilized the in-situ test and DIC method, in order to examine failure mechanisms in microstructure of DP1000 steels. Kahziz et al. [40] investigated damage propagation during bending of DP600 steel using laminography. Zhang et al. [41] evaluated the fracture mechanisms in two different morphologies of the martensite phase. Here, two different damage mechanisms were observed. 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 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 experimentally 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 damage 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 notchedtensile tests. Finally, the in-situ test setup was used to compare the damage scenario (i.e., strain localization, micro-crack initiation, and coalescence 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 received 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 different orientations (parallel to rolling, normal to loading, and 45 degree 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 repeated three times.
Material
Table 1. Chemical composition of steels used in this study. Element (Mass contents %) Al
Mo
Mn
Si
P
S
Cr
Ni
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
V 0.01
Cu
Co
C
DP600
0.022 0.003
Fig. 1. Standard tensile specimen prepared from DP steels after DIN EN ISO 6892-1.
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 68921, which is shown in Fig. 2. All the tests were conducted at the strain rate of 0.01 .
(a) (b) (c) (d) Fig. 2. Experimental specimens prepared from DP steels: (a) tensile, (b) Notched tensile, (c) shear, and (d) bulge specimens.
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 ). Also, ARAMIS measurements were utilized to analyze the deformation history and strain localization pattern during loading. Fig. 3 shows the experimental setup and a tensile specimen prepared with a speckle pattern for capturing the deformation on the surface during the test.
(a)
(b)
Fig. 3. ARAMIS Testing Setup (a) ARAMIS system, (b) prepared specimen during ARAMIS testing.
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 [42]. 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 screwdriven 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 following 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 (Error! Reference source not found.(a) and 4(b)). The changes in the macroscopic dimensions were measured at each deformation 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 observation of deformational behavior of microstructure at the last steps before the failure of the specimen (Error! Reference source not found.(c) and 4(d)). Finally, image processing techniques were applied for local plastic deformation analysis.
(a)
(b)
(c)
(d)
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.
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 [16]:
̅
{
√
*
(
√
̅
*
(
̅
)
)+ [√
(
̅
)
(
(
̅
))]}
Eq.1
Eq.2 ̅
where η and ̅ are triaxiality and Lode angle parameters, respectively. A total of six parameters ( , , , , , ) need to be defined. The parameters and are material strain hardening parameters and are determined using curve fitting for the stress-strain curve by a power function. and are two basic Mohr–Coulomb parameters and are calibrated using material tests carried up to fracture. The parameter controls dependence on the Lode angle, and the parameter controls the asymmetry of fracture locus. Their default value is 1.0 if no additional 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 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 simulations were extracted from uniaxial experiments performed in the section 2 (Fig.2) and material damage was not considered. The local fracture strain ( ̅ ) and two stress state parameters, stress triaxiality (η) and Lode angle ( ̅ ) 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 [15] and Bai ad Wierzbicki [16] calculated the average histories of stress triaxiality and Lode angle parameters using numerical simulations. They utilized a concept of average stress triaxiality and Lode angle parameters which are defined by Eq. 3 and Eq. 4, respectively. In this paper, the proposed approach was applied to calculate the average values of stress states parameters. A detailed description of the simulation approach can be found in Refs. [15-16, 43]. A summary of stress state parameters, and ̅ , and the equivalent strain to fracture ̅ for DP600 and DP980 are shown in Table 2. ̅
∫ ( ̅ ) ̅
Eq. 3 ̅
̅
̅ ̅
∫ ̅( ̅ ) ̅
Eq. 4
where ε ̅_p is the calculated equivalent local plastic strain in each increment and (̅ ) and ̅ ( ̅ ) are unique functions of equivalent plastic strain.
Table 2. Summary of 3D simulations carried out to calibrate the MMC model for DP600 and DP980 steels.
No
Specimen
1 2 3 4
Tensile Simple shear Notched-tensile Bulge
̅ 0.34 0.015 0.57 0.658
0.995 0.02 0.15 -0.994
̅ DP600 1.398 1.048 0.542 0.66
DP980 0.552 0.868 0.342 0.496
In order to model damage evolution, as suggested in Ref. [16] a linear incremental relationship based on the damage indicator, D, and local equivalent plastic strain under monotonic loading conditions was assumed: ̅
( ̅ )
∫
̅ ̅
Eq. 5
̅ or ̅ is the MMC function from Eq. 1 which should be calculated in each increment based where on triaxiality and Lode parameters. The final failure based on Eq. 3 happens when D=1, so that ̅ ̅.
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 ( ) and, r-ratio in three directions (rolling direction, transverse direction, and 45 degree 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 anisotropic behavior in the flow curve. Eq. 6 In order to investigate fracture behavior, tensile tests were performed 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 differences being greater in DP980 than DP600. It can be concluded that at higher martensite volume fractions, the rolling process results in more anisotropic material behavior. Fracture behavior of DP600 steel could be assumed as isotropic, but for DP980 steel this assumption is inaccurate.
Table 3. Tensile test data for DP600 and DP980 steels. Material
(-)
(-)
(-)
365.5
0.9
0.809
1.034
681.5
0.635
0.927
0.724
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
(MPa)
DP600
644
649
648
357
372
DP980
1009
1026
1044.5
665.5
667
Table 4. The values of the fracture strain in three different directions. Material
(-)
(-)
(-)
DP600
0.288
0.273
0.2696
DP980
0.128
0.132
0.094
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.
(a)
(b)
(c)
(d)
Fig. 5. Experimental stress-strain curves obtained from (a) tensile, (b) notched tensile, (c) shear, and (d) bulge tests.
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 compared 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 specimens, 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 observed 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 experiments. Consequently, the numerical approach could be used to calculate the value of the equivalent plastic strain during different loading conditions.
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.
(a)
(b)
(c)
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.
(a)
(b)
(c)
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.
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.
(a)
(b)
(c)
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.
(a)
(b)
(c)
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.
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. Therefore, 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. Table 5. Calibrated MMC damage parameters. Material DP600 DP980
A (MPa) 1105 1695.12
n (-) 0.2079 0.153
(-) 1.048 0.925
(-) 1 1
(-) 0.15 0.15
(a) (b) Fig. 11: Numerical fracture loci of DP600 (a) and DP980 (b).
(MPa) 685 900
(a) (b) 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).
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. According to [44], 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 mechanically activated plastic deformations.
(a)
(b)
Fig. 13. Experimental engineering stress–strain curves of notched tensile specimens of (a) DP600 and (b) DP980 steels.
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 ( ) was calculated according to ASTM E562-08 [45] 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.
OLM SEM
DP600 (
)
DP980 (
)
Fig. 14. Optical light microscopy and scanning electron microscopy images of DP steels.
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 x 50 . 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.
(a)
(b)
Fig. 15. EBSD grain orientation maps method for (a) DP600, and (b) DP980 steels.
Fig. 16. Pole EBSD texture plot in (100), (110), and (111) orientations for DP600 (top) and DP980 (bottom).
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 applied strains in tensile specimens. As reported in previous studies [37, 46], 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 martensite 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. 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.
(a)
(b)
(c)
(d)
Fig. 17. Damage initiation and propagation in DP600 after (a) 7%, (b) 14%, (c) 21%, and (d) 28% strain. Loading direction is vertical.
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 [47]. 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 martensite 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 martensite 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.
(a)
(b)
c)
(d)
Fig. 18. Damage initiation and propagation in DP980 after (a) 6%, (b) 9%, (c) 11%, and (d) 12.5% strain. Loading direction is vertical.
5. Conclusion In this paper, the mechanical behavior and damage evolution of commercial DP600 and DP980 dualphase 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 materials demonstrated isotropic hardening behavior. DP600 had roughly isotropic behavior at fracture point whereas fracture behavior of DP980 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 discrepancy 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 specimens 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 mechanisms 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 important damage initiation mechanisms in DP600 and DP980 were (a) and (b), respectively. At high strains, two effective micro-crack initiation 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.
Author 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.
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 Materials IWM (BU 3184/2-1), in title: micro-mechanical investigation of deformation and failure scenario in dual phase steel using experimental and numerical methods.
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Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: