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Damage and fracture of dual-phase steels: Influence of martensite volume fraction
Author’s Accepted Manuscript Damage and fracture of dual-phase steels: Influence of martensite volume fraction Q. Lai, O. Bouaziz, M. Gouné, L. Brassart, M. Verdier, G. Parry, A. Perlade, Y. Bréchet, T. Pardoen www.elsevier.com
PII: DOI: Reference:
S0921-5093(15)30317-8 http://dx.doi.org/10.1016/j.msea.2015.08.073 MSA32707
To appear in: Materials Science & Engineering A Received date: 27 February 2015 Revised date: 21 August 2015 Accepted date: 22 August 2015 Cite this article as: Q. Lai, O. Bouaziz, M. Gouné, L. Brassart, M. Verdier, G. Parry, A. Perlade, Y. Bréchet and T. Pardoen, Damage and fracture of dualphase steels: Influence of martensite volume fraction, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2015.08.073 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Damage and fracture of dual-phase steels: influence of martensite volume fraction Q. Lai1,*, O. Bouaziz2, M. Gouné3, L. Brassart4, M. Verdier1, G. Parry1, A. Perlade5, Y. Bréchet1, T. Pardoen4 SIMaP, CNRS UMR 5266, Université de Grenoble Alpes, F-38402 St Martin d’Hères Cedex, France 2 Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux (LEM3), CNRS UMR 7239, F-57045 Université de Lorraine, Metz, France 3 ICMCB-CNRS-UPR 9048, F-33608 Pessac Cedex, France 4 Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, 2 Pl. Sainte-Barbe, Bâtiment Réaumur, B-1348 Louvain-la-Neuve, Belgium 5 R&D Automotive Products, ArcelorMittal, Voie Romaine, BP 30320, F-57283 Maiziéres-lés-Metz Cedex, France 1
Abstract: The influence of the martensite volume fraction (Vm) on the damage and fracture behavior of dual-phase steels was studied from experimental and modeling approaches. A transition in the dominating damage mechanism is observed when varying Vm. Martensite fracture dominates the void nucleation process at high Vm, while interface decohesion prevails at low Vm. Damage accumulation accelerates when Vm increases, resulting in a decrease of the fracture strain. Brittle fracture areas are observed in uniaxial tensile specimens for a sufficiently high Vm. The damage mechanisms and evolution are rationalized using a micromechanical analysis based on periodic finite element cell calculations. The results show that Vm is a key factor for controlling the balance between strength and fracture resistance. Keywords: dual-phase steels; damage; fracture. *
Corresponding author. Currently a post-doc research fellow at the University of British Columbia. E-mail address: [email protected] (Q. Lai); [email protected] (T. Pardoen)
1
1
Introduction The reduction of weight in order to limit fuel consumption and gas emissions has
become, for several decades, the main driving force for the development of advanced high strength steels (AHSS) [1, 2]. In addition, AHSS exhibit superior performances regarding passenger safety and crashworthiness [2]. Among the grades of AHSS, ferrite-martensite (FM) dual-phase (DP) steels are the most widely used in the automotive industry owing to attractive mechanical properties, lean alloy content and robust processing. A DP steel is a composite essentially consisting of a hard martensite phase embedded in a soft ferrite matrix. The DP steels are characterized by a low yield/tensile strength ratio, high initial strain hardening capacity, and good bake-hardening properties [1]. However, the moderate fracture strain is one of, if not the main, limitation for extending the range of applications for this steel grade, especially when the components undergo substantial deformation during forming. The trade-off between strength and fracture strain leads to microstructure engineering challenges depending on the specific requirements of application. A proper optimization adapted to each application requires the knowledge of the influence of microstructural features as well as quantitative micromechanical models. Ductile fracture of DP steels results from a process of nucleation, growth and coalescence of internal voids [3-5]. Intense research activity has been devoted to understanding the damage behavior of DP steels [3-17]. Ghadbeigi et al. [7] studied the damage mechanisms in DP600 steel, and found that the failure of martensite islands mostly occurs as a result of micro-crack initiation at the boundaries with the 2
surrounding ferrite followed by crack propagation to the centre of the islands. An extreme case of martensite fracture is the failure of continuous martensite bands, which occurs very early during deformation and is detrimental to fracture resistance [14, 15]. However, Kadkhodapour et al. [9] observed that the dominant void nucleation mechanism for the DP800 grade is ferrite grain-boundary decohesion in the neighborhood of martensite islands with no substantial contribution of martensite fracture. The variety of void nucleation mechanisms reveals the complexity related to the proper understanding and prediction of the damage behavior in DP steels. Additional efforts are needed to identify the respective influences of the various microstructural parameters. The volume fraction of martensite (Vm) is considered as the most important parameter in the balance between strength and fracture strain [18], and a clear understanding of its effects is of primary importance. In the present work, the impact of Vm on the damage and fracture mechanisms and on the evolution of the damage accumulation is studied by detailed experimental investigations on specifically designed microstructures with well controlled morphology and phase properties. The results of damage characterization are rationalized by investigating the local response of martensite, which is provided by Finite Element (FE) unit cell calculations [19, 20]. The FE unit cell calculations were performed in order to achieve a balance between computational cost and the capability to predict the deformation and damage characteristics of DP steels, compared to the microstructure-based FE models [9, 21-24]. 3
The paper is organized as follows. The experimental procedure is presented in section 2. The experimental results, including microstructure processing, tensile data, damage and fracture characterization, are shown in section 3. The micromechanical model and the results are presented in section 4. The main points regarding the damage and fracture mechanisms are discussed in section 5, before concluding.
2
Experimental procedure
2.1
Microstructure processing and characterization
The steel grade used in this work (0.1wt% C, 3.5wt% Mn) was processed in a research center of the company ArcelorMittal. After casting, the ingot was held at 1200°C and then hot-rolled above 900°C. A martensitic microstructure was produced by quenching, followed by cold-rolling to 1mm thickness involving 70% reduction. Tempering of the as-received material was performed in order to produce a spheroidized microstructure. The spheroidized microstructure was than intercritically annealed at 700°C for durations varying from 20 minutes to 6 hours. Samples for Scanning Electron Microscope (SEM) observations were prepared by standard mechanical grinding and polishing procedures, finishing with 8 min colloidal silica polishing. The samples were etched with 2% Nital to reveal the microstructure. The microstructures were analyzed by quantitative image analysis. The SEM images were binarized into black-white in order to distinguish the ferrite and martensite phases. The area fraction of martensite, which corresponds to the volume fraction in 3-dimension [25], was measured with ImageJ [26]. The method of intercepts was used 4
to quantify the average size of martensite [25].
2.2
Mechanical tests
Nanoindentation was used to locally probe the hardness of martensite. A matrix of indents was performed on the specimens after colloidal silica polishing to eliminate the plastically deformed surface layer. The location of each indent was identified under Back Scatter Electron (BSE) mode in SEM and only the indents exactly located within the martensite islands were analyzed. The hardness of the phases was continuously measured during the loading thanks to the Continuous Stiffness Measurement (CSM) mode which imposes small load oscillations during the indentation [27]. The hardness was extracted as a mean value between 60 and 90nm penetration depths. The nanohardness of martensite in each sample is an average of five to ten indents. The mechanical properties were measured by uniaxial tensile testing using dog-bone specimens with 25mm gauge length and 5mm width. The tests were performed at room temperature and 1.5mm/min displacement rate which corresponds to an engineering strain rate of 0.001/s. The yield strength is defined as the stress corresponding to 0.2% plastic strain. The uniform elongation is quantified through the true strain at the onset of necking determined by Considère criterion [28], and the corresponding stress is the true tensile strength. Three specimens of each grade were tested.
2.3
Fracture and damage characterization
The fracture surfaces were observed in a SEM. For ductile fracture surfaces, the 5
dimple density was characterized by the mean distance between all neighboring dimple centers, which was done manually on the SEM micrographs. The fracture strain is defined as the cross-sectional area reduction measured on the fracture surface and expressed by
f ln
A0 Af
(1)
where A0 and Af are the initial and final cross-sectional area measured on SEM images. Damage accumulation was characterized through the evolution of the density and area fraction of voids as a function of strain. One specimen per condition was selected for damage analysis. Post-mortem 2D analysis of the voids was performed on broken tensile specimens. A half fractured specimen was sectioned through the thickness approximately along the midwidth, in the longitudinal direction. These samples were then polished and cleaned with ethanol. The specimens were observed in a SEM using BSE mode, which is more sensitive to porosity at the surface [29]. The SEM micrographs have a grid of 1022×680 pixels. The images with 1000× magnification were adjusted with the adequate brightness and contrast, and binarization was applied in order to properly differentiate voids from the non-porous surrounding material. The density and area fraction of voids were analyzed with ImageJ. A threshold void size was fixed to the value of 0.11μm2, which corresponds to 9 pixels, and this is used for the comparison of damage accumulation between different microstructures. In addition, the evolution of void size distribution with deformation is also evaluated. After quantifying the damage accumulation, the samples were etched with 2% Nital and observed in a SEM. 6
The local strain is taken as the true thickness strain εthickness given by
thickness ln
h0 h
(2)
where h0 and h are the initial and current thickness in the corresponding zone [16]. The measurements of the damage parameters are averaged over five micrographs for each level of deformation, and the evolution of damage accumulation with thickness strain is compared among the samples with different Vm.
3
Experimental results
3.1
Microstructure and characterization
The as-received spheroidized microstructure (QT) is shown in Figure 1a. After an intercritical annealing at 700°C, DP microstructures were produced with Vm equal to 15%, 19%, 28% and 37%, as shown in Figure 1b-e. The martensite islands form mainly at ferrite grain boundaries. The dual-phase microstructure is relatively uniform and equiaxed when Vm is low (Figure 1b), but the martensite islands tend to organize in clusters elongated along the rolling direction at Vm above 19%, see Figure 1c. Continuous martensite bands develop for Vm equal to 28% (Figure 1d) and the banded structure is significant when Vm reaches 37%, see Figure 1e. The mean linear size of martensite increases with increasing Vm, as shown in Figure 1f. The nanoindentation results provided in Table 1 show that the hardness of martensite is relatively constant, around 8GPa, whatever the volume fraction of austenite at 700°C. The fact that the hardness is constant for the different Vm is a result of the austenite growth from a Mn-enriched cementite, and can be explained by the constant C and Mn 7
content within austenite. Indeed, a simple mass balance shows that the carbon content in austenite depends on the ratio of austenite growth to cementite dissolution rate [30]. Some recent calculations by DICTRA on the spheroidized microstructure in this study demonstrate that the austenite growth and cementite dissolution rates are such that both carbon and manganese content in austenite are relatively constant during austenitization at 700°C [30]. Therefore, in the model, the martensite hardness will be assumed constant among all DP microstructures.
3.2
Flow properties
Figure 2 shows the true stress/true strain curves of the DP steels with Vm of 15%, 19%, 28% and 37%. The flow stress increases with increasing Vm, which is associated to a more progressive elasto-plastic transition. The tensile properties are summarized in Table 2. The tensile strength increases with increasing Vm, while the uniform elongation and fracture strain exhibit an opposite trend. The effect of Vm on fracture is very significant. For instance, the fracture strain of QT-700-15% is 1.06, while it drops to 0.33 for QT-700-37%.
3.3
Damage analysis
Figure 3 a-d are SEM micrographs showing damage events in QT-700-15% closed to the fracture surface. The tensile axis is horizontal. The deformed microstructure is significantly elongated and the distribution of martensite aligns with the tensile axis (Figure 3a). Elongated voids are observed and the so-called “necklace” coalescence mechanisms [31] occurs in QT-700-15% (Figure 3a). Both martensite fracture (Figure 8
3b) and interface decohesion (Figure 3c and d) operate as damage nucleation mechanisms in QT-700-15%. Notice that several microcracks can be initiated at a single martensite island (Figure 3b). Interface decohesion tends to occur at the triple junction between martensite islands and ferrite grain boundaries, and grows along the grain boundary as a void (Figure 3c) or propagates as a crack (Figure 3d). Damage dominantly nucleates by interface decohesion in QT-700-15%. As Vm increases to 28%, wide continuous martensite bands have formed and large voids nucleate inside the bands (Figure 4a). Cavities nucleate as penny-shape voids by martensite fracture (Figure 4b) and this local fracture seems to be initiated from the edge of the martensite phase (Figure 4c). The dominating damage nucleation mechanism for QT-700-28% is martensite fracture. But interface decohesion is still observed around the small martensite islands and, again, is related to triple junctions (Figure 4d). The damage mechanisms in QT-700-37% are shown in Figure 5, which are supposed to be characteristic for the DP steels involving large Vm. Similar to QT-700-28%, large voids nucleate inside the wide continuous martensite bands (Figure 5a), and the coalescence between two adjacent large voids through martensite fracture is observed as well (Figure 5b). Penny-shape voids can be formed by martensite fracture (Figure 5c), possibly along the block boundary, as shown in Figure 5d. Figure 6a shows a micrograph of deformed QT-700-19% used for damage quantification. No significant influence of surface pollutant is observed. But, according to the systematic error analysis in Ref. [29], the influence of voids smearing-out by 9
mechanical polishing cannot be excluded. Figure 6b corresponds to the same image after binarization, as used to distinguish the pores and the matrix. Compared to the in-situ XRD tomography studies with the non-interrupted conditions in the literature [3, 5, 17, 32] that clearly show the 3D distribution of voids and the growth behavior of individual voids but have the drawback of resolution (about 2μm), the SEM observation has higher resolution and can detect the formation of smaller voids, providing complementary information to in-situ XRD tomography. Figure 7 shows the effect of Vm on damage accumulation as quantified by the density and area fraction of voids. Only the voids larger than 110nm2 are taken into account for these plots. Figure 7a shows first that the damage nucleation strain is negligibly affected by Vm. Some defects are initially present due to the processing of cold-rolled martensite [30] and there is no significant damage occurrence before necking. The damage nucleation strain is defined here as the thickness strain at which the density of voids starts to increase from the initial defect density (about 0.002/μm2). The acceleration of void nucleation (by martensite fracture) after necking, which is similar to the damage quantifications in Ref. [3] where interface decohesion is dominant, is probably due to the increase of stress triaxiality in the necking zone. Figure 7a also shows that the damage nucleation rate significantly increases by increasing Vm. As a result, the void density increases with increasing Vm for the same thickness strain. The evolution of the area fraction of voids shown in Figure 7b involves the variation of both the void density and void size. The area fraction of voids in QT-700-19% starts to increase only after a thickness strain of 0.25, while in QT-700-37%, it starts at around 10
0.1. This difference is much larger than the comparison with damage nucleation strain, which is defined according to void density only. For the same thickness strain, the area fraction of voids also increases with increasing Vm. The evolution of the void size distribution with thickness strain in QT-700-19% and in QT-700-37% is shown in Figure 8. Both QT-700-19% and 37% exhibit a continuous void nucleation and growth processes. Indeed, the number of small voids (with 10~20 pixels) increases with increasing deformation, which is a proof of continuously increasing void nucleation events. In addition, the number of larger voids is also increased with thickness strain, especially for QT-700-19% (Figure 8a), indicating an on-going void growth process participating to the accumulation of porosity. For QT-700-37% (Figure 8b), there is a significant increase in the density of small voids, but the number of large voids is still limited even at the strain close to the onset of void coalescence.
3.4
Fracture analysis
Within the range of Vm addressed in this work (from 15% to 37%), the DP microstructures generally fail by ductile fracture, in agreement with the mechanisms presented in the former section. Dimples dominate the fracture surfaces of the tensile specimens. The mean distance between dimple centers in QT-700-15%, 19%, 28% and 37% is about 2.9±0.7μm, 3.0±0.3μm, 3.2±0.5μm and 2.9±0.4μm, respectively. These values are the same considering the error bars, even though Vm changes a lot. Considering the decrease of the fracture strain with increasing Vm, the trend in the mean 11
distance between dimple centers actually indicates an increased probability of forming a void at each martensite island with increasing Vm. The fracture surface of QT-700-37% exhibits more complicated features. Figure 9a shows both ductile and brittle regions. Dimples cover the center of the fracture surface (Figure 9b). But, flat cleavage facets dominate the edges of the fracture surface, some being surrounded by regions with dimples, see Figure 9c. The size and area fracture of the facets indicate that it is the result of the cleavage of the ferrite grains.
4
Micromechanical modeling
4.1
Model description
A stacked hexagonal array (SHA) Finite Element (FE) based model [33] is used in this study. The idealized microstructure consists of a periodic stack of hexagonal prism, each of which contains a ferrite shell and a single spherical martensite particle. This hexagonal prism is approximated by an axisymmetric cell. The simulations are performed using the FE commercial code ABAQUS [34]. The unit cell is shown in Figure 10. The elements are quadrangular axisymmetric with second-order interpolation function (CAX8R). The volume fraction of martensite is given by
2d 3 3L3
where d is the
radius of martensite inclusion and L is the radius of the axisymmetric cell. The boundary conditions applied to the unit cell model simulate the conditions of a uniaxial tensile test. Volume averaging is employed to generate the true stress—true strain curves, and the true strain and true stress of the representative volume element (RVE) correspond to the mean of these values at each integration point. 12
The constitutive law selected for each phase is the classical, rate-independent J2 flow theory with isotropic hardening. The Young’s modulus of ferrite and martensite is taken identical with E equal to 210GPa and the Poisson ratio ν equal to 0.3. The plastic behavior of martensite was fitted based on the experimental responses of bulk martensitic samples [35] using the exponential law
y , ' y , ' k ' [1 exp( p n ' )] 0
(3)
where y0 , ' is the yield strength of martensite; p is the accumulated plastic strain;
y , ' , k ' are material parameters affected by the martensite carbon content only. The 0
dependency of y0 , ' and k ' on martensite carbon content is described in details in [35]. According to DICTRA calculation [30], the carbon content in martensite is assumed equal to 0.3wt%. Therefore, y0 , ' and k ' are equal to 969 and 967MPa, respectively. The parameter n ' is equal to 120, which is the same value used in [35] as well. The plastic response of ferrite is described by
y , y , 0
[1 exp( p )] for y , ytr
y , ytr IV ( p trp )
for
y , ytr
(4a) (4b)
where y0 , is the yield strength of ferrite, is the initial work-hardening rate and is the dynamic recovery coefficient; ytr and trp correspond, respectively, to the
values of the flow stress and of the plastic strain at the transition from stage-III to stage-IV hardening. These material parameters of ferrite are a priori unknown, and they are identified by fitting the model predictions to the mechanical response of the DP steels, see ref [36] and Table 3. 13
4.2
Macroscopic and microscopic responses in the unit cell
Figure 11 shows that the FE unit cell model can simulate the macroscopic response of DP steels with various martensite volume fractions, including the elasto-plastic transition and the work-hardening behavior. The FE calculations are also capable of predicting the variation of the mean phase stresses and strains as a function of the applied overall deformation. As shown in Figure 12a, the plastic strain in the martensite increases with increasing Vm for a given overall deformation level, indicating an enhanced co-deformation with the ferrite. For Vm equal to 15% and 19%, the martensite inclusions undergo very limited plastic deformation. The average Maximum Principal Stress (MPS) in martensite tends to saturation at large strains (Figure 12b). The MPS level in martensite increases with increasing Vm for a given deformation level, which implies a higher probability of martensite fracture if we assume a brittle mechanism controlled by the attainment of a critical stress level. For QT-700-37%, the MPS in martensite saturates at about 1500MPa; while for QT-700-15%, it only reaches 1000MPa. According to the Eshelby theory, the stress at the interface is almost equal to the stress in the particle. In Ref. [3], the critical stress for ferrite/martensite interface decohesion is identified as 1200MPa, which is in agreement with the values found in this work, especially for the case Vm=15%. But this agreement can only be seen as qualitative because the FE cell calculations show some variations of the stress inside the particle and thus with respect to the interface value.
14
5
Discussion
5.1
Damage in DP steels
The martensite phase acts as the reinforcement constituent in a composite. A significant part of the load is transferred to the martensite islands due to the plastic incompatibility between ferrite and martensite. The high stress level in martensite provides the driving force for martensite fracture. On the other hand, plastic strains accumulate at the matrix/reinforcement interface with the piling-up of dislocations, and facilitate the occurrence of interfacial decohesion [3, 37, 38]. These are the two main damage mechanisms in these composite microstructures, which may compete with one another [39]. According to the results presented in section 3.3, there is a transition in the dominating damage mechanism due to a variation of Vm. At small Vm, interface decohesion is the dominant damage mechanism. As Vm increases, the proportion of damage by martensite fracture significantly increases until becoming dominant. A similar observation is reported in ref [6], where no particle cracking was reported for Vm below 20%. This trend can be captured by looking at the stress and strain evolutions in the martensite predicted by FE cell calculations. As shown in Figure 12a, the co-deformation between ferrite and martensite is promoted by increasing Vm. An enhanced co-deformation lowers the strain concentration in the ferrite, which partly explains a smaller proportion of damage by interface decohesion with high Vm. On the other hand, as shown in Figure 12b, the MPS in martensite increases with deformation 15
and tends to saturate at large strains. The level of MPS in martensite significantly decreases with decreasing Vm. For Vm=15%, MPS in martensite barely reaches 1000MPa, which is close to the yield strength of martensitic steels with 0.3wt% carbon [35]. Therefore, martensite fracture should not occur when Vm is small enough. In this case, the strain concentration at the matrix/inclusion interface leads to the occurrence of interface decohesion, dominating the damage nucleation process. The comparison of the level of MPS attained in martensite provides an explanation for the differences in damage nucleation when changing Vm, assuming a brittle fracture mode of martensite. Actually, the fracture strain of martensite with more than 0.3wt% of carbon is rather low, and the assumption of brittle fracture can be considered acceptable [40]. A high MPS means a high probability of martensite fracture [31]. Indeed, at the same thickness strain, the void density in QT-700-37% is much larger than in QT-700-19%. In addition, the void nucleation rate is much higher for QT-700-37%. These observations can be explained by the higher MPS level in the martensite inclusion. The unit cell model adequately predicts the response of DP steels at moderate strain, as shown in [36].
However, some of the observations about the damage process
cannot be explained by the local responses provided by the predictions of the FE unit cell model. For instance, martensite fracture can still be observed when Vm is equal to 15% (Figure 3b), while the predicted MPS is rather low. In addition, the void nucleation strains in QT-700-19% and QT-700-37% are very similar, while the calculations in Figure 12b predict markedly different levels of macroscopic strain at which a critical 16
stress (for instance, 1300MPa as used in [35]) is reached. The shortcomings of the micromechanical model can be attributed to the oversimplified morphology considered in the simulations, consisting of a spherical, isolated inclusion. Actually, the martensite islands are interconnected and somewhat banded, which favors more load transfer between the soft and the hard phase. In addition, local bending can be imposed on elongated martensite islands, resulting in a stress concentration [7]. The stress in some parts of the martensite phase is thus probably higher than the model prediction, explaining why martensite fracture can be observed in QT-700-15%. Also, the connected sections of martensite islands constitute the preferred site for damage nucleation [41], which results in a similar void nucleation strain among the different DP microstructures with different Vm. As Vm increases, the average size of martensite islands increases, and the martensite banding becomes significant (Figure 1). Large voids are formed at the wide martensite bands (Figure 4 and 5) and they contribute to a large extent to damage accumulation. These microstructure features should be taken into account to improve the prediction of damage in DP steels.
5.2
Fracture of DP steels
Cleavage in DP steels under uniaxial tension conditions has been reported to take place within ferrite grains but not in the martensite phase [10, 12, 42-45]. A direct observation of cleavage in a ferrite grain, which is blocked by the martensite islands, is reported in Ref. [45]. The brittle fracture of DP steels is attributed to the presence of interconnected martensite islands [12, 43] and/or to a coarse microstructure [10, 42, 44]. 17
In contrast to the case of isolated martensite islands, the interconnected martensite in DP steels constrains the plastic flow in the ferrite matrix by confining the active slip systems [12] and/or by imposing a high triaxiality state of stress [46]. Once the martensite breaks, a cleavage crack in ferrite grain can be triggered due to the very large local stress building up at the crack tip. The results in this paper show that DP steels mainly fracture in a ductile manner while cleavage becomes operative at high Vm. As Vm increases, the size of the martensite phase increases and continuous wide martensite bands form, so that large cracks can initiate inside the martensite phase. A large Vm also leads to enhanced martensite connectivity that constrains the plastic flow of the ferrite. These microstructural features at high Vm favor the occurrence of cleavage in the ferrite. The points mentioned above are not sufficient to fully explain the occurrence of brittle fracture events observed in this study. For the largest Vm, dimples still cover the major part of the fracture surface of QT-700-37%. In addition, cleavage is not uniformly distributed over the fracture surface but is only located at the edges of the specimens (Figure 9a). These observations indicate that ductile fracture is the intrinsic or dominating mode of failure under uniaxial tension, because ductile fracture is the first mechanism to initiate in the center of the specimens [9, 17]. The occurrence of brittle fracture at the edges of specimen is probably induced by geometrical and dynamic effects. A large principal crack can be formed during the failure of a tensile specimen, as reported in [7]. As Vm increases, the flow stress is increased. Once the principal crack is formed, a high opening stress level builds up at the tip of the crack, involving a higher 18
local stress triaxiality. This promotes the occurrence of brittle crack propagation by locally attaining the cleavage stress of ferrite.
6
Conclusions The influence of martensite volume fraction on the damage and fracture behavior of
dual-phase steels was analyzed with detailed characterizations and FE unit cell calculations. The main conclusions are the following. 1) The tensile strength increases with increasing Vm, while the fracture strain decreases. A trade-off between these two properties can be found as Vm is varied. 2) Interface decohesion is an important void nucleation mechanism when Vm is low. Interface decohesion mainly takes place at triple junctions, and the defects grow as voids or propagate as cracks along the ferrite grain boundary. 3) Martensite fracture is the dominating void nucleation mechanism when Vm is high, and it often initiates at the edge of the martensite phase. Large voids are formed by fracture of wide martensite bands. 4) Simple periodic FE unit cell calculations predict an increase of the maximum principal stress in martensite with increasing Vm, which allows rationalizing the transition of the dominating damage mechanism and the accelerated void nucleation. 5) The dual-phase steels mainly fail by ductile fracture. However, partial brittle fracture can occur at the end of the failure process when Vm is high, when the crack approaches the edges of the specimens. 19
Acknowledgement The authors acknowledge Prof. J.D. Embury for helpful discussions. Q.L. acknowledges the financial support of ArcelorMittal Research. L.B. is mandated by the National Fund for Scientific Research (FNRS, Belgium). The support of BELSPO through IAP 7/21 network is also gratefully acknowledged.
References [1] W. Bleck, JOM, 48 (1996) 26-30. [2] O. Bouaziz, H. Zurob, M.X. Huang, Steel Res. Int., 84 (2013) 937-947. [3] C. Landron, O. Bouaziz, E. Maire, J. Adrien, Scr. Mater., 63 (2010) 973-976. [4] C. Landron, O. Bouaziz, E. Maire, J. Adrien, Acta Mater., 61 (2013) 6821-6829. [5] C. Landron, E. Maire, O. Bouaziz, J. Adrien, L. Lecarme, A. Bareggi, Acta Mater., 59 (2011) 7564-7573. [6] A.F. Szewczyk, J. Gurland, Metall. Trans. A, 13 (1982) 1821-1826. [7] H. Ghadbeigi, C. Pinna, S. Celotto, Mater. Sci. Eng. A, 588 (2013) 420-431. [8] D.L. Steinbrunner, D.K. Matlock, G. Krauss, Metall. Trans. A, 19 (1988) 579-589. [9] J. Kadkhodapour, A. Butz, S.Z. Rad, Acta Mater., 59 (2011) 2575-2588. [10] N.J. Kim, G. Thomas, Metall. Trans. A, 12 (1981) 483-489. [11] M. Mazinani, W.J. Poole, Metall. Mater. Trans. A, 38A (2007) 328-339. [12] T. Kunio, M. Shimizu, K. Yamada, H. Suzuki, Eng. Fract. Mech., 7 (1975) 411-417. [13] A.R. Marder, Metall. Trans. A, 13 (1982) 85-92. [14] C.C. Tasan, J.P.M. Hoefnagels, M.G.D. Geers, Scr. Mater., 62 (2010) 835-838. [15] G. Avramovic-Cingara, Y. Ososkov, M.K. Jain, D.S. Wilkinson, Mater. Sci. Eng. A, 516 (2009) 7-16. [16] G. Avramovic-Cingara, C.A.R. Saleh, M.K. Jain, D.S. Wilkinson, Metall. Mater. 20
Trans. A, 40A (2009) 3117-3127. [17] E. Maire, O. Bouaziz, M. Di Michiel, C. Verdu, Acta Mater., 56 (2008) 4954-4964. [18] G.R. Speich, R.L. Miller, in: Structure and Properties of Dual Phase Steels, 1979, 145-182. [19] F.M. Al-Abbasi, J.A. Nemes, Comput. Mater. Sci., 39 (2007) 402-415. [20] F.M. Al-Abbasi, J.A. Nemes, Int. J. Mech. Sci., 45 (2003) 1449-1465. [21] J. Kadkhodapour, A. Butz, S. Ziaei-Rad, S. Schmauder, Int. J. Plast., 27 (2010) 1103-1125. [22] K.S. Choi, W.N. Liu, X. Sun, M.A. Khaleel, Metall. Mater. Trans. A, 40A (2009) 796-809. [23] X. Sun, K.S. Choi, A. Soulami, W.N. Liu, M.A. Khaleel, Mater. Sci.Eng. A, 526 (2009) 140-149. [24] N. Vajragupta, V. Uthaisangsuk, B. Schmaling, S. Munstermann, A. Hartmaier, W. Bleck, Comput. Mater. Sci., 54 (2011) 271-279. [25] H.E. Exner, Qualitative and quantitative surface microscopy, in: Physical Metallurgy (4th edition), Elsevier, Amsterdam, 1996. [26] http://imagej.nih.gov/ij/. [27] W.C. Oliver, G.M. Pharr, J. Mater. Res., 19 (2004) 3-20. [28] A. Considère, in: Annales des ponts et chaussées I sem, 1885, pp. 574. [29] C.C. Tasan, J.P.M. Hoefnagels, M.G.D. Geers, Acta Mater., 60 (2012) 3581-3589. [30] Q. Lai, PhD thesis , Université de Grenoble, 2014. [31] A. Pineau, T. Pardoen, Failure of Metals, in: Comprehensive Structural Integrity, Pergamon, Oxford, 2007, pp. 684-797. [32] C. Landron, E. Maire, J. Adrien, O. Bouaziz, M. Di Michiel, P. Cloetens, H. Suhonen, Nucl. Instrum. Methods Phys. Res. B, 284 (2012) 15-18. [33] V. Tvergaard, Int. J. Fract., 17 (1981) 389-407. [34] ABAQUS, Analysis User' s Manual, Version 6.8, 2008. [35] A.P. Pierman, O. Bouaziz, T. Pardoen, P.J. Jacques, L. Brassart, Acta Mater., 73 (2014) 298-311. [36] Q. Lai, Int. J. Plast., submitted. 21
[37] A.S. Argon, J. Im, R. Safoglu, Metall. Trans. A, 6 (1975) 825-837. [38] Y. Charles, R. Estevez, Y. Brechet, E. Maire, Eng. Fract. Mech., 77 (2010) 705-718. [39] L. Babout, Y. Brechet, E. Maire, R. Fougeres, Acta Mater., 52 (2004) 4517-4525. [40] R. Roumina, J.D. Embury, O. Bouaziz, H.S. Zurob, Mater. Sci. Eng. A, 578 (2013) 140-149. [41] K. Park, M. Nishiyama, N. Nakada, T. Tsuchiyama, S. Takaki, Mater. Sci. Eng. A, 604 (2014) 135-141. [42] M. Calcagnotto, Y. Adachi, D. Ponge, D. Raabe, Acta Mater., 59 (2011) 658-670. [43] P. Uggowitzer, H.P. Stuwe, Mater. Sci. Eng., 55 (1982) 181-189. [44] X.L. Cai, J. Feng, W.S. Owen, Metall. Trans. A, 16 (1985) 1405-1415. [45] Q. Lai, O. Bouaziz, M. Goune, A. Perlade, Y. Brechet, T. Pardoen, Mater.Sci. Eng. A, 638 (2015) 78-89. [46] S.K. Yerra, G. Martin, M. Veron, Y. Brechet, J.D. Mithieux, L. Delannay, T. Pardoen, Eng. Fract. Mech., 102 (2013) 77-100.
Figure captions: Figure 1. The spheroidized microstructure (a) and DP microstructures with 15% (b), 19% (c), 28% (d) and 37% (e) of martensite, and the evolution of mean linear size of martensite with Vm(f).
22
23
f
mean linear size of martensite
3.0
Dimension (μm)
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Vm
Figure 2. Uniaxial true stress-true strain curves of DP steels with martensite volume fractions equal to 15%, 19%, 28% and 37%. All the curves are shown up to necking. 1200
true stress (MPa)
1000
QT-700-37% QT-700-28%
800
QT-700-19% QT-700-15%
600 400 200 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
true strain Figure 3. SEM micrographs showing the damage mechanisms in QT-700-15%. The voids are observed closed to the fracture surface.
24
Figure 4. SEM micrographs showing the damage mechanisms in QT-700-28%. The voids are observed closed to the fracture surface.
25
Figure 5. SEM micrographs showing the damage mechanisms in QT-700-37%. The voids are observed closed to the fracture surface.
26
Figure 6. Micrographs showing the voids on the as-polished surface of QT-700-19% (a) and the representation after binarization (b).
27
Figure 7. Variation of damage accumulation of QT-700-19% and QT-700-37% with thickness strain in terms of (a) void density and of (b) area fraction of voids. Only the voids larger than 110nm2 are taken into account for these plots.
a
0.020 0.018
QT-700-19%
2
void density (/μm )
0.016 0.014 0.012 0.010
QT-700-37%
0.008 0.006 0.004 0.002
initial defect density
0.000 0.1
0.2
0.3
0.4
0.5
0.6
thickness strain
b area fraction of voids (%)
3.0 2.5
QT-700-19% 2.0 1.5 1.0
QT-700-37%
0.5
initial area fraction of defects
0.0 0.1
0.2
0.3
0.4
0.5
0.6
thickness strain
Figure 8. Variation of damage as a fuction of thickness strain for different ranges of void size in (a) QT-700-19% and (b) QT-700-37%.
28
a
εthickness=0.095
6
εthickness=0.236
-3
2
void density (10 /μm )
7
εthickness=0.531
5 4 3
QT-700-19%
2 1 0 10 ~20
20 30 40 80 100 120 150 200 >300 50 60 ~30 ~40 ~50 ~60 ~70 ~90 ~110 ~130 ~200 ~300
pixel
3.5
εthickness=0.104
3.0
εthickness=0.136 εthickness=0.22
2.5
-3
2
void density (10 /μm )
b
2.0 1.5
QT-700-37%
1.0 0.5 0.0 10 ~20
20 ~30
40 50 30 ~40 ~50 ~60
70 100 120 150 200 >300 60 ~70 ~80 ~110 ~130 ~200 ~300
pixel Figure 9. SEM micrographs of the fracture surface in QT-700-37%; (a) a low-magnification graph showing both ductile and brittle features; (b) surface covered by dimples; (c) surface showing significant cleavage.
29
Figure 10. Configuration, dimensions and mesh of the axisymmetric FE unit cell.
Figure 11. Comparison of the simulated (with FE unit cell model) and experimental stress-strain response
30
1200
× Vm=37% × Vm=28%
true stress (MPa)
1000 800
×
600
Vm=19%
× V =15% m
400
experiment
200 0 0.00
× model 0.05
0.10
0.15
0.20
0.25
true strain Figure 12. Variation of the mean plastic strain (a) and MPS (b) in the martensite with overall strain for different martensite volume fractions.
plastic strain in martensite
a
0.20
Vm = 37%
0.15
0.10
Vm = 28% 0.05
Vm = 19% 0.00 0.00
Vm = 15% 0.05
0.10
0.15
0.20
0.25
0.30
macroscopic strain
MPS in martensite (MPa)
b
1800
Vm = 37%
1600
Vm = 28% Vm = 19%
1400 1200
Vm = 15%
1000 800 600 400 200 0 0.00
0.05
0.10
0.15
0.20
macroscopic strain
Tables: 31
0.25
0.30
Table 1. Nanohardness of martensite in the DP samples. Samples Martensite hardness (GPa) QT-700-19% 8.4608 ±1.64936 QT-700-28% 7.7718±0.67976 QT-700-37% 8.0692±0.68784 Table 2. Mechanical properties of the DP steels involving different martensite volume fractions. Samples Tensile Uniform Fracture strain strength (MPa) elongation QT-700-15% 691±4 0.164±0.002 1.06±0.06 QT-700-19% 765.5±13 0.143±0.009 0.75±0.11 QT-700-28% 928±25 0.124±0.011 0.4±0.01 QT-700-37%
1058±18
0.116±0.002
0.33±0.02
Table 3. Identified ferrite parameters. Vm
y , (MPa)
(MPa)
15% 19% 28% 37%
250 279 300 307
4895 5980 8925 10260
11 13 17 20
0
32
PII: DOI: Reference:
S0921-5093(15)30317-8 http://dx.doi.org/10.1016/j.msea.2015.08.073 MSA32707
To appear in: Materials Science & Engineering A Received date: 27 February 2015 Revised date: 21 August 2015 Accepted date: 22 August 2015 Cite this article as: Q. Lai, O. Bouaziz, M. Gouné, L. Brassart, M. Verdier, G. Parry, A. Perlade, Y. Bréchet and T. Pardoen, Damage and fracture of dualphase steels: Influence of martensite volume fraction, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2015.08.073 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Damage and fracture of dual-phase steels: influence of martensite volume fraction Q. Lai1,*, O. Bouaziz2, M. Gouné3, L. Brassart4, M. Verdier1, G. Parry1, A. Perlade5, Y. Bréchet1, T. Pardoen4 SIMaP, CNRS UMR 5266, Université de Grenoble Alpes, F-38402 St Martin d’Hères Cedex, France 2 Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux (LEM3), CNRS UMR 7239, F-57045 Université de Lorraine, Metz, France 3 ICMCB-CNRS-UPR 9048, F-33608 Pessac Cedex, France 4 Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, 2 Pl. Sainte-Barbe, Bâtiment Réaumur, B-1348 Louvain-la-Neuve, Belgium 5 R&D Automotive Products, ArcelorMittal, Voie Romaine, BP 30320, F-57283 Maiziéres-lés-Metz Cedex, France 1
Abstract: The influence of the martensite volume fraction (Vm) on the damage and fracture behavior of dual-phase steels was studied from experimental and modeling approaches. A transition in the dominating damage mechanism is observed when varying Vm. Martensite fracture dominates the void nucleation process at high Vm, while interface decohesion prevails at low Vm. Damage accumulation accelerates when Vm increases, resulting in a decrease of the fracture strain. Brittle fracture areas are observed in uniaxial tensile specimens for a sufficiently high Vm. The damage mechanisms and evolution are rationalized using a micromechanical analysis based on periodic finite element cell calculations. The results show that Vm is a key factor for controlling the balance between strength and fracture resistance. Keywords: dual-phase steels; damage; fracture. *
Corresponding author. Currently a post-doc research fellow at the University of British Columbia. E-mail address: [email protected] (Q. Lai); [email protected] (T. Pardoen)
1
1
Introduction The reduction of weight in order to limit fuel consumption and gas emissions has
become, for several decades, the main driving force for the development of advanced high strength steels (AHSS) [1, 2]. In addition, AHSS exhibit superior performances regarding passenger safety and crashworthiness [2]. Among the grades of AHSS, ferrite-martensite (FM) dual-phase (DP) steels are the most widely used in the automotive industry owing to attractive mechanical properties, lean alloy content and robust processing. A DP steel is a composite essentially consisting of a hard martensite phase embedded in a soft ferrite matrix. The DP steels are characterized by a low yield/tensile strength ratio, high initial strain hardening capacity, and good bake-hardening properties [1]. However, the moderate fracture strain is one of, if not the main, limitation for extending the range of applications for this steel grade, especially when the components undergo substantial deformation during forming. The trade-off between strength and fracture strain leads to microstructure engineering challenges depending on the specific requirements of application. A proper optimization adapted to each application requires the knowledge of the influence of microstructural features as well as quantitative micromechanical models. Ductile fracture of DP steels results from a process of nucleation, growth and coalescence of internal voids [3-5]. Intense research activity has been devoted to understanding the damage behavior of DP steels [3-17]. Ghadbeigi et al. [7] studied the damage mechanisms in DP600 steel, and found that the failure of martensite islands mostly occurs as a result of micro-crack initiation at the boundaries with the 2
surrounding ferrite followed by crack propagation to the centre of the islands. An extreme case of martensite fracture is the failure of continuous martensite bands, which occurs very early during deformation and is detrimental to fracture resistance [14, 15]. However, Kadkhodapour et al. [9] observed that the dominant void nucleation mechanism for the DP800 grade is ferrite grain-boundary decohesion in the neighborhood of martensite islands with no substantial contribution of martensite fracture. The variety of void nucleation mechanisms reveals the complexity related to the proper understanding and prediction of the damage behavior in DP steels. Additional efforts are needed to identify the respective influences of the various microstructural parameters. The volume fraction of martensite (Vm) is considered as the most important parameter in the balance between strength and fracture strain [18], and a clear understanding of its effects is of primary importance. In the present work, the impact of Vm on the damage and fracture mechanisms and on the evolution of the damage accumulation is studied by detailed experimental investigations on specifically designed microstructures with well controlled morphology and phase properties. The results of damage characterization are rationalized by investigating the local response of martensite, which is provided by Finite Element (FE) unit cell calculations [19, 20]. The FE unit cell calculations were performed in order to achieve a balance between computational cost and the capability to predict the deformation and damage characteristics of DP steels, compared to the microstructure-based FE models [9, 21-24]. 3
The paper is organized as follows. The experimental procedure is presented in section 2. The experimental results, including microstructure processing, tensile data, damage and fracture characterization, are shown in section 3. The micromechanical model and the results are presented in section 4. The main points regarding the damage and fracture mechanisms are discussed in section 5, before concluding.
2
Experimental procedure
2.1
Microstructure processing and characterization
The steel grade used in this work (0.1wt% C, 3.5wt% Mn) was processed in a research center of the company ArcelorMittal. After casting, the ingot was held at 1200°C and then hot-rolled above 900°C. A martensitic microstructure was produced by quenching, followed by cold-rolling to 1mm thickness involving 70% reduction. Tempering of the as-received material was performed in order to produce a spheroidized microstructure. The spheroidized microstructure was than intercritically annealed at 700°C for durations varying from 20 minutes to 6 hours. Samples for Scanning Electron Microscope (SEM) observations were prepared by standard mechanical grinding and polishing procedures, finishing with 8 min colloidal silica polishing. The samples were etched with 2% Nital to reveal the microstructure. The microstructures were analyzed by quantitative image analysis. The SEM images were binarized into black-white in order to distinguish the ferrite and martensite phases. The area fraction of martensite, which corresponds to the volume fraction in 3-dimension [25], was measured with ImageJ [26]. The method of intercepts was used 4
to quantify the average size of martensite [25].
2.2
Mechanical tests
Nanoindentation was used to locally probe the hardness of martensite. A matrix of indents was performed on the specimens after colloidal silica polishing to eliminate the plastically deformed surface layer. The location of each indent was identified under Back Scatter Electron (BSE) mode in SEM and only the indents exactly located within the martensite islands were analyzed. The hardness of the phases was continuously measured during the loading thanks to the Continuous Stiffness Measurement (CSM) mode which imposes small load oscillations during the indentation [27]. The hardness was extracted as a mean value between 60 and 90nm penetration depths. The nanohardness of martensite in each sample is an average of five to ten indents. The mechanical properties were measured by uniaxial tensile testing using dog-bone specimens with 25mm gauge length and 5mm width. The tests were performed at room temperature and 1.5mm/min displacement rate which corresponds to an engineering strain rate of 0.001/s. The yield strength is defined as the stress corresponding to 0.2% plastic strain. The uniform elongation is quantified through the true strain at the onset of necking determined by Considère criterion [28], and the corresponding stress is the true tensile strength. Three specimens of each grade were tested.
2.3
Fracture and damage characterization
The fracture surfaces were observed in a SEM. For ductile fracture surfaces, the 5
dimple density was characterized by the mean distance between all neighboring dimple centers, which was done manually on the SEM micrographs. The fracture strain is defined as the cross-sectional area reduction measured on the fracture surface and expressed by
f ln
A0 Af
(1)
where A0 and Af are the initial and final cross-sectional area measured on SEM images. Damage accumulation was characterized through the evolution of the density and area fraction of voids as a function of strain. One specimen per condition was selected for damage analysis. Post-mortem 2D analysis of the voids was performed on broken tensile specimens. A half fractured specimen was sectioned through the thickness approximately along the midwidth, in the longitudinal direction. These samples were then polished and cleaned with ethanol. The specimens were observed in a SEM using BSE mode, which is more sensitive to porosity at the surface [29]. The SEM micrographs have a grid of 1022×680 pixels. The images with 1000× magnification were adjusted with the adequate brightness and contrast, and binarization was applied in order to properly differentiate voids from the non-porous surrounding material. The density and area fraction of voids were analyzed with ImageJ. A threshold void size was fixed to the value of 0.11μm2, which corresponds to 9 pixels, and this is used for the comparison of damage accumulation between different microstructures. In addition, the evolution of void size distribution with deformation is also evaluated. After quantifying the damage accumulation, the samples were etched with 2% Nital and observed in a SEM. 6
The local strain is taken as the true thickness strain εthickness given by
thickness ln
h0 h
(2)
where h0 and h are the initial and current thickness in the corresponding zone [16]. The measurements of the damage parameters are averaged over five micrographs for each level of deformation, and the evolution of damage accumulation with thickness strain is compared among the samples with different Vm.
3
Experimental results
3.1
Microstructure and characterization
The as-received spheroidized microstructure (QT) is shown in Figure 1a. After an intercritical annealing at 700°C, DP microstructures were produced with Vm equal to 15%, 19%, 28% and 37%, as shown in Figure 1b-e. The martensite islands form mainly at ferrite grain boundaries. The dual-phase microstructure is relatively uniform and equiaxed when Vm is low (Figure 1b), but the martensite islands tend to organize in clusters elongated along the rolling direction at Vm above 19%, see Figure 1c. Continuous martensite bands develop for Vm equal to 28% (Figure 1d) and the banded structure is significant when Vm reaches 37%, see Figure 1e. The mean linear size of martensite increases with increasing Vm, as shown in Figure 1f. The nanoindentation results provided in Table 1 show that the hardness of martensite is relatively constant, around 8GPa, whatever the volume fraction of austenite at 700°C. The fact that the hardness is constant for the different Vm is a result of the austenite growth from a Mn-enriched cementite, and can be explained by the constant C and Mn 7
content within austenite. Indeed, a simple mass balance shows that the carbon content in austenite depends on the ratio of austenite growth to cementite dissolution rate [30]. Some recent calculations by DICTRA on the spheroidized microstructure in this study demonstrate that the austenite growth and cementite dissolution rates are such that both carbon and manganese content in austenite are relatively constant during austenitization at 700°C [30]. Therefore, in the model, the martensite hardness will be assumed constant among all DP microstructures.
3.2
Flow properties
Figure 2 shows the true stress/true strain curves of the DP steels with Vm of 15%, 19%, 28% and 37%. The flow stress increases with increasing Vm, which is associated to a more progressive elasto-plastic transition. The tensile properties are summarized in Table 2. The tensile strength increases with increasing Vm, while the uniform elongation and fracture strain exhibit an opposite trend. The effect of Vm on fracture is very significant. For instance, the fracture strain of QT-700-15% is 1.06, while it drops to 0.33 for QT-700-37%.
3.3
Damage analysis
Figure 3 a-d are SEM micrographs showing damage events in QT-700-15% closed to the fracture surface. The tensile axis is horizontal. The deformed microstructure is significantly elongated and the distribution of martensite aligns with the tensile axis (Figure 3a). Elongated voids are observed and the so-called “necklace” coalescence mechanisms [31] occurs in QT-700-15% (Figure 3a). Both martensite fracture (Figure 8
3b) and interface decohesion (Figure 3c and d) operate as damage nucleation mechanisms in QT-700-15%. Notice that several microcracks can be initiated at a single martensite island (Figure 3b). Interface decohesion tends to occur at the triple junction between martensite islands and ferrite grain boundaries, and grows along the grain boundary as a void (Figure 3c) or propagates as a crack (Figure 3d). Damage dominantly nucleates by interface decohesion in QT-700-15%. As Vm increases to 28%, wide continuous martensite bands have formed and large voids nucleate inside the bands (Figure 4a). Cavities nucleate as penny-shape voids by martensite fracture (Figure 4b) and this local fracture seems to be initiated from the edge of the martensite phase (Figure 4c). The dominating damage nucleation mechanism for QT-700-28% is martensite fracture. But interface decohesion is still observed around the small martensite islands and, again, is related to triple junctions (Figure 4d). The damage mechanisms in QT-700-37% are shown in Figure 5, which are supposed to be characteristic for the DP steels involving large Vm. Similar to QT-700-28%, large voids nucleate inside the wide continuous martensite bands (Figure 5a), and the coalescence between two adjacent large voids through martensite fracture is observed as well (Figure 5b). Penny-shape voids can be formed by martensite fracture (Figure 5c), possibly along the block boundary, as shown in Figure 5d. Figure 6a shows a micrograph of deformed QT-700-19% used for damage quantification. No significant influence of surface pollutant is observed. But, according to the systematic error analysis in Ref. [29], the influence of voids smearing-out by 9
mechanical polishing cannot be excluded. Figure 6b corresponds to the same image after binarization, as used to distinguish the pores and the matrix. Compared to the in-situ XRD tomography studies with the non-interrupted conditions in the literature [3, 5, 17, 32] that clearly show the 3D distribution of voids and the growth behavior of individual voids but have the drawback of resolution (about 2μm), the SEM observation has higher resolution and can detect the formation of smaller voids, providing complementary information to in-situ XRD tomography. Figure 7 shows the effect of Vm on damage accumulation as quantified by the density and area fraction of voids. Only the voids larger than 110nm2 are taken into account for these plots. Figure 7a shows first that the damage nucleation strain is negligibly affected by Vm. Some defects are initially present due to the processing of cold-rolled martensite [30] and there is no significant damage occurrence before necking. The damage nucleation strain is defined here as the thickness strain at which the density of voids starts to increase from the initial defect density (about 0.002/μm2). The acceleration of void nucleation (by martensite fracture) after necking, which is similar to the damage quantifications in Ref. [3] where interface decohesion is dominant, is probably due to the increase of stress triaxiality in the necking zone. Figure 7a also shows that the damage nucleation rate significantly increases by increasing Vm. As a result, the void density increases with increasing Vm for the same thickness strain. The evolution of the area fraction of voids shown in Figure 7b involves the variation of both the void density and void size. The area fraction of voids in QT-700-19% starts to increase only after a thickness strain of 0.25, while in QT-700-37%, it starts at around 10
0.1. This difference is much larger than the comparison with damage nucleation strain, which is defined according to void density only. For the same thickness strain, the area fraction of voids also increases with increasing Vm. The evolution of the void size distribution with thickness strain in QT-700-19% and in QT-700-37% is shown in Figure 8. Both QT-700-19% and 37% exhibit a continuous void nucleation and growth processes. Indeed, the number of small voids (with 10~20 pixels) increases with increasing deformation, which is a proof of continuously increasing void nucleation events. In addition, the number of larger voids is also increased with thickness strain, especially for QT-700-19% (Figure 8a), indicating an on-going void growth process participating to the accumulation of porosity. For QT-700-37% (Figure 8b), there is a significant increase in the density of small voids, but the number of large voids is still limited even at the strain close to the onset of void coalescence.
3.4
Fracture analysis
Within the range of Vm addressed in this work (from 15% to 37%), the DP microstructures generally fail by ductile fracture, in agreement with the mechanisms presented in the former section. Dimples dominate the fracture surfaces of the tensile specimens. The mean distance between dimple centers in QT-700-15%, 19%, 28% and 37% is about 2.9±0.7μm, 3.0±0.3μm, 3.2±0.5μm and 2.9±0.4μm, respectively. These values are the same considering the error bars, even though Vm changes a lot. Considering the decrease of the fracture strain with increasing Vm, the trend in the mean 11
distance between dimple centers actually indicates an increased probability of forming a void at each martensite island with increasing Vm. The fracture surface of QT-700-37% exhibits more complicated features. Figure 9a shows both ductile and brittle regions. Dimples cover the center of the fracture surface (Figure 9b). But, flat cleavage facets dominate the edges of the fracture surface, some being surrounded by regions with dimples, see Figure 9c. The size and area fracture of the facets indicate that it is the result of the cleavage of the ferrite grains.
4
Micromechanical modeling
4.1
Model description
A stacked hexagonal array (SHA) Finite Element (FE) based model [33] is used in this study. The idealized microstructure consists of a periodic stack of hexagonal prism, each of which contains a ferrite shell and a single spherical martensite particle. This hexagonal prism is approximated by an axisymmetric cell. The simulations are performed using the FE commercial code ABAQUS [34]. The unit cell is shown in Figure 10. The elements are quadrangular axisymmetric with second-order interpolation function (CAX8R). The volume fraction of martensite is given by
2d 3 3L3
where d is the
radius of martensite inclusion and L is the radius of the axisymmetric cell. The boundary conditions applied to the unit cell model simulate the conditions of a uniaxial tensile test. Volume averaging is employed to generate the true stress—true strain curves, and the true strain and true stress of the representative volume element (RVE) correspond to the mean of these values at each integration point. 12
The constitutive law selected for each phase is the classical, rate-independent J2 flow theory with isotropic hardening. The Young’s modulus of ferrite and martensite is taken identical with E equal to 210GPa and the Poisson ratio ν equal to 0.3. The plastic behavior of martensite was fitted based on the experimental responses of bulk martensitic samples [35] using the exponential law
y , ' y , ' k ' [1 exp( p n ' )] 0
(3)
where y0 , ' is the yield strength of martensite; p is the accumulated plastic strain;
y , ' , k ' are material parameters affected by the martensite carbon content only. The 0
dependency of y0 , ' and k ' on martensite carbon content is described in details in [35]. According to DICTRA calculation [30], the carbon content in martensite is assumed equal to 0.3wt%. Therefore, y0 , ' and k ' are equal to 969 and 967MPa, respectively. The parameter n ' is equal to 120, which is the same value used in [35] as well. The plastic response of ferrite is described by
y , y , 0
[1 exp( p )] for y , ytr
y , ytr IV ( p trp )
for
y , ytr
(4a) (4b)
where y0 , is the yield strength of ferrite, is the initial work-hardening rate and is the dynamic recovery coefficient; ytr and trp correspond, respectively, to the
values of the flow stress and of the plastic strain at the transition from stage-III to stage-IV hardening. These material parameters of ferrite are a priori unknown, and they are identified by fitting the model predictions to the mechanical response of the DP steels, see ref [36] and Table 3. 13
4.2
Macroscopic and microscopic responses in the unit cell
Figure 11 shows that the FE unit cell model can simulate the macroscopic response of DP steels with various martensite volume fractions, including the elasto-plastic transition and the work-hardening behavior. The FE calculations are also capable of predicting the variation of the mean phase stresses and strains as a function of the applied overall deformation. As shown in Figure 12a, the plastic strain in the martensite increases with increasing Vm for a given overall deformation level, indicating an enhanced co-deformation with the ferrite. For Vm equal to 15% and 19%, the martensite inclusions undergo very limited plastic deformation. The average Maximum Principal Stress (MPS) in martensite tends to saturation at large strains (Figure 12b). The MPS level in martensite increases with increasing Vm for a given deformation level, which implies a higher probability of martensite fracture if we assume a brittle mechanism controlled by the attainment of a critical stress level. For QT-700-37%, the MPS in martensite saturates at about 1500MPa; while for QT-700-15%, it only reaches 1000MPa. According to the Eshelby theory, the stress at the interface is almost equal to the stress in the particle. In Ref. [3], the critical stress for ferrite/martensite interface decohesion is identified as 1200MPa, which is in agreement with the values found in this work, especially for the case Vm=15%. But this agreement can only be seen as qualitative because the FE cell calculations show some variations of the stress inside the particle and thus with respect to the interface value.
14
5
Discussion
5.1
Damage in DP steels
The martensite phase acts as the reinforcement constituent in a composite. A significant part of the load is transferred to the martensite islands due to the plastic incompatibility between ferrite and martensite. The high stress level in martensite provides the driving force for martensite fracture. On the other hand, plastic strains accumulate at the matrix/reinforcement interface with the piling-up of dislocations, and facilitate the occurrence of interfacial decohesion [3, 37, 38]. These are the two main damage mechanisms in these composite microstructures, which may compete with one another [39]. According to the results presented in section 3.3, there is a transition in the dominating damage mechanism due to a variation of Vm. At small Vm, interface decohesion is the dominant damage mechanism. As Vm increases, the proportion of damage by martensite fracture significantly increases until becoming dominant. A similar observation is reported in ref [6], where no particle cracking was reported for Vm below 20%. This trend can be captured by looking at the stress and strain evolutions in the martensite predicted by FE cell calculations. As shown in Figure 12a, the co-deformation between ferrite and martensite is promoted by increasing Vm. An enhanced co-deformation lowers the strain concentration in the ferrite, which partly explains a smaller proportion of damage by interface decohesion with high Vm. On the other hand, as shown in Figure 12b, the MPS in martensite increases with deformation 15
and tends to saturate at large strains. The level of MPS in martensite significantly decreases with decreasing Vm. For Vm=15%, MPS in martensite barely reaches 1000MPa, which is close to the yield strength of martensitic steels with 0.3wt% carbon [35]. Therefore, martensite fracture should not occur when Vm is small enough. In this case, the strain concentration at the matrix/inclusion interface leads to the occurrence of interface decohesion, dominating the damage nucleation process. The comparison of the level of MPS attained in martensite provides an explanation for the differences in damage nucleation when changing Vm, assuming a brittle fracture mode of martensite. Actually, the fracture strain of martensite with more than 0.3wt% of carbon is rather low, and the assumption of brittle fracture can be considered acceptable [40]. A high MPS means a high probability of martensite fracture [31]. Indeed, at the same thickness strain, the void density in QT-700-37% is much larger than in QT-700-19%. In addition, the void nucleation rate is much higher for QT-700-37%. These observations can be explained by the higher MPS level in the martensite inclusion. The unit cell model adequately predicts the response of DP steels at moderate strain, as shown in [36].
However, some of the observations about the damage process
cannot be explained by the local responses provided by the predictions of the FE unit cell model. For instance, martensite fracture can still be observed when Vm is equal to 15% (Figure 3b), while the predicted MPS is rather low. In addition, the void nucleation strains in QT-700-19% and QT-700-37% are very similar, while the calculations in Figure 12b predict markedly different levels of macroscopic strain at which a critical 16
stress (for instance, 1300MPa as used in [35]) is reached. The shortcomings of the micromechanical model can be attributed to the oversimplified morphology considered in the simulations, consisting of a spherical, isolated inclusion. Actually, the martensite islands are interconnected and somewhat banded, which favors more load transfer between the soft and the hard phase. In addition, local bending can be imposed on elongated martensite islands, resulting in a stress concentration [7]. The stress in some parts of the martensite phase is thus probably higher than the model prediction, explaining why martensite fracture can be observed in QT-700-15%. Also, the connected sections of martensite islands constitute the preferred site for damage nucleation [41], which results in a similar void nucleation strain among the different DP microstructures with different Vm. As Vm increases, the average size of martensite islands increases, and the martensite banding becomes significant (Figure 1). Large voids are formed at the wide martensite bands (Figure 4 and 5) and they contribute to a large extent to damage accumulation. These microstructure features should be taken into account to improve the prediction of damage in DP steels.
5.2
Fracture of DP steels
Cleavage in DP steels under uniaxial tension conditions has been reported to take place within ferrite grains but not in the martensite phase [10, 12, 42-45]. A direct observation of cleavage in a ferrite grain, which is blocked by the martensite islands, is reported in Ref. [45]. The brittle fracture of DP steels is attributed to the presence of interconnected martensite islands [12, 43] and/or to a coarse microstructure [10, 42, 44]. 17
In contrast to the case of isolated martensite islands, the interconnected martensite in DP steels constrains the plastic flow in the ferrite matrix by confining the active slip systems [12] and/or by imposing a high triaxiality state of stress [46]. Once the martensite breaks, a cleavage crack in ferrite grain can be triggered due to the very large local stress building up at the crack tip. The results in this paper show that DP steels mainly fracture in a ductile manner while cleavage becomes operative at high Vm. As Vm increases, the size of the martensite phase increases and continuous wide martensite bands form, so that large cracks can initiate inside the martensite phase. A large Vm also leads to enhanced martensite connectivity that constrains the plastic flow of the ferrite. These microstructural features at high Vm favor the occurrence of cleavage in the ferrite. The points mentioned above are not sufficient to fully explain the occurrence of brittle fracture events observed in this study. For the largest Vm, dimples still cover the major part of the fracture surface of QT-700-37%. In addition, cleavage is not uniformly distributed over the fracture surface but is only located at the edges of the specimens (Figure 9a). These observations indicate that ductile fracture is the intrinsic or dominating mode of failure under uniaxial tension, because ductile fracture is the first mechanism to initiate in the center of the specimens [9, 17]. The occurrence of brittle fracture at the edges of specimen is probably induced by geometrical and dynamic effects. A large principal crack can be formed during the failure of a tensile specimen, as reported in [7]. As Vm increases, the flow stress is increased. Once the principal crack is formed, a high opening stress level builds up at the tip of the crack, involving a higher 18
local stress triaxiality. This promotes the occurrence of brittle crack propagation by locally attaining the cleavage stress of ferrite.
6
Conclusions The influence of martensite volume fraction on the damage and fracture behavior of
dual-phase steels was analyzed with detailed characterizations and FE unit cell calculations. The main conclusions are the following. 1) The tensile strength increases with increasing Vm, while the fracture strain decreases. A trade-off between these two properties can be found as Vm is varied. 2) Interface decohesion is an important void nucleation mechanism when Vm is low. Interface decohesion mainly takes place at triple junctions, and the defects grow as voids or propagate as cracks along the ferrite grain boundary. 3) Martensite fracture is the dominating void nucleation mechanism when Vm is high, and it often initiates at the edge of the martensite phase. Large voids are formed by fracture of wide martensite bands. 4) Simple periodic FE unit cell calculations predict an increase of the maximum principal stress in martensite with increasing Vm, which allows rationalizing the transition of the dominating damage mechanism and the accelerated void nucleation. 5) The dual-phase steels mainly fail by ductile fracture. However, partial brittle fracture can occur at the end of the failure process when Vm is high, when the crack approaches the edges of the specimens. 19
Acknowledgement The authors acknowledge Prof. J.D. Embury for helpful discussions. Q.L. acknowledges the financial support of ArcelorMittal Research. L.B. is mandated by the National Fund for Scientific Research (FNRS, Belgium). The support of BELSPO through IAP 7/21 network is also gratefully acknowledged.
References [1] W. Bleck, JOM, 48 (1996) 26-30. [2] O. Bouaziz, H. Zurob, M.X. Huang, Steel Res. Int., 84 (2013) 937-947. [3] C. Landron, O. Bouaziz, E. Maire, J. Adrien, Scr. Mater., 63 (2010) 973-976. [4] C. Landron, O. Bouaziz, E. Maire, J. Adrien, Acta Mater., 61 (2013) 6821-6829. [5] C. Landron, E. Maire, O. Bouaziz, J. Adrien, L. Lecarme, A. Bareggi, Acta Mater., 59 (2011) 7564-7573. [6] A.F. Szewczyk, J. Gurland, Metall. Trans. A, 13 (1982) 1821-1826. [7] H. Ghadbeigi, C. Pinna, S. Celotto, Mater. Sci. Eng. A, 588 (2013) 420-431. [8] D.L. Steinbrunner, D.K. Matlock, G. Krauss, Metall. Trans. A, 19 (1988) 579-589. [9] J. Kadkhodapour, A. Butz, S.Z. Rad, Acta Mater., 59 (2011) 2575-2588. [10] N.J. Kim, G. Thomas, Metall. Trans. A, 12 (1981) 483-489. [11] M. Mazinani, W.J. Poole, Metall. Mater. Trans. A, 38A (2007) 328-339. [12] T. Kunio, M. Shimizu, K. Yamada, H. Suzuki, Eng. Fract. Mech., 7 (1975) 411-417. [13] A.R. Marder, Metall. Trans. A, 13 (1982) 85-92. [14] C.C. Tasan, J.P.M. Hoefnagels, M.G.D. Geers, Scr. Mater., 62 (2010) 835-838. [15] G. Avramovic-Cingara, Y. Ososkov, M.K. Jain, D.S. Wilkinson, Mater. Sci. Eng. A, 516 (2009) 7-16. [16] G. Avramovic-Cingara, C.A.R. Saleh, M.K. Jain, D.S. Wilkinson, Metall. Mater. 20
Trans. A, 40A (2009) 3117-3127. [17] E. Maire, O. Bouaziz, M. Di Michiel, C. Verdu, Acta Mater., 56 (2008) 4954-4964. [18] G.R. Speich, R.L. Miller, in: Structure and Properties of Dual Phase Steels, 1979, 145-182. [19] F.M. Al-Abbasi, J.A. Nemes, Comput. Mater. Sci., 39 (2007) 402-415. [20] F.M. Al-Abbasi, J.A. Nemes, Int. J. Mech. Sci., 45 (2003) 1449-1465. [21] J. Kadkhodapour, A. Butz, S. Ziaei-Rad, S. Schmauder, Int. J. Plast., 27 (2010) 1103-1125. [22] K.S. Choi, W.N. Liu, X. Sun, M.A. Khaleel, Metall. Mater. Trans. A, 40A (2009) 796-809. [23] X. Sun, K.S. Choi, A. Soulami, W.N. Liu, M.A. Khaleel, Mater. Sci.Eng. A, 526 (2009) 140-149. [24] N. Vajragupta, V. Uthaisangsuk, B. Schmaling, S. Munstermann, A. Hartmaier, W. Bleck, Comput. Mater. Sci., 54 (2011) 271-279. [25] H.E. Exner, Qualitative and quantitative surface microscopy, in: Physical Metallurgy (4th edition), Elsevier, Amsterdam, 1996. [26] http://imagej.nih.gov/ij/. [27] W.C. Oliver, G.M. Pharr, J. Mater. Res., 19 (2004) 3-20. [28] A. Considère, in: Annales des ponts et chaussées I sem, 1885, pp. 574. [29] C.C. Tasan, J.P.M. Hoefnagels, M.G.D. Geers, Acta Mater., 60 (2012) 3581-3589. [30] Q. Lai, PhD thesis , Université de Grenoble, 2014. [31] A. Pineau, T. Pardoen, Failure of Metals, in: Comprehensive Structural Integrity, Pergamon, Oxford, 2007, pp. 684-797. [32] C. Landron, E. Maire, J. Adrien, O. Bouaziz, M. Di Michiel, P. Cloetens, H. Suhonen, Nucl. Instrum. Methods Phys. Res. B, 284 (2012) 15-18. [33] V. Tvergaard, Int. J. Fract., 17 (1981) 389-407. [34] ABAQUS, Analysis User' s Manual, Version 6.8, 2008. [35] A.P. Pierman, O. Bouaziz, T. Pardoen, P.J. Jacques, L. Brassart, Acta Mater., 73 (2014) 298-311. [36] Q. Lai, Int. J. Plast., submitted. 21
[37] A.S. Argon, J. Im, R. Safoglu, Metall. Trans. A, 6 (1975) 825-837. [38] Y. Charles, R. Estevez, Y. Brechet, E. Maire, Eng. Fract. Mech., 77 (2010) 705-718. [39] L. Babout, Y. Brechet, E. Maire, R. Fougeres, Acta Mater., 52 (2004) 4517-4525. [40] R. Roumina, J.D. Embury, O. Bouaziz, H.S. Zurob, Mater. Sci. Eng. A, 578 (2013) 140-149. [41] K. Park, M. Nishiyama, N. Nakada, T. Tsuchiyama, S. Takaki, Mater. Sci. Eng. A, 604 (2014) 135-141. [42] M. Calcagnotto, Y. Adachi, D. Ponge, D. Raabe, Acta Mater., 59 (2011) 658-670. [43] P. Uggowitzer, H.P. Stuwe, Mater. Sci. Eng., 55 (1982) 181-189. [44] X.L. Cai, J. Feng, W.S. Owen, Metall. Trans. A, 16 (1985) 1405-1415. [45] Q. Lai, O. Bouaziz, M. Goune, A. Perlade, Y. Brechet, T. Pardoen, Mater.Sci. Eng. A, 638 (2015) 78-89. [46] S.K. Yerra, G. Martin, M. Veron, Y. Brechet, J.D. Mithieux, L. Delannay, T. Pardoen, Eng. Fract. Mech., 102 (2013) 77-100.
Figure captions: Figure 1. The spheroidized microstructure (a) and DP microstructures with 15% (b), 19% (c), 28% (d) and 37% (e) of martensite, and the evolution of mean linear size of martensite with Vm(f).
22
23
f
mean linear size of martensite
3.0
Dimension (μm)
2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Vm
Figure 2. Uniaxial true stress-true strain curves of DP steels with martensite volume fractions equal to 15%, 19%, 28% and 37%. All the curves are shown up to necking. 1200
true stress (MPa)
1000
QT-700-37% QT-700-28%
800
QT-700-19% QT-700-15%
600 400 200 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
true strain Figure 3. SEM micrographs showing the damage mechanisms in QT-700-15%. The voids are observed closed to the fracture surface.
24
Figure 4. SEM micrographs showing the damage mechanisms in QT-700-28%. The voids are observed closed to the fracture surface.
25
Figure 5. SEM micrographs showing the damage mechanisms in QT-700-37%. The voids are observed closed to the fracture surface.
26
Figure 6. Micrographs showing the voids on the as-polished surface of QT-700-19% (a) and the representation after binarization (b).
27
Figure 7. Variation of damage accumulation of QT-700-19% and QT-700-37% with thickness strain in terms of (a) void density and of (b) area fraction of voids. Only the voids larger than 110nm2 are taken into account for these plots.
a
0.020 0.018
QT-700-19%
2
void density (/μm )
0.016 0.014 0.012 0.010
QT-700-37%
0.008 0.006 0.004 0.002
initial defect density
0.000 0.1
0.2
0.3
0.4
0.5
0.6
thickness strain
b area fraction of voids (%)
3.0 2.5
QT-700-19% 2.0 1.5 1.0
QT-700-37%
0.5
initial area fraction of defects
0.0 0.1
0.2
0.3
0.4
0.5
0.6
thickness strain
Figure 8. Variation of damage as a fuction of thickness strain for different ranges of void size in (a) QT-700-19% and (b) QT-700-37%.
28
a
εthickness=0.095
6
εthickness=0.236
-3
2
void density (10 /μm )
7
εthickness=0.531
5 4 3
QT-700-19%
2 1 0 10 ~20
20 30 40 80 100 120 150 200 >300 50 60 ~30 ~40 ~50 ~60 ~70 ~90 ~110 ~130 ~200 ~300
pixel
3.5
εthickness=0.104
3.0
εthickness=0.136 εthickness=0.22
2.5
-3
2
void density (10 /μm )
b
2.0 1.5
QT-700-37%
1.0 0.5 0.0 10 ~20
20 ~30
40 50 30 ~40 ~50 ~60
70 100 120 150 200 >300 60 ~70 ~80 ~110 ~130 ~200 ~300
pixel Figure 9. SEM micrographs of the fracture surface in QT-700-37%; (a) a low-magnification graph showing both ductile and brittle features; (b) surface covered by dimples; (c) surface showing significant cleavage.
29
Figure 10. Configuration, dimensions and mesh of the axisymmetric FE unit cell.
Figure 11. Comparison of the simulated (with FE unit cell model) and experimental stress-strain response
30
1200
× Vm=37% × Vm=28%
true stress (MPa)
1000 800
×
600
Vm=19%
× V =15% m
400
experiment
200 0 0.00
× model 0.05
0.10
0.15
0.20
0.25
true strain Figure 12. Variation of the mean plastic strain (a) and MPS (b) in the martensite with overall strain for different martensite volume fractions.
plastic strain in martensite
a
0.20
Vm = 37%
0.15
0.10
Vm = 28% 0.05
Vm = 19% 0.00 0.00
Vm = 15% 0.05
0.10
0.15
0.20
0.25
0.30
macroscopic strain
MPS in martensite (MPa)
b
1800
Vm = 37%
1600
Vm = 28% Vm = 19%
1400 1200
Vm = 15%
1000 800 600 400 200 0 0.00
0.05
0.10
0.15
0.20
macroscopic strain
Tables: 31
0.25
0.30
Table 1. Nanohardness of martensite in the DP samples. Samples Martensite hardness (GPa) QT-700-19% 8.4608 ±1.64936 QT-700-28% 7.7718±0.67976 QT-700-37% 8.0692±0.68784 Table 2. Mechanical properties of the DP steels involving different martensite volume fractions. Samples Tensile Uniform Fracture strain strength (MPa) elongation QT-700-15% 691±4 0.164±0.002 1.06±0.06 QT-700-19% 765.5±13 0.143±0.009 0.75±0.11 QT-700-28% 928±25 0.124±0.011 0.4±0.01 QT-700-37%
1058±18
0.116±0.002
0.33±0.02
Table 3. Identified ferrite parameters. Vm
y , (MPa)
(MPa)
15% 19% 28% 37%
250 279 300 307
4895 5980 8925 10260
11 13 17 20
0
32