Influence of microstructure and pre-straining on the bake hardening response for ferrite-martensite dual-phase steels of different grades

Author’s Accepted Manuscript Influence of Microstructure and Pre-straining on the Bake Hardening Response for Ferrite-Martensite Dual-Phase Steels of Different Grades Dengpeng Ji, Mei Zhang, Delong Zhu, Siwei Luo, Lin Li www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(17)31294-7 https://doi.org/10.1016/j.msea.2017.09.127 MSA35594

To appear in: Materials Science & Engineering A Received date: 4 July 2017 Revised date: 12 September 2017 Accepted date: 28 September 2017 Cite this article as: Dengpeng Ji, Mei Zhang, Delong Zhu, Siwei Luo and Lin Li, Influence of Microstructure and Pre-straining on the Bake Hardening Response for Ferrite-Martensite Dual-Phase Steels of Different Grades, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2017.09.127 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.

Influence of Microstructure and Pre-straining on the Bake Hardening Response for Ferrite-Martensite Dual-Phase Steels of Different Grades Dengpeng Ji a, Mei Zhang a,b,c,, Delong Zhu a, Siwei Luo a, Lin Li a,b a b c

School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China

State Key Laboratory of Advanced Special Steel, Shanghai University, Shanghai 200072, China

Shanghai Key Laboratory of Advanced Ferro Metallurgy, Shanghai University, Shanghai 200072, China

Abstract: This work aims to investigate the effects of pre-straining and microstructure on bake hardening (BH) response of dual phase (DP) steels. Four kinds of different grades of commercial DP steels, DP340/600, DP420/780, DP500/780 and DP550/980, were pre-strained in tension to 0.5, 1, 2, 4, 6 and 8%, then baked at 170 °C for 20 min followed by restraining, or just baked at 170, 190, 210, 230, 250 °C for 20 min and at 250 °C for 40 min followed by straining without pre-straining. Electron backscattered diffraction (EBSD) measurements and temperature-dependent internal friction measurements were conducted to characterize geometrically necessary dislocations (GNDs) and analyze solute carbon content and interactions between point defects and dislocations in DP steels. The results show that for all grades of DP steels investigated, BH values increase to peak values at pre-straining ranging from 0.5 to 2% and then decline with further pre-straining. At BH condition of 170 °C/20 min, peak BH values with pre-straining are 33 MPa for DP340/600, 34 MPa for DP420/780, 78 MPa for DP500/780 and 90 MPa for DP550/980 respectively. Pre-straining can cause increase in tensile strength and decrease in total elongation after baking, especially for DP500/780 and DP550/980. DP steels without pre-straining can reach very high BH0 values by applying either higher temperature or longer holding time. Solute carbon content in ferrite controls the speed of BH response in DP steels. Microstructures of higher volume fraction of martensite, smaller martensite islands and smaller ferrite grains can produce higher BH values. Keywords: Bake-hardening; Dual-phase steel; Geometrically necessary dislocation; Internal friction 1. Introduction Advanced high strength steels (AHSS) have been increasingly used in automotive industry for the purpose of weight saving and crash safety improving of vehicles. As the first generation of AHSS, dual phase (DP) ferrite-martensite steel presents unique combination of high strength and good formability and its special mechanical properties can be tailored and adjusted by alloying and processing with respect to the requirements of specific structural application for auto-body, which offers promising application prospect [1-4]. The microstructure of DP steel consists of hard martensite particles dispersed in a soft and ductile ferrite matrix [5]. This combined microstructure gives DP steel some interesting properties such as combination of high strength and good ductility, continuous yielding, high initial work-hardening rate (n value) and a low ratio of yield stress to tensile strength (YS/TS) [6]. Furthermore, the continuous yielding behavior, no yield-point elongation, makes the absence of Lüders bands during plastic flow of DP steel, 

Corresponding author: Dr. Mei Zhang Tel: +86-13611822313 Fax: +86-21-56331466 E-mail: [email protected] 1 / 26

resulting in an excellent surface finish without the need for additional skin-passes [7]. Also, DP steel costs less because it is low-carbon and low-alloy and can be processed using traditional routes [8-10]. For press formed car body structural components, paint baking is the last operation which is performed typically at a temperature around 170 °C for about 20 min in order to bind the paint coat. In addition, bake hardening (BH) of the steel after paint baking operation contributes to the improved strength in service, e.g., the increased dent resistance of the outer car body parts. A lot of efforts have been focused on the research of BH effects of DP steels and it is revealed that DP steels can show a considerable BH effect after some pre-straining [11-14]. Different from the extra low carbon (ELC, C ~ 200 ppm) and ultralow carbon (ULC, C < 50 ppm) steels, where the aging behavior is mainly controlled by the amount of dislocations and interstitial carbon atoms, the BH in DP Steels can have more complex nature stemming from the relatively complex two-phase microstructure. Interstitial carbon atoms in ferrite, carbon in the grain boundaries, carbon released from martensite due to tempering, dislocations produced by martensitic transformation as well as external pre-straining and internal stress due to martensitic transformation are all expected to exert influence on BH mechanism for DP steels. With efforts of researchers, three main strengthening stages of BH in DP steels can be identified. During heating, solute carbon atoms in steel diffuse and segregate to the vicinities of dislocations in ferrite, forming the Cottrell atmospheres blocking dislocations [15, 16], and this is often referred as the first stage. The second strengthening stage is associated with carbon-clustering or precipitation of low temperature carbides in ferrite [17], which can also block the movement of dislocations. With bake proceeding, the effects induced by tempering of martensite work, which can be referred as the third strengthening stage where internal stress relief in ferrite due to volume contraction of martensite during tempering and carbon clustering or precipitation near the ferrite/martensite interfaces will both influence the yielding behaviors of DP steels [18, 19]. It is worth noting that these strengthening stages may overlap at elevated baking temperatures. Considering BH mechanism in DP steel, the BH response of a specific DP steel can be affected by the external processing factors, i.e., baking temperature, holding time and pre-straining, and factors of the steel itself, i.e., the original chemical composition and microstructure which includes the volume fraction of martensite, the size distribution for ferrite and martensite, and the morphology of ferrite and martensite. Chang [20] and Davies [21] studied the effect of aging temperature on the mechanical properties of DP steels and observed the yield strength increasing with temperature below 225 °C. Discontinuous yielding behavior returned for specimens aged at 200 °C and above. The formation of Cottrell atmospheres around dislocations and relief of residual stress may be responsible for the variation of yielding behavior in the temperature range below 225 °C. Ramazani et al. [13] quantified the BH effect in DP600 steel. In terms of the BH0 (yielding stress increment of a 0% pre-strained sample after an aging treatment) kinetics of DP600 steel, the yielding stress increment increases with holding time to a plateau which depends on the aging temperature. The yielding stress increment gets higher with a higher degree of pre-straining and reaches the peak value at 2% pre-straining. Gündüz [22] conducted an investigation on the cold deformation aging susceptibility of a carbon steel and a microalloyed steel both with dual phase microstructure. It was revealed that the aging of the microalloyed steel occurred more slowly than that of the carbon steel. This was attributed to the chemical composition of microalloyed dual phase steel which, in addition to carbon atoms, contained nitrogen and carbide forming elements such as titanium, vanadium and aluminum. With respect to microstructure of DP steels, although the relationship between microstructure and mechanical properties of DP steels has been discussed by many researchers [3, 7, 23, 24], not much specific investigation has been reported about microstructural effect on BH response for DP steels. The roles of volume fraction of martensite, size distribution and morphology for two phases in affecting BH 2 / 26

response of DP steels have not been understood in detail. Due to excellent combination of strength and formability of DP steels and weight saving demand in automotive industry, the usage amount of DP steels in the total weight of the car is increased and DP steels of higher strength grades are considered for producing car parts. Paint baking process, performed on press formed car parts which typically contain strain in the range of 0 to 5% [25], can produce additional increment of yielding stress, increasing dent resistance of outer car body parts. Various grades of DP steels correspond to various patterns of microstructure. Investigating the influence of microstructure and pre-straining on BH response, namely strain aging behavior, for DP steels is of great significance not only to enhance the fundamental understanding of DP steel structure but also to provide practical guidelines for the application of DP steels in automotive industry. In the present work, different grades of DP steels, corresponding to different combinations of yielding strength and tensile strength, are selected to investigate the influence of microstructure and pre-straining on the BH response of DP steels. 2. Experimental procedure 2.1. Materials and characterization of microstructure Four kinds of different grades of industrially processed cold rolled DP steels were investigated in this research and they are DP340/600, DP420/780, DP500/780 and DP550/980 respectively, where DPx/y denotes a kind of DP steel with a combination of yielding strength of x MPa and tensile strength of y MPa. The chemical compositions of the four materials are given in Table 1. The microstructures of as-received steels were revealed using scanning electron microscope (SEM) technique with specimen preparation of polishing and 2% Nital etching. Based on the SEM micrographs of as-received steels, image processing software “Photoshop CC 2015” was used to separate martensite and ferrite. Then the processed micrographs were used for determining volume fraction of martensite and grain size distributions for ferrite and martensite with the help of image analyzing software “Image Pro Plus 6.0”. Table 1 Chemical compositions of the four investigated DP steels (wt.%). Steel

C

Si

Mn

P

Cr

Al

t (mm) 1)

DP340/600 DP420/780 DP500/780 DP550/980

0.076 0.102 0.078 0.098

0.415 0.142 0.429 0.139

1.84 2.06 1.81 2.07

0.020 0.027 0.031 0.013

0.013 0.276 0.006 0.407

0.048 0.041 0.048 0.036

2.0 1.6 1.6 2.0

Note: 1) t shows the thickness of the steel sheets (in mm). 2.2. Mechanical property test The mechanical properties of steels before and after baking were tested using uniaxial tensile test. Tensile specimens were cut from the four kinds of steel sheets according to the national standard of China GB/T 228.1-2010 [26] with their tensile axis parallel to the rolling direction. The specimen geometry used for tensile test is given in Fig. 1. Tensile tests were carried out at room temperature with a crosshead speed of 10 mm/min on a MTS C45.305 machine. Three parallel tests were carried out for each baking treatment and average values were calculated.

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Fig. 1. Specimen geometry for tensile testing (dimensions are given in mm). 2.3. Bake hardening treatment and method of determining BH values For each kind of DP steel, one portion of tensile specimens were pre-strained at room temperature in tension to 0.5, 1, 2, 4, 6 and 8%, then baked at 170 °C for 20 min in air oven followed by restraining at room temperature and the other portion of tensile specimens without pre-straining were baked at 170, 190, 210, 230, 250 °C for 20 min or at 250 °C for 40 min directly in air oven followed by straining at room temperature. Bake hardening (BH), namely strain aging phenomenon, occurs in the final paint baking process of a car component. BH value is defined as the increase of yielding stress, relative to the flow stress at the end of pre-straining, after paint baking treatment. The definition of BH as well as the major BH mechanism of diffusion of interstitial atoms forming Cottrell atmospheres locking dislocations is illustrated in Fig. 2. However, absence of a marked yield point for DP steel even after pre-straining and aging in some cases makes it difficult to determine the BH value due to aging only. If apply 0.2% offset criterion to determine yielding stress of specimens after pre-straining and aging, and subtract the flow stress at the end of pre-straining from the yielding stress after pre-straining and aging, to obtain the BH value, then a relatively higher portion of work hardening (WH) caused by 0.2% strain will be contained in the BH value, especially in the case of lower amount of pre-straining due to the high work hardening rate in this strain stage for DP steels, as illustrated in Fig. 3.Therefore, in the case of absence of marked yield point after pre-straining and aging, the method introduced by Waterschoot et al. [17] was applied to determine the BH value. In this method, the flow curve after pre-straining and aging was superimposed on the flow curve without pre-straining and aging, resulting in ∆𝜎 values, the difference between flow stresses with aging and without aging, as a function of the strain. The ∆𝜎 goes through a maximum, BH* depicted in Fig. 3, and then decreases at much higher strain. The maximum of ∆𝜎, BH*, is determined as the BH value due to aging only. In the case of presence of marked yield point after pre-straining and aging, the standard method determining BH value, depicted in Fig. 2, was applied. For aged specimens without pre-straining, BH value is the increase of 0.2% offset yield stress after baking, relative to the 0.2% offset yield stress of a specimen without aging. In the rest of this paper, the uniform BHx is used to describe the bake hardening degree, where x denotes pre-straining of x pct. The difference in determining methods will not be mentioned any more.

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Fig. 2. Schematic illustration of BH definition and major BH mechanism of diffusion of interstitial atoms forming Cottrell atmosphere blocking dislocations.

Fig. 3. Determining method of BH value in the case of absence of a marked yield point after pre-straining and aging. 2.4. EBSD measurements for calculating densities of GNDs In order to characterize the Geometrically necessary dislocations (GNDs) in ferrite due to martensitic transformation in DP steels, microstructures of the four DP steels were also mapped by electron backscattered diffraction (EBSD) using a field-emission gun scanning electron microscopy (FEG-SEM, Apollo 300) equipped with an EBSD system operated at an accelerating voltage of 15 kV. EBSD specimens were prepared by mechanical grinding and polishing, followed by electropolishing in a 5% perchloric acid and 95% acetic acid solution (by volume) with an applied voltage of 30 V. A high-speed CCD camera was used for pattern acquisition. Data were recorded at 100 nm step size and analyzed using the HKL CHANNEL 5 software. Martensite was indexed as bcc iron and distinguished from ferrite using band contrast (BC) parameter in the resulting data sets. A Matlab-based program was developed to calculate the kernel average misorientation (KAM) parameter from original data exported by CHANNEL 5 software. The KAM parameter of a point is the average of misorientations between this point and its neighbors in a 200 nm distance, where misorientations over 2° are excluded from the average calculation because these neighbor points are assumed to belong to adjacent grains or subgrains [27]. For calculating GND densities in ferrite, the method proposed by Kubin and Mortensen was applied [28]. Based on the strain gradient model of Gao et al. [29], they define a GND array for simple cylinder torsion. A series of twist subgrain boundaries is assumed to exist in the cylinder and each contains two 5 / 26

perpendicular arrays of screw dislocations. Considering assumption above, the following relationship between GND density 𝜌𝑔𝑛𝑑 and misorientation angle 𝜗 can be obtained, 2𝜗

𝜌𝑔𝑛𝑑 = 𝑢𝑏

(1)

where 𝑢 is the unit length (In this research, 𝑢 = 200 nm) and 𝑏 is the magnitude of the Burgers vector (For bcc iron, 𝑏 = 0.248 nm). The misorientation angle 𝜗 is assumed to be the KAM parameter calculated from EBSD original data. 2.5. Temperature-dependent internal friction measurements Temperature-dependent internal friction measurements were conducted to analyze the solute carbon content and interactions between point defects and dislocations in the four DP steels. The samples were cut to sheets having dimensions of 1 mm × 2 mm × 55 mm from tensile specimens of three different states which are the as-received state, the states of 2% and 6% pre-straining followed by baking treatment at 170 °C for 20 min respectively. Internal friction measurements were performed in an inversed torsion pendulum by free decay method from 0 °C to 300 °C with heating rate of 1 °C/min at a frequency of 2 - 4 Hz. 3. Results 3.1. Microstructures and mechanical properties of as-received steels Representative micrographs of microstructures for the four DP steels in as-received condition are depicted in Fig. 4 a-d and the corresponding grain size distributions of two phases, ferrite and martensite, for the four materials are exhibited in Fig. 5 a-b. Microstructure parameters obtained from SEM micrographs of the as-received steels as well as mechanical properties of as-received condition are shown in Table 2.

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Fig. 4. SEM micrographs of microstructures of (a) DP340/600, (b) DP420/780, (c) DP500/780 and (d) DP550/980 steels in as-received condition.

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Fig. 5. Grain size distribution of (a) ferrite and (b) martensite for the four DP steels. Table 2 Microstructure parameters obtained from SEM micrographs and mechanical properties of as-received condition presented as average value of three tensile specimens for each material. Steel

MVF (%)

df (μm)

dm (μm)

YS (MPa)

UTS (MPa)

UE (%)

TE (%)

n-value

DP340/600 DP420/780 DP500/780 DP550/980

21.8 28.3 38.4 33.4

8.7 4.1 7.4 2.1

1.9 1.4 4.1 1.5

388±10 480±8 656±15 659±14

627±11 805±24 886±10 977±14

17.6±0.6 13.9±0.8 7.6±0.3 8.9±0.6

28.2±0.6 21.6±1.5 14.1±1.0 15.8±1.5

0.17±0.01 0.17±0.01 0.10±0.005 0.12±0.006

Standard abbreviations are given. MVF: martensite volume fraction; df: ferrite grain size (the average, weighted by area fraction, of diameters of all grains); dm: martensite grain size (the same calculating method as df); YS: 0.2% offset yield strength; UTS: ultimate tensile strength; UE: uniform elongation; TE: total elongation. 8 / 26

3.2. BH response with pre-straining Mechanical properties of four studied DP steels after pre-straining and aging at 170 °C/20 min were recorded in stress-strain curves, as shown in Fig. 6 a-b. For DP340/600 and DP420/780 steels, with pre-straining increasing from 0 to 8% and aging treatment of 170 °C/20 min staying the same, tensile strength and total elongation change slightly. However, it is not the case for DP500/780 and DP550/980 steels. From stress-strain curves of DP500/780 steel after different degrees of pre-straining and identical aging treatment, it can be observed that total elongation presents slight decline and the corresponding tensile strength presents slight increase with pre-straining increasing from 0 to 1%. Further increasing pre-straining to 2%, total elongation of DP500/780 decreases sharply. When pre-straining increases to 6%, increment of tensile strength of DP500/780 after aging treatment, in comparison with that of the as-received condition, reaches to the maximal value of 70 MPa. Similar phenomenon is observed in the DP550/980 steel, where total elongation of DP550/980 decreases sharply when the pre-straining increases to 4% and increment of tensile strength of DP550/980 reaches to the maximal value of 60 MPa when the pre-straining increases to 6%.

Fig. 6. Stress-strain curves of (a) DP340/600, DP420/780, (b) DP500/780 and DP550/980 steels at the BH condition of 170 °C/20 min with various degrees of pre-straining. DP steel shows continuous yielding behavior in the as-received condition. Appropriate combination of pre-straining and baking treatment can cause the return of discontinuous yielding behavior. Among the four DP steels, only DP420/780 steel does not present discontinuous yielding behavior when the specimens were pre-strained to different degrees from 0 to 8% and then baked at 170 °C for 20 min. DP340/600, DP500/780 and DP550/980 steels can all present discontinuous yielding behavior when the specimens were pre-strained to a certain degree and then baked at 170 °C for 20 min. For DP340/600 and DP500/780 steels, well-defined yield point elongation can be observed after baking when pre-straining increases to 0.5%. With further increasing pre-straining to 2%, marked yielding point could not be observed any more in DP340/600 and flow stress, after yielding, of DP500/780 presents a continuous decline with strain up to fracture, where yield point elongation of DP500/780 becomes non-obvious. DP550/980 steel begins to present well-defined yield point elongation when pre-straining increases to 2% and the corresponding Lüders strain is the highest among DP340/600, DP500/780 and DP550/980 steels. When pre-straining increases to 4%, the yield point elongation of DP550/980 becomes non-obvious. For all the four DP steels with various degrees of pre-straining, the aging treatment of 170 °C/20 min can cause a yielding strength increase and the corresponding BH values vary with amount of 9 / 26

pre-straining and vary from one grade of DP steel to another, as depicted in Fig. 7. BH0 values of the four DP steels are relatively low and in the range of 0 to 25 MPa. The BH value gets higher with a higher degree of pre-straining. DP340/600 and DP420/780 steels reach highest BH values at 0.5% pre-strain while DP500/780 and DP550/980 steels reach highest BH values at 2% pre-strain. After pre-straining corresponding to the highest BH value, further pre-straining does not improve the BH effect and the BH value presents a tendency of decline. Comparing the four DP steels, BH effects in DP500/780 and DP550/980 are relatively stronger than those in DP340/600 and DP420/780 steels.

Fig. 7. BH values of DP340/600, DP420/780, DP500/780 and DP550/980 steels at the BH condition of 170 °C/20 min with various degrees of pre-straining. 3.3. BH0 behaviors of the DP steels in dependence on the aging temperature and time Given the relatively low BH0 values of the four DP steels at BH condition of 170 °C/20 min, several higher BH temperatures and longer holding time, including 190 °C/20 min, 210 °C/20 min, 230 °C/20 min, 250 °C/20 min and 250 °C/40 min, were applied to the specimens without pre-straining to study the BH0 behavior of the four DP steels. Fig. 8 a-d show the stress-strain curves at various BH conditions of DP340/600, DP420/780, DP500/780 and DP550/980 respectively. For all the four DP steels, tensile strength after different aging treatments of specimens without pre-straining changes insignificantly, which is different from the case observed in pre-strained specimens. Total elongation after aging treatment presents a decline especially in the case of return of discontinuous yielding when the BH temperature increases. All the four DP steels still display continuous yielding behavior at typical BH condition of 170 °C/20 min without pre-straining. With various BH condition being applied to the specimens without pre-straining, it can be seen that discontinuous yielding behavior can return in all the four DP steels as long as the BH temperature and holding time increase to a certain level which is 230 °C/20 min for DP340/600, 250 °C/40 min for DP420/780, 230 °C/20 min for DP500/780 and 250 °C/20 min for DP550/980. Comparing BH0 behaviors of four DP steels, DP500/780 steel is the easiest to produce discontinuous yielding after baking and the following are DP340/600, DP550/980 and DP420/780 respectively.

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Fig. 8. Stress-strain curves of (a) DP340/600, (b) DP420/780, (c) DP500/780 and (d) DP550/980 steels at various BH conditions without pre-straining. 0.2% offset yield strength increment (BH0 value), in comparison with the as-received condition, after various baking treatments for the four DP steels are given in Fig. 9. BH0 value of each DP steel presents an increasing tendency with baking process getting stronger from 170 °C/20 min to 250 °C/40 min. When the baking treatment of 250 °C/40 min was applied, all the four materials display discontinuous yielding and BH0 values of DP340/600, DP420/780, DP500/780 and DP550/980 steels reach 40, 111, 173 and 234 MPa respectively, which correlates well with the strength grades of DP steels. From the above, it is easy to find that BH of DP steel is a process in dependence of BH temperature and holding time. Comparing BH responses of pre-strained specimens and specimens without pre-straining, pre-strained specimens can reach higher BH value and produce discontinuous yielding more easily when the identical baking treatment was applied.

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Fig. 9. BH0 values of DP340/600, DP420/780, DP500/780 and DP550/980 steels at various BH conditions without pre-straining. 4. Discussion 4.1. Geometrically necessary dislocations It has been well known that the industrially used BH effect is a kind of strain aging phenomenon which is based on locking of mobile dislocations, produced by pre-straining, by interstitial atoms in solid solution such as C or N atoms [13, 17]. Due to the special microstructure configuration of martensite islands dispersed in ferrite matrix, a high density of inhomogeneous GNDs, which are not pinned, can be generated in ferrite near to the ferrite-martensite interfaces during the martensitic transformation. The mobile GNDs in combination with residual stress induced by martensitic volume expansion control the initial yield and flow behavior of DP steels [30, 31]. Compared to conventional BH steels, the presence of mobile GNDs in ferrite in DP steels of as-received condition is expected to produce interesting BH response. For evaluating densities and distributions of GNDs around martensite islands, 2D EBSD measurements were conducted on the four DP steels. Figure. 10 a-d show the band contrast (BC) maps of the four DP steels. The higher the lattice distortion, the lower is the BC value and the darker the color in the grey scale maps of BC, which can be used to distinguish the martensite from the ferrite due to higher lattice distortion of martensite. The respective KAM maps of the same area for the four DP steels are exhibited in Figure. 10 e-h. Because martensite has high lattice distortion, diffraction pattern of martensite is hard to identify. Therefore, compared to ferrite, lower rate of identification of martensite in terms of diffraction pattern is found in the region of martensite. The unidentified regions in the KAM maps are marked as red which corresponds to high KAM values in martensite regions. In terms of identified regions, the largest KAM values are found in martensite islands and zones of high KAM values can also be observed in ferrite at the ferrite-martensite phase boundaries. The orientation gradient in ferrite is affected by the size of adjacent martensite islands as larger martensite islands produce larger absolute volume expansion during martensitic transformation, hence affecting larger extent of the adjacent ferrite. However, it is interesting to note that some smaller martensite particles can produce bigger areas of plastic deformation. For example, the martensite particle marked as 1 in Fig. 10 e, corresponding to 1′ in Fig. 10 a, is smaller than the martensite particle marked as 2 in Fig. 10 e, corresponding to 2′ in Fig. 10 a. It is easy to find that area of plastic deformation produced by particle 1 12 / 26

is bigger than that produced by particle 2. One possible explanation for this phenomenon is that smaller austenite particles possess higher carbon content and produce larger volume expansion during transformation. Another possible explanation is that the smaller martensite particle in 2D section is just a small part of larger martensite particle in 3D space and the considerable areas of plastic deformation arise from the rest of the martensite particle lying below or above the 2D section. The KAM maps also show that there are some visible minor plastic deformation zones at the ferrite-ferrite boundaries while they are less frequent and less pronounced than that at the ferrite-martensite boundaries, which can possibly be attributed to the presence of martensite particles above or below the ferrite-ferrite boundaries. In addition, the distribution of martensite islands is recognized from the KAM maps. The more a ferrite grain is surrounded by martensite islands, the larger extent of this ferrite grain undergoes a plastic deformation, which is observed more clearly in the KAM map of DP550/980 where a larger number of martensite islands locate at the grain boundaries of ferrite. In general, similar observations are found in all the KAM maps of the four DP steels except that microstructures containing more martensite islands, such as DP420/780, DP500/780 and DP550/980 when compared to DP340/600, show more zones of high KAM values in ferrite.

Fig. 10. Band contrast maps of (a) DP340/600, (b) DP420/780, (c) DP500/780, and (d) DP550/980 steels and respective kernel average misorientation (KAM) maps of (e) DP340/600, (f) DP420/780, (g) DP500/780, and (h) DP550/980 steels. The KAM maps show the orientation gradients near ferrite-ferrite grain boundaries and ferrite-martensite phase boundaries in DP steels. The method proposed by Kubin and Mortensen [28] was applied to calculate GND densities from KAM values. A Matlab-based program was developed to convert the KAM maps into GND density maps which are shown in Figure. 11 a-d. The GND density values vary from about 3.2 × 1014 m-2 close to the martensite particles to about 6.0 × 1013 m-2 in the grain interior of ferrite for all the four DP steels. The dislocation densities calculated in the present work are slightly lower than the data reported in the literature based on TEM [32]. Calcagnotto et al. [27] attributed this to that statistically stored dislocations (SSDs) are also included in the results based on TEM. Comparing GND maps of the four DP steels, it is easy to find that more zones of high dislocation density exist in DP420/780, DP500/780 and DP550/980 steels.

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Fig. 11. GND densities, calculated from KAM values, of (a) DP340/600, (b) DP420/780, (c) DP500/780 and (d) DP550/980 steels. 4.2. Evaluation of internal stress In DP steels, the residual stress induced by martensitic transformation acts on the ferrite and a plastic zone is generated around each martensite particle. Further out from this zone, the residual stress is in the elastic range and decays rapidly with increasing distance from the martensite particle. Thus, many preferentially yielding zones are produced in DP steels [31]. When a lower applied stress, even below the normal yield stress, is added to the residual elastic stress, the plastic deformation can take place, which is expected to be closely related to the continuous yielding behavior of DP steel [33]. After baking treatment, the discontinuous yielding can return in DP steels, where the internal stress relief may play an important role. For evaluating the role of residual stress in DP steels, the model of DP steel developed by T. Sakaki et al. [31] is considered. Suppose that one spherical martensite particle with a radius a is embedded in an infinite ferrite matrix and then a simple steel with dual phase microstructure is produced. Let the spherical martensite particle locate at the origin of the coordinate system 𝑥𝑖 (i = 1, 2, 3) and any point in the steel can be denoted by 𝒓 = (𝑥1 , 𝑥2 , 𝑥3 ). In this way, the distance between a point and the origin of the coordinate system can be denoted by 𝑟 = (𝑥12 + 𝑥22 + 𝑥32 )1/2. Let equivalent stress be denoted by 𝜎̅. If the ferrite phase does not yield at all, the internal stress in the ferrite (r > a) due to the martensitic volume expansion can be stated as follows 𝐸

𝑎3

∗ 𝜎̅ 𝑜 (𝑟) = 1−𝑣 𝑒𝑀 𝑟3

(2)

where E is Young’s modulus of the ferrite and the martensite (2.06 × 105 MPa), v is Poisson’s ratio ∗ (0.28), 𝑒𝑀 is the isotropic expansion strain of martensite volume and its expression is given: ∗ 𝑒𝑀 = 0.0058 + 0.45𝐶𝛼′ (3) where 𝐶𝛼′ is the mass percent of carbon in martensite. Neglecting the very small solubility of carbon in the ferrite, the carbon content in martensite, 𝐶𝛼′ , can be related to the total carbon content, 𝐶𝑡𝑜𝑡𝑎𝑙 , and volume fraction of martensite, 𝑉𝛼′ , by: 𝐶𝛼 ′ =

𝐶𝑡𝑜𝑡𝑎𝑙 𝑉𝛼′

(4)

∗ For DP340/600, DP420/780, DP500/780 and DP550/980 steels, 𝑒𝑀 = 0.0073, 0.0074, 0.0067 and 𝑜 0.0071 respectively. The corresponding equivalent stress, 𝜎̅ , acting on the ferrite for DP340/600, DP420/780, DP500/780 and DP550/980 steels are 2108a3/r3, 2123a3/r3, 1920a3/r3 and 2037a3/r3 MPa respectively. Immediately outside of the ferrite-martensite interface, 𝜎̅ 𝑜 is high enough to yield the

14 / 26

ferrite. However, 𝜎̅ 𝑜 decreases rapidly with 1/r3, leading to that the ferrite will only yield within a finite radius R. The yielding resulting from the martensite transformation is called transformation induced yielding in order to distinguish it from yielding under external stress. The radius R of the transformation induced yielding zone can be determined using the following equation: 𝑅3 𝑎3

𝐸𝑒 ∗

𝑀 = (1−𝑣)𝑌

0

(5)

where 𝑌0 is the yield strength of the ferrite at the temperature of transformation induced yielding and is estimated as 210 MPa for DP340/600, 290 MPa for DP420/780, 230 MPa for DP500/780 and 380 MPa for DP550/980, in consideration of grain size dependence [34] and testing temperature dependence [34, 35] of the yield strength of pure irons, and the solid-solution hardening by substitutional elements [36]. The values of (R/a) calculated are 2.15, 1.94, 2.03 and 1.75 for DP340/600, DP420/780, DP500/780 and DP550/980 respectively. For all the four DP steels containing various sizes of ferrite and martensite, the values of (R/a) are around 2.0, indicating that extent of plastic deformation zone around martensite is affected by the size of martensite island markedly. This phenomenon has been verified using experimental results by Ramazani et al. [37] elsewhere. They reported that the thickness of the GND layer around martensite depends on the size of martensite island and is insignificantly affected by the ferrite grain size. Considering the transformation induced yielding zones, internal stress acting on ferrite can be stated as follows: In the transformation induced yielding zone of the ferrite (a < r < R), 𝜎̅(𝑟) = 𝑌0 + 𝐻0 𝜀(𝑟) (6) In the elastic zone of the ferrite (r > R), 𝑅3

𝜎̅(𝑟) = 𝑌0 𝑟 3

(7)

where 𝐻0 is initial strain-hardening rate of the ferrite at the transformation induced yielding. In the transformation induced yielding zone of the ferrite, 𝜀(𝑟) is low and 𝐻0 𝜀(𝑟) is far less than 𝑌0 , thus, 𝐻0 𝜀(𝑟) in equation (6) can be omitted. The internal stress acting on the ferrite in the transformation induced yielding zone is controlled by 𝑌0. From the above, it is easy to find that magnitude of internal stress acting on the ferrite is correlated with the ferrite grain size which markedly affects the yield strength, 𝑌0, of ferrite at transformation induced yielding and that extent of ferrite affected by internal stress is correlated with the size of martensite island and volume fraction of martensite. For the four DP steels of various grades corresponding to different microstructure features, the role of internal stress in BH response can be different, which will be discussed in detail in the following section. 4.3. Internal friction variation BH behavior in steel is believed to be controlled by the concentration of interstitial carbon in solid solution conventionally because interstitial carbons diffuse to vicinity of mobile dislocations to pin the dislocations, producing bake hardening. Solute carbon and the interactions between point defects and dislocations in the four DP steels were analyzed by low frequency temperature-dependent internal friction measurements. Fig. 12 a-d shows the internal friction spectrums of DP340/600, DP420/780, DP500/780 and DP550/980 respectively. Two kinds of relaxation peaks can be identified evidently in the internal friction spectrums for all the four DP steels. One kind of peak occurs at around 41 °C, which is considered to be the Snoek relaxation peak of C interstitial atoms [38]. The other kind of peak occurs at 15 / 26

around 220 °C, which is considered to be the Snoek-Köster relaxation peak [39, 40].

Fig. 12. Temperature-dependent internal friction spectrums of (a) DP340/600, (b) DP420/780, (c) DP500/780 and (d) DP550/980 steels in three different states which are the state of as-received, the state of 2% pre-straining followed by baking treatment at 170 °C/20 min and the state of 6% pre-straining followed by baking treatment at 170 °C/20 min. The stress induced reorientation of the interstitial atoms results in a mechanical loss peak, the Snoek peak [38]. The Snoek relaxation peak can be used to characterize interstitial foreign atoms in bcc metals, which is mainly based on the two experimental observations: the one is that the position of the Snoek peak in terms of temperature and frequency is correlated with the species of solute atoms (O, N or C) in a distinct metal and the other is that the magnitude of the Snoek peak is proportional to the concentration −1 of interstitial solute atoms. For a given species of interstitial, the internal friction peak height, 𝑄𝑚 , is related to interstitial concentration, 𝐶0, by: −1 𝑄𝑚 = 𝐴𝐶0 (8) Determination of the factor A needs calibration by some other methods, such as chemical analysis. As anisotropy of the Snoek relaxation strength exists in single crystals and Snoek relaxation strength in a polycrystal is the result of an average over all grains, there is no doubt that texture is the primary structural factor which affects the relaxation strength per unit concentration of interstitials for a polycrystalline sample [41]. The Snoek relaxation peak at around 41 °C in DP steels is solely caused by the carbon interstitials in the ferrite because a significant Snoek-type relaxation peak could not be observed when the martensite was tested separately [17]. Thus, the height of Snoek peak reflects solute carbon content in ferrite of DP steel. Comparing the Snoek peaks of the four DP steels, the height of Snoek peak of DP420/780 in the as-received state is the lowest among the four materials, as shown in Fig. 12 b, indicating that DP420/780 steel has the lowest carbon content in solid solution in ferrite if the potential texture difference with grain size is neglected. Using the calibration of Fe-C Snoek peak by 16 / 26

Hirscher et al. [42] and dividing the measured amount of carbon atoms by the fraction of ferrite, the carbon content in solid solution in ferrite is estimated as 19 at. ppm for DP340/600, 8 at. ppm for DP420/780, 24 at. ppm for DP500/780 and 21 at. ppm for DP550/980. Compared to the other three DP steels, the lower carbon content in solid solution in ferrite of DP420/780 steel may be responsible for the absence of discontinuous yielding when the specimens were pre-strained to different degrees from 0 to 8% and then baked at 170 °C for 20 min, which is consistent with the experimental observation of Waterschoot et al. [17]. They reported that lower solute carbon content produces slower yield stress increase. When the samples were pre-strained to a degree of 2% and then baked at 170 °C for 20 min, the heights of Snoek peaks of all the four DP steels present a decline. Pre-straining leads to an increase of dislocation density in ferrite and interstitial carbon atoms diffuse to vicinity of dislocations forming so-called Cottrell atmospheres or precipitation during the following baking process, which results in a decline of solute carbon content in ferrite, thus a decline of Snoek relaxation strength. With further pre-straining to 6%, more dislocations are produced and Snoek relaxation strength declines furtherly, indicating lower carbon content in solid solution, as depicted in Fig. 12. The Snoek-Köster relaxation in cold-worked ferrite containing carbon or nitrogen has been thoroughly studied and mechanism of the relaxation involves the dragging of interstitials by bowing dislocation segments [43]. The Snoek-Köster relaxation strength in cold-worked ferrite increases linearly with interstitial content to a saturation value and the saturation value increases roughly as the square root of the plastic strain [39]. Köster et al. [44] interpreted the saturation effect to mean that the Snoek-Köster peak is caused by a specific dislocation-interstitial configuration where any excess of either dislocations or interstitials is ineffective. A relaxation peak similar to the Snoek-Köster peak in cold-worked ferrite has also been observed in ferrous martensite, the mechanism of which was considered to be similar to that in cold-worked ferrite [45]. As DP steel consisting of ferrite and martensite, the relaxation peak at around 220 °C should be a combination of Snoek-Köster peak in ferrite and Snoek-Köster-like peak in martensite. Thus, when various degrees of pre-straining were applied, variation of Snoek-Köster peak in DP steel should be different from that in pure ferrite or martensite. Solute carbon in ferrite and martensite as well as the volume fraction of martensite should be taken into account to interpret the experimental observation. As Fig. 12 shows, heights of Snoek-Köster peaks in DP340/600 present a continuous increase with strain and the contrary is the case in DP420/780. Heights of Snoek-Köster peaks with strain in DP500/780 present the same tendency as that in DP420/780 does, but the tendency in DP500/780 is not so significant as that in DP420/780. Height of Snoek-Köster peak in DP550/980 increases when straining increases from 0 to 2%. With further increasing straining to 6%, height of Snoek-Köster peak in DP550/980 presents a decline. For all the four studied DP steels, the martensite can contain more than 0.2 mass% of C and dislocations in martensite are practically saturated with segregated C atoms [46]. Therefore, strength of Snoek-Köster-like relaxation in martensite, according to the dragging model, should depend on the density and mean length of dislocation segments. When DP steels were pre-strained and then baked at 170 °C for 20 min, the pre-straining leads to a rapid stress-induced ordering of solute carbon atoms into preferred positions according to the stress fields of the dislocations [15]. Carbon atoms migrate to dislocations in the following baking process and heating process of internal friction measurement with additional carbon atoms migrating to dislocations to form carbides pinning the dislocations. The pinning of dislocations in martensite could reduce the mean length of dislocation segments, leading to a decrease of Snoek-Köster-like relaxation strength in martensite. When pre-straining gets higher, higher stress could be applied on martensite and the decrease of Snoek-Köster-like relaxation strength in martensite 17 / 26

could get higher. So, with considerable solute carbon content existing in ferrite, the increase of Snoek-Köster relaxation strength with strain in ferrite and decrease of Snoek-Köster-like relaxation strength with strain in martensite should be two opposite trends and the overall response is a combination of them. In this condition, the volume fraction of martensite can of course control the overall response of Snoek-Köster relaxation of DP steels. Variation of Snoek-Köster peak in DP steels could be explained. For DP340/600 steel containing 21.8 vol.% martensite, the lowest amount of martensite among the four materials, the increase of Snoek-Köster relaxation strength with strain in ferrite may contribute greater influence to the overall response and thus heights of Snoek-Köster peaks in DP340/600 present a continuous increase with strain. With increasing volume fraction of martensite, decrease of Snoek-Köster-like relaxation strength with strain in martensite could produce larger influence, which leads to the variation of Snoek-Köster relaxation strength with strain in DP500/780 steel containing 38.4 vol.% martensite and DP550/980 steel containing 33.4 vol.% martensite. When relatively lower solute carbon content exists in ferrite, dislocations created in ferrite by pre-straining could not be saturated with segregated C atoms and excess of dislocations will be ineffective in producing increase of Snoek-Köster relaxation strength with strain. So, the decrease of Snoek-Köster-like relaxation strength with strain in martensite could control the overall response, which is the case in DP420/780 steel where a continuous decline of Snoek-Köster relaxation strength of the steel is observed, as depicted in Fig. 12 b. From the above, it can be revealed that carbides formation in martensite can be detected indirectly by internal friction measurement and higher stress applied on martensite induced by higher degree of pre-straining may help in the formation of carbides in martensite. Timokhina et al. [15] confirmed the formation of rod-like carbides in martensite after pre-straining/baking with a composition close to that of low temperature Fe32C4 or Fe4C0.63 by using APT techniques. The carbides formation in martensite could be accompanied by the volume contraction of martensite, resulting in internal stress relief in ferrite, which could play an important role in BH response of DP steels. 4.4. Effect of pre-straining on the BH response of DP steels Obviously, variations in pre-straining can produce different BH responses for DP steels, which can be seen from the stress-strain curves presented in Fig. 6 a-b. When evaluating the role of pre-straining in BH responses of DP steels, attention should be mainly focused on variations of dislocations and internal stress in ferrite produced by pre-straining. When 0.5% pre-straining was applied, discontinuous yielding has returned for DP340/600 and DP500/780 after baking and a BH value equal to or near the highest BH value with strain is reached (Fig. 7), which could not be explained solely by the increase of dislocations in ferrite produced by 0.5% pre-straining. When the unstrained specimens were baked at 170 °C for 20 min, all the four DP steels still present continuous yielding with a relatively low BH0 value ranging from 0 to 25 MPa. From the experimental results, it can be inferred that dislocations in ferrite in unstrained DP steels have been pinned by interstitials during the baking at 170 °C for 20 min, but a number of preferentially yielding zones around martensite islands, as mentioned in previous section, are still preserved because internal stress in ferrite is just relieved slightly at 170 °C for 20 min, thus the steels still yield continuously after baking [31]. Upon pre-straining, the number of preferentially yielding zones decreases rapidly and the pre-strained DP steels yield discontinuously after baking with return of yielding elongation and considerable BH value. When various degrees of pre-straining were applied, the absence of yielding elongation for DP420/780 after baking can be attributed to the low solute carbon content in ferrite and 18 / 26

DP420/780 steel will not be discussed in terms of this point. Discontinuous yielding returns at 0.5% pre-straining for DP340/600 and DP500/780, and at higher pre-straining of 2% for DP550/980 after baking. Difference in pre-straining at which discontinuous yielding returns for the three DP steels after baking is related to the microstructures. As DP340/600 steel contains the lowest volume fraction of martensite and DP500/780 steel the highest, the volume fraction of martensite could not be the sole factor leading to the difference. Although DP500/780 steel contains higher volume fraction of martensite than DP340/600 steel, the size of martensite island in DP500/780 steel is also larger than that in DP340/600 steel, thus the number of preferentially yielding zones in DP500/780 may be comparable to or less than that in DP340/600. However, DP550/980 steel has relatively high volume fraction of martensite and small size of martensite island, thus the number of preferentially yielding zones in specific volume of material in DP550/980 could be significantly larger than that in DP340/600 and DP500/780 steels. In addition to this, the magnitude of internal stress (controlled by 𝑌0, 210 MPa for DP340/600, 230 MPa for DP500/780 and 380 MPa for DP550/980) in ferrite in DP550/980 is also larger than that in DP340/600 and DP500/780. All the preferentially yielding zones in DP steels are unlikely to be subjected to the same local flow process, thus as strain continues the number of preferentially yielding zones gradually decreases. The larger number of preferentially yielding zones and higher magnitude of internal stress in DP550/980 could contribute to the higher pre-straining required to extinguish the preferentially yielding zones. After the discontinuous yielding returns, further increasing pre-straining to a certain degree has slight positive contribution to the increase of BH value (DP500/780) or slight negative contribution to the increase of BH value (DP340/600 and DP550/980), which can be attributed to that dislocations produced by martensitic transformation plus dislocations produced by a small amount of pre-straining have been sufficient for interstitials to pin in the baking condition of 170 °C/20 min. As pre-straining continues to increase, well-defined yielding elongation disappears gradually and BH values present a decline tendency. Several reasons could account for this phenomenon. The higher the pre-straining is, the higher the dislocation density is, thereby the longer it takes at a given temperature for the yielding elongation to be generated [21] and the amount of carbon segregated to per dislocation decreases [47], resulting in the disappearance of yielding elongation and the decrease of BH value. Furthermore, the greater the increase in flow stress produced by pre-straining, the harder a given BH value can be obtained by aging. For DP500/780 and DP550/980 steel, when pre-straining increases to a certain degree which is 2% for DP500/780 and 4% for DP550/980, an increase in tensile strength and a decrease in total elongation can be observed obviously. Similar phenomena were also reported in literatures [22, 48, 49], which supports the validity of the present results. Changes in yielding behaviors are generally associated with the classical Stage Ι of strain aging related to atmosphere formation at dislocation. An increase in tensile strength and a decrease in total elongation due to precipitation on dislocation are classically observed in Stage Ⅱ of strain aging [22]. At higher aging temperatures, these strain aging stages are expected to overlap [17]. With respect to precipitation behavior, the most interesting variables are the dissolved solute content and the dislocation density [48]. Increasing pre-straining may increase tensile strength after aging by increasing dislocation density which enhances precipitation hardening in ferrite. Wilson et al. [48] suggested that if most of this precipitation is on dislocations, the precipitates must form lines of very small, closely spaced particles through which free dislocations can be forced only with difficulty. Effects of changing the spacing of the dislocation network on which precipitation occurs could be analogous to that of change in dispersion for a dispersion hardened alloy. In dispersion hardened alloys, 19 / 26

a moderate change in dispersion has a relatively minor effect on the yield stress but an appreciable alteration on the strain hardening rate [50]. Hart [50] and Fisher et al. [51] assume that the spacing between individual particles is sufficient for dislocations to be forced forward and dislocation loops are left behind surrounding the particles, then an appreciable hardening increment is expected during plastic strain and the additional hardening increment 𝜏ℎ , due to trapped dislocation loops, can be given by: 𝑟 3 𝑁𝑏

𝜏ℎ = 𝐺𝐾 (Λ) ( 𝑟 )

(9)

Where 𝐺 is the rigidity modulus, 𝑏 the Burgers vector, 𝑁 the mean number of loops surrounding a barrier and 𝐾 a constant  3. In the present research, 𝑟 is the diameter of precipitate particles and Λ their mean spacing. Equation (9) predicts that 𝜏ℎ will be inversely proportional to Λ3 for precipitates of equal strengths. Thus, when pre-straining increases, dislocation density in ferrite increases, thereby the mean spacing between precipitate particles which precipitate on dislocations decreases, resulting in the increased additional strain hardening for strain aged DP steels. This may account for the increase in tensile strength for DP steels after pre-straining and aging. Actually, dislocations in deformed metals are not always distributed homogenously on a microscale, especially for metals which have been strained heavily. Complex dislocation structure could also affect the BH behaviors. Timokhina et al. [52] conducted TEM microanalysis on a DP steel after pre-straining/baking. They reported that significant microstructural changes except an increase in the average dislocation density of the ferrite were not found for the DP steel after 5% pre-straining and that the formation of dislocation cell structure with a high number of carbides in the walls was observed in the microstructure of the DP steel after 10% pre-straining/baking. The mechanical properties of the 10% pre-strained DP steel after the BH treatment displayed a sharp decrease in the total elongation. The DP steel in their research contains ~15 ± 4 pct of martensite, which is similar to DP340/600 in the present research. As martensite is hard to deform, ferrite in DP steels containing higher volume fraction of martensite undergoes heavier deformation when a given strain is applied. Large deformation and high stress can favor the formation of dislocation cell structure [53, 54]. For DP500/780 and DP550/980, compared to DP340/600 and DP420/780, the volume fraction of martensite as well as flow stress during straining is higher. Therefore, the pre-straining required to produce dislocation cell structure in ferrite for DP500/780 and DP550/980 could be lower and pre-straining of 2 to 4% may be sufficient. In dislocation cell structures, the overwhelming majority of dislocations are actually located in the cell walls [54]. The high density of dislocations in the cell walls provide suitable sites for the formation of carbides at the BH temperature. The local high density of precipitates in the cell walls may significantly enhance the additional strain hardening due to precipitation, leading to a further increase in tensile strength. However, heterogeneous distribution of dislocations causes heterogeneous distribution of precipitates after aging. The local regions containing more precipitates are strengthened, which can induce inhomogeneous strain partitioning during straining, leading to significant decrease in total elongation. In contrast, For DP340/600 and DP420/780 steel, increase in tensile strength and decrease in total elongation in the pre-straining range of 0.5 to 8% are relatively slight. The possible reason may be higher pre-straining required, over 8%, to produce complex dislocation structure in ferrite due to relatively low volume fraction of martensite and relatively low flow stress during pre-straining in DP340/600 and DP420/780. It is worth noting that the low solute carbon content in ferrite in DP420/780 steel may also weaken the precipitation of carbides on dislocations, causing the difference from DP500/780 and DP550/980 steels.

20 / 26

4.5. Effect of microstructure on the BH response of DP steels As is mentioned in the last section, microstructure of DP steels could affect the pre-straining required to extinguish the preferentially yielding zones, which is one of the aspects in which microstructure affects the BH response in DP steels. When comparing the peak BH values with strain of the four DP steels (Fig. 7) as well as the BH0 behaviors under different baking treatments (Fig. 8), differences among the four DP steels are impressive, indicating that microstructure of DP steel has significant influence on the BH response. With respect to BH0 behaviors of DP steels under different baking treatments, when the BH condition of 250 °C/40 min was applied, all the four DP steels can present discontinuous yielding, which is the combined effect of locking of dislocations by Cottrell atmospheres or precipitates in ferrite and internal stress relief, caused by volume contraction of martensite due to precipitation of carbides in martensite during tempering at BH temperature, which weakens the function of preferentially yielding zones. The mechanism responsible for BH in DP steels without pre-straining is illustrated in Fig. 13 briefly. BH0 values of DP340/600, DP420/780, DP500/780 and DP550/980 steels at BH condition of 250 °C/40 min reach 40, 111, 173 and 234 MPa respectively. In order to interpret the significant difference among the BH0 values of the four DP steels, attention should be focused on the internal stress relief and locking of dislocations during baking. For analyzing the effect of residual stresses on initial work-hardening behavior of DP steels, Gerbase et al. [55] use a simple distribution of residual stresses and predict that the flow stress, 𝜎𝑓 , is related to the residual stress by: 𝜎𝑓 = 𝜎𝑦 − 𝑓𝜎𝑅 (10) where 𝜎𝑦 is the yield stress of the material without influence of residual stress, 𝜎𝑅 the magnitude of residual stress and 𝑓 the volume fraction of material subject to residual stress. Assuming that the internal stress acting on ferrite in the four DP steels is relieved completely at BH condition of 250 °C/40 min, contribution in BH0 values produced by internal stress relief can be stated as 𝑓𝜎𝑅 where 𝑓 is strongly affected by volume fraction of martensite and 𝜎𝑅 is controlled by 𝑌0 which is correlated with ferrite grain size by a Hall-Petch relationship with increasing yield stress at decreasing grain size. The smallest grain size of ferrite and the relatively high volume fraction of martensite in DP550/980 steel lead to the high magnitude of internal stress acting on ferrite and the large volume fraction of material subject to the stress. Thus, internal stress relief at BH condition of 250 °C/40 min could play a primary role in the great BH0 value of 234 MPa for DP550/980 steel. On the contrary, contribution of internal stress relief to the BH0 value in DP340/600 steel should be smaller due to both of the large grain size of ferrite and low volume fraction of martensite.

Fig. 13. Schematic illustration of BH mechanism in DP steel without pre-straining. After baking, internal stress acting on ferrite relieves and dislocations around martensite are locked by precipitates or 21 / 26

interstitials in ferrite as well as released by martensite. In addition to internal stress relief, locking of dislocations by Cottrell atmospheres or precipitates during BH is another mechanism responsible for BH in DP steels. As a large number of geometrically necessary dislocations (GNDs) resulting from the martensitic transformation exist in ferrite of DP steels, interstitials can diffuse to these dislocations forming Cottrell atmospheres or precipitating as carbides to lock the mobile dislocations and DP steels can present discontinuous yielding after baking even without pre-straining. Due to special microstructure configuration in DP steels, martensite islands can serve as additional C sources [11]. C atoms released from martensite at higher BH condition diffuse to GNDs around martensite islands, locking the dislocations. So, even if solute carbon content in ferrite is low, discontinuous yielding can also present by applying either longer holding time or higher temperature, which is the case in DP420/780 steel. With increasing volume fraction of martensite in DP steel, more GNDs are produced and more martensite islands serve as C sources releasing C atoms to lock the dislocations, thereby BH response in DP steel is improved. At a fixed volume fraction of martensite, decreasing the size of martensite islands increase the total area of ferrite-martensite interfaces, which could also improve the BH response in DP steel. It has been reported that a decrease in the grain size leads to considerable increase in bake hardenability [56, 57]. In the present research, the impressive BH response in DP550/980 steel containing the smallest ferrite grain size among the four DP steels could be also associated with the small grain size of ferrite. In addition to higher magnitude of internal stress correlated with smaller grain size of ferrite, the smaller grain size of ferrite could also exert influence on bake hardenability by affecting solute carbon content required for BH in DP steels. With decreasing grain size of ferrite, the volume fraction of grain boundaries gets higher. High angle grain boundaries can serve as preferential deposition sites for interstitials due to the higher energy. Therefore, higher volume fraction of grain boundaries can increase the solid solubility of carbon atoms. The solute carbon atoms segregated at grain boundaries is so-called “hidden” carbon atoms which cannot be detected by internal friction measurements [58]. Also, when DP steels are baked, in case of finer grain, diffusion path toward dislocations of carbon atoms, segregated at grain boundaries as well as released from martensite located at grain boundaries, is shorter. Consequently, the smaller the grains are, the greater the BH response will be. 5. Conclusions Bake hardening responses of four kinds of industrially processed cold rolled DP steels were studied in order to characterize the role of pre-straining and microstructure in BH responses for DP steels. The following conclusions can be drawn in the present research. 1. The role of pre-straining in BH responses of DP steels can be divided into two aspects: extinguishing preferentially yielding zones around martensite and producing more dislocations. Larger number of preferentially yielding zones associated with microstructure require higher pre-straining to extinguish. 2. For all grades of DP steels, BH values increase to peak values at pre-straining ranging from 0.5 to 2% and then decline with further pre-straining. At BH condition of 170 °C/20 min, peak BH values with pre-straining are respectively 33 MPa for DP340/600, 34 MPa for DP420/780, 78 MPa for DP500/780 and 90 MPa for DP550/980. Microstructures of higher volume fraction of martensite, smaller martensite islands and smaller ferrite grains can produce higher BH values. 3. Pre-straining can cause increase in tensile strength and decrease in total elongation after baking, 22 / 26

especially in DP500/780 and DP550/980, due to precipitation on dislocations and complex dislocation structure. 4. By applying either higher temperature or longer holding time, DP steels can reach very high BH0 values, 40, 111, 173 and 234 MPa for DP340/600, DP420/780, DP500/780 and DP550/980 respectively. Internal stress relief and locking of geometrically necessary dislocations are responsible for the high BH0 values. 5. The solute carbon content in ferrite of DP steel controls the speed of aging, but it is not the dominating factor resulting in high BH value of DP steel. 6. The amount of geometrically necessary dislocations in DP steel increases with martensite volume fraction increasing. Precipitation of carbides in martensite and effect of pre-straining helping in the precipitation can be indirectly detected by internal friction measurements. Acknowledgements This work is financially supported by National Natural Sciences Foundation of China (Grant Nos. 50934011 and 50971137). References [1] P. Li, J. Li, Q. Meng, W. Hu, D. Xu, Effect of heating rate on ferrite recrystallization and austenite formation of cold-roll dual phase steel, J. Alloys Compd. 578 (2013) 320-327. [2] H. Seyedrezai, A.K. Pilkey, J.D. Boyd, Effect of pre-IC annealing treatments on the final microstructure and work hardening behavior of a dual-phase steel, Mater. Sci. Eng. A 594 (2014) 178-188. [3] A. Ghaheri, A. Shafyei, M. Honarmand, Effects of inter-critical temperatures on martensite morphology, volume fraction and mechanical properties of dual-phase steels obtained from direct and continuous annealing cycles, Mater. Des. 62 (2014) 305-319. [4] X. Cai, C. Liu, Z. Liu, Process design and prediction of mechanical properties of dual phase steels with prepositional ultra fast cooling, Mater. Des. 53 (2014) 998-1004. [5] G.R. Speich, R.L. Miller, Mechanical properties of ferrite-martensite steels, in: R.A. Kot, J.W. Morris (Eds.), Structure and Properties of Dual-Phase Steels, AIME, New York, 1979, pp. 145-182. [6] Y. Cao, J. Ahlström, B. Karlsson, The influence of temperatures and strain rates on the mechanical behavior of dual phase steel in different conditions, J. Mater. Res. Technol. 4 (2015) 68-74. [7] A.P. Pierman, O. Bouaziz, T. Pardoen, P.J. Jacques, L. Brassart, The influence of microstructure and composition on the plastic behaviour of dual-phase steels, Acta Mater. 73 (2014) 298-311. [8] A. Ramazani, K. Mukherjee, H. Quade, U. Prahl, W. Bleck, Correlation between 2D and 3D flow curve modelling of DP steels using a microstructure-based RVE approach, Mater. Sci. Eng. A 560 (2013) 129-139. [9] M.S. Rashid, Dual Phase Steels, Annu. Rev. Mater. Sci. 11 (1981) 245-266. [10] A. Ramazani, K. Mukherjee, U. Prahl, W. Bleck, Modelling the effect of microstructural banding on the flow curve behaviour of dual-phase (DP) steels, Comput. Mater. Sci. 52 (2012) 46-54. [11] A. Ramazani, S. Bruehl, M. Abbasi, W. Bleck, U. Prahl, The Effect of Bake-Hardening Parameters on the Mechanical Properties of Dual-Phase Steels, Steel Res. Int. 87 (2016) 1559-1565. [12] C.F. Kuang, S.G. Zhang, J. Li, J. Wang, H.F. Liu, Effects of pre-strain and baking parameters on the microstructure and bake-hardening behavior of dual-phase steel, Int. J. Miner. Metall. Mater. 21 (2014) 766-771. 23 / 26

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