Influence of microstructure and strain rate on the strain partitioning behaviour of dual phase steels

Accepted Manuscript Influence of microstructure and strain rate on the strain partitioning behaviour of dual phase steels Anindya Das, Soumitra Tarafder, S. Sivaprasad, Debalay Chakrabarti PII:

S0921-5093(19)30397-1

DOI:

https://doi.org/10.1016/j.msea.2019.03.084

Reference:

MSA 37701

To appear in:

Materials Science & Engineering A

Received Date: 21 February 2019 Revised Date:

18 March 2019

Accepted Date: 19 March 2019

Please cite this article as: A. Das, S. Tarafder, S. Sivaprasad, D. Chakrabarti, Influence of microstructure and strain rate on the strain partitioning behaviour of dual phase steels, Materials Science & Engineering A (2019), doi: https://doi.org/10.1016/j.msea.2019.03.084. 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 proof before it is published in its final 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.

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Influence of Microstructure and Strain Rate on the Strain Partitioning Behaviour of Dual Phase Steels Anindya Das 1 2

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, Soumitra Tarafder1 , S. Sivaprasad1 , Debalay Chakrabarti2

MST Division, CSIR-National Metallurgical Laboratory, Jamshedpur, India – 831007 Metallurgical and Materials Engineering Department, IIT Kharagpur, India – 721134

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*E-mail address: [email protected]

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Abstract: Two dual phase steels with varying martensite content (∼10 and 33 percent) have been deformed in tensile mode at various strain rates (0.001 to 800 /s). The microstructural parameters after deformation have been studied in detail using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The minute details of deformation features within the ferrite matrix have been investigated using EBSD based misorientation analysis. The influence of metallurgical parameters like ferrite grain size and its spatial distribution, the size and fraction of martensite on the deformation at different strain rates have also been investigated along with evolution of crystallographic texture. It has been found that strain rate influences the gradient in deformation in the ferrite grains between the interface and the grain interiors. Increase in martensite although enhances the dislocation density in the ferrite grains, but it also restricts the rotational ability of ferrite, which led to restricted sub-structural recovery at high strain rates. By observing the misorientation development ahead of the interphase boundaries, the failure mechanisms of these dual phase steels have been explained.

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Introduction

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Keywords: Dual-phase steel, strain rate, EBSD, Strain-partitioning, Kernell average misorientation, Grain orientation spread

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Dual phase (DP) steels are low-carbon and low-alloy steels in which the martensite volume fraction varies between 10 to 30 percent within a ferrite matrix. The combination of high strength and ductility with excellent formability makes it a widely beneficial alloy for automobile production [1,2]. In response to the increasing demand of weight reduction of the automobile components and improved crashworthiness, it is obligatory to determine the material properties at strain rates resembling crash regimes (>10 /s). Various studies have already highlighted the combined influence of strain rate and martensite fraction on the strength and ductility of the dual phase steels [3-9]. There is a broad agreement that increase in the volume fraction of martensite diminishes the strain rate sensitivity of the dual phase steels. It is also true that martensite plasticity is negligible in these low carbon dual phase steels during deformation compared to that of ferrite. As a result, the overall plasticity of the dual phase steels is largely governed by the ferrite matrix, although it is influenced by the distribution, size and volume fraction of martensite present in the matrix [10]. Consequently, the strain partitioning behaviour in the dual phase steels are also dependent on the metallurgical factors along with the type of deformation [11]. The difference in the strength of the individual phases (ferrite being softer than martensite) can provide a preliminary idea about the strain partitioning between the two phases. The overall deformation in ferrite depends on the partitioning of strain between the two phases [11-13]. With the increase in the volume fraction and the strength of martensite, the strain accumulation in ferrite 1

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regions adjacent to the ferrite –ACCEPTED martensite interface increases. However, the same amount of MANUSCRIPT strain does not develop across the entire ferrite regions especially at the interiors of the ferrite grains and in those ferrite grains which are away from martensite interfaces. Such a strain localization in ferrite decreases with the decrease in the fraction and strength of martensite [12]. The heterogeneity in damage evolution can be influenced by the ferrite grain size, distribution and fraction of the martensite islands [14]. It is reported that the plastic deformation initiates within the coarser ferrite grains and regions having lesser martensite content [14]. The influence of grain size on the stress – strain partitioning between these two phases have been studied by Calcagnotto et al., 2011 [15]. With ferrite grain refinement, martensite plasticity enhances which improves the uniformity in deformation of ferrite and martensite. As a result of the uniform deformation, the crack formation by the process of decohesion at the interfaces is restricted [15]. The dependency of ferrite morphology on strain partitioning was quantified by Han et al., 2013 [16], although they could not find any effect of orientation of ferrite grains and the nature of interface in the strain partitioning behaviour.

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This supposedly sums up the characteristics of deformation, primarily of the ferrite matrix in DP steels. Even though the metallurgical parameters are known to govern the stress – strain partitioning behaviour, these explanations are valid for deformations at quasi-static, i.e. loading at low strain rates. At higher strain rates, the strain rate sensitivity of the individual phases along with the microstructure are expected to play a major role in the deformation of these phases. As a result, the strain partitioning behaviour will differ at high strain rates which can possibly be influenced further by the size and spatial distribution of the individual phases. Moreover, the deformation mechanism also changes at high strain rates for these dual phase steels [9], which possibly alter the damage evolution at a local scale within the microstructure. It is thus important to characterize the local deformation response within the microstructure of the DP steels at various strain rates. Such information can provide a detail understanding on how the two phases in DP steels respond to deformation and how the failure ultimately occurs under the influence of tensile loading at various strain rates.

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In this study tensile tests have been performed on two dual phase steels (DP600 and DP800) having varying martensite content, at strain rates ranging from 0.001 to 800 /s. Detail SEMEBSD studies have been performed on the deformed specimens to elucidate the micro-damage involved in the microstructure and how it is influenced by the strain rate as well as by the various microstructural variations. The observed details have been analysed to understand the strain partitioning nature of the DP steels and how its dependence on the strain rate.

Materials and Methods Materials

Two ferrite – martensite dual phase steel sheets (DP600 and DP800) with varying martensite content has been selected for this study. The composition of the two dual phase steels is shown in Table 1. The average size of the individual phases and the volume fraction of martensite in the two steels are mentioned in Table 2. The sheets have been received in the form of cold rolled and annealed condition. The representative microstructure of the two steels are shown in Fig. 1.

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Table 1: Chemical compositions (Wt. %) of the dual phase steels

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Material DP600 DP800

C 0.085 0.11

Mn 0.91 1.8

S P Si Cr Cu 0.008 0.015 0.36 0.022 0.027 0.006 0.016 0.32 0.019 0.021

N (ppm) Fe 30 Bal 56 Bal

Table 2: Microstructural parameters of the as-received materials determined by image analysis

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DP800 6.3±2.4 3.8±1.3 33.2±3.6 4.0±2.0

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Microstructural Parameters DP600 Ferrite grain size (µm) 9.4±3.6 Martensite colony size (µm) 3.9±1.1 Martensite area fraction (%) 10.2±1.0 Martensite island interspacing (µm) 10.9±4.8

Figure 1: Microstructure of as-received (a) DP600 and (b) DP800

Tensile tests at different strain rates

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For tensile tests at quasi-static i.e. low strain rates (6 1 /s), specimens of 25 mm gauge length were used and the tests were performed according to ASTM standard E-8M [17]. Fig. 2 shows the drawing of the specimen used for quasi-static strain rate tensile tests. Tests were carried out in a servo-hydraulic test frame (Instron 8502), covering a strain rate range of 0.001 to 1 /s. A 25 mm gauge length extensometer was used for the strain measurement. Tensile tests at strain rates of 100, 400 and 800 /s were conducted using a high-speed servo-hydraulic test system (Instron VHS 8800), capable of achieving displacement velocities up to 20 m/s. The specimen for these tests were fabricated as per ISO 26203 standard [18] and a typical specimen drawing is shown in Fig. 2. The methodology suggested by Wood and Schley [19] was followed for the positioning of the strain gauges and the corresponding data extraction procedure for both load and strain measurements. All specimens were prepared with the loading direction along the rolling direction of the as-received sheets. Multiple tests were carried out at all strain rates and the representative data is reported.

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Microstructural investigation through EBSD

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Figure 2: Specimen dimensions used for tensile testing at quasi-static and low strain rates (6 1/s) and dynamic strain rates (> 100/s). All dimensions are in mm

To understand the characteristics of deformation in both the steels after tensile deformations, EBSD studies were carried out. Both the as-received and deformed specimens were subjected to EBSD scans using TSL OIM AnalysisT M 5.3 (EDAX, Mahwah, USA) in a FEI Nova Nanosem 430 FEG scanning electron microscope at 70° tilting condition. The EBSD scans covered an area of 200 µm x 200 µm at a step size of 0.2 µm in all the cases. All the EBSD scans were performed on the RD – TD plane of the specimens.

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Results

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The post processing of the EBSD data was conducted using TSL AnalysisT M 7.0. No cleanup of the dataset was performed using the conventional neighbour CI (confidence index) correlation technique. The points corresponding to CI value less than 0.1 were discarded. The martensite present in the microstructure was partitioned by IQ (image quality) based thresholding method (martensite already being heavily strained shows inferior IQ compared to ferrite) [20]. All the deformation and crystallographic analysis have been performed on the ferrite phase after separating out the martensite from the respective EBSD scans.

Tensile properties at different strain rates

The engineering stress – strain curves obtained after tensile deformation of the two DP steels is shown in Fig. 3. The variation in yield strength, ultimate tensile strength and uniform elongation is presented elsewhere [9]. The higher volume fraction of martensite in DP800 is the main reason behind the substantial increase in strength and reduced ductility when compared with DP600.

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Influence of strain rate on the local strain evolution in DP steels

Figure 4 displays the inverse pole-figure colour maps along the normal direction (ND-IPF) showing the microstructure of the two dual phase steels when deformed at certain strain rates. In Fig. 4, the ferrite grains are marked using a white arrow. The martensite regions (marked with yellow arrows) appear black since the low indexed points of martensite are partitioned 4

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Figure 3: Engineering stress – strain curves obtained after tensile deformation at different strain rates for (a) DP600 and (b) DP800

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out. Due to the difference in the orientation of the ferrite grains, the colours of these grains differ according to the IPF colour code for BCC materials (the colour legend in Fig. 4). The ferrite grains in Fig. 4 are deformed in nature having an orientation gradient as reflected by the colour difference within the grains.

Figure 4: ND-IPF colour maps showing the microstructure of DP600 when deformed at (a) 0.001 /s, (b) 800 /s and DP800 when deformed at (c) 0.001 /s, (d) 800 /s strain rate 5

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The EBSD study is primarily intended toMANUSCRIPT obtain detail information about the local scale ACCEPTED deformation of the phases in DP steels when exposed to tensile deformation at different strain rates. Local average misorientation techniques like Kernell average misorientation (KAM) gives a firsthand insight about the evolution of the local strain in the microstructure [21]. In this work, the KAM values are reported only for the ferrite phase and in all cases KAM is calculated for maximum of 5 degrees of misorientation considering the first neighbour. Figure 5(a) shows that the average KAM values increase with strain rate for both the DP steels. This supposedly indicates that the local strain increases in the matrix with strain rate. In a previous work by the authors, it has been reported that increasing the strain rate also increase the dislocation density in the ferrite matrix of DP steels [9]. In ferrite – martensite dual phase steels, measuring dislocation density using X-Ray diffraction is very difficult since the peaks corresponding to ferrite and martensite merge with each other. On the other hand, by measuring the size of the dislocation cells, the dislocation density in the ferrite grains can be estimated [22]. In general, the dislocation density and dislocation cell size follow an inverse relationship [22]. It was found that, DP800 always produced higher dislocation density than DP600 and the dislocation density increased with increasing strain rate for both the steels [9]. It reasonably explains that the increase in the strain rate increases the local strain in the ferrite matrix by enhancing the dislocation density. Interestingly, DP800 also shows higher KAM values compared to DP600 at all the applied strain rates.

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Moreover, the rate of increase in KAM at the high strain rate regime (100 to 800 /s) is also more in case of DP800. This further indicates that the volume fraction as well as the spatial distribution of martensite in the ferrite matrix, plays a major role in the evolution of local strain in the DP steel, even at high strain rates. Higher volume fraction in DP800 not only aggravates the dislocation density, but it also influences the process of deformation. The martensite colonies are heavily deformed at high strain rates and eventually fragments [9]. As a result the interaction between the ferrite matrix and the fragmented martensite laths at high strain rates serve as fresh sources of dislocation generation, significantly increasing the dislocation density at high strain rates in DP800.

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In Fig. 5 (b to e) the representative KAM maps of DP steels deformed at the lowest (0.001 /s) and highest (800 /s) strain rate is shown. These KAM maps are generated from the same microstructural region which is shown in Fig. 4. Since the KAM is calculated over the entire ferrite matrix (excluding the dark points corresponding to martensite), the individual grains are not distinguished in the KAM maps. The black patches are the martensite colonies which have been partitioned out from the IQ data. In DP600 at 0.001 /s strain rate (Fig. 5(b)), the KAM map clearly shows that the local deformation in the ferrite matrix is high near to the ferrite / martensite interface (as pointed in the figure). This is in resemblance to previous studies [21,23]. It is well known that during deformation in ferrite – martensite DP steels, the dislocations pile up at the vicinity of the interface. Thus the local strain within the ferrite grains differs between the regions close to the interface with high local strain and relatively lower strain at the grain interior. The KAM map in Fig. 5(b) also shows similar behaviour for ferrite grains, where the interior possess very less deformation compared to the interface regions. At high strain rate, in DP600, the overall intensity of the local deformation increases (as shown in Fig. 5) which is also reflected in KAM map, as shown for 800 /s in Fig. 5(c). Unlike that in 0.001 /s strain rate, the gradient in deformation between the interior and interface area of ferrite grains decreases at high strain rate. Considerable amount of ferrite grains have a high KAM values ( 2 to 3 degrees) at the interior of the grains. In DP800, the evolution of local strain in the ferrite grains at 0.001 /s (Fig. 5(d)) is similar to that in DP600 at the same strain rate (Fig. 5(b)). But at 800 /s, the ferrite grains show high amount of local strain (high KAM values) and the grains have experienced uniform deforma6

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Figure 5: (a) variation of average KAM value with strain rate for DP600 and DP800. KAM maps of DP600 at (b) 0.001 and (c) 800 /s, and KAM maps of DP800 at (d) 0.001 and (e) 800 /s strain rates

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tion throughout the matrix (Fig. 5(e)). At high strain rates, there exist negligible gradient in deformation between the grain interior and the interface area in DP800, unlike that in DP600 where few ferrite grains are present in which the gradient still exists.

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The above results portray the variation within the deformation in the ferrite grains of the DP steels when the strain rate is increased from 0.001 to 800 /s. It is apparent from the present results that strain rate influences the deformation in the ferrite grains by making the deformation more uniform across the grain volume when it is increased from quasi-static to high strain rates. The evolution of local misorientation primarily depends on the martensite fraction of the steels. The influence of ferrite grain size and spatial distribution to be discussed in the following sections.

Influence of ferrite grain size on the deformation of the DP steels when deformed at various strain rates

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Apart from the local strain evolution in the ferrite matrix as estimated by KAM, the grain orientation spread (GOS) values were also compared for both the steels at all the strain rates. Figure 6 shows the average GOS values of the two DP steels when deformed at various strain rates. Unlike the variation of KAM, GOS values were higher in DP600 at all the strain rates, as shown in Fig. 6. This suggests that the ferrite grains in DP600 are subjected to large change in local orientation when deformed as compared to DP800, possibly due to the substantial microstructural recovery. It should be noted that in DP600, the average ferrite grain size is approximately 9.4 µm whereas, in DP800 it is 6.3 µm. When the grain size is coarse, severe strain gradient develops upon deformation, where the grain exteriors (closer to grain boundaries) undergo intense straining, unlike the grain interior. Such an inhomogeneous deformation promotes the recovery process as well as the formation of micro-shear bands within the larger grains. In contrast, for the fine grains, the strain can easily penetrate inside the grains resulting 7

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Figure 6: Variation of average GOS values of the ferrite grains in DP600 and DP800 with strain rate in a more uniform deformation over the entire grain volume. As a result, in DP800 the ferrite grains undergo lesser recovery and micro-shear banding compared to that in DP600 contributing to the consistently higher GOS values in DP600. Apart from the overall GOS of the ferrite grains, the corresponding grain diameter were also measured. In Fig. 7(a and b), the GOS values for individual ferrite grains are plotted against their respective diameter at 0.001 and 800 /s strain rate for both the DP steels.

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Although in case of DP600, not much of variation in the distribution of GOS exist at two different strain rates, it can be reasonably found that finer ferrite grains lead to lower GOS values when compared to that of the coarser grains, at both the strain rates. At 800 /s, in DP600, there exists a few ferrite grains which are finer but having very high GOS values as indicated in Fig. 7(a). In case of DP800, there exists a distinct difference in the distribution of GOS values with diameter between two extreme strain rates. In both the strain rates, for DP800, the GOS values increase with the ferrite grain size, but with increase in strain rate to 800 /s, the finer grains undergo heavy deformation increases the GOS values.

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Since the GOS values are dependent on the grain size [24], the values obtained for the individual grains have been normalized by their respective diameter. The variation in GOS/D (where D is the grain diameter), for the DP steels at the extreme strain rates (0.001 and 800 /s) is plotted in Fig. 7(c and d). The finer ferrite grains have higher GOS/D values, as reported in an earlier study [24]. On increasing the strain rate, the GOS/D values increases for finer grains whereas it remain same for the coarser grains. Interestingly, for DP800, the increase in strain rate from 0.001 to 800 /s significantly increase the GOS/D values, unlike DP600. Therefore, the deformation in finer grains intensifies with the increase in the strain rate, which is more severe than DP600. Along with the local strain evolution and influence of grain size on the deformation, it is also worthwhile to investigate the relative spatial distribution of the ferrite grains in the deformation of DP steels. Since, DP steels are comprised of two contrasting phases, the relative volumetric positions of these two phases affect the deformation behaviour [10]. But it is also worthwhile to investigate the combined influence of strain rate and the spatial distribution

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Figure 7: (a, b) Variation of GOS values with diameter of ferrite grains at 0.001 and 800 /s strain rates for (a) DP600 and (b) DP800. (c, d) Variation of GOS/D values with diameter of ferrite grains at 0.001 and 800 /s strain rates for (c) DP600 and (d) DP800

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of the ferrite grains in the investigated steel having different relative fractions of ferrite and martensite. As a result, the specific location of the ferrite grains with different GOS values are separately investigated for both the steels at 0.001 and 800 /s strain rates. Figure 8 and 9 show the ferrite grains (marked in yellow) having different GOS values for the DP steels at the two extreme strain rates. In DP600, at both the strain rates, the lowest GOS values (0 to 3 degrees) are present within the ferrite grains which are completely surrounded by martensite as shown in Fig. 8(a and e). The trapped ferrite grains are heavily constrained by the surrounding martensite and hence, retain their orientation during deformation even at high strain rates. Eventually, the coarser ferrite grains show higher GOS values at both the strain rates for DP600. Interestingly, at 0.001 /s, most of the ferrite grains with 3 to 9 degrees of GOS (Fig. 8(b and c)) share ferrite – ferrite grain boundaries, as pointed in the figures. Moreover, these grains are not heavily surrounded by martensite in general. At 800 /s for DP600, the number of grains showing GOS in the range of 6 to 9 degrees have increased as compared to that at 0.001 /s. Moreover, ferrite grains having GOS values of 3 to 6 degrees share lesser extent of ferrite – ferrite grain boundaries, which otherwise is significant for grains showing 6 to 9 degrees at 800 /s strain rate. In DP800, at 0.001 /s, the lower GOS values are not associated with the ferrite grains which are completely trapped within the martensite regions, rather discretely scattered (Fig. 9(a)). At 0.001 /s, DP800 show most of the ferrite grains to possess GOS values in the range of 3 to 9

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Figure 8: Corresponding ferrite grains in DP600 at different ranges of GOS values when deformed at (a-d) 0.001 /s and (e-h) 800 /s

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6 degrees and only a few grains have the GOS values greater than 6 degrees. However, at 800 /s, appreciable amount of ferrite grains are present with GOS values greater than 6 degrees. Moreover, at 800 /s, in DP800 the finer and trapped ferrite grains show lowest GOS values (Fig. 9(e)). In DP800, due to higher martensite fraction (around 33 percent in DP800 compared to 10 percent in DP600, as mentioned in Table 2), the amount of ferrite – ferrite boundaries are less, and thus the grains with ferrite – ferrite boundaries are not found to produce any preferential GOS values. Interestingly, presence of some martensite islands in DP800 within a ferrite grain pose additional constraint to the deformation of ferrite, which also helped to restrict the GOS values within 3 to 6 degrees at 0.001 /s strain rate, which otherwise increased at the high strain rate regime.

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Concerning the GOS values in the ferrite, it is also important to investigate the influence of crystallographic orientation of the ferrite grains on the deformation. Therefore, the crystallographic orientation of the ferrite grains having different GOS values are separately investigated. Figure 10 and 11 report the ND-IPF of the ferrite grains having different GOS values at 0.001 and 800 /s strain rate for both the DP steels. At 0.001 /s, in DP600, ferrite grains with GOS values up to 9 degrees are oriented primarily along the 〈111〉 crystallographic direction, followed by the 〈001〉 direction. Whereas, ferrite having GOS values greater than 9 degrees are only oriented preferentially along 〈001〉 crystallographic direction. At 800 /s, almost all the ferrite grains are only oriented along 〈111〉 crystallographic direction irrespective of the GOS values. For DP800, at 0.001 /s the ferrite grains were oriented both along 〈111〉 and 〈001〉 crystallographic directions for the lower GOS values (< 3 degrees). For higher GOS values (> 3 degrees), 〈001〉 oriented ferrite grains are not present substantially at 0.001 /s strain rate. But at 800 /s strain rate, significant amount of grains which attain up to 9 degrees of GOS are oriented along 〈001〉 crystallographic direction.

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Figure 9: Corresponding ferrite grains in DP800 at different ranges of GOS values when deformed at (a-d) 0.001 /s and (e-h) 800 /s

Figure 10: Corresponding ND-IPF maps of ferrite grains in DP600 of different ranges of GOS values when deformed at (a-d) 0.001 /s and (e-h) 800 /s 11

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Figure 11: Corresponding ND-IPF maps of ferrite grains in DP800 of different ranges of GOS values when deformed at (a-d) 0.001 /s and (e-h) 800 /s

Influence of strain rate and microstructure on the grain rotation behaviour in dual phase steels

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It has been highlighted in the previous sections that, the spatial distribution of the individual phases in dual phase steel play a major role on the deformation of the softer ferrite phase. Martensite restricts the deformation of the ferrite grain at its vicinity compared to ferrite – ferrite regions, which is further influenced by the size of the ferrite grains and the fraction of martensite. Consequently, the resultant GOS values of the ferrite grains vary, depending on the strain rate of deformation. In Fig. 12 and 13, the ferrite grains which have produced the highest GOS values in DP600 and DP800 are shown for strain rates of 0.001 and 800 /s. The corresponding map of grain reference orientation deviation (GROD) is also displayed for the same set of ferrite grains. The GROD gives the distribution of angular deviation at each point within the grain considering the reference orientation of that particular grain. Therefore, it gives an insight into the lattice rotation at different locations and its spatial distribution within a grain.

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Figure 12: Cropped portion of (a-c) DP600 and (d-f) DP800 at 0.001 /s strain rate showing its (a,d) IQ image overlapped with LAGB in red, (b,e) corresponding grain orientation spread map and (c,f) map corresponding to orientation deviation angle within the grains

Figure 13: Cropped portion of (a-c) DP600 and (d-f) DP800 at 800 /s strain rate showing its (a,d) IQ image overlapped with LAGB in red, (b,e) corresponding grain orientation spread map and (c,f) map corresponding to orientation deviation angle within the grains 13

At 0.001 /s strain rate, it can be seen thatMANUSCRIPT the GROD is much larger in DP600. Moreover, ACCEPTED the highest angular deviation (lattice rotation) is near to the ferrite / martensite interfaces. As the strain rate increases to 800 /s, in DP600 the angular deviation spreads across the entire grain area whereas, it still remains high at the vicinity of the interfaces in DP800. Therefore, the strain rate intensifies the lattice rotation associated with the deformation of the ferrite grains, provided, the ferrite grains are not too fine and the amount of martensite is limited.

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The difference in the lattice rotation in the ferrite grains due to strain rate and microstructure can alter the overall crystallographic orientation of the matrix after deformation. In Fig. 14, the ND-IPF crystallographic texture maps corresponding to the ferrite matrix at two different strain rates is shown. In DP600, on increasing the strain rate from 0.001 to 800 /s, the ferrite grains tend to rotate more towards the 〈111〉 crystallographic direction, as shown in Fig. 14(a and b). Whereas in DP800, the ferrite grains retained the overall crystallographic orientation irrespective of the strain rates as observed in Fig. 14(c and d).

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Figure 14: ND-IPF maps of DP600 at (a) 0.001 and (b) 800 /s strain rates and of DP800 at (c) 0.001 and (d) 800 /s strain rates

Variation of hardening ahead of interfaces with strain rate

The restriction to lattice rotation also creates additional hardening in the ferrite regions adjacent to martensite. Although, the formation of localized hardened regions is also dependent on the strain rate and microstructural variables, which is explained earlier. Figure 15 shows the magnified view of a portion of IQ image obtained for DP600 and DP800 both at 0.001 and 800 /s. For DP600, in both the IQ maps at different strain rates, line 1 correspond to ferrite – ferrite grain boundaries and line 2 corresponds to ferrite – martensite interfaces. The corresponding point – to – point and point – to – origin misorientation details along the marked lines are presented. With the increase in strain rate the misorientation (point – to – origin) increases for both ferrite grain boundaries and interphase boundaries. Such an increase in the misorientation 14

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Figure 15: IQ maps and corresponding misorientation details of the marked lines in (a, b) DP600 and (c, d) DP800 at (a, c) 0.001 and (b, d) 800 /s strain rates respectively

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across the boundaries at high strain rates further confirms that the boundary area of the ferrite grains experience higher plastic flow in DP600. In case of DP800, appreciable change in the misorientation across the ferrite – ferrite grain boundaries with strain rate was not found. At 0.001 /s strain rate, two different types of interfaces were detected, marked as line 3 and 4 in Fig. 15(c). While the characteristic shown for line 3 is similar to the most of the interfaces in dual phase steel (e.g. line 1 and 2), some of the interfaces (represented by line 4) show a different variation. Regarding the misorientation details of line 4 in Fig. 15(c), within the martensite crystal (distance from 1.0 to 3.5 micrometer along the x-axis) the point – to – origin misorientation does not drop (marked by arrow) even though the corresponding point – to – point misorientation drops significantly. It can be inferred that the deformation in that marked zone within the martensite is considerably high. However, at high strain rates, no such behaviour was observed across the interfaces. The misorientation across the interface shown in Fig. 15(d) represents typical nature as observed in various other instances. Rather, the misorientation ahead of the interface (pointed in the figure) shows a marginal increase, due to the enhancement of plastic flow at the ferrite regions close to the interface.

Discussion

The results presented above show the difference in the deformation of ferrite in the two DP steels when deformed at various strain rates. The major difference in microstructure for the two DP steels are their martensite fraction. There are also difference in the size of ferrite grains and martensite colonies, although it is marginal. Present study shows the size dependency, effect of spatial distribution and crystallographic orientation of ferrite grains on the localized deformation in ferrite. Martensite was not found to show any plasticity over the applied range of strain rates in DP600. Martensite fragmentation however occurred at high strain rates for DP800 [9]. Due to the higher carbon content in DP800, the strength of martensite is almost 6 percent higher in DP800 compared to DP600, although the strength of ferrite remains the same in both the steels [25]. Even this minor variation in the strength of martensite can signif15

icantly influence the accommodation of strain MANUSCRIPT between the two phases in the investigated steels ACCEPTED especially due to the much higher fraction of martensite in DP800. It is certain that martensite shows minimal or no plasticity whereas ferrite contributes to the plastic deformation. Apart from the individual strength of the two phases, the local plastic deformation of the ferrite grains is also dependent on (a) microstructural factors like grain size, distribution and fraction of the individual phases and on (b) the type of deformation (loading path as well as strain rate). It is well known that martensite in DP steels acts as a barrier to the dislocation flow in ferrite, and thus the dislocations accumulate near to the interface regions [26], resulting in a strain gradient within the adjacent ferrite grains.

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Using local average misorientation as represented by the KAM it is shown that at low strain rates, the local misorientation is much higher near to the interface whereas it decreases towards the grain interior. With the increase in strain rate, the deformation tends to become uniform, especially in DP800. Therefore, the degree of uniformity of deformation across the ferrite grains increases with the strain rate and is also dependent on the grain size and the martensite fraction. In DP800, due to higher martensite fraction, the constraint imposed by the martensite on to the ferrite grains is also high, limiting the degrees of freedom for these ferrite grains to rotate during the plastic flow. Similarly, the ferrite grains which are surrounded by martensite in DP600 have the least GOS values. Hence, the sub-structural evolution within the ferrite grains, surrounded by martensite and containing high dislocation density, become restricted. This is also applicable to the finer ferrite grains. When the grain size increases, the coarser ferrite grains experience minimal constraints from the nearby martensite regions. In other words, the constraint imposed by the martensite acts primarily at the interface regions, and it gradually diminishes towards the ferrite grain interior. Consequently, the local orientation changes within the coarser grains to a greater extent in DP600. As shown in Fig. 12 and 13, lattice rotation is high at the interface regions. In DP600, with strain rate, the lattice rotation spreads uniformly in the ferrite grains and a larger volume of the grain gets deformed. Whereas, in DP800, change in strain rate does not create much difference in the lattice rotation, since the ferrite grains are completely locked by the surrounding martensite (higher interface area in DP800). The heterogeneous deformation of coarser ferrite grains creates local strain fields, due to which the extent of recovery varies within the different portions of the individual ferrite grains. As a result, individual portions of the grains rotate differently to homogenize the overall deformation in the matrix. With the increase in strain rate, due to the additional strain imposed on the ferrite grains, the local strain restricts the movement of the interface and thus intensifies the lattice rotation within the ferrite grains. This also justifies the strain rate dependency of the crystallographic orientations of the deformed ferrite grains for the DP steels with varying martensite fractions, as shown in Fig. 14. The influence of microstructure and strain rate on the deformation mechanisms of ferrite grains is important to explain the deformation instability (i.e. necking) and ultimate fracture in DP steels. The deformation induced damage in the microstructure is translated into the process of fracture. The lattice rotation and the strain gradient within the ferrite grains depend on the microstructural parameters as well as on the strain rate. In other words, a ferrite grain divides into different regions having different levels of work hardening. Due to the stronger dislocation activity near to the ferrite – martensite interface, those regions become strain hardened to a greater extent than the grain interior. Thus, in DP steels, the phase interface becomes the potential sites for the initiation of the crack, which propagates to cause the fracture. The increase in strain rate also enhances the hardening across the ferrite – ferrite grain boundaries along with the ferrite – martensite interfaces in DP600, Fig. 15(a and b). The enhanced plastic strain ahead of the interfaces is the precursor of interface decohesion, which prevails at high strain rates in DP600. In Fig. 16(a and b), representative images of the microstructures of DP600 at 0.001 and 800 /s are shown, revealing profound interface decohesion. 16

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In DP800, the interface hardening also increases with the increase in strain rate. Higher martensite fraction and strength induce high dislocation density at the neighbouring ferrite regions which contributes to a high degree of hardening. Similar to DP600, with the increase in strain rate, the hardening across the interface also increases in DP800. As a result, the interface decohesion prevails at all the strain rates. However, at the quasi-static strain rates, in DP800, due to higher martensite fraction (i.e. lesser ferrite region to consume the strain), some of the strain also partitions towards the martensite regions, Fig. 15(c). Such a straining of martensite can result in the martensite cracking. Fig. 16(c) shows a martensite region in DP800 in which cracks have originated after deformation at 0.001 /s strain rate. This demonstrates that the strain rate influences the failure mechanism in DP steel by altering the strain partitioning between the harder and softer phases.

Figure 16: Microstructure of DP600 showing interface decohesion at (a) 0.001, (b) 800 /s and (c) DP800 at 0.001 /s showing cracks developing in the martensite colonies

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Conclusions

This work comprehensively explains the variation in the deformation of ferrite grains in two ferrite / martensite DP steels (DP600 and DP800) with different fraction and strength of martensite and different ferrite grain size upon tensile deformation at the various strain rates. The salient conclusions of this work are presented below: 1. The strain accumulation occurs at the ferrite regions adjacent to the ferrite-martensite interface resulting in a high dislocation density at those regions, whereas the interiors of 17

the ferrite grains experience lower strain. Increasing the strain rate and decreasing the ACCEPTED MANUSCRIPT ferrite grain size, diminish the gradient in the local strain across the grain. 2. The GOS values of the finer ferrite grains is less compared to the coarser ferrite grains. With the increase in strain rate, the finer ferrite grains show higher GOS values. The normalized GOS values (GOS/D where D is the grain size) also show a sharp increase for finer grains in DP800 as the strain rate is increased.

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3. Due to the heavy constraint imposed by the martensite regions, ferrite grains in DP600 that are completely surrounded by martensite regions show negligible GOS values. The coarser ferrite grains that share ferrite – ferrite grain boundaries reveal high GOS values after deformation at 0.001 /s strain rate. At higher strain rate, the number of ferrite grains showing high GOS values increase and these grains do not share ferrite – ferrite grain boundaries.

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4. The less constraint from martensite regions in DP600 (due to the low martensite fraction) allows the ferrite grains to rotate during deformation which otherwise is restricted heavily by the martensite regions in DP800. In DP600, at 800 /s ferrite grains are found to preferentially orient along the 〈111〉 crystallographic direction. But in DP800, restricted rotation of the ferrite grains does not change their crystallographic orientations even at the high strain rates.

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5. In DP600, increase in strain rate enhances the local hardening of ferrite at the vicinity of the interfaces and rapid accumulation of strain ahead of the interfaces mostly trigger the damage evolution by the interface decohesion irrespective of the strain rate. In the case of DP800, high misorientation (i.e. strain gradient) exists within the martensite regions at 0.001 /s strain rate, which leads to the martensite cracking. At high strain rates, the interfaces experience heavy deformation, and thus it only triggers the interface decohesion.

Acknowledgements

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The authors like to thank M/S Tata Steel Ltd., for providing the financial aid and the materials to conduct the study. The authors like to thank Prof. Indradev Samajdar of IIT Mumbai, India for providing experimental help to conduct EBSD scans at his laboratory.

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Data Availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study

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