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Acta Materialia 59 (2011) 5462–5471

Microtexture development during equibiaxial tensile deformationin monolithic and dual phase steels

Do Hyun Kim a, Se-Jong Kim a, Sung-Hwan Kim a, Anthony D. Rollett b, Kyu Hwan Oh a,Heung Nam Han a,⇑

a Department of Materials Science and Engineering and Center for Iron and Steel Research, RIAM, Seoul National University, Seoul 151-744, Republic

of Koreab Department of Materials Science and Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213, USA

Received 5 February 2011; received in revised form 4 May 2011; accepted 10 May 2011Available online 3 June 2011

Abstract

Subgrain texture and microstructure evolution in individual ferrite grains in single (so called interstitial-free) and dual phase (DP) steelsheets with various martensitic fractions during stepwise equibiaxial deformation was observed by high resolution electron backscatterdiffraction (EBSD) measurement on a special deformation stage positioned inside a scanning electron microscope chamber. The micro-mechanical effect of hard martensite islands on adjacent ferrite grains in DP steels was analyzed by comparing the microstructuralchanges in the two steels. The strain partitioning between ferrite and martensite in DP steel, the development of orientation gradientsin ferrite grains near martensite islands, and the surface height variation were observed via a combination of high resolution transmissionelectron microscopy, EBSD, and atomic force microscopy. From these microstructural and geometrical observations the main effect ofthe hard martensite islands was to shed strain into the adjacent ferrite, thus inducing strain gradients, orientation spread, geometricallynecessary dislocations and increased surface height variation.� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Electron backscatter diffraction; Equibiaxial; Orientation; Dual phase; Martensite

1. Introduction

Modern high strength steels have been developed for theautomotive industry for the purpose of reducing the weightof the car body, which improves fuel efficiency and satisfiesthe consumer’s increasing demand for safer and more com-fortable vehicles. Among the high strength steels, generally,dual phase (DP) steels are low carbon, low alloy materialswith �5–30 vol.% hard martensite in a ductile ferritematrix. As they combine high strength and good formabil-ity with low production costs they have also been widelyused recently for automotive applications [1–7]. In general,the martensite fraction in low carbon DP steel could becontrolled by the deformation of ferrite–pearlite steel and

1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2011.05.020

⇑ Corresponding author.E-mail address: hnhan@snu.ac.kr (H.N. Han).

a subsequent intercritical annealing condition. Duringdeformation DP steels show complex inhomogeneousdeformation behavior, due to the presence of differentmicrostructural constituents. The complex deformationbehavior might act as a drawback to the broad applicationof DP steel. To ensure reliable application of DP steels it isimportant to understand the influence of the complexdeformation behavior on the microstructural changes.Therefore, there has been much research analyzing themicrostructural changes in DP steel with respect to sub-grain texture evolution during deformation [8–17].

It is well known that the mechanical properties of poly-crystalline materials during plastic deformation are stronglyaffected by their initial microstructures and microstructualchanges, such as rotation of the crystallographic orienta-tions of individual grains, the subgrain evolution, or thequantity and distribution of dislocations, including both

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Fig. 1. Schematic diagram and digital images of the equibiaxial tensiledeformation device for EBSD measurement. (a) Sample shape forequibiaxial tensile deformation. (b) Schematic diagram of the equibiaxialtensile deformation device controlled by rotation of a screw. Digitalimages of equibiaxial tensile deformation device (c) before and (d) afterdeformation.

D.H. Kim et al. / Acta Materialia 59 (2011) 5462–5471 5463

geometrically necessary dislocations (GND) and statisti-cally stored dislocations (SSD). Finally, the macroscopicmechanical behavior of materials such as DP steels is gov-erned by a combination of microstructural changes andtheir micromechanical responses, which are influenced bygrain or phase interactions during deformation. Lebensohnet al. simulated the microstructural changes and subgrainevolution in polycrystalline copper during uniaxial tensiledeformation and the results were compared with experi-mentally measured data [18]. Dillien et al. measured the lat-tice curvature in ferrite of a DP steel during cold rolling [19].It was revealed that a strong lattice curvature predomi-nantly develops around martensite grains, leading to a steeporientation gradient in ferrite grains adjacent to martensitegrains. As for the GND [20–22], recently, the accumulatedGND density in a DP steel was estimated based on the mis-orientation distribution with the help of high resolutionelectron backscatter diffraction (HREBSD) [23,24]. How-ever, most works were related to GND formation in DPsteels, which originated from the volume expansion duringthe austenite to martensite transformation without furtherdeformation.

In this study, in order to understand the subgrain tex-ture and microstructural evolution in individual ferritegrains in interstitial-free (IF) and DP steel sheets with var-ious martensitic fractions during plastic deformationHREBSD measurement on a special deformation stagefor equibiaxial tension was carried out inside a scanningelectron microscope chamber. The micromechanical effectof hard martensite islands on adjacent ferrite grains inDP steels was analyzed by comparing the microstructuralchanges in the IF and DP steels. The distribution ofGND and the height distribution inside ferrite grains nearmartensite islands, as well as the overall texture evolutionfor each deformation step, were observed through high res-olution transmission electron microscopy (HRTEM) andatomic force microscopy (AFM), respectively. From themeasured microstructural and geometrical changes in theIF and DP steels the effect of hard martensite on the micro-structure of the steels during plastic deformation was inves-tigated and is discussed.

2. Experimental

2.1. Equibiaxial tensile deformation inside the scanning

electron microscope and microstructure measurement

A quantitative measurement of orientation changes dur-ing stepwise biaxial tensile deformation of individual ferritegrains and grain aggregates in IF and DP steels wasattempted by combining EBSD and the specially designedmechanical device shown in Fig. 1. The device was installedin a scanning electron microscope chamber and operatedso as to develop the equibiaxial tensile mode in the cen-ter-top part of the sheet specimens as the screw was rotatedupwards, as shown in Fig. 1b. Fig. 1c and d is digitalimages of the specimen on the device before and after equ-

ibiaxial tensile deformation, respectively. A lubricantbetween the hemispherical cap and specimen was used todecrease the frictional stress between the specimen andthe screw. A disk-shaped specimen with a diameter of16 mm was prepared by a wire cutting method, as shownin Fig. 1a. The specimen was mechanically polished downto a thickness of 300 lm using a diamond suspension. Thena final surface polish using colloidal silica and Ar+ plasmacleaning were conducted for high quality digital imaging.

To trace the microstructure of the same area on thespecimen during stepwise equibiaxial tensile deformationfour rectangular micro-indentation marks were made onthe specimen surface before loading, as shown in Fig. 1a.From the shape change of the rectangular indentationmarks during deformation it was confirmed that equibiax-ial tensile deformation was applied. Macroscopic strains ateach deformation step were obtained by measuring the rel-ative displacement of the indentation marks in both thehorizontal and vertical directions in the scanning electronmicroscopy (SEM) images. The tensile strain was measuredas up to about 13% in one direction.

All experiments were carried out in a scanning electronmicroscope (JEOL JSM-6500F) equipped with a field emis-sion gun. The crystallographic orientation changes ofstrained grains were analyzed by an EBSD system (INCACrystal and HKL Channel 5, Oxford Instruments). Theaccelerating voltage and probe current were set at 20 kVand 4 nA, respectively. The band detection numbers andresolution of the Hough transformation were also main-tained constant at 5 and 50, respectively, for consistentEBSD measurement conditions. It is known that an appro-priate spatial resolution, which is simply the distancebetween two adjacent pixels, should be chosen accordingto the grain size [25]. Given ferrite grain sizes of 17 and6.5 lm in IF and DP steels, respectively, the spatial resolu-tions used were 1 and 0.1 lm, respectively.

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AFM (PSIA model XE-150) was used to investigate thethickness directional displacement in ferrite grains nearmartensite islands after equibiaxial tensile deformation.The distribution of thickness directional strain was evalu-ated in the ferrite phase in DP steels from the measuredsurface morphology. After EBSD measurements ofdeformed DP steel the dislocation structure in ferrite adja-cent to martensite islands was observed by high resolutionTEM (JEOL 3000F). For the TEM observations of the spe-cial ferrite region a cross-sectional sample was fabricatedusing a focused ion beam (FIB) (Nova NanoLab 200)equipped with a Schottky field emission gun column,Ga+ ion beam column, Pt gas injection system, andOmniprobe internal micromanipulator. The damagecaused by the Ga+ ion beam during FIB sample prepara-tion was reduced by Ar+ plasma cleaning.

2.2. Materials and determination of martensite area fraction

The present investigation was carried out for IF and DPsteels whose chemical compositions are listed in Table 1.While IF steel consists of only a monolithic ferrite phase,DP steels consist of soft ferrite and hard martensite. Theproportion of martensite in DP steels is controlled bydeformation of the initial ferrite–pearlite steel and subse-quent intercritical annealing treatments at temperaturesof 720 �C, 760 �C, and 850 �C for 30 min. These treatmentsresulted in area fractions of 7%, 18%, and 27%, respec-tively. The above values were determined through a phaseanalysis of the EBSD patterns of the specimens.

A conventional tool for phase volume fraction measure-ment is diffraction profile analysis using an X-ray or neu-tron beam [26,27]. This method is based on the differencein lattice symmetry. However, this method tends to failwhen attempting to discriminate between various phasesof steels that form by the decomposition of austenite,because these phases, such as ferrite, bainite, and martens-ite, in most cases have almost identical lattice structures.Recently it was shown that the quantitative measure ofEBSD pattern quality is very useful for mapping micro-structures [28–30]. Since the pattern quality is sensitive tolattice defects and surface topology, a map constructedwith it shows detailed features of the microstructure, suchas the boundaries. Also, because different phases generallyhave different diffraction intensities, the map can presentphase contrast. The phases that form at low temperatures,such as bainite and martensite, usually have higher disloca-tion contents, which leads to degraded EBSD patterns withlower pattern quality. Thus in this study the initial area

Table 1Chemical composition of steel specimens used for equibiaxial tensiledeformation.

wt.% C Mn Si Al Cu P Ti

IF steel 0.004 0.07 – 0.035 – <0.015 0.05DP steel 0.1 1.46 0.29 1.51 0.52

fraction and position of martensite in the DP steels weredetermined based on EBSD band contrast (BC) imagesusing the subset selection function in an HKL Channel 5system, where BC quantifies the pattern quality.

Fig. 2 shows the BC image map and profile, which wasscaled to the byte range 0–255 for the DP steel with 18%martensite area fraction as an example. For grain identifi-cation and subsequent grain averaging of the BC the mis-orientation angle in the grain boundary definition was setto 5�. The BC histogram in Fig. 2b indicates that the mar-tensite phase has initial BC values ranging from 20 to 120.Accordingly, grains with a grain average BC below 98 wereassigned to martensite, while grains with BC over 98 wereassigned to ferrite.

3. Results and discussion

Equibiaxial tensile deformation of IF and DP steels withmartensite area fractions of 0%, 7%, 18%, and 27% wascarried out in a scanning electron microscope chamberusing the device shown in Fig. 1. For the deformation steps

Fig. 2. (a) Band contrast image and (b) histogram for martensite selectionin DP steel. Blue in (a) indicates martensite phase. (For interpretation ofthe references to colour in this figure legend, the reader is referred to theweb version of this article.)

D.H. Kim et al. / Acta Materialia 59 (2011) 5462–5471 5465

corresponding to horizontal directional strains of 0%, 5%,9%, and 13% the orientation images at the center-top of thesheet specimens were measured by EBSD. We confirmedthat the strain developed at the center-top of the specimenwas almost equibiaxial based on the finding that the rectan-gular indentation marks on the specimen surface remainednearly rectangular. The measured orientation image mapsfrom the surface normal direction (ND) overlaid onto theBC image maps are shown in Fig. 3. For the zero straincase (before equibiaxial tensile deformation) the ferriteand martensite in the DP steels could be identified fromthe BC image maps, as shown in Figs. 2 and 3. It is clearthat martensite islands (dark area) are well distributed attriple junctions of ferrite grain boundaries in DP steels.

Fig. 3. EBSD orientation maps of IF and DP steels with martensite area fradeformation.

In order to observe the effects of the martensite islandson texture change in the ferrite phase, although the initialcrystallographic orientations in the IF and DP steels aredissimilar due to the different thermomechanical treat-ments, IF and DP steels with various martensite fractionswere compared. In Fig. 3 the red, green, and blue colorsrepresent the h1 0 1i, and h1 1 1i crystallographic directionsparallel to the ND of the specimen, respectively. It was evi-dent that the area of the green region, which is close toh1 0 1i||ND, decreases as the biaxial strain increases. Thismeans that h1 0 1i||ND rotates towards h1 1 1i||ND orh0 0 1i||ND under biaxial strain. This was expected becauseequibiaxial stretching is similar to compression and the sta-ble end orientations for bcc materials deforming in com-

ctions of (a) 0%, (b) 7%, (c) 18% and (d) 27% during equibiaxial tensile

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pression are h0 0 1i||ND and h1 1 1i||ND. The tendency oforientations between h1 0 1i||ND and h1 1 2i||ND to splitand become unstable was noted by Katoh and Hutchinson,who also noted its importance for subsequent annealing[31,32]. In addition to the overall texture change, thepost-deformation images of the IF and DP steels clearlyindicate the development of intragranular misorientationsin terms of noticeable color gradations inside the ferritegrains. Note that the dark area broadens as deformationprogresses in the DP steels. This indicates that the BC val-ues of ferrite regions adjacent to martensite islands weredramatically reduced as biaxial deformation increased.This tendency was stronger in the DP steels with largermartensite fractions and was rarely observed in the IF steel.In this study we investigated why differences in microstruc-tural change occur in IF and DP steels during equibiaxialdeformation.

In order to investigate the overall texture change duringequibiaxial tensile deformation a visco-plastic self-consis-tent (VPSC) model was used. The self-consistent approxima-tion is a commonly used method for estimating themacroscopic behavior of polycrystalline aggregates. How-ever, since this method is based on a mean field approach[33–35], the actual micromechanical fields and orientationchanges that develop inside the grains of a polycrystallinematerial may vary from the predictions. In this study a veloc-ity gradient of equibiaxial tension in the plane of the materialwith random bcc grains was applied. Version 7c of the LosAlamos VPSC code was employed [36]. The slip systemswere assumed to be {1 1 0}h1 1 1i and {1 1 2}h1 1 1i. Forcrystallographic slip a standard rate-dependent plastic sliplaw [37] was employed in the VPSC code.

_eijðxÞ ¼ _c0

Xs

msij

msklrklðxÞ

ss0

� �n

ð1Þ

where msij, _c0, _eijð�xÞ and rklð�xÞ are the symmetric Schmid

tensor associated with the slip system(s), a normalizationfactor, the differential strain rate and stress, respectively.The rate sensitivity exponent (n) and the initial shear stress

Fig. 4. Inverse pole figures of steel (a) with random orientation before equibiaxdirection of rotation of orientation. Red and blue dots indicate two different rerespectively. (For interpretation of the references to colour in this figure legen

(ss0) resolved onto the slip plane were assumed to be 20 and

2 MPa, respectively.The simulated texture at a von Mises equivalent strain

of 0.75 is shown in Fig. 4 as ND inverse pole figures. Bypartitioning grains into two regions divided by a line con-necting h113i and h304i two different stable orientationsfor equibiaxial tensile deformation were found. Thosecolored red tended to rotate towards h1 0 0i||ND, whilethe blue grains moved towards h1 1 1i||ND. Orientationsstarting near the h1 0 1i corner rotated towards theh1 0 0i–h1 1 1i line in the early stages of deformation. Thissimulation result macroscopically matches the experimen-tal observation in Fig. 3 which indicates that the area frac-tion colored green, which represents orientations close toh1 0 1i||ND, decreases as the biaxial strain increases.Fig. 5shows orientation density function (ODF) sections foru2 = 45� measured in ferrite grains of IF (Fig. 5a) andDP (Fig. 5b) steels with a martensite area fraction of27%. The texture data were obtained by EBSD at the sameposition of the specimen before (left-hand column) andafter (right-hand column) biaxial deformation. In the IFsteel the ferrite grains have an initially strong c-fiber(h1 1 1i||ND) and a weak h1 0 0i||ND component. Sinceh1 1 1i||ND is the stable orientation for the equibiaxial ten-sile deformation mode, as shown in the VPSC simulation,the intensity of c-fibers in the IF steel increased after defor-mation. On the other hand, in the DP steel, although theinitial ferrite texture is very similar to that in the IF steel,the rotated cube texture components (0 0 1)[1 �1 0] and(0 0 1)[�1�1 0], which are another stable orientation for equ-ibiaxial tensile deformation, intensified along with theincrease in c-fibers. This difference between the IF andDP steels may be a consequence of the interphase interac-tion between hard martensite and soft ferrite.

To investigate the microtexture development inside indi-vidual ferrite grains and the intergranular and interphaseinteractions several grains with the initial orientationsmarked in black in the inverse pole figures of Fig. 6 werechosen and examined in detail. In both IF and DP steels

ial strain and (b) after equibiaxial strain of 40%. Black arrows indicate thegions with h0 0 1i||ND and h1 1 1i||ND for equibiaxial tensile deformation,d, the reader is referred to the web version of this article.)

Fig. 5. ODF sections with u2 = 45� obtained for the same area of (a) IF and (b) DP steels with 0% and 27% martensite area fraction before (left-handcolumn) and after (right-hand column) equibiaxial tensile deformation.

Fig. 6. Inverse pole figures of measured initial and final orientations of several grains in (a) IF and (b–e) DP steels with 0% and 18% martensite areafraction.

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the grains in the regions close to the h0 0 1i and h1 1 1i cor-ners rotate towards the stable orientations h0 0 1i andh1 1 1i, respectively. This trend agrees with the VPSC pre-diction. However, in the experimental measurements

increasing orientation spread was observed inside grainsas the deformation increased. Notably, the orientationspread in the DP steels was much greater than that in theIF steel. Taking into consideration the smaller grain size

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in DP steel (6.5 lm) than in IF steel (17 lm), the differencein orientation spread between the IF and DP steels is sub-stantial. In the IF steel orientations starting near the h1 0 1icorner move towards the midsection of the h0 0 1i–h1 1 1iline, a feature that was reproduced by the VPSC calcula-tion. On the other hand, it should be noted that theh6 1 6i||ND and h4 1 6i||ND grains in the DP steels (Fig. 6d and e) exhibit entirely different rotation historiesin comparison with the similar h5 1 6i||ND grain in the IFsteel. Notably, the h4 1 6i||ND grain in the DP steels splitsinto different grains based on the h1 1 3i–h3 0 4i borderline. It can be seen that one part of the grain moves toh0 0 1i and the other part to h1 1 1i. This grain fragmenta-tion in DP steels during deformation might be closelyrelated to the strengthening of the rotated cube texturecomponent, as shown in Fig. 5.

Fig. 7. (a) EBSD BC image, (b) AFM topography and (c) AFM line profiles mmartensite area fraction after 5% equibiaxial tensile deformation. F and M in

Based on the above obvious difference in micromechan-ical behavior and microtexture development between IFand DP steels during equibiaxial deformation, severaleffects of hard martensite in DP steels have been consid-ered. One of these is strain partitioning between ferriteand martensite [38–40] due to the difference in their hard-ness. The nanoindenter–EBSD correlation technique[30,41,42] was used to compare the small-scale mechanicalproperties of two phases. The mean hardnesses of the fer-rite and martensite phases in the DP steel with 18% mar-tensite area fraction were determined to be 2.9 and7.3 GPa, respectively. The difference in hardness increasesthe accumulated strain in the ferrite phase relative to themartensite in the DP steels. Therefore, at the same biaxialstrain the strain actually applied in the ferrite region of DPsteels is effectively larger than that in the ferrite region of

atching lines 1 and 2 in (b), respectively, measured in DP steel with 18%dicate ferrite and martensite, respectively.

D.H. Kim et al. / Acta Materialia 59 (2011) 5462–5471 5469

the IF steel, and the enhancement is dependent on the mar-tensite fraction. In addition to the concentration of strainin the ferrite phase, several researchers have reported thatlocal shear strain adjacent to the ferrite–martensite inter-face develops in DP steels due to strain partitioning[39,43,44]. Local shear strain is likely to result in a localizedhigh dislocation density in the ferrite adjacent to martensiteislands and induce a low BC in this region, as shown by theEBSD measurements, shown in Fig. 3.

Another important effect of the strain partitioning in DPsteels is the dramatic increase in surface roughness duringdeformation. Fig. 7 shows the surface morphology andheight distribution of DP steels with an 18% martensitearea fraction after 5% biaxial strain, measured by AFM.The martensite islands are high relative to the ferrite grainsbecause of the strain concentration in the soft ferrite grains.It is also apparent that the ferrite regions near the phaseinterfaces were constrained in the thickness directionbecause of continuity with neighboring hard martensite

Fig. 8. (a) EBSD orientation map of DP steel with martensite area fraction 1eliminate the surface roughness. (b) Calculated distribution of GND density inthe dashed box depicted in (b).

islands, which were deformed significantly less. The strainconstraint in the ferrite regions near ferrite–martensiteinterfaces induced a steep inclination of the surface in theseregions, which also contributes to low BC near the phaseinterfaces in the EBSD measurements, as shown in Fig. 3.

The variation in strain near the ferrite–martensite inter-face should give rise to strain gradients in the ferrite matrixadjacent to martensite islands that induce GND [20–22].To confirm the GND in ferrite regions near martensite aspecimen was re-prepared after 5% biaxial deformationby light mechanical polishing with colloidal silica to elimi-nate the surface roughness induced by deformation. Forthe EBSD measurements of a smaller region the spatial res-olution was set to 0.05 lm. Fig. 8a shows an orientationimage after re-preparation of the specimen. Orientationgradients (white arrows) in ferrite grains (marked F) adja-cent to a martensite island (marked M) were evident. Themethod suggested by Kubin and Mortensen [45] was usedto calculate the GND density from the orientation gradi-

8% after 5% biaxial deformation. The specimen surface was repolished tothe ferrite grain indicated by the dashed box in (a). (c) HAADF image of

5470 D.H. Kim et al. / Acta Materialia 59 (2011) 5462–5471

ent. Assuming a series of twist subgrain boundaries in thecylinder, each containing two perpendicular arrays ofscrew dislocations, the GND density qg is related to themisorientation angle h as follows:

qg ¼ 2h=ub ð2Þ

where u and b are the length between two consecutive pixelsand the Burgers vector, respectively. Fig. 8b shows the cal-culated GND density distribution in the ferrite grains ofthe region indicated by the dashed box area in Fig. 8a.The GND density is higher in the ferrite region that is nearmartensite, where the orientation transition occurs. To ob-serve the dislocation structure directly the dashed box areadepicted in Fig. 8b was prepared as a cross-sectional sam-ple by FIB and analyzed by HRTEM. Fig. 8c shows a highangle angular dark field (HAADF) image of this region inthe [1 1 0] ferrite zone axis. It is clear that a high density oftangled dislocations is present in the ferrite region [22]where the orientation transition occurs. The TEM observa-tions are in good agreement with the calculated GND den-sity distribution based on the EBSD measurements. Fromthis observation it was confirmed that the strain constraintin ferrite regions near ferrite–martensite interfaces duringdeformation induces a high density of GND. The high dis-location density contributes to the low BC near phase inter-faces observed in the EBSD measurements, as shown inFig. 3, and the large orientation spread in the DP steels.

4. Summary

Microtexture development during equibiaxial deforma-tion in IF and DP steel sheets with various martensite frac-tions was investigated by performing HREBSDmeasurement on a special deformation stage positionedinside a scanning electron microscope chamber. The effectsof the hard martensite phase on the microstructuralchanges during deformation were as follows.

1. In both the IF and DP steels orientations close to theh0 0 1i and h1 1 1i corners rotated towards the stableorientations h0 0 1i and h1 1 1i, respectively. Grains withinitial orientation near h1 0 1i tended to move towardsthe midsection of the h0 0 1i–h1 1 1i line in the earlystages of deformation. These trends were reproducedby the VPSC calculations. However, the grains in theDP steels tended to develop higher internal misorienta-tions inside grains as deformation proceeded in compar-ison with the IF steel. Notably, this trend was strong ingrains with initial orientations near h1 0 1i. These couldbe described by strain partitioning and the developmentof additional local strain above the imposed equibiaxialstrain in ferrite regions near martensite–ferriteinterfaces.

2. The BC values in ferrite regions adjacent to martensiteislands decreased dramatically as the biaxial deforma-tion increased. This tendency was more evident in theDP steels with larger martensite fractions, and was

rarely observed in the IF steel. The loss of pattern qual-ity was induced by the strain gradient and the steep incli-nation of the surface in the ferrite regions nearmartensite–ferrite interfaces. The strain gradient wasconfirmed through the observation of GND in thisregion by EBSD and TEM.

Acknowledgements

This study was supported by the National ResearchFoundation of Korea grant funded by the Ministry of Edu-cation, Science and Technology (2010-0018936) and POS-CO research program. The authors would like to thankDr Suk Hoon Kang at KAERI, Dr Jun-Hyun Han atKIST, Dr Sukbin Lee at CMU, Mr Hyun-Sik Choi atSNU and Dr Ricardo A. Lebensohn at LANL for valuableconversations on the EBSD measurements and VPSC cal-culations. The work at CMU, where H.N.H. had a sabbat-ical period, was primarily supported by the MRSECprogram of the National Science Foundation under awardno. DMR-0520425.

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