M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

Ava i l ab l e on l i ne a t www.sc i enced i r ec t . com

www.e l sev i e r . com/ loca te /matcha r

Assessment of local deformation using EBSD: Quantification oflocal damage at grain boundaries

Masayuki Kamaya⁎

Institute of Nuclear Safety System, Inc., 64 Sata, Mihama-cho, Mikata-gun, Fukui 919-1205, Japan

A R T I C L E D A T A

⁎ Tel.: +81 770 379114; fax: +81 770 372009.E-mail address: kamaya@inss.co.jp.

1044-5803/$ – see front matter © 2012 Elseviedoi:10.1016/j.matchar.2012.02.001

A B S T R A C T

Article history:Received 5 July 2011Received in revised form 5 December2011Accepted 3 February 2012

Electron backscatter diffraction (EBSD) in conjunction with scanning electron microscopywas used to assess localization of the local misorientation to grain boundary. In order toquantify the degree of localization, a parameter, which was referred to as the grainboundary local misorientation, was proposed. Through crystal orientation measurementsusing deformed Type 316 stainless steel, it was shown that the grain boundary localmisorientation increased with the applied plastic strain. Particularly, at several grainboundaries, the grain boundary local misorientation was more than 3 times the localmisorientation averaged for the whole area. Surface observations revealed that the largelocal misorientation near the grain boundaries was attributed to the impeded slip stepsrather than the number of slip steps observed on the surface. The magnitude of the grainboundary local misorientation had a week correlation with grain boundary length or grainboundary misorientation, and no correlation was found for twin boundaries. Finally, itwas shown that the maximum grain boundary local misorientation could be estimatedstatistically, and the estimated maximum value for the specimen surface with an area of80 mm2 was 10.6 times the averaged value.

© 2012 Elsevier Inc. All rights reserved.

Keywords:Electron backscatter diffraction(EBSD)MisorientationLocal misorientationGrain boundaryPlastic strain

1. Introduction

Electron backscatter diffraction (EBSD) in conjunction withscanning electron microscopy (SEM) has been used for asses-sing damage accumulated in materials. Tensile or fatigueloading, for example, causes a change in crystal orientationlocally [1,2], and the change can by quantified by crystal orien-tation measurements using EBSD (hereafter, EBSD measure-ments). Commercial apparatuses for EBSD measurementscan measure crystal orientations of more than 600 points persecond by scanning sample surfaces [3] and provide mappingdata of crystal orientations. The misorientation parameters,such as the kernel averaged misorientation (KAM) [1], localmisorientation [4] and local gradient [5], can be calculatedfrom the measured orientations and they correlate well withthe degree of damage due to plastic strain [6–12], fatigue[13,14] and creep [15].

r Inc. All rights reserved.

Even if the damage induced in the material is uniformmacroscopically, its spatial distribution is not homogeneousin a microscopic scale. Anisotropy of deformation propertiesof crystal grains and the random nature of the crystal orienta-tion in polycrystalline material cause the inhomogeneity[16–19]. In low-cycle fatigue, it was observed that microstruc-turally small cracks were preferentially initiated from thearea of relatively large local misorientation [20]. Therefore, inorder to assess the degree of damage prior to the crack initia-tions, it is important to pay attention to the localized localmisorientation rather than the averaged value. In particular,the damage near grain boundaries is one of the key parame-ters because many cracks are initiated from grain boundariesin fatigue, stress corrosion cracking, and creep, which aremajor degradation phenomenon of materials used in nuclearpower plant components. Furthermore, it was shown thatthe local misorientation tended to be large near grain

57M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

boundaries [14,21–23]. The density of the geometrically neces-sary dislocations correlated well with the magnitude of thelocal misorientation [24–31]. It was shown that the dislocationdensity could be estimated using the local misorientationwith an optimization technique such as the energy minimiza-tion method [12,32].

This study aims to quantify the local misorientation whichis localized at individual grain boundaries. Firstly, crystal ori-entations were measured using deformed Type 316 stainlesssteel. Then, after defining a parameter representing the de-gree of localization near grain boundaries, the change in accu-mulated damage near grain boundaries was investigated.Discussions were made on the characteristics of highly local-ized grain boundaries. Finally, it was shown that the maxi-mum value of the grain boundary local misorientation in anextensive area larger than the measured area can be estimat-ed statistically.

2. Experimental Procedure

The material used in the experiment was solution heat-treated Type 316 austenitic stainless steel, and its alloying el-ements are listed in Table 1. Plate tensile specimens (gaugelength=20 mm and cross section=2×4 mm2) were machinedand deformed by a tensile test up to the nominal global plasticstrain, εp, of 3.0%. The deformation rate was 1.0 mm/min atthe cross-head of the tensile test machine and the strainwas identified by the change in distance between indentationmarks. The test was interrupted at εp=0.55% and 1.7% in orderto measure the crystal orientations of the surface of the spec-imen. The observed surface was polished using up to 3 μm di-amond paste followed by colloidal silica polishing before thetensile test.

Crystal orientations were measured using commercialsoftware (OIM Data Collection ver. 5.2) and an EBSD detectorinterfaced to a field emission electron gun SEM (Carl ZeissULTRA55) operating at 20 keV. The observation was made by300 magnifications under the working distance of 20 mm.The crystal orientation maps were obtained from EBSD mea-surement scanning with the step size of ho=0.5 μm. Therange of the measurement was approximately 250×250 μm2.The measurement conditions were selected carefully inorder to identify accurate misorientations [5]. The possiblefactors which affect the accuracy of crystal orientation mea-surement are SEM conditions (e.g. electron gun type, acceler-ating voltage, beam current, beam stability for long timeoperation), observation conditions of EBSD (e.g. working dis-tance, focus and magnification of observation), EBSD patternacquisition (e.g. shape of screen, background noise adjust-ment, video gain), conditions for data processing of obtainedEBSD pattern (Hough transform settings, indexing, calibra-tion) and so on. Particularly, the number of pixels of the CCD

Table 1 – Element content (wt.%) of test material.

Fe C Si Mn P S Ni Cr Mo

Bal. 0.05 0.41 0.83 0.026 0.001 10.08 16.14 2.08

camera for diffraction image acquisition has large influenceon the accuracy, and it was set to the maximum, which was640×480 pixels, in the current measurement system. The ex-posure time for pattern acquisition was 0.027 s with thevideo gain of 19. The pattern size for the Hough transformand θ step size, which were setting parameters in the mea-surement software, were set to 120 and 0.5°, respectively.The orientation data were analyzed using in-house softwareMADAM (Misorientation Analyzer for DAmage Measurement)[33].

3. Filtering Process for Reducing MeasurementError

Even if the orientation measurements are carried out careful-ly, some error will be included in the identified crystal orienta-tions. Misorientation identification has an error associatedwith it of 0.1–1° [5,34] depending on measurement conditions.The influence of the error can be ignored if the measured mis-orientations are large enough compared to the magnitude ofthe error. In other words, by increasing the plastic strain, theinfluence of the error can be reduced. However, for the pre-sent specimen, large plastic strain could not be applied be-cause surface roughness and slip steps induced by theplastic strain were significant. In particular, the surface wasnot flat locally and this could make orientation measure-ments difficult. Therefore, the tensile test was stopped at3.0% plastic strain. The measured misorientations were notso large compared to the magnitude of error. Then, in orderto capture the change in the local misorientation from rela-tively small plastic strain, the error in measurement was re-duced by applying a filtering process [35] to the measuredorientations.

In the filtering process, to remove the error in the crystalorientations obtained, the average of the crystal orientationsof surrounding points (up to nine points) was calculated asschematically shown in Fig. 1. The orientation of each mea-surement point was replaced with the averaged value. In theaveraging, orientation of different grains was not included. Aline was drawn between two adjacent points when the

Fig. 1 – A schematic drawing of the smoothing filter forcrystal orientations.

58 M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

misorientation was larger than 5°. If a series of these linesformed a closed region, the lines were defined as a grainboundary. It has been confirmed that the selected thresholdvalue of 5° for grain boundary definition worked well for thecurrent material [4]. By applying this filtering process, theerror in misorientation identification was drastically reduced.This makes it possible to capture slight change in crystal ori-entations caused by the relatively small plastic strain. Itshould be noted, however, that the filtering cuts down peaksin local misorientation. Therefore, the spatial resolution ofthe mapping may deteriorate. The step size should be smallenough to make up for blurred distribution.

Fig. 3 – Definition of the points for calculation of extendedlocal misorientation for origin point po.

4. Local Misorientation

4.1. Calculation Procedure

Based on the filtered crystal orientations, the local change inthe crystal orientation was evaluated using the local misor-ientationML; its value at point po is calculated by the followingequation [4]:

ML poð Þ ¼ 14

X4i¼1

β po;pið Þ ð1Þ

where β(po, pi) denotes the misorientation between the pointpo and neighboring points pi in the same grain as shown inFig. 2.

Similarly, the extended local misorientations were definedby using not only the neighboring points but also remotepoints defined in Fig. 3 [5]. For example, the local misorienta-tion for number 3 points, ML

3rd, was calculated by:

M3rdL poð Þ ¼ 1

4

X4i¼1

β po;p3ð Þi

� �ð2Þ

where pi(3) denotes the points numbered 3 in Fig. 3. The ex-

tended local misorientation is the averaged misorientationbetween the points of the same distance, which is denotedas h, from the central point po. The distances h are 20.5ho,2ho, 50.5ho and 80.5ho forML

2nd,ML3rd,ML

4th andML5th, respectively,

where ho is the step size of the measurement.

Fig. 2 – Definition of local misorientation.

Themean value ofML, which is denoted asMave, was calcu-lated for each mapping datum by the following equation [4]:

Mave ¼ exp1N

XNi¼1

ln ML pið Þf g" #

ð3Þ

where N is the number of data. It should be noted that onlygrains consisting of more than 10 measurement points wereincluded in the calculation. It was difficult to identify the crys-tal orientations at grain boundaries, inclusions and particleson the surface. Incorrectly identified crystal orientations atsuch points were different from those of surrounding pointsand they were recognized as isolated small grains. Suchsmall grains, which typically consisted of a few points, wereignored for the calculation of Mave.

The extended averaged local misorientations were alsocalculated for ML

2nd, ML3rd, ML

4th and ML5th and denoted as Mave

2nd,Mave

3rd, Mave4th and Mave

5th, respectively.

4.2. Experimental Results

Fig. 4 shows the distribution of ML at different degrees ofstrain. The same area was observed by the interrupted test.Due to the plastic strain, the local misorientation developedinhomogeneously. Particularly, the local misorientationtended to be large near grain boundaries, which are indicatedby solid lines in the figures. The magnitude of the local misor-ientation increased as the plastic strain increased, althoughmore than half area showed small change.

The change in the extended averaged local misorientationswith the distance h is shown in Fig. 5. The regression line wasextrapolated and the intercept value at h=0 was defined asthe error index Bn [5]. The lattice curvature caused a gradientin the crystal orientation and gave rise to the misorientation.Therefore, the local misorientation caused by the orientationgradient was proportional to step size and, if no error was in-cluded in the local misorientation, it would be zero when thestep size became infinitely small. In other words, the interceptvalue Bn emanated from the error in the local misorientationidentification and it was 0.019° at the maximum. Since Bnwas small compared to Mave, the influence of the error wasnot significant and this made it possible to observe the localmisorientation distributions in Fig. 4 even when the plastic

Fig. 4 – Distribution of local misorientation for strained stainless steel (grain boundaries are superimposed).

59M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

strain was less than 1.0%. The roughness of the sample sur-face increased due to induced plastic strain increased, ant itmay reduce the measurement accuracy. The almost identicalBn at difference plastic strains implied that the change in ac-curacy due to the plastic strain was negligibly small and thelocal misorientation of different plastic strains could be com-pared quantitatively. For comparison, the change in the ex-tended averaged local misorientations using the originalcrystal orientations (orientations before applying the filteringprocess) is shown in Fig. 5(b). Bn of the original crystal orienta-tions was about 0.12° and tended to increase with the plasticstrain, and these values were larger than the net local misor-ientation, which was almost identical to Mave−Bn. Fig. 6shows the distribution of ML obtained using the original crys-tal orientation. Due to the error in measurement, it was diffi-cult to conduct a detailed observation of the localization.Thus, the filtering process was a practical method for quanti-tative evaluation of the local misorientation and essential forthe observation of such small local misorientations.

The effect of filtering process is similar to that obtained bytaking moving average. In the calculation of the moving aver-age of a series data, several neighboring points are averaged.In the smoothing filter, the moving averaged was adopted in

two-dimensional crystal orientation field. By averaging sever-al crystal orientations, the spatial resolution for local misor-ientation was deteriorated. However, instead of the reductionin spatial resolution, ripple change brought about bymeasure-ment error was suppressed and the apparent accuracy of thecrystal orientationmeasurement was improved. By increasingthe range of averaging, the measurement accuracy can be im-proved more, though it reduces the spatial resolution further.From the results shown in Figs. 4 and 6, the range for averagingseemed to work well for the current observations.

The distribution of EBSD pattern quality is shown in Fig. 7.The quality depended on the crystal orientation and deterio-rated due to applying plastic strain. The dislocations inducedby the plastic strain disturbed the diffraction of electronbeam. Due to overlap of multiple patterns from differentgrains, the quality tended to be poor near grain boundaries, al-though the width of such poor quality area at grain boundarywas less than ho.

Fig. 8 shows the relationship between the averaged localmisorientation and the degree of plastic strain. The linear cor-relation implied that the local misorientation was a goodmeasure for the local plastic strain as shown in previous stud-ies [4,13].

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Distance from center h, µm

Distance from center h, µm

0%0.55%1.7%3.0%

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 0.5 1.0 1.5

0.0 0.5 1.0 1.5

Ext

ende

d M

ave

, deg

.E

xten

ded

Mav

e , d

eg.

0%0.55%1.7%3.0%

a) After applying filtering process5thaveMaveM 2nd

aveM 3rdaveM 4th

aveM

b) without filtering process5thaveMaveM 2nd

aveM 3rdaveM 4th

aveM

Bn

Bn

εp

εp

Fig. 5 – Change in extended Mave with distance from centerfor ML calculation (ho=0.5 mm).

Fig. 6 – Distribution of local misorientation obtained usingcrystal orientations with applying the filtering process(εp=3.0%).

Fig. 7 – Quality of EBSD pattern for crystal orientationidentification.

0.00

0.05

0.10

0.15

0.20

0.0 1.0 2.0 3.0

Mav

e , d

eg./µ

m

Plastic strain p,%

[ ] [ ]p ave% 27.3 deg./ µm 1.74Mε = −

ε

Fig. 8 – Change in averaged local misorientation with plasticstrain.

60 M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

Fig. 10 – Partitioning of the grain for defining the grainboundary local misorientation MGB.

61M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

5. Grain Boundary Local Misorientation

5.1. Definition of Grain Boundary Local Misorientation

In order to correlate themagnitude of the local misorientationto the grain boundaries, each measurement point wasassigned to a specific grain boundary. As schematicallyshown in Fig. 9, the shortest distance from the grain bound-aries was defined as distance d and the point was assignedto the nearest grain boundary. Fig. 10 shows a result of the as-signment. The points were colored according to their grainboundary assignment. As mentioned earlier, the small grainswhich consisted of less than 10 points were ignored. The divi-sions were intricate near short grain boundaries and no grainboundary was assigned at some measurement points, whichare indicated in white, because the assignment procedurecould not take the complex grain boundary configurationinto account. These points and the points assigned to grainboundaries for which length LGB was less than 10 μm werenot used for the calculation of the grain boundary localmisorientation.

The log-normal average of local misorientation for pointswhere the distance d was less than the threshold distancedth was defined as the grain boundary local misorientationMGB. Fig. 11 shows the spatial distribution of MGB in the caseof dth=3 μm (6ho). MGB was calculated for each side (for indi-vidual grain) of the grain boundaries. As shown in Fig. 4, themagnitude of the local misorientation was different for eachgrain boundaries and changed discontinuously at some grainboundaries. By normalizing the MGB by Mave, it is possible toassess how much the local misorientation was localized tothe grain boundaries. If there was no localization, MGB/Mave

should be unity. In Fig. 11(a), even when no plastic strainwas induced, the local misorientation was localized to thegrain boundary. The solution treatment and quenching dur-ing the material preparation could cause the localized localmisorientation at grain boundary, although the magnitude ofthe local misorientation was relatively small. The increase inthe normalized MGB with the plastic strain implies that the lo-calization became more significant as the plastic strain in-creased. MGB/Mave became more than 3.0 at several grainboundaries and, from the results shown in Fig. 8, which

Fig. 9 – A schematic drawing for definition of the distancefrom grain boundary for each point (smallest distance isdefined as d for each point).

corresponds to more than 12% in the plastic strain. Thismeans that the magnitude of plastic strain becomes morethan 4 times the global plastic strain locally.

5.2. Change with Distance from Grain Boundary

Fig. 12 shows the change in normalized MGB with the thresh-old distance dth for two grain boundaries (A) and (B). Thegrain boundary (B) was the twin boundary, which is indicatedby red lines in the figure.MGB/Mave tended to increase with thedistance dth decrease, although it was not always the maxi-mum at the smallest dth. The magnitude of the localizationwas not significant at the beginning of the experiment, andtended to increase with the plastic strain. In particular, side2 of grain boundary (B) had MGB/Mave of more than 2.5 at thestrain of 3.0%. However, the change in MGB/Mave was not mo-notonous and it was different for grain boundaries (A) and(B), and sides 1 and 2.

The averaged local misorientation at which dwas less thandth was defined as Mave(GB). Mave(GB) corresponds to the

Fig. 11 – Grain boundary local misorientation (dth=3 μm).

62 M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

averaged value of MGB for all grain boundaries. Fig. 13(a)shows the change in normalized Mave(GB) together withthe number of points used for the calculation of Mave(GB).Mave(GB)/Mave increased as the distance dth decreased. The num-ber points increased with distance dth and became almost 0.5Nall

for the distance dth=8ho=4 μm, where Nall is the total number ofpoints of the measurements. Since the grain boundaries of lessthan 10 μm were not included for the calculation Mave(GB), thenumber of points did not reach Nall even for large threshold dis-tance dth. The change inMave(GB)/Mave with the strain is shown inFig. 13(b). Increase in Mave(GB)/Mave for smaller dth implied the lo-calization of the local misorientation to the grain boundaries,and the localization extended almost 10 μm from the grainboundaries.

There was no significant change in the averaged Mave(GB)/Mave observed under different magnitudes of strain, althoughthe localization was surely developed by the deformation atseveral grain boundaries as shown in Figs. 11 and 12. Further-more, at small dth, the magnitude of Mave(GB)/Mave was largestfor the unstrained material. The localization did not occur atall grain boundaries, but only at specific grain boundaries.Therefore, the localization should be investigated not for the

averaged change of all grain boundaries but for an individualgrain boundary.

It should be noted that the local misorientation might berelatively large near the grain boundary because of the poorEBSD pattern quality, which is shown in Fig. 7, and the rela-tively small number of points for averaging in the filteringprocess. Therefore, MGB and Mave(GB) at dth/ho=1 might be af-fected, although they changed continuously at dth/ho=1 inFigs. 12 and 13.

5.3. SEM surface Observation of Localized Area

Fig. 14 shows SEM surface images at the strain of 3.0%. Thelocal misorientations together with the expected directionsof the slip step are also shown. The direction was derivedby the maximum Schmid factor. In Fig. 14(a), many slipsteps were observed on the surface of the specimen particu-larly at grain (A). However, the local misorientation was notso large at grain (A) except near the boundary with grain(B). The direction of the slip steps was identical to thatexpected by the maximum Schmid factor, and they passedthrough boundary (C) to the neighboring grains. The main

0.0

0.5

1.0

1.5

2.0

2.5

3.0

MG

B/M

ave

MG

B/M

ave

MG

B/M

ave

MG

B/M

ave

Distance from grain boundary dth/ho Distance from grain boundary dth/ho

Distance from grain boundary dth/ho Distance from grain boundary dth/ho

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

8 10 8 10

8 10

0 2 4 6 0 2 4 6

0 2 4 6 0 2 4 6 8 10

0%0.55%

c) Grain boundary B (Side: 1)

A(side:1)A(side:2)

B(side:2)

B(side:1)

a) Grain boundary A (Side: 1)

d) Grain boundary B (Side: 2)

b) Grain boundary A (Side: 2)

1.7%3.0%

0%0.55%1.7%3.0%

0%0.55%1.7%3.0%

0%0.55%1.7%3.0%

Fig. 12 – Change in grain boundary local misorientation at each grain boundary.

63M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

source of the local misorientation is the curvature of crystallattice which is attributed to so-called geometrically neces-sary dislocations. The glide of dislocations does not alwayscontribute the development of the curvature. The crystal lat-tice keeps the same orientation, even if it glides like a slideof a card stack. Therefore, the local misorientation was notso large near grain boundary (C), which did not impede glid-ing of the dislocation. On the other hand, the local misorien-tation became large at grain boundary (D). The localmisorientation tended to develop when gliding of the dislo-cation was impeded. Piled-up dislocations caused the local

change in crystal orientation as observed at grain boundary(D), where the slip steps did not pass through to the neigh-boring grain. The junction point (E) and grain (B) also showedrelatively large local misorientation. In these areas, slip stepswere not observed clearly, but many steps were observedaround them. Slip steps disappeared at the junction point(E) and the boundary of grain (B), and this assumed to en-hance evolution of the local misorientation. Thus, the mag-nitude of local misorientation correlated with impeded slipsteps rather than with the number slip steps observed onthe surface.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

3.0%1.7%0.55%0%

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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1.2

1.4

1.6

1.8

2.0

0 10 20 30

0 10 20 30 40

Num

ber

of p

oint

s N

/Nal

l

Gave(GB)Number of points

a) Changes for εp = 3.0%

b) For all strains

εp

Distance from grain boundary dth/ho

Distance from grain boundary dth/ho

Mav

e(G

B)/M

ave

Mav

e(G

B)/M

ave

Fig. 13 – Change in averaged local misorientation Mave(GB)

with threshold distance dth.

A

D

C

E

B

ML (deg./μm)

0.4

0.0

0.2

a)

B

C

D

A

E

ML (deg./μm)

0.4

0.0

0.2

b)

Fig. 14 – SEM surface images and corresponding localmisorientation distribution (arrows shows the direction ofslip steps expected by themaximum Schmid factor, red linesshow twin boundaries) (εp=3.0%).

64 M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

Grain boundary (B) in Fig. 14(b) corresponds to grainboundary (B) in Fig. 12. As shown in Fig. 12, the local misor-ientation was relatively large near boundary (B), particularlyin the right side grain of the boundary. In Fig. 14(b), manyslip steps were observed in the right side grain of boundary(B) and the slips did not pass through the boundary. On theother hand, the slip steps in the left side grain were notclear and multiple steps were observed. This resulted inlarger local misorientation in the right side grain than inthe left side one. Near grain boundary (C), the local misor-ientation was small because the slip steps were not imped-ed. However, it became large near the grain (A). Thedetailed observation showed that the slip steps disappearednear grain (A) along grain boundary (C). Hence, the grainboundary local misorientation may not be homogeneousalong the grain boundary. In the case of grain boundary(C), the junction point at grain (A) rather than the grainboundary (C) played an important role in the developmentof the local misorientation. As shown in Fig. 12, grainboundary (B) was a twin boundary and showed a relativelylarge local misorientation. On the other hand, the twinboundaries (D) and (E) showed no localization. The directionof the slip plane was deduced to be the same as the grainboundaries and there was little accumulation of dislocationsat the boundaries.

0

1

2

3

4

5

6

0 1 2 3 4 5 6

MG

B/M

ave

(Sid

e:2)

MGB/Mave (Side:1)

Twin

not Twin

Fig. 15 – Correlation of grain boundary local misorientation ofthe both sides of the grain boundary (dth=3 μm, εp=3.0%).

-2

-1

0

1

2

3

4

5

Maximum MGB/Mave

98%

90%

80%

70%

50%30%

10%

0 2 4 6 8 10

y =

____

x - σ

=__1 k

k[1

-{-ln

(F)}

]μ

Fig. 17 – GEV probability plot for normalized grain boundarylocal misorientation (dth=3 mm, εp=3.0%).

65M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

5.4. Influence Factors for Grain BoundaryLocal Misorientation

Fig. 15 shows the correlation between the MGB of sides 1 and 2at εp=3.0% obtained for dth=3 μm. There was large scatter par-ticularly for large MGB. Since only a weak correlation could befound, MGB should be evaluated individually for each side. Nocorrelation was observed for twin boundaries. Mave(GB)/Mave

values were 1.33, 1.27 and 1.29 for no twin boundaries, twinboundaries and both boundaries, respectively.

The correlation with the grain boundary length LGB isshown in Fig. 16. The averaged boundary lengths were18.8 μm, 26.6 μm and 23.3 μm for no twin boundaries, twinboundaries and all boundaries, respectively. Large MGB valuesappeared at relatively short grain boundaries. On the otherhand, at relatively long grain boundaries (more than 60 μm),the maximum MGB was less than 2Mave.

5.5. Estimation of Maximum MGB

In order to quantify the damage prior to the crack initiation, itis important to quantify the maximum MGB in all grain

0

1

2

3

4

5

6

0 50 100 150 200

Length of grain boundary LGB/ho

MG

B/M

ave

Twin

not Twin

Fig. 16 – Relationship between the grain boundary localmisorientation and grain boundary length (dth=3 μm,εp=3.0%).

boundaries. However, due to the area limitation for the EBSDmeasurements, it is difficult to obtain the maximum MGB inthe whole area of interest. Then, a statistical approach wasmade in order to estimate the maximum MGB.

Additional EBSD measurements were carried out for 20areas, of which size was 250×250 μm2. The maximum MGB

for dth=3 μm was calculated for each measurement includingthe results shown in Fig. 4(d). Fig. 17 shows the generalizedextreme value (GEV) probability plot of the obtained maxi-mum MGB/Mave. The cumulative distribution function of theGEV distribution can be expressed by,

G x; μ;σ ; kð Þ ¼ exp − 1−kx−μσ

� �n o1k

� �ð4Þ

Constants μ, σ and k were identified as −0.104, 0.797 and4.79, respectively. The maximumMGB/Mave in the 21 measure-ments was 7.97. The linear relationship implied that the max-imum MGB/Mave could be described by the GEV probabilityplot. Here, for example, the maximum MGB/Mave on the speci-men surface, with an area of 4×20 mm2, was estimated. Sincethe area of one measurement was 0.252 mm2, cumulativeprobability, F, for the specimen surface could be obtained byF=(80/0.0625)/ (80/0.0625+1). By substituting F to G in Eq. (4),the maximum MGB/Mave could be obtained from x. The esti-mated maximum MGB/Mave was 10.6, which corresponded to48.5% in plastic strain from the relation shown in Fig. 8. Itshould be noted, however, that the correlation shown inFig. 8 was not linear at such a large plastic strain. Anyhow, ex-tremely large grain boundary local misorientation was de-duced to appear locally, and the damage for crack initiationshould be assessed referring to the maximum value.

6. Conclusions

In order to assess the localization of the local misorientationto grain boundaries, the distribution of local misorientationwas investigated using deformed stainless steel specimen. Aparameter, which was referred to as the grain boundary localmisorientation, was proposed for quantification of the

66 M A T E R I A L S C H A R A C T E R I Z A T I O N 6 6 ( 2 0 1 2 ) 5 6 – 6 7

localization. Then, by using the parameter, characteristics ofthe localization of the local misorientation were evaluated.The results obtained are summarized as follows.

(1) By applying a filtering process, the error in misorienta-tion identification was significantly reduced, and itwas possible to observe the localization of the local mis-orientation to grain boundaries at small plastic strain.

(2) The local misorientation tended to localize to the grainboundary and the magnitude of the localization in-creased with the applied plastic strain. At severalgrain boundaries, the normalized value, MGB/Mave,was more than 3.0, which corresponded to more than12% plastic strain.

(3) On the other hand, Mave(GB) showed little change withthe plastic strain. Therefore, in order to evaluate the lo-calization, the local misorientation should be assessednot for the averaged change of all grain boundaries,but for the individual grain boundary.

(4) The large local misorientation near the grain bound-aries was attributed to the impeded slip steps ratherthan the number of slip steps observed on the surface.

(5) The correlations between MGB and grain boundarylength and between MGB and misorientation of thegrain boundary were small, and no correlation wasfound for twin boundaries.

(6) ThemaximumMGB could be estimated by the GEV prob-ability plot, and it was deduced to be 10.6Mave for thespecimen surface with an area of 80 mm2.

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