Work Hardening and Microstructural Developmentduring High-Pressure Torsion in Pure Iron

Akihide Hosokawa1,+, Seiichiro Ii1 and Koichi Tsuchiya1,2

1Structural Materials Unit, Research Center for Strategic Materials, National Institute for Materials Science,Tsukuba 305-0047, Japan2Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8577, Japan

The work hardening behavior and the developments of microstructure and crystallographic texture during high-pressure torsion (HPT) inpure iron were investigated. A set of the 3D electron backscatter diffraction (EBSD) measurements were also performed to characterize themicrostructure in 3D using an orthogonally arranged focused ion beam-scanning electron microscope (FIB-SEM) instrument. It was found thatthe image quality (IQ) values of the EBSD data obtained by the FIB-SEM are better compared to the conventional mechanical polishingprocedure. A detailed analysis on the distribution of misorientation angle was performed, being fitted with the Mackenzie plot. The use of theHencky equivalent strain made it possible to compare the work hardening behaviors and the microstructural evolutions observed in the currentinvestigation with those reported for accumulative roll bonding (ARB). This comparison has revealed that the Hall­Petch coefficient k obtainedby HPT deformation drastically increases with the grain refinement by HPT deformation. [doi:10.2320/matertrans.M2013462]

(Received December 26, 2013; Accepted April 21, 2014; Published June 25, 2014)

Keywords: severe plastic deformation, electron back-scattered diffraction (EBSD), three dimensional electron back-scattered diffraction (3D-EBSD), work hardening, Hencky strain, cut and see

1. Introduction

Ultrafine grained (UFG) metals with an average grain sizebelow 1µm are known to exhibit excellent strength andreasonable ductility. It is widely known that severe plasticdeformation (SPD) such as high-pressure torsion (HPT) is apromising method to produce UFG metals.1­4) The grainrefinement for various metallic materials by HPT have beenextensively reported by numerous authors,1,5­7) and theknowledge for the resultant mechanical properties and themicrostructure formed after HPT deformation have been wellestablished.

Meanwhile, for pure bcc iron, the evolution of mechanicalproperties and microstructure during HPT deformation is notwell understood. A few investigations have been performedon the texture development by HPT deformation,8­11) butthey involve some drawbacks. The works by Valiev et al.8)

and by Edalati et al.9) presented detailed microstructuraldevelopments during HPT deformation by TEM, but nocrystallographic texture analysis was performed. The work byDescartes et al.10) presented a detailed study on the develop-ment of the microstructure/texture for pure iron during HPTdeformation by means of electron back-scatter diffraction(EBSD) measurements, but the imposed hydrostatic pressureis only 500MPa. This pressure is much smaller than the otherexperimental investigations (Typically several GPa. SeeRefs. 5, 7, 8) for examples), making us wonder if the resultsreported in Ref. 10) is truly comparable with the other worksfor HPT deformation in the literature. Ivanisenko et al.11)

also performed TEM and SEM/EBSD study, showing thedevelopment of microstructures and texture as well as thegrain boundary character distribution by misorientation

angles for Armco iron. However, that EBSD analysis hasfocused on the grain morphologies, and no analysis wasperformed on the crystallographic texture formed by HPTdeformation. It is thus reasonable to conduct a set of EBSDanalyses to investigate the crystallographic texture formed byHPT deformation in bcc iron.

Deformation texture due to simple shear or torsion hasbeen studied by several researchers,12,13) whereby themaximal equivalent strain applied was about 5. One of theadvantages of HPT deformation over conventional torsiontests is that HPT can apply infinite strain avoiding material’sfailure because of a high quasi-hydrostatic pressure. It isthus expected that HPT deformation makes it possible toapply much larger strain to bcc iron than those reported inRefs. 12, 13). It would be interesting to investigate whetherthe deformation textures formed by conventional torsion andHPT deformation differ or not.

Moreover, it is of particular interest to compare the work-hardening behavior and the development of microstructureand texture in bcc iron at such large strain between severaldifferent deformation modes such as HPT, wire drawing andaccumulative roll bonding (ARB). These three deformationmethods are capable of applying quite large equivalent plasticstrain, and the experimental results for wire drawing andARB are available in the literature.3,14,15)

The aim of the current study is to investigate the workhardening behavior and the evolutions in microstructure andtexture for pure iron during HPT. Furthermore, an attemptwas made to characterize the 3D grain morphology by 3D-EBSD technique using the recently developed FIB-SEM dualbeam instrument.16) This technique can potentially clarify theinfluence of the 3D grain morphology on work hardeningbehavior. The obtained work hardening behavior is comparedwith those reported for other deformation modes in theliterature.

+Corresponding author, E-mail: hosokaa@mech.kyushu-u.ac.jp. Presentaddress: Department of Mechanical Engineering, Kyushu University,Fukuoka 819-0395, Japan

Materials Transactions, Vol. 55, No. 7 (2014) pp. 1097 to 1103©2014 The Japan Institute of Metals and Materials

2. Experimental

Pure electrolytic iron (which contains 12 ppmC) wasarc-melted under an argon atmosphere, followed by castinginto a cylindrical rod with a diameter of 10mm. The ingotwas heat treated at 1173K for 1 h in an argon atmosphere,which was followed by wire electro-discharge machining(EDM) to slice HPT discs (10mm in diameter, 0.85mmin thickness). The final thickness of the HPT discs wascontrolled by mechanical polishing. The discs were thensubjected to HPT deformation with a rotation speed of0.2 rpm. The number of HPT turns, N, ranged from 0.5to 10.

The deformed discs were cut into two half discs, and thenembedded in resin for cross-sectional metallography byoptical microscopy (OM) and by scanning electron micro-scope (SEM) equipped with electron backscatter diffraction(EBSD) system. The same samples were also subjected to theVickers microhardness testing. The surface was finished by0.5 µm colloidal silica for EBSD analyses, and further etchedby nital (HNO3 : ethanol ¼ 1 : 9) for optical microscopy.Vickers microhardness was also measured with a load of1.96N on the well-polished cross sections, whereby the radialposition of the individual indentations were measured toquantify the local strain.

Transmission electron microscopy (TEM) were performedusing the JEOL-2010F TEM equipped with a field-emissiongun operated at 200 kV. In preparing the TEM foils, circulardiscs with a diameter of 2mm were cut out of the HPTeddiscs. The thickness of those discs were then reduced to0.1mm by mechanical grinding the outer regions from boththe sides so that the discs are taken out from the centralregion along the thickness direction. Each disc was thenglued on a Pt grid. The inner diameter of a grid was 0.5mmwhile the outer diameter was 3mm. Afterward, twin-jetelectropolishing was performed to prepare TEM foils usingan electrolyte composed of 10% HCl4 and 90% ethanolat 253K.

The 3D-EBSD measurements were carried out for thesample after HPT (N = 10, r = 4mm) using an orthogonallyarranged FIB-SEM instrument16) to characterize the micro-structure as well as the crystallographic orientation in 3D. Arectangular piece (2mm © 2mm © 0.85mm) was cut out ofthe HPTed sample, followed by mechanical polishing andelectropolishing using the same electrolyte for TEM samplesat 253K. The acceleration voltages for SEM and FIB were 15and 30 kV, respectively. The FIB current was set to 600 pAduring the serial sectioning for the 3D-EBSD measurement.The measurement time for the whole single process to collecta series of the 2D-EBSD scans was approximately 14 h. Toprevent the drift during this long-term measurement, a markerpoint was used for the drift correction. The marker point wascreated by depositing carbon in the small square form at thevicnity of the area of interest. A series of the collected 2Dinverse pole figure (IPF) maps were used to visualize a 3Dimage using a commercial software Avizo. The size of a non-isotropic voxel is 1.96 nm © 1.96 nm © 10 nm, and the totalvisualized volume is 588 nm © 625 nm © 390 nm. The totalnumber of the EBSD scans for this 3D visualization wasthus 39.

3. Results

3.1 Work hardening behaviorConventional tensile testing is not suitable to measure the

plastic constitutive behavior at large strain.17) Instead, anequivalent stress­strain curve were drawn based on theresults of Vickers microhardness testing that were performedon the different HPTed discs. The strain introduced by HPTdeformation is quantified in the following manner. The shearstrain, £, is given by the equation:1)

£ ¼ 2³rN

tð1Þ

where r is the distance from the center along the radialdirection, N the number of turns, and t is the thickness of thedisc. The equivalent strain heq is obtained by substituting £

into the following equation.18)

heq ¼1ffiffiffi3

p ln2þ £2 þ £

ffiffiffiffiffiffiffiffiffiffiffiffiffi4þ £2

p2

!ð2Þ

According to the recent review by Onaka,18) thisequivalent strain heq for simple shear deformation isessentially the same with the so-called von Mises equivalentstrain, ¾V:M:, and thus it can be used as a convenient measureof strain for large scale deformation to compare differentdeformation modes. Thus one can compare the value of heqcalculated for an HPT deformation with the axial logarithmicstrain of wire drawing, ¾V:M: ¼ lnðA0=AÞ where A0 is theinitial cross sectional area of the sample and A the currentcross sectional area. The result of the comparison is shown inFig. 1, where the evolution of the microhardnessas a functionof this equivalent strain is shown. The inevitable preliminarydeformation by compression (equivalent strain ³0.4) wasincluded in the equivalent strain. Note that the strain in anHPT disc is dependent on the distance from the center alongthe radial direction r, and also dependent on the number ofturns, N. The Vickers microhardness data points shown inFig. 1 were measured from the various different positions ofthe various different discs (i.e., different r, different N) toillustrate the continuous evolution of the hardness as a

Fig. 1 The evolution of Vickers microhardness (i.e., flow stress) plotted asa function of equivalent strain. The curve of wire-drawing reported byLangford and Cohen14) is also plotted for a comparison.

A. Hosokawa, S. Ii and K. Tsuchiya1098

function of equivalent strain heq. The flow stress (in MPa) isalso indicated in the secondary y-axis, which was calculatedfrom the following equation.19) �· ’ 3:33Hv, where Hv is thevalue of the Vickers microhardness. Since the curve obtainedfrom the evolution in hardness shown in Fig. 1 is equivalentto the uniaxial stress­strain curve of electrolytic pure iron,this can be compared with the stress­strain curve for ultra-low carbon steel obtained by repeated wire-drawing process-es14) shown in the solid line. The stress­strain curve obtainedfor the HPT samples was found to show an almost linearhardening behavior and then shows an inflection at aroundheq ¼ 3­4, above which the rate of hardening becamesignificantly lower, while the curve for a wire-drawn samplekept exhibiting linear work-hardening up to heq � 7.Similarly, good agreement was observed between wire-drawing and HPT deformations below heq ¼ 3­4, but theagreement suddenly poor with further deformation. Thisdisagreement will be further discussed in later section.

3.2 Evolution in microstructure3.2.1 Optical microscopy

The evolution of microstructure due to the HPT deforma-tion was first characterized by OM as shown in Fig. 2. Thegrain structure is clearly seen in the sample before HPTdeformation. These microstructure drastically evolves withHPT deformation, particularly in the perimeter region of thediscs. Although the grain structure marginally remains in thecentral region, it was found that those grain boundariesbecome invisible with optical microscopy even after justa half turn of HPT deformation. Electron microscopy isdefinitely required to investigate the microstructure in theseregions.3.2.2 TEM

The microstructures of the perimeter (r = 4mm) of theHPTed discs were observed by TEM as shown in Fig. 3. Theapproximate average grain size was estimated to be 200 nm,which was found not to change with the increasing strainfurther. This tendency is consistent with the more quantitativeresults obtained by means of SEM/EBSD as will be shownlater. Another remarkable point is that the dislocation densitydoes not drastically differ between the samples after HPTdeformation with various different number of turns, N. Itseems that the dislocation density stops increasing around theheq ¼ 4, bringing no significant contribution to the increasein flow stress any further.

3.2.3 SEM/EBSDSEM/EBSD measurements were carried out to investigate

the crystallographic texture as well as the microstructuremore quantitatively. The evolutions in IPF maps and thecorresponding IPFs with the increasing strain are shown inFig. 4. Note that the grain boundary maps were super-imposed on the IPF maps. In this figure, the evolutions in themicrostructures and the texture with an increasing distancefrom the center r is presented. It can be seen from the grainboundary maps that the low angle grain boundary (LAGB =boundaries with misorientation angle 2° < ª < 15°, indicatedby the thin lines) and the high angle grain boundary(HAGB = misorientation angle 15° < ª < 180°, indicatedby the thick lines) are almost equally mixed at the strain of

Fig. 2 The evolution of microstructure with the increasing number of turns, N.

Fig. 3 The bright field and dark field TEM images for the HPTed sampleswith different N. (a) N ¼ 1=2 (heq ¼ 3:51) (b) N ¼ 1 (heq ¼ 4:31)(c) N ¼ 10 (heq ¼ 6:98).

Work Hardening and Microstructural Development during High-Pressure Torsion in Pure Iron 1099

heq ¼ 1:98. The fraction of the LAGBs then seems to becomegradually dominant with further deformation, and eventuallymost of the grain boundaries become HAGBs beyondheq � 4. The grain size was found to decrease with anincreasing strain, and eventually reaches 246 nm at heq �7:62, as will be shown later quantitatively in Fig. 7.

It is also observed that deformation texture is developedduring HPT from the IPF in Fig. 4(b) whereby the crystallo-graphic orientation is represented based on a cylindricalcoordinate (Thickness, Radial, and Hoop directions) insteadof the ordinary Cartesian coordinate (i.e., ND, TD, RD) forEBSD analyses. Considering the local deformation mode, itwould be natural that the shear plane is perpendicular to thethickness direction of the HPT discs and the shear direction isparallel to the hoop direction in HPT deformation. Similarly,the shear plane should be parallel to the rolling plane and theshear direction should be parallel to the rolling direction ifneglect the local strain concentration in the vicinity of thesheet surfaces. However, a clear feature of the deformationtexture formed by HPT deformation beyond the strain ofheq � 4 shown in Fig. 4(b) is that ©110ª is parallel to the discnormal (thickness direction), which differs from the deforma-tion texture components observed on the sheet normal planesin cold-rolled bcc iron. The texture component pointing in thehoop direction (which corresponds to the shear direction)is also ©111ª with some scatter. Indeed, several researchershave reported that torsion of ferritic steels results in sheardeformation texture that is composed of {110}©112ª and{110}©001ª.12,13) These texture components are consistentwith those observed in the current EBSD analysis, and alsoexplain the inflection point in work hardening at heq � 4.

The distribution of misorientation angle ª also changeswith increasing strain as shown in Fig. 5. As wasqualitatively demonstrated in the grain boundary maps inFig. 4, the boundaries with misorientation angle below 15°were found to be more frequently counted when the strain heqis small. By the time strain exceeds heq ¼ 4, the frequenciesof the HAGBs becomes much higher showing good agree-ment with the Mackenzie model.20)

One may notice that there are three spikes in thedistribution (i.e., abnormally high number fraction) at themisorientation angles of 30, 45 and 60° which are quite closeto the angles of the coincidence site lattice (CSL) boundariesof �13b, �19b and �3, respectively. Several researchershowever pointed out that these peaks are artifacts originatedfrom misindexing by the software.21) We therefore do notpursue further discussion about these peaks. It seemsconclusive, at least based on the EBSD observation fromthe cross-section, that misorientation of the grain boundariesbecomes randomized after the strain heq exceeds 3.3.2.4 3D EBSD

The three dimensional morphology of individual grainsafter HPT (heq ¼ 6:96) was visualized by 3D EBSDtechnique as shown in Fig. 6. Figures 6(a) and 6(b) show atypical IQ map and an IPF map of each 2D scan whileFig. 6(c) is the visualized 3D image from a series of thecollected 2D EBSD scans. It is remarkable that the IQ valuesobtained from the surface milled by FIB (1380­6710) werefound to be higher than those obtained for the mechanicallypolished surface (500­3400). Removal of sample surface

with the FIB inside the vacuum chamber seems useful toprevent the surface from oxidization, making the IQ better.

A measurement of 3D EBSD is generally very time-consuming and thus the slicing pitch of FIB cutting and thescanning time of each EBSD scan have to be compromisedwith the quality. To keep the measurement time reasonable,the pixel size along the thickness direction (i.e., the slicingpitch) of the current measurement could not be made too smalland thus the quality of the visualized image necessarilybecame slightly poor. The jaggy grain boundaries in Fig. 6(c)are also due to the poor number of scans. Nevertheless, nosuccessful example of 3D visualization of UFG pure ironfabricated by HPT deformation has ever been reported inliterature and thus the current result is considered to be quiteprecious. Although the orientation is indicated based on thecolor key in this figure, it is of course possible to assign theother parameters that are used in conventional EBSD analysessuch as IQ, Kernel Average Misorientation (KAM) and so on.

It has been reported that the grains are generally elongatedalong the shear direction after HPT (see Ref. 22) forexample). In the current 3D image, however, the grains donot appear elongated very much.

4. Discussion

4.1 Inflection point observed in Vickers hardness resultIt is of interest to discuss the origin of the inflection point of

the work hardening behavior as observed in Fig. 1. Beyondthis inflection point, the work hardening behavior obtainedwith HPT deformation clearly differs from that for wire-drawing. Such an inflection can also be found in a classicalwork by Young et al.,23) whereby they compared the stress­strain curves for torsion (without hydrostatic pressure) andwire drawing in Fe­0.17mass%Ti alloy. That paper demon-strated that the work hardening in torsion ceases at around¾V:M: (i.e., heq) ³ 2 while that for wire drawing continuesto exhibit work-hardening. Gil Sevillano et al.17) mentionedthe possibility that this linear hardening observed in wiredrawing is due to the development of ©110ª fiber texture beingparallel to the drawing axis. Such a texture is of course neverformed by torsion, as confirmed by the texture analysis onsteels after torsion.12,13) This is consistent with our currentEBSD result.

One might be curious about the microstructures (i.e., grainmorphology) formed by wire-drawing and torsion. Thedetailed micrographs of the microstructure are provided inRefs. 14, 23) In wire-drawing, the grains are elongated alongthe drawing direction while the thickness of the grains keepdecreasing all the way up to 100 nm at the equivalent strainof 7. Although the grain size of the pure iron formed by wire-drawing is surely smaller than that for the HPTed iron, thelinear hardening behavior observed in wire-drawing cannot beexplained solely by the grain size. The microstructure formedby torsion is not very different from those observed by thecurrent observation for the HPTed iron.23) It is thereforeconcluded that the inflection in the equivalent stress­strain curve in Fig. 1 is ascribed to the texture formed bytorsion.

It might be worth mentioning here that if we use theequivalent strain proposed by Shrivastava et al.24) (defined by

A. Hosokawa, S. Ii and K. Tsuchiya1100

£=ffiffiffi3

p), the disagreement between the stress­strain curve

obtained by HPT and that of wire-drawing becomes moresignificant. It follows that the Shrivastava strain seriouslyoverestimates the actual strain and thus is not an appropriatemeasure of shear deformation especially for heq > 4. Thecurrent authors are aware of that the research group of Jonasand his co-workers have been claiming that the use of theHencky strain (the version recommended by Onaka18,25))

is not applicable for large simple shear deformation.26,27)

However, Onaka25) pointed out that the version recommendedby Jonas and his co-workers, £=

ffiffiffi3

p, is indeed a nominal

equivalent strain which is not appropriate when we deal withlarge deformation. Moreover, we feel that the current resultsshown in Fig. 1 support the viewpoint of Onaka.18,25)

Fig. 4 The evolutions of IPF maps and the corresponding IPFs with increasing equivalent strain. The maximal intensity of each IPF, Imax is also indicated.The scale bars represent 1 µm.

Fig. 5 The evolution in the distribution of misorientation angle withincreasing equivalent strain.

(a) (b)

(c)

Fig. 6 The results of the 3D EBSD measurement for the HPTed pure iron.(a) A typical IQ map and (b) the corresponding IPF map out of a series ofthe 2D EBSD scans used for the 3D visualization. (c) A visualized 3Dimage based on a set of 2D EBSD scans.

Work Hardening and Microstructural Development during High-Pressure Torsion in Pure Iron 1101

4.2 Evolution in microstructure: HPT vs. other defor-mation methods

To discuss the ratio between the amounts of LAGBs andHAGBs more quantitatively, the fraction of HAGBs, fH (i.e.,defined by the ratio of the number of HAGBs to the totalnumber of grain boundaries) is plotted as a function ofequivalent strain heq as shown in Fig. 7(a). The evolution ofgrain size is also plotted in the same figure. The fH increasedrapidly and reached the saturation value of about 90% atheq � 4, and further deformation does not seem to change thefH. The grain refinement proceeded rapidly with increasingstrain in the beginning of deformation, and then the rate ofgrain refinement significantly slowed down beyond heq ¼3­4. The grain size then very gradually decreased withfurther deformation, except for a slight increase at heq ¼6:16, and finally reaches the minimum grain size of 254 nm atheq ¼ 6:96.

As was done by Young et al.,23) it is worth trying tocompare these tendency obtained by HPT with a similar setof data obtained by other deformation modes, for example,ARB.15) The von Mises equivalent strain after ten passes ofARB is 8, which is comparable with the equivalent strainapplied by HPT with N = 30 and r = 5mm. The dataobtained for IF (= Interstitial-Free) steels deformed at roomtemperature by ARB reported by Kamikawa and Tsuji arealso plotted in Fig. 7(a) for a comparison. It seems that ARBcan reduce the grain size (= lamellae thickness) slightly moreeffectively than HPT around equivalent strain 4­7 while thevalue of fH does not increase as steeply as HPT.

4.3 Hall­Petch relationNow that the grain size and the microhardness and the flow

stress of the HPTed iron samples are known, a Hall­Petchplot can be produced as shown in Fig. 7(b). The Hall­Petchplot for IF steels whereby the grain size was controlled bypost-ARB annealing treatments3) is also indicated as areference. The Hall­Petch coefficient of the HPTed iron,kHPT, was estimated to be 447MPa(µm)¹0.5. Here, it is worthcomparing this value with those in literature. Significantamount of works on Hall­Petch coefficients on ferritic steelshave been reported for example by Takaki and his co-workers.28­30) As reported by them, the Hall­Petch coefficient

is highly influenced by contents of carbon and nitrogen.Takeda et al.28) proposed that the relation between the k(MPa(µm)¹0.5) value and the carbon content Cppm (ppm) isprovided by the following equation.

k ¼ 100þ 120Cppm ð3ÞThe k value for the pure iron used in the current study(12 ppmC) is then estimated from this equation as 359MPa(µm)¹0.5, which is not as large as the value of kHPT. Thishigher k value in the HPTed samples (kHPT) might be due tothe grain refinement, as for example proposed by Kamikawaet al.4) They have performed a series of tensile tests forARBed pure Al samples and reported that a significantlylarger k value for UFG Al was obtained compared toconventional pure Al containing much coarser grains. Theyascribed this extraordinary k value to the depletion of mobiledislocations in the highly refined grains. It is thus not veryunnatural to consider that the higher k values are obtainedalso in bcc iron due to the similar mechanism. In fact, Tsujiet al.3) reported that the Hall­Petch coefficient for IF steelobtained by ARB and the post-deformation annealingtreatments was estimated as kARB = 500MPa(µm)¹0.5 asshown in Fig. 7(b). This is markedly higher than the valuereported by Takaki and his co-workers,28,30) whereby theyestimated the k value for IF steel with coarser grains tobe around 180MPa(µm)¹0.5. This value kcoarse and thecorresponding data points are also plotted in Fig. 7(b).The difference between kARB and kcoarse also supports theidea that the Hall­Petch coefficient is enhanced by grainrefinement.

Another remarkable point is that the interceptions are quitedifferent between the slopes of the HPTed and ARBedsamples but nevertheless their inclinations are relativelysimilar. The interceptions in this figure represent the strengthindependent of the grain boundary strengthening mechanism.In this particular situation, the main contribution ispresumably due to the intragranular dislocations that wouldhave been annihilated by post-ARB annealing. Hence, it issupposed that the density of the intragranular dislocations inas-HPTed samples is higher than in the samples after thepost-ARB annealing treatments, resulting in the the differ-ence in the interceptions.

Fig. 7 (a) The evolution of grain size and the fraction of high angle grain boundaries with increasing equivalent strain. The data obtained by ARB15) are alsoplotted as a reference. (b) The Hall­Petch plot of the HPTed pure iron. The k values reported in literature are also included.28) C. R. in this figure stands forcold rolling.

A. Hosokawa, S. Ii and K. Tsuchiya1102

4.4 3D grain morphology vs. work hardening behaviorThe biggest advantage of the 3D-EBSD technique is that

the 3D morphology of the grains can be visualized. Workhardening behavior is probably influenced by the evolution ofthe grain morphology during deformation. Unfortunately, wehave performed the 3D-EBSD measurement only for onsingle HPTed sample (heq ¼ 6:96) at this moment. It is thusdifficult to discus how the 3D grain morphology affect thework hardening behavior from the current investigation.Nevertheless, it is remarkable that the 3D-EBSD techniqueallows us to visualize the 3D grain morphology in the as-HPTed fine grained structure with a quite good IQ value. The3D observations of the region with much lower strain(heq ¼ 1­2) are the tasks to be performed, providing asolution to the discussion here.

5. Conclusions

The work hardening behavior of pure iron was studied bycoupling the HPT deformation with Vickers microhardnesstesting. Moreover, the microstructure and the texturedevelopment during HPT deformation were also investigatedby means of the EBSD technique. The 3D EBSD techniquealso successfully visualized the 3D grain structure and theorientations of the UFG pure iron produced by HPTdeformation. Work-hardening in iron observed in HPT wasfound to be less than that of wire drawing probably due to thedifferent deformation texture. The final texture obtained byHPT is {110} being parallel to the disc plane which preventsthe linear work hardening beyond the equivalent strainheq � 4, resulting in an inflection in the equivalent stress­strain curve. The distribution of misorientation anglebecomes quite randomized, showing good agreement withthe Mackenzie plot at larger strain. The grain size seems tokeep decreasing moderately up to heq � 7, following therapid grain refinement up to heq ¼ 4. It was found that theHall­Petch coefficient (k) obtained in the HPTed pure ironbecomes much larger due to the significant grain refinement,showing reasonable agreement with the k obtained by ARB.It is the Hencky strain that makes it possible to compare themagnitude of the accumulative plastic strain applied by HPTwith that by ARB.

Acknowledgment

This work is supported by a Grant-in-Aid for ScientificResearch from the MEXT, Japan, in Innovative Areas “Bulk

Nanostructured Metals”. Ms. Yuka Hara is acknowledged forher assistance in the FIB-SEM experiments. The authorsthank Dr. Julien Rosalie for his valuable comments and proofreading.

REFERENCES

1) R. Z. Valiev, R. K. Islamgaliev and I. V. Alexandrov: Prog. Mater. Sci.45 (2000) 103­189.

2) M. A. Meyers, A. Mishra and D. J. Benson: Prog. Mater. Sci. 51 (2006)427­556.

3) N. Tsuji, Y. Ito, Y. Saito and Y. Minamino: Scr. Mater. 47 (2002) 893­899.

4) N. Kamikawa, X. Huang, N. Tsuji and N. Hansen: Acta Mater. 57(2009) 4198­4208.

5) K. Edalati and Z. Horita: Acta Mater. 59 (2011) 6831­6836.6) M. Hafok and R. Pippan: Int. J. Mater. Res. 101 (2010) 1097­1104.7) Y. Todaka, M. Yoshii, M. Umemoto, C. Wang and K. Tsuchiya: Mater.

Sci. Forum 584­586 (2008) 597­602.8) R. Z. Valiev, Y. V. Ivanisenko, E. F. Rauch and B. Baudelet: Acta

Mater. 44 (1996) 4705­4712.9) K. Edalati, T. Fujioka and Z. Horita: Mater. Trans. 50 (2009) 44­50.10) S. Descartes, C. Desrayaud and E. F. Rauch: Mater. Sci. Eng. A 528

(2011) 3666­3675.11) Y. V. Ivanisenko, R. Z. Valiev and H.-J. Fecht: Mater. Sci. Eng. A 390

(2005) 159­165.12) J. Baczynski and J. J. Jonas: Acta Mater. 44 (1996) 4273­4288.13) E. Aernoudt and J. G. Sevillano: J. Iron Steel Inst. 211 (1973) 718­725.14) G. Langford and M. Cohen: Trans. ASM 62 (1969) 623­638.15) N. Kamikawa and N. Tsuji: Mater. Trans. 53 (2012) 30­37.16) T. Hara, K. Tsuchiya, K. Tsuzaki, X. Man, T. Asahata and A. Uemoto:

J. Alloy. Compd. (2013) S717­S721.17) J. G. Sevillano, P. van Houtte and E. Aernoudt: Prog. Mater. Sci. 25

(1981) 69­412.18) S. Onaka: Philos. Mag. Lett. 90 (2010) 633­639.19) R. Hill: The Mathematical Theory of Plasticity, (Oxford University

Press, 1950).20) J. K. Mackenzie: Biometrika 45 (1958) 229­240.21) A. A. Gazder, W. Cao, C. H. J. Davies and E. V. Pereloma: Mater. Sci.

Eng. A 497 (2008) 341­352.22) A. Hohenwarter and R. Pippan: Mater. Sci. Eng. A 527 (2010) 2649­

2656.23) C. M. Young, L. J. Anderson and O. D. Sherby: Metall. Trans. 5 (1974)

519­520.24) S. C. Shrivastava, J. J. Jonas and G. Canova: J. Mech. Phys. Solids 30

(1982) 75­90.25) S. Onaka: Philos. Mag. 92 (2012) 2264­2271.26) S. C. Shrivastava, C. Ghosh and J. J. Jonas: Philos. Mag. 92 (2012)

779­786.27) J. J. Jonas and S. C. Shrivastava: Mater. Trans. 54 (2013) 415­416.28) K. Takeda, N. Nakada, T. Tsuchiyama and S. Takaki: ISIJ Int. 48

(2008) 1122­1125.29) S. Takaki, K. Kawasaki and Y. Kimura: J. Mater. Process. Technol. 117

(2001) 359­363.30) S. Takaki: Mater. Sci. Forum 654­656 (2010) 11­16.

Work Hardening and Microstructural Development during High-Pressure Torsion in Pure Iron 1103