Evaluation of Dislocation Density for 1100 Aluminum with Different Grain Sizeduring Tensile Deformation by Using In-Situ X-ray Diffraction Technique+1

Hiroki Adachi1,+2, Yoji Miyajima2, Masugu Sato3 and Nobuhiro Tsuji4

1Graduate School of Engineering, University of Hyogo, Himeji 671-2280, Japan2Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan3Japan Synchrotron Radiation Research Institute (JASRI), Hyogo 679-5198, Japan4Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan

Ultra-fine-grained (UFG) aluminum with a grain size of 260 nm was fabricated by annealing a severely plastically deformed A1100 alloy.The resulting UFG aluminum exhibited a 0.2% proof stress (·0.2) that was four times larger than that predicted by the conventional Hall-Petchrelation. In this study, the UFG aluminum, the fine-grained aluminum with a grain size of 960 nm and the coarse-grained aluminum with a grainsize of 4.47 µm were prepared. The change in the dislocation density, μ was investigated during tensile deformation using in-situ X-raydiffraction measurements at SPring-8. It was found that as the strain increased, the μ changed in four distinct stages. The first stage wascharacterized by elastic deformation, and little change in the μ occurred. For the coarse-grained aluminum, this stage was almost absent. In thesecond stage, the μ rapidly increased until the stress reaches ·II in which the plastic deformation begins to occur at a constant strain rate. In thethird stage, only a moderate change in the μ occurred. Finally, in the fourth stage, the μ rapidly decreased as the test pieces underwent fracture.Additionally, it was found that the ·0.2-·I was followed by the conventional Hall-Petch relation in all grain size range.[doi:10.2320/matertrans.L-M2015803]

(Received December 21, 2014; Accepted February 10, 2015; Published April 10, 2015)

Keywords: ultra-fine grained aluminum, in-situ measurement, dislocation density, Hall-Petch relation

1. Introduction

The development of severe plastic deformation technique,such as accumulative roll-bonding (ARB),1­3) high-pressuretorsion (HPT),4) equal channel angular pressing (ECAP),5)

has facilitated fabrication of ultrafine-grained aluminum withaverage crystal grain sizes of several 100 nm. When the grainsize in materials with conventional grain sizes is refined, theirstrength is known to empirically rise with the inverse squareroot of the average grain size, in accordance with the Hall-Petch relation.6,7) Kamikawa et al. have reported, however,that although the relation between grain size and 0.2% proofstress (·0.2; MPa) in 99.99% pure aluminum alloy with grainsizes of 20 to 405 µm is ·0.2 = 9.7 + 41d¹1/2,8) where d [µm]is the average grain size, further decreases in grain size bysevere plastic deformation resulted in substantially largerstress than predicted by this equation.8) For d = 1µm, forexample, the previous equation predicts a value of ·0.2 =50.7MPa, but the actual 0.2% proof stress is approximately100MPa, or twice the predicted value. This phenomenon isalso observed for IF steel,9) thus indicating that fine-grainedmaterials sometimes exhibit yield stresses higher thanconventionally predicted by the Hall-Petch curve. Low-temperature annealing of ultrafine-grained aluminum with agrain size of 200 nm fabricated by ARB results insubstantially lower ductility and higher strength than thoseof the as-ARBed material. It has also been reported that whenthe annealed material is rolled at a low reduction ratio itsductility rises to about the same level as-ARBed materi-al.10,11) This phenomenon, known as “hardening by anneal-ing, softening by deformation”, is just the reverse to what

occurs for materials with conventional grain sizes. Thesevarious mechanical phenomena specific to ultrafine-grainedaluminum are not exhibited by materials with conventionalgrain sizes. This suggests that the dislocation behaviorleading to deformation in ultrafine-grained aluminum isdiffers from it in conventional grained aluminum, but thedetails remain unclear. In the present study, we consideredthe dislocation behavior and investigated in particular thedislocation multiplication that occurs during tensile deforma-tion, as a means of clarifying how it changes with grainsize.

Several methods can be used to evaluate the dislocationdensity, including electrical resistance measurements,12)

transmission electron microscopy (TEM),13) and X-raydiffraction (XRD). However, electrical resistance measure-ments and TEM encounter specific problems. The contribu-tion of dislocations to the electrical resistance is smaller thanthat of the grain size,12) which may make it difficult toaccurately determine the dislocation density of fine-grainedmaterials, in which the grain boundary density is high. TEMobservations require the preparation of thin-film samples,during which the dislocation density can be reduced near thesurface,14) permitting only local measurement of dislocationdensities. In addition, surface effects may be induced thatchange the dislocation source activity and behavior relativeto those of the bulk material. In the present study, wetherefore applied a method based on XRD, which canprovide averaged information within the scattering volume.The method proposed by Williamson et al. for calculation ofthe dislocation density from the results of XRD measure-ments15­17) requires accurate measurement of the full width athalf maximum (FWHM) for multiple diffraction peaks, andlong measurement times are required in order to obtaindiffraction profiles with a good S/N ratio for a wide range ofdiffraction angles. For this purpose, the crosshead movement

+1This Paper was Originally Published in Japanese in J. JILM 64 (2014)463­469.

+2Corresponding author, E-mail: adachi@eng.u-hyogo.ac.jp

Materials Transactions, Vol. 56, No. 5 (2015) pp. 671 to 678©2015 The Japan Institute of Light Metals

is suspended midway through during tensile testing and thediffraction profile is measured while maintaining thestroke.18,19) In this intermittent measurement procedure,however, stress relaxation occurs while maintaining thestroke, possibly resulting in a lower dislocation density thanin continuous tensile deformation, and thus in underestima-tion. Tomota et al. have reported, for example, that duringtensile testing of IF steel which they suspended midwaythrough, a decline in stress of approximately 25MPaoccurred when neutron diffraction testing was performedwhile the stroke was maintained for 2 ks or 4 ks.18)

For in-situ measurement of the dislocation density duringtensile deformation, it is therefore necessary to develop asystem that permits diffraction profile measurements through-out a wide range of diffraction angles in a very short time.For this reason, we performed the experiments of the presentstudy using the high brightness X-rays available at theSPring-8 synchrotron radiation facility.

2. Experimental Procedures

An A1100 alloy of 1mm thickness was homogenized at673K for 7.2 ks and then cooled to room temperature.Table 1 shows the chemical compositions of A1100 alloy.The specimen was then subjected to 8 cycles of ARB at roomtemperature, thus the specimens of 0.5mm thickness wereobtained.1) Because the thickness reduction is 50% per cycleby rolling in the ARB process, the total applied equivalentstrain was 6.4. The crystal grain size was then adjusted bylow-temperature annealing, to obtain three types of materials:(1) materials annealed at 373K for 1.8 ks, (2) materialssubjected to pre-annealing at 448K for 21.6 ks and then post-annealed at 498K for 1.8 ks; and (3) materials subjected topre-annealing at 448K for 21.6 ks and then post-annealed at573K for 1.8 ks. The two-step annealing was performed insome materials to suppress abnormal grain growth during thepost-annealing using a low-temperature pre-annealing.8)

From the resulting sheet materials, tensile-test specimenswere prepared so that the rolling direction (RD) would agreein the tensile direction. The shape of the tensile-testspecimens is shown in Fig. 1.

Normal direction-transverse direction (ND-TD) crosssections of the specimens were mechanically mirror polishedusing SiC polishing paper, chemical-mechanical polishingusing colloidal silica, and then subjected to electron beambackscatter diffraction (EBSD) measurements at an accel-eration voltage of 15 kV, in an oriented imaging microscopy(OIM) system provided by TSL, and equipped on a JSM-6500F scanning electron microscope provided by JEOL Ltd.The ND spacing of high-angle grain boundaries was thenmeasured, thus this spacing was considered to be a grain size.

In-situ measurement for changes in dislocation densityduring tensile deformation requires diffraction profilechanges over a wide range of diffraction angles in a short

time. We utilized the high-brightness X-ray BL-19B2 beamline of the SPring-8 synchrotron radiation facility for thisstudy, with the measurement system shown schematically inFig. 2. The X-ray energy was 25 keV, and the beam size was3mm along the test specimen width direction and 110 µm inthe tensile direction. An imaging plate (IP) was used as thedetector, to allow simultaneous measurement at a wide rangeof diffraction angles with high angular resolution. As an IPdoes not provide time resolution, a slit with a width of 4mmwas placed in front of the IP, and from the start of the tensiletest the IP was moved at 2mm/s perpendicularly to the slit toobtain a record of the diffraction profiles at different times atdifferent positions on the IP. The time resolution of thisexperiment was accordingly 2 s, and the maximum measure-ment time as determined by the IP width was 80 s. Theincident X-rays were perpendicular to the tensile-test speci-men and the IP was tilted 14.7° upward from the horizontaltransmission direction, with a distance of 716.6mm from thespecimen to the IP, thus enabling simultaneous measurementof diffraction peaks associated with (111), (200), (220), (311),and (222) planes. Profile fitting of the obtained diffractionpeaks was performed using the pseudo-Voigt function, andthe FWHM was obtained. The tensile test was performedwith an initial strain rate of 8.3 © 10¹4 s¹1 at room temper-ature. The area of necking or fracture in a specimen was notirradiated with X-rays, and the measurement results are notfor regions near fractures.

3. Results

Figures 3(a), (b) and (c) show ND-RD cross-sectional

Table 1 Chemical composition of A1100 alloy in mass%.

Si Fe Cu Mn Zn Al

0.12 0.53 0.13 0.02 0.01 99.19

Fig. 1 The shape of tensile test pieces.

Fig. 2 A schematic illustration of the in-situ XRD measurement system.

H. Adachi, Y. Miyajima, M. Sato and N. Tsuji672

grain boundary maps of specimens with grain size adjustedunder different annealing conditions. The specimen inFig. 3(a) was annealed at 448K for 21.6 ks and then 573Kfor 1.8 ks. Its crystal grains are almost equiaxed, and themeasurements showed an average high-angle grain boundaryspacing of 4.47 µm in the ND. Such specimens are hereafterdenoted to as the coarse-grained (CG) material. The specimenin Fig. 3(b) was annealed at 448K for 21.6 ks and then 498Kfor 1.8 ks. Its grains are somewhat more equiaxed than thoseof the specimen shown in Fig. 3(c). In this specimen, graingrowth had occurred. The measurements showed an averageND spacing of 960 nm between high-angle grain boundaries.Such specimens are hereafter referred to as the fine-grained(FG) material. The specimen shown in Fig. 3(c) wasannealed at 373K for 1.8 ks. Many of its grains exhibit RDelongation, and it contains rather few observable low-anglegrain boundaries within its grains. The measurements showedan average ND spacing of 260 nm between high-angle grainboundaries. This value was taken as the grain size, and suchspecimens are hereafter denoted to as the ultrafine-grained(UFG) material.

Figure 4 shows the stress-strain curves obtained by in-situXRD measurements. The strain was calculated from changesin strokes of tensile tester, and therefore includes deformationof the tensile tester. The UFG material exhibited a continuous

(a)(b)

(c)

Fig. 3 TD inverse pole figure maps of ND-RD planes, (a) in the coarse grained (CG) aluminum, (b) in the fine grained (FG) aluminum and(c) in the ultra-fine grained (UFG) aluminum. Black lines correspond to the boundaries of misorientation angle > 15 degree. White linescorrespond to the boundary of misorientation angle < 15 degree.

Fig. 4 Nominal stress-strain curves for the CG, FG and UFG aluminumduring in-situ XRD measurements.

Evaluation of Dislocation Density for 1100 Aluminum with Different Grain Size during Tensile Deformation 673

yield. Its 0.2% proof stress (·0.2) at a strain of ¾0.2 = 1.22%was 302MPa. When work hardened to a strain of 3%, itreached a tensile strength of 373MPa and thereafter exhibiteda gradual decline in stress accompanying local deformation,and fractured at a strain of 4.9%. The FG material exhibiteda 0.2% proof stress of ·0.2 = 205MPa at ¾0.2 = 0.98%,immediately followed by its indication of a maximumstrength of 207MPa, and thereafter exhibited a sharp declinein stress by approximately 10 Pa. Its strength at a strain of1.16% was 193MPa. As an fcc metal, aluminum usuallyexhibits a continuous yield, but discontinuous yields reportedto occur in cases where its grains have been refined.8) The FGmaterial subsequently exhibited a gradual decline in stressaccompanying local deformation, and fractured at a strain of2.3%. Despite the annealing further progressed and the grainsbecame coarser, its ductility declined. The CG materialexhibited a continuous yield, but the slope in the linear strainregion from 0% to 0.8% was smaller than that for the UFGand FG materials. With this linear region taken as a region ofelastic deformation, the 0.2% proof stress was ·0.2 = 78MPa.If calculated on the basis of the same slope observed for theelastic regions of the UFG and FG materials, the 0.2% proofstress would then be ·0.2 = 28MPa at ¾0.2 = 0.31%. Abovea strain of 0.8%, the CG material exhibited moderatelyincreasing strength with rising strain. Because of its highplastic elongation, it did not fracture during the in-situ XRDmeasurements.

Figure 5 shows the effect of strain on the (111) diffractionpeak for the UFG material. The shape of the diffraction peakat a strain of 0.66% was largely unchanged from that of thenon-loaded state, but the peak angle shifted downward. Thisdownward shift of the peak angle represents an increase inthe (111) plane spacing in the tensile direction as a result ofelastic deformation.

At a strain of 1.49%, the elastic deformation resulted in afurther downward shift in the peak position beyond that at astrain of 0.66%, and an increase in diffraction peak width. Anincrease in the strain to 2.49% resulted in a further increasein the peak width but little or no change in the angle. Theincrease in the peak width may be caused by a heterogeneousincrease in strain or by a decrease in crystallite size, either orboth of which might have occurred in the progress of theplastic deformation. The effects of heterogeneous strain andcrystallite size on the peak width can be distinguished byapplying the Williamson-Hall equation15)

�2ª cos ª

­¼ 0:9

Dþ 2¥

sin ª

­ð1Þ

where ¦2ª is the FWHM of the diffraction peak, ª is thediffraction angle, ­ is the wavelength of the incident X-ray, ¾is the heterogeneous strain, and D is the crystallite size. Bymeasuring ª and ¦2ª for the diffraction peaks and taking2 sin ª/­ as the horizontal axis and ¦2ª cos ª/­ as the verticalaxis, it is possible to determine the heterogeneous strain fromthe slope and the crystallite size from the inverse of thevertical-axis intercept. Figure 6 shows a Williamson-Hallplot for the UFG material, with all of the points on theirrespective straight lines in close accordance with theWilliamson-Hall equation. The plots for the UFG materialin the unloaded state and at strain of 0.66% show little or no

change in both slope and intercept, and also little or nochange in heterogeneous strain and crystallite size. Withfurther increases in strain to 1.49% and 2.49%, the slope ofthe plot gradually increased, indicating increasing heteroge-neous strain, and the intercept also increased slightly,indicating a slight decline in crystallite size due to theincrease in strain.

Based on the heterogeneous strain and crystallite sizeindicated by this Williamson-Hall plot, the dislocationdensity μ can be calculated using17)

μ ¼ 2ffiffiffi

3p

¥

Db; ð2Þ

where b is the magnitude of the Burgers vector.Figure 7 shows the change in the dislocation density of

the UFG material during tensile deformation, as determinedby the in-situ XRD measurement. The change comprisesfour stages, labeled Region I to Region IV in the figure.In Region I, extending from strains of 0% to 0.75%, thedislocation density showed little or no change following thestart of tensile deformation. This is a region of elasticdeformation alone, as indicated in Fig. 5 by the downwardshift in the diffraction angle, but with little or no change in

Fig. 5 (111) diffracted peaks at various nominal strains for the UFGaluminum during in-situ XRD measurements.

Fig. 6 Williamson-Hall plots at various nominal strains for the UFGaluminum.

H. Adachi, Y. Miyajima, M. Sato and N. Tsuji674

shape of the diffraction peak between strains of 0% and0.66%. Plastic deformation arose in the transition fromRegion I to Region II around the onset of sharply risingdislocation density, as is also indicated by the smaller slopeof the stress-strain curve in Region II than in Region I.Denoting the stress, strain, and dislocation density at the timeof transition from Region I to Region II as ·I, ¾I, and μI,respectively, their values were approximately ·I = 220MPa,¾I = 0.75%, and μI = 0.61 © 1014m¹2. The stress ·I was82MPa smaller than the ·0.2 proof stress, dislocationmultiplication began at a substantially lower stress than the0.2% proof stress, and the dislocation density rose toμ0.2 = 1.20 © 1014m¹2 at the strain of the 0.2% proof stress.The dislocation density thereafter rose monotonically to alevel near a strain of 2.16%. On reaching Region III, thedislocation density became essentially constant. Denoting thestress, strain, and dislocation density at the time of transitionfrom Region II to Region III as ·II, ¾II, and μII, respectively,their values were approximately ·II = 361MPa, ¾II = 2.16%,and μII = 2.2 © 1014m¹2. In Region IV, in which the strainwas in excess of 4.65%, the dislocation density fell sharply.This agrees with the strain at the onset of fracturing in the testspecimen, which indicates that the decline in dislocationdensity in Region IV is attributed to a reduction in stressaccompanying fracture. The dislocation density decrease was0.6 © 1014m¹2.

Figure 8 shows the change in the dislocation density in theFG material during tensile deformation, as determined byin-situ XRD measurement. As in the UFG material, thedislocation density changed in four stages, labeled Region Ito Region IV. The dislocation density showed little or nochange following tensile test initiation in Region I but beganto rise when the strain ¾I exceeded 0.60%, marking thetransition to Region II, in which the slope of the stress-straincurve became smaller than in Region I. The stress and thedislocation density at a strain ¾I = 0.60% were ·I = 153MPaand μI = 0.28 © 1014m¹2, respectively. As was the case withthe UFG material, the FG material stress ·I was lower thanthe 0.2% proof stress ·0.2 = 205MPa and the onset ofdislocation multiplication occurred at a stress lower than the0.2% proof stress. The dislocation density was approximatelyμ0.2 = 0.6 © 1014m¹2 at the 0.2% proof stress and increaseduntil the strain reached approximately 1.16%. In Region II, a

decline in stress of approximately 10MPa was observed inthe stress-strain curve, but the cause could not be clearlydetermined given the time resolution and measurementaccuracy of the in-situ measurements in the present study.The decline in stress was not attributed to the onset of mobiledislocation multiplication, as it occurred at a level of stresshigher than ·I. The boundary between Region II andRegion III is not definitive, but if the boundary is taken tobe located at ¾II = 1.16%, the corresponding stress anddislocation densities are then ·II = 194MPa and μII = 0.79 ©1014m¹2. Little or no change in dislocation density wasobserved in Region III until the strain reached approximately2.3%, which marks the onset of test specimen fracture andentry to Region IV, a region in which the dislocation densitysubstantially fell by approximately 0.3 © 1014m¹2, or abouthalf the corresponding fall observed for the UFG material.This indicates the annihilation during unloading of somedislocations that had formed by multiplication underdeformation, more often for fine grain sizes. Since thedislocation density decreases during stress relaxation, it alsomeans that the dislocation densities for pure fine-grainedaluminum under deformation are underestimated in TEMmeasurements after loading and unloading, and also bymeasurements of the diffraction profiles with suspendedcross-head movement in tensile testing. It is also possible thatthe dislocation substructure itself after unloading differs fromthe substructure under deformation. The mechanism of thedislocation annihilation was not clearly determined in thepresent study, but in view of the high crystal grain-boundarydensities in the UFG and FG materials, it may be that thedeformation accompanying the unloading induces movementof the dislocations to the grain boundaries, which act as asink for their annihilation.

Figure 9 shows the changes in the dislocation density ofthe CG material during tensile deformation, as measured byin-situ XRD. In the CG material, at a strain of 0.166%, whichwas the first measurement point following tensile testinitiation, the dislocation density started rising with noobservable presence of Region I. The stress at a strain of0.166% was 14MPa, which indicates that in the CG materialthe stress ·I at which dislocation multiplication begins is lessthan 14MPa. In Region II, the rise in dislocation density withincreasing strain is approximately linear and the dislocation

Fig. 7 Change in the dislocation density with the nominal strain for theUFG aluminum during the in-situ XRD measurement. Greek letterindicates each region. Vertical broken line is the region boundary.

Fig. 8 Change in the dislocation density with the nominal strain for the FGaluminum during the in-situ XRD measurement. Greek letter indicateseach region. Vertical broken line is the region boundary.

Evaluation of Dislocation Density for 1100 Aluminum with Different Grain Size during Tensile Deformation 675

density at a strain of 0% falls on the resulting straight line.This indicates that the stress ·I, marking the onset ofdislocation multiplication, is quite small and very close to0MPa. We accordingly find ·I = 0MPa, ¾I = 0%, andμI = 0.10 © 1014m¹2. The dislocation density then risessubstantially up to a strain of 0.83%, which indicates thatthe stress and strain are linearly related in the region in whichthe strain is less than or equal to 0.83%, but because it is nota region of elastic deformation characteristic of Region I,but rather a region of plastic deformation characteristic ofRegion II, the slope in this Region II of the stress-straincurve of the CG material is smaller than those found in theregion of elastic deformation for the UFG and FG materials.Accordingly, we conclude on the basis of the slope of thestress-strain curves for the UFG and FG materials in Region Ithat the 0.2% proof stress of the CG material is ·0.2 =28MPa, and that ¾0.2 = 0.31% and μ0.2 = 0.18 © 1014m¹2.Beyond a strain of 0.83%, the increase rate in dislocationdensity in the CG material is more moderate than in itsRegion II, which indicates this region may be identified asRegion III. The boundary between Region II and Region IIIis taken as being located at ¾II = 0.83%, and the stress anddislocation density at that time are then ·II = 70MPa andμII = 0.26 © 1014m¹2, respectively.

4. Discussion

The in-situ XRD measurements clearly indicated thatchanges in dislocation density during tensile deformationproceed in four stages, represented as Region I to Region IV.Region I is characterized by elastic deformation with little orno change in dislocation density, Region II by sharplyincreased dislocation multiplication, Region III by moderatedislocation multiplication, and Region IV by a sharp fall indislocation density due to unloading accompanying fracture.

In considering the factors determining the transitionthrough these four regions, let us begin with the transitionfrom Region II to Region III. Region II is a stage of rapidlymultiplying dislocations that proceeds until the dislocationdensity reaches μII, which marks the transition to Region III.As shown by the relation between μII and grain size inFig. 10, μII varies roughly in proportion to the inverse of thegrain size. In Region II and Region III, plastic deformation

proceeds and the shear deformation rate d£/dt may beexpressed as20)

d£

dt¼ μvb ð3Þ

where v is the mean speed of dislocation movement, μ is thedislocation density, and b is the length of Burgers vector. Inconstant-speed tensile testing such as the measurements ofthe present study, d£/dt is constant. In the initial period ofplastic deformation, the dislocation density is low, and inorder to maintain a constant shear deformation rate after thetransition from elastic deformation to plastic deformation it isnecessary to increase the dislocation density or the speed ofdislocation movement. Grain boundaries inhibit dislocationmovement. If the grain size is taken as the approximatemaximum distance of ready movement by the dislocations,then a decrease in grain size should also shorten the movingdistance of ready movement by the dislocation.21) Theaverage speed of dislocation movement is presumably lowerthan that of uninhibited dislocation movement because thetime spent moving within the grains becomes shorter and thetime of immobilization near the grain boundaries becomeslonger. It follows that the maintenance of a constant speed ofdeformation requires a larger increase in dislocation densityin the FG or UFG materials than in the CG materials. Here,let us assume as a rough approximation that the dislocationsmove sufficiently fast within the grains but stop moving nearthe grain boundaries. The average speed of dislocationmovement v is then determined by the density of themovement-inhibiting grain boundaries, and is thus propor-tional to the crystal grain size. It is for this reason that thedislocation density required for constant-speed plasticdeformation is inversely proportional to the crystal grainsize. In short, the sharp rise in dislocation density observed inRegion II presumably occurred to meet the need to attain thedislocation density μII necessary for a constant-speed plasticdeformation. This also explains the larger increase indislocation density in Region II for the UFG material thanfor the FG and CG materials to prevent a decline in the slopeof the stress-strain curve much below that of the plastic-deformation region, and the occurrence of a 0.2% proof stress·0.2 that was substantially higher than the stress ·I at whichdislocation multiplication actually began.

Fig. 9 Change in the dislocation density with the nominal strain for the CGaluminum during the in-situ XRD measurement. Greek letter indicateseach stage. Vertical broken line is the stage boundary.

Fig. 10 Change in dislocation density, μII with the grain size. μII is thedislocation density at the transition point from the stage II to III.

H. Adachi, Y. Miyajima, M. Sato and N. Tsuji676

Figure 11 shows the changes in ·I, ·0.2, and the differencebetween the two, relative to the inverse square root of thegrain size. The dotted line shows the Hall-Petch relation(·0.2 = 9.7 + 41d¹1/2) reported for 99% coarse-grained purealuminum,22) together with its extrapolation to smaller grainsizes. The value of the stress ·0.2 for the CG material, with itsgrain size of 4.47 µm, agrees the value given by the coarse-grain Hall-Petch relation, but those for the FG and UFGmaterials are well above the extension of the coarse-grainHall-Petch relation.

As revealed by the in-situ XRD measurements anddescribed above, ·0.2 occurs in a part of Region II in whichthe dislocation density rises to μII required for constant-speedplastic deformation, and where the dislocation density forthe UFG and FG materials in particular has alreadyrisen substantially. The proof stress ·0.2 therefore does notrepresent the yield stress, which is a measure of the stress atthe start of plastic deformation. If ·I, at which dislocationmultiplication begins, is taken as the stress at the start ofplastic deformation, its value for the UFG and FG materials issubstantially larger than those derived by extension of thecoarse-grain Hall-Petch relation. For the CG material, on theother hand, the measured value of ·I is very close to·I = 0MPa, and thus below the value given by the coarse-grain Hall-Petch relation. Though grain sizes larger than 5 µmwere not investigated in the present study, they too may beexpected to show a ·I value very close to 0MPa in view ofthe known tendency for coarser grains to yield more easily.

It is therefore reasonable to conclude that in purealuminum, dislocation multiplication occurs even underslight stress loading for grain sizes down to approximately5 µm, but is suddenly inhibited for grain sizes of less thanthis. For dislocation multiplication from a Frank-Read sourcewithin the grains, the stress · necessary for activation of thatsource is expressed as23)

· ¼ M®b

Lð4Þ

where M is Taylor’s constant, ® is the shear modulus, b is thelength of the Burgers vector, and L is the dislocation source

length. Given the values · = ·I, M = 3.06, ® = 26GPa andb = 0.286 nm for aluminum, this equation yields dislocationsource lengths of L = 103 nm and L = 149 nm for the UFGand FG materials, respectively. If intra-grain forest disloca-tions are regarded as the Frank-Read sources, as a roughapproximation the forest dislocations are arrayed in a latticeconfiguration with a spacing L, and the dislocation density isthus μ = L¹2. For the UFG and FG materials, this yieldsμ = 0.93 © 1014m¹2 and 0.45 © 1014m¹2, respectively.These values are similar to the values of μI = 0.61 ©1014m¹2 and μI = 0.28 © 1014m¹2, determined from thein-situ XRD measurements for the UFG and FG materials,respectively. This suggests that the small grain size in thesetwo materials resulted in a dislocation source length forready activation that was smaller, and a correspondingincrease in the level of stress required for dislocationmultiplication.

We may now ask what is represented by the conventionallyreported Hall-Petch relation for coarse-grained aluminum.The term ·0.2 is defined as the stress at the time of 0.2%plastic deformation. For the CG material, the stress ·I at theonset of dislocation multiplication is very close to 0MPa andin that case ·0.2 = ·0.2-·I. If we also plot the differencebetween the ·I and ·0.2 values for the FG and UFG materials,as shown in Fig. 11, we find that they are in fact very close tothe values derived by extension of the Hall-Petch relation forcoarse-grained aluminum. This clearly suggests what wasconventionally investigated in the derivation of the Hall-Petch relation for coarse-grained aluminum was not thedependence of the 0.2% proof stress ·0.2 alone on the grainsize, but rather the dependence of a combination of the 0.2%proof stress and the stress at the onset of dislocationmultiplication, expressed as ·0.2-·I.

5. Conclusions

In this investigation on changes in dislocation densityduring tensile deformation of UFG, FG, and CG materialswith grain sizes of 260 nm, 960 nm, and 4.47 µm, respec-tively, the findings obtained by in-situ XRD measurementemploying synchrotron radiation were as follows.(1) The changes in dislocation density that accompany

increasing strain proceed in four stages. The firstcomprises a region of elastic deformation with little orno change in dislocation density, the second a region ofsharply rising dislocation density, and the third a regionof moderate change in dislocation density.

(2) The fourth stage comprises a region of sharplydeclining dislocation density accompanying test speci-men fracture, with a substantially decrease in disloca-tion density in the UFG and FG materials. This decreasebecomes larger with decreasing grain size. This clearlyindicates that the dislocation substructure of FGmaterials during their deformation differs substantiallyto that subsequent to unloading, and that for UFGmaterials, in order to measure the changes in dislocationdensity during deformation, in-situ measurement isnecessary.

(3) In the CG material, the measured value of ·I, whichis the stress at the onset of dislocation multiplication,

Fig. 11 Change in the 0.2% proof stress, ·0.2, the stress ·I and thedifference between ·0.2 and ·I with the grain size. ·I is the stress at thetransition point from the stage I to II. The dash line indicates the Hall-Petch relationship for coarse grained pure aluminums reported by N.Kamikawa.8)

Evaluation of Dislocation Density for 1100 Aluminum with Different Grain Size during Tensile Deformation 677

was close to 0MPa and little or no stage-1 elasticdeformation was observed. In the FG and UFGmaterials, the measured ·I values rose to 153MPa and220MPa, respectively, thus showing that ·I increaseswith decreasing grain size. The ·I values for the lattertwo materials were well above those derived byextension of the Hall-Petch relation for coarse-grainedaluminum.

(4) The dislocation density μII, which marks the transitionfrom the second to the third stage, was found to varyinversely with the grain size, thus increasing withdecreasing grain size. This tendency is presumablyattributed to the required constant-speed plastic defor-mation in the second stage and a consequent rise in thedislocation density for attainment of μII.

(5) It was found that the difference between the value of ·I,the stress at the onset of dislocation multiplication, andthat of ·0.2, the 0.2% proof stress, derived by extensionof the Hall-Petch relation for coarse-grained aluminum.This clearly indicates that the conventionally reportedHall-Petch curve represents the dependence of ·0.2-·I ongrain size, rather than ·0.2 alone.

Acknowledgments

This study was financially supported by the LightMetal Education Foundation, Inc. and the Grant-in Aidfor scientific Research on Innovative Area, “Bulk Nano-structured Metals”, through MEXT, Japan (contract No.22102002), and support is gratefully appreciated. Thesynchrotron radiation experiments were performed atBL19B2 of SPring-8 with the approval of the JapanSynchrotron Radiation Research Institute (JASRI), (ProposalNo. 2011B1923 and 2012A1123).

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