on the generation of nanograins in pure copper through uniaxial single compression

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On the generation of nanograins inpure copper through uniaxial singlecompressionB. Zhang a & V.P.W. Shim aa Impact Mechanics Laboratory, Department of MechanicalEngineering , National University of Singapore , 9 EngineeringDrive 1, Singapore 117576, Republic of SingaporePublished online: 05 Jul 2010.

To cite this article: B. Zhang & V.P.W. Shim (2010) On the generation of nanograins in purecopper through uniaxial single compression, Philosophical Magazine, 90:24, 3293-3311, DOI:10.1080/14786435.2010.484405

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Philosophical MagazineVol. 90, No. 24, 28 August 2010, 3293–3311

On the generation of nanograins in pure copper through

uniaxial single compression

B. Zhang and V.P.W. Shim*

Impact Mechanics Laboratory, Department of Mechanical Engineering,National University of Singapore, 9 Engineering Drive 1, Singapore 117576,

Republic of Singapore

(Received 15 January 2010; final version received 4 April 2010)

Attempts at generating nanograins through uniaxial single compressionwere made by deforming copper samples at 298K and 77K. At 298K,dynamically-deformed samples (DDS) become softer, in contrast toquasi-statically deformed samples (QDS), which show a hardness closeto the saturation value. The microstructure of DDS is characterised bydeformation twins and equiaxed micron-sized grains, and the observedsoftening is due to the occurrence of recrystallisation (RX). At a reducedtemperature of 77K, nanograins are generated in DDS, whereas QDS showforest dislocations and twins. The generation of nanograins, which evolvethrough rotational DRX, is associated with the formation of shear bandswith an amorphous structure. Compared with twinning, it appears thatamorphisation plays a more pronounced role in high strain rate deforma-tion at reduced temperatures (77K). The hardness of DDS, obtained fromcompression at 77K, exceeds the saturation value by 16%, whereas that ofQDS corresponds approximately to saturation.

Keywords: uniaxial single compression; temperature effect; strain rate;nanograin; twinning; shear band; amorphisation; recrystallisation

1. Introduction

Severe plastic deformation (SPD) is a well-accepted approach to synthesise ultrafineor nanograined metals and alloys, and possesses advantages in overcomingdifficulties associated with other techniques, such as the introduction of porosityfrom inert gas condensation and of impurities from mechanical alloying [1].Equal-channel angular pressing (ECAP) [2], high-pressure torsion (HPT ) [3],accumulative roll-bonding (ARB) [4] and multiple forging (MF) [5] are typicalSPD techniques, which lead to significant grain refinement. However, theseapproaches display two limitations: firstly, the processing time needed is protractedbecause of the generally low strain rates (51 s�1) applied during deformation of asample, and repeated deformation is required to reduce the grain size to the ultrafine(100–1000 nm) or nano (5100 nm) range, e.g. eight passes and four full rotationsare needed respectively for ECAP and HPT to generate a structure with grain sizes

*Corresponding author. Email: [email protected]

ISSN 1478–6435 print/ISSN 1478–6443 online

� 2010 Taylor & Francis

DOI: 10.1080/14786435.2010.484405

http://www.informaworld.com

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of 0.25–0.26 mm in copper [6,7]. Secondly, the grains produced by these techniques,

usually at room temperature (298K), display a minimum size limit, regardless of

the processing method – viz. unidirectional and multidirectional deformation [8].

By employing high strain-rate compression (�104 s�1) on hat-shaped specimens at

room temperature (RT), the microstructure of copper and zirconium were

successfully refined after a single impact, but they still correspond to the ultrafine

regime [9,10]. At a lower temperature (195K) and a low strain rate (10�3 s�1), the

grain size obtained in copper was 0.16 mm after a multiple-forging (MF) process [11];

this is smaller than the saturation value of 0.2mm for RT deformation [12]. However,

multiple forging still involves a sequence of repeated deformation processes. By

combining high strain rate (102� 2� 103 s�1) with low temperature (77K),

nanograins can be induced in copper, but this still necessitates a multiple

deformation process [13].The aim of the present work was to explore the possibility of generating

nanograined structures by a single deformation process. Uniaxial single compression

(USC), which is much simpler to execute and requires less complex equipment

compared to ECAP, HPT, etc., was selected as the deformation mode. Pure copper,

which displays a saturation minimum grain size of 0.2mm based on conventional

SPD (cSPD) – i.e. processing at low strain rate (51 s�1) and RT – was the target

material investigated. As highlighted in the literature [14], the saturation grain size

decreases with an increase in the dislocations that can be stored in a deformed

material. Therefore, the dislocation storage capacity required to facilitate generation

of nanograins should be higher than that associated with the saturation grain size

resulting from cSPD. Since material hardness increases with dislocation density, as

described by Taylor [15], this parameter is used for comparison with the value for

cSPD samples comprising saturation-sized grains; consequently, it is also regarded as

a preliminary indicator of the formation of nanograins. It is noted that the saturation

(Vickers) hardness of severely deformed copper lies within a wide range (100–150)

as reported by various researchers (see Figure 1 of [16]). This study was

directed at investigating the hardness that can be achieved by a single deformation

process – uniaxial compression – in relation to the hardness associated with

saturation-sized grains generated by multiple forging. The approach adopted in this

study focusses on enhancement of dislocation storage by compressing samples at

high strain rates (104–105 s�1) and/or at a low temperature, both of which are

20 m

m

1

3

2

(b)(a)

Figure 1. (a) Optical micrograph showing microstructure of annealed copper. (b) Schematicdrawing showing the 1, 2 and 3 axes.

3294 B. Zhang and V.P.W. Shim

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considered effective in suppressing dislocation recovery, and hence may elevatedislocation density. Uniaxial single compression of samples is conducted at twotemperatures – RT and liquid nitrogen temperature (77K); for both, samples aredeformed quasi-statically and dynamically, and the resulting microstructure andstrength examined. For plastic deformations at RT, Andrade et al. [9] found that theinitial state of a sample (i.e. annealed or initially work hardened to different degrees)affects the final microstructure and mechanical properties after it is subjected tosubsequent impact, whereas Mishra et al. [16] reported that for samples subjected toECAP, the initial state has no influence. This motivates the accompanying objectiveof investigating whether USC leads to a difference in the microstructure(and mechanical properties) arising from different initial states. Two initialconditions are examined – annealed copper and samples work hardened viacompression in two directions.

2. Experimental

2.1. Deformation

As-received polycrystalline OFHC copper (99.99% purity) in the form of 35mmdiameter rods were used to fabricate 12� 12� 20mm cuboid samples by means ofwire-cutting. The samples were then heat treated at 450�C for 3 h; the grain structureafter annealing is shown in Figure 1a. As depicted schematically in Figure 1b,annealed samples were compressed sequentially along mutually orthogonal axes (1, 2and 3); this was repeated several times to yield a refined structure for comparisonwith uniaxially compressed samples. Sequential compression in two-directions(2DC) was also conducted along the 2 and 3 axes to produce hardened samples thatwere subsequently subjected to USC. MF and 2DC at room temperature were bothperformed using a Shimadzu Universal Testing Machine, at a loading rate of0.5mm/min to induce a final true strain ef¼ ln(L0/L) of 0.69 (corresponding to 50%engineering strain) for each axial compression, where L0 and L are, respectively, theinitial and final length of the sample. Table 1 lists the initial conditions of USCsamples, as well as ef and the true strain rate (_e) induced during compression.(The small annealed samples listed in Table 1 were cut from the large sample shownin Figure 1b, taking into consideration the loading capacity of the Universal TestingMachine and the maximum allowable diameter of projectiles launched by thegas gun.)

Table 1. Initial condition of samples; ef and _e induced during uniaxial single compression.

Initial

temperature

Initial

state

Initial size

(Axis ‘2’� ‘3’� ‘1’)

Direction of

compression

Equipment

SUTM Gas gun

ef _e (s�1) ef _e (s�1)

RT Hardened by

2DC

2.1� 2.1� 5.7mm Axis 1 2.7 4� 10�3 2.7 1.3� 105

Annealed

LNT Annealed 2.3 9.4� 10�2 2.3 6.9� 104

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2.2. Tests for microhardness

Deformed samples were polished using 800 grit SiC abrasive paper, followed byanother polishing sequence using 5, 1 and 0.3 mm aluminium oxide abrasive in awater suspension. Subsequently, the Vickers microhardness was measured usinga Matsuzawa Seiko tester model MXT50, which applied a load of 50 gf for 15 s.Care was taken to ensure that the diagonal length of each indentation was no largerthan 1/5 the sample size, and that all indentations were located sufficiently far fromeach other and from the sample edge.

2.3. Microstructure characterisation

Metallographic analysis was carried out based on observations made via an Olympusoptical microscope (model BH2). Prior to examination, sample surfaces werepolished and etched with a solution comprising a mix of HNO3, H3PO4 and C2H4O5

in a 9 : 2 : 9 volume ratio. The microstructure was examined by means of aJEM-2010F transmission electron microscope (TEM) operating at 200 kV. Samplesfor TEM observation were in the form of 3mm diameter discs punched fromdeformed test samples; the discs were mechanically ground to a thickness of around25 mm, and the resulting foil further thinned by ion milling until perforation at thecentre was achieved.

3. Results and discussion

3.1. Microhardness of multiple-forged (MF) and two-direction compression(2DC) samples

Figure 2 shows the variation of the Vickers microhardness (HV) with cumulativestrain for MF and 2DC samples. A pronounced increase in hardness with cumulativestrain is observed up to a true strain of 2.8, after which the hardness appears tofluctuate around a constant value, irrespective of the sequence and mode ofdeformation, such as MF and 2DC. This suggests a saturation value for the HV,which remains essentially unchanged with further strain. The dashed line in Figure 2marks the saturation level of the microhardness, which is obtained by averaging theHV values of MF samples corresponding to different amounts of cumulative strain.For comparison, the saturation HV levels for pure copper studied by others(Belyakov et al. [12], whereby the HV shown is converted from stress by multiplyinga factor of 3/10) or other techniques (ECAP [17]; HPT [18]) are also shown, and thisdemonstrates close correlation with results from the current study. The HVsaturation indicates the occurrence of dynamic recovery, whereby dislocationannihilation accompanies their generation during plastic deformation.

Despite saturation in the HV, the microstructure was observed to evolve withincreasing strain. Figures 3a and 3b show TEM bright-field (BF) images ofMF samples that correspond, respectively, to cumulative true strains of 12.5 and 27in Figure 2. As can be seen, the (sub)grain structure is finer for larger cumulativestrains; this results from further subdivision of existing grains with increasing strain.However, subdivision does not occur when the grain size has been reduced to a


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critical value, as pointed out by Humphreys et al. [19]; this defines the existence ofa saturation minimum grain size.

3.2. Evolution of mechanical properties and microstructure of uniaxial singlecompression (USC) samples at 298K

Quasi-statically deformed 2DC samples (Figure 2) with a cumulative true strain of8.3 (sum of uniaxially-applied true strains) were subjected to subsequent uniaxialsingle compression (USC); this was done at quasi-static rates for some samples andunder impact loading for others. Samples subjected to six cycles of 2DC deformation

Figure 2. Variation of HV with cumulative true strain for MF and 2DC copper samples.

(a) (b)

Figure 3. Bright-field TEM images of samples after multiple forging: (a)P

e¼ 12.5;(b)

Pe¼ 27.


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(denoted as 2D6C samples) assume a geometry similar to that of a short rod with a

square cross-section of about 2mm. The resulting rod is then cut into several shorterlengths, measuring 5.7mm each. These are then deformed by impact compression

along their longer length, by means of a cylindrical steel projectile propelled by a gasgun. The strain-rate imposed on these specimens depends on their length and theprojectile velocity. (Details of the test samples are given in Table 1.)

Figure 4 shows how the resulting HV of 2D6C samples varies with the strain rate

imposed during the final uniaxial compression. For low strain rates, there isnegligible change in the HV, which is consistent with the results in Figure 2;

however, the hardness decreases significantly for samples deformed by impact.This observation suggests that high-rate deformation affects the microstructure, andtherefore warrants investigation.

Figure 5 shows the microstructure of a 2D6C sample before and after impact;

Figure 5a depicts elongated grains, whereas twins (indicated by arrows) andnewly-formed equiaxed grains are observed in Figure 5b. The significant drop in the

HV (Figure 4) and the difference in microstructures between Figures 5a and 5b pointto the occurrence of recrystallisation (RX).

The generation of deformation twins is a typical characteristic of high strain-ratedeformation, which has been reported for oxygen-free electronic copper [20] and

copper alloys [21]. As discussed in [22], the thickness of twins measured using opticalmicroscopy is overestimated compared to values derived from TEM. Current TEM

measurements show that the thickness of twins ranges from 60 nm to a few mm.A noteworthy feature of the twins generated in the present study is their intersections

at various angles (e.g. TW1 and TW2 in Figure 6). Figure 6a shows that dislocationsare present at the boundaries of twins, a typical characteristic of deformation twins,

whereas annealing twins usually display dislocation-free boundaries [23]. Theboundary defining the intersection between TW1 and TW2 comprises straight lines.Another result of the interaction between TW1 and TW2 is the generation of a short

Figure 4. Variation of HV with strain rate for compression of 2D6C copper.


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third twin (TW3), which does not align with either TW1 or TW2. Figures 6b and 6cshow, respectively, the diffraction patterns of TW2 and TW3; the diffraction spotsassociated with the matrix surrounding the twin and that of the twin are denoted,respectively, by the subscripts ‘M’ and ‘T’, and are symmetric with respect tothe {111} plane, indicating a typical {111}/[112] type twin relationship.

The HV of initially annealed samples compressed at low and high strain rates are,respectively, 121.2 and 71.3. The former is consistent with Figure 2, whereas the

Figure 6. (a) Bright-field TEM image showing intersection of TW1 and TW2 and twinning ata third orientation (TW3). (b) (110) diffraction pattern of TW2. (c) (011) diffraction patternof TW3.

(a) (b)

Figure 5. Optical images showing microstructure of 2D6C copper. (a) Before impact;(b) after impact.


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latter indicates the occurrence of RX, similar to that for 2D6C samples subjectedto impact.

3.3. Evolution of mechanical properties and microstructure of samples subjected touniaxial single compression at 77K

Unlike the USC tests at 298K, in which both initially hardened and annealedsamples are used (Table 1), the tests at 77K involve only annealed samples becausethe results in Section 3.2 have demonstrated that a difference in the initial state(i.e. work hardened vis-a-vis annealed) yields negligible differences in the mechanicalproperties (and the grains) of deformed samples. Figure 7 shows the HV of copperafter compression at a common initial temperature (77K) but at different strainrates. The average HV of quasi-statically deformed samples is slightly higher than thesaturation HV of samples prepared at RT, whereas that of dynamically deformedsample exceeds the saturation HV by 16%.

Figure 8 shows TEM bright-field images of quasi-statically deformed samples.The roughly homogenous distribution of dislocations, identified by arrows,indicates the suppression of dynamic recovery because of the low temperature,which retards the formation of low-energy cells in these regions. This maintains thehigher dislocation density compared to cases where recovery occurs at RT, and thusmay account for the slight increase in the HV compared to quasi-statically deformedspecimens. In addition, a structural feature of significance is the aggregation ofbands of nano-sized width within the white dashed frame in Figure 8a; this isdiscernible by the varying contrast defining the bands. A higher magnification imageof the outlined region is given in Figure 8b, and selected area electron diffraction(SAED) patterns are shown in Figures 8c and 8d, which correspond, respectively, tothe areas bounded by the small and the big circles in Figure 8b. Figures 8c and 8ddisplay identical diffraction spots, which reveal a twin-relationship among the bands,as can be seen from the indices in Figure 8c. These nano-sized multiple twins arecomparable in size with those produced by dynamic plastic deformation at strain rate

Figure 7. HV values of samples deformed at different strain rates. (a) 9.4� 10�2 s�1;(b) 6.9� 104 s�1.


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of 103 s�1 [24,25], though smaller in amount. This generation of twins reflectslocalised deformation in regions where the stress is sufficiently high to nucleate them.

Figure 9 shows typical TEM images of dynamically deformed samples (DDS).Figure 9a is a bright-field image, whereby a white band is surrounded bynanoparticles identified by a distinct contrast, whereas Figure 9b is the dark-fieldimage corresponding to Figure 9a. SAED patterns are obtained, respectively, forareas outlined by the small and big circles in Figure 9a, and these are shown inFigures 9c and 9d. The uniform colour intensity of the band in Figures 9a and 9b, aswell as the diffused halo rings in Figure 9c, indicates the formation of an amorphousstructure in the band. The SAED pattern in Figure 9d, is characterised by theoverlapping of two patterns that correspond respectively to an amorphous and apolycrystalline structure, with their indices annotated. This suggests that in thevicinity of the amorphous band, nano-sized grains with a wide range ofmisorientation angles are generated.

The amorphous bands in DDS, usually 20–500 nm in thickness, either cut acrossthe crystalline area with a nearly straight boundary, or form an enclosed areasurrounded by crystalline regions; they occur at random separations from oneanother. Figure 10a shows an image with a region wherein two bands, denoted by

Figure 8. (a) Bright-field TEM images of quasi-statically deformed samples. (b) Magnificationof area outlined in (a). (c, d) Respective SAED patterns of the areas in the small and largecircles in (b).


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(c)

(111)

(200) (220)(222)

(311)(d)

(a) (b)

Figure 9. TEM images of dynamically deformed samples: (a) BF image; (b) DF image;(c) SAED pattern corresponding to small circle in (a); (d) SAED pattern corresponding tolarge circle in (a).

(c) (d)

(a)

B1 B2

(b)

B1

B2

Figure 10. TEM images showing area with two shear bands: (a) BF image; (b) DF image;(c) BF image corresponding to circle in (b); (d) DF image of (c).


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‘B1’ and ‘B2’, are close to each other. These two bands are similar in shape to that inFigure 9. However, a dark-field image of B1 in Figure 10b displays a few regions thatare notably whiter, indicating the diffraction of electron beams there, possibly due tothe presence of crystals. In contrast, B2 and the band in Figure 9 are totally dark.(The possible coexistence of amorphous and crystalline structures in the band isdiscussed later.) The microstructure in the region between B1 and B2 is analogous tothat around the band in Figure 9. A magnified bright-field image of the area circledin Figure 10b is shown in Figure 10c, whereas Figure 10d is the dark-field imagecorresponding to Figure 10c. The continuous rings of the SAED pattern, depicted bythe inset of Figure 10c, demonstrate the formation of a polycrystalline structure withrandom crystallographic orientations. The grain size, as seen from Figures 10cand 10d, is of the order of several nanometres.

Figure 11a depicts a bright-field TEM image in which bands are discernible fromthe areas of distinct contrast. The inset in Figure 11a is the corresponding SAEDpattern; this indicates the presence of both amorphous and polycrystalline structures.A comparison of Figures 11a and 11b reveals regions (indicted by dashed arrows)within a band that exhibit significant contrast with the band, but are similar inappearance to areas outside the bands. This feature of the bands is identical to thatof B1 in Figure 10. Figures 11c and 11d show, respectively, SAED patterns of areas‘1’ and ‘2’ in Figure 11a. In contrast to Figure 11c, a number of diffraction spotsemerge in Figure 11d and tend to form rings corresponding to those forpolycrystalline copper. This confirms that the regions indicated by the arrows in

(d)(c)

(b)(a)

1

2

Figure 11. (a) Bright-field TEM image. (b) Dark-field TEM image corresponding to (a).(c) SAED pattern of area ‘1’ in (a). (d) SAED pattern of area ‘2’ in (a).


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Figure 11a maintain a crystalline microstructure. The existence of crystals within theamorphous bands indicates that the strain or strain rate is non-uniform, even withina band, and that a critical strain is required to transform the crystalline structure intoan amorphous one; a strain lower than this leads only to the generation of smallergrains but no amorphisation. The crystalline region, indicted by the solid arrow inFigure 11a, separates that particular band into two parts. This is possibly thelocation where the two separated bands initiate or terminate, or a localised area ofrelatively small strain within a band like those marked by the dashed arrows.

Figure 12a shows a region with multiple bands. The SAED patterns of thenarrowest and thickest bands, indicated by solid arrows, are shown, respectively,

A

B

C

(a) (b) (c)

(d) (e) (f)

(g) (i)(h)B

C

Figure 12. (a) Bright-field TEM image showing multiple bands. (b, c) Respective SAEDpatterns corresponding to the narrowest and thickest bands in (a). (d) Magnification ofbright-field image of area outlined in (a). (e) Dark-field image of (d). (f) SAED pattern ofcircle in (d). (g) Bright-field image of area adjoining that in (h). (h) Region left of B and C in(a). (i) Bright-field image of area remote from the bands.


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in Figures 12b and 12c, and demonstrate the formation of an amorphous structurethere. The area outlined in Figure 12a is examined in detail, and Figures 12d and 12eare, respectively, the bright-field and dark-field images of this area at highermagnification. The SAED pattern of the region circled in Figure 12d is shown inFigure 12f, and indicates the generation of fine polycrystalline grains between thetwo amorphous bands. However, the grains located at a relatively far distance fromthe amorphous bands, such as those bounded by the dashed lines in Figure 12e, arelarger than those nearer the bands. This is different from Figure 10, where the grainsize is roughly uniform in the region between shear bands, and the difference isaccounted for as follows. The shear strain decreases with distance from a shear band(this is indicated by an increase in grain size), and the direction of shearing followsthat of the shear band. When two shear bands which have the same direction of shearoccur in close proximity to each other, the superposition of their influence on theregion between them is constructive, resulting in a smaller variation of strain(i.e. more uniform small grains). The converse takes place when the directions ofshearing in neighbouring shear bands oppose each other; this produces an increasedvariation in the shear strain between the bands, and thus a noticeable variation ingrain size as that shown in Figure 12e. The assumption that regions closer to a shearband have larger local strains is supported by Figures 12g–12i. The shear bands,indicated by the letters B and C in Figure 12h correspond, respectively, to the bandswith the same labels in Figure 12a, while the region shown in Figure 12g connects tothe left of that in Figure 12h. It is observed that, the size of crystalline grainsincreases with distance from a band, reflecting a decrease in the localised strain.Figure 12i shows an area relatively far (about 10 mm) from a band, where the grainsare noticeably larger. These results indicate that deformation inside the sample isheterogeneous, and that the generation of nanograins is associated with theformation of amorphous bands.

With regard to the bands mentioned, which display SAED patterns correspond-ing to an amorphous structure, it could be postulated that they formed duringthinning of samples by ion milling for TEM observation. However, amorphousregions that are associated with TEM sample preparation usually exist at the edge ofthe hole in the sample. The amorphous regions, such as those shown in Figures 9–12,are not at the periphery of the hole. Furthermore, the diffused ring SAED patterns,such as those in Figures 9c and 11c, correspond only to the shear bands, whereas theregions adjacent to the bands show SAED patterns comprising continuous rings(e.g. Figures 10c and 12f ), which are characteristic of a polycrystalline structure.This indicates that the amorphous phase of the shear bands originates from plasticdeformation rather than post-deformation treatment, such as ion milling ofdeformed samples; if it were the latter, there would not be such distinct differencesbetween an amorphous band and its adjacent regions. Figure 13 shows a typicalhigh-resolution TEM (HRTEM) image of a shear band displaying a diffused ringSAED pattern. Although a crystal lattice (marked by the solid arrow) is discernible,the dominant structure within the band comprises a disordered arrangement ofatoms, as indicated by the dashed arrows. This gives rise to SAED patternscharacteristic of an amorphous state. Bearing in mind that the purity of the OFHCcopper samples in this study is rated at 99.99%, it is reasonable to assume thatinclusions, and therefore their possible participation in precipitating amorphous


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phases during plastic deformation, are negligible. Moreover, the diffraction spots

corresponding to a generic area in the band, shown in Figure 11d, are indicativesolely of copper, confirming the absence of inclusions in contributing to the

formation of the amorphous phase. Therefore, the generation of the amorphous

regions arises from localised deformation at high strain rates rather than thepossibility of inclusions being present and playing a part in this. It is noted that the

amorphous phases are found in only some of the shear bands (others comprisedsolely ultrafine and nanograins, similar to the observations of [9,26,27]); in general,

they do not occur on their own, but together with nanograins (e.g. Figures 11a

and 13). This indicates that these amorphous structures emerge after grains withinthe bands have been reduced below a critical size. The critical grain size and thus the

localised strain corresponding to the generation of amorphous phases within shear

bands cannot be deduced from the current study. Consequently, the localisedtemperature and strain rate at which amorphisation takes place, as well as the

duration of this process (which is definitely shorter than that for the entiredeformation), are unknown and constitute a topic for future consideration.

Nevertheless, the current work substantiates the results of previous molecular

dynamics simulations [28], which show that amorphisation is a mechanismassociated with plastic deformation of pure copper.

The microstructure of dynamically-deformed specimens can be summarised as

follows: (1) amorphous bands form in regions where the localised strain is large,whereas in other regions, a crystalline structure is preserved; (2) nanograins generally

occur near the amorphous bands, but the grain size increases to exceed 100 nm in

regions sufficiently far from the amorphous bands; (3) the distribution of nanograinsbetween amorphous bands is related to the direction of shearing by which the bands

are formed. Twinning is an important mechanism to accommodate plastic

deformation, as concluded by Tao and Lu [29]. However, they are rarely found inDDS in the current study. Instead, amorphous bands are readily observed. This is

consistent with simulation results that point to amorphisation playing a role inaccommodating plastic deformation at high strain rates, in the same way twining

Figure 13. HRTEM image of a shear band displaying a diffused ring pattern (inset is the liveFFT view of the entire image).


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does at low strain rates [28]. It appears that a strain rate in the order of 104/s is ableto produce amorphous structures in polycrystalline copper at 77K.

3.4. Formation of nanograins in dynamically-deformed specimens

Grain refinement in the vicinity of amorphous bands indicates a RX processassociated with impact deformation. The instantaneous temperature during impactdeformation is estimated from:

T ¼ Ti þ�

�c

Z� de, ð1Þ

where �, e, �, Ti, c and � represent, respectively, the stress, strain, fraction of plasticwork transformed into heat, initial temperature, specific heat and density of copper.The value of c varies with temperature, which is modelled by Banerjee as [30]:

c ¼0:0000416T 3 � 0:027T 2 þ 6:21T� 142:6 forT5 270K

0:1009Tþ 358:4 forT � 270K

�: ð2Þ

� is experimentally determined as 0.7 from uniaxial single compression tests [31],which is similar to values obtained by others for tension and compression, whereasthe often-assumed value of �¼ 0.9 has been reported for samples subjected totorsion [32]. The modified Steinberg–Cochran–Guinan–Lund (SCGL) constitutivemodel, which is considered to predict the stress–strain response for annealed OFHCcopper deformed at 77K and high strain rates more accurately than the frequently-used Johnson–Cook, Zerilli–Armstrong, mechanical threshold stress and Preston–Tonks–Wallace models [30], is adopted to calculate the change in temperature duringimpact and defined by

�ðe, _e,T Þ ¼ ½�a f ðeÞ þ �tð_e,T Þ��ð p,T Þ

�0

, ð3Þ

where �a and �t are respectively the athermal and thermally-activated components ofthe flow stress, f (e) represents strain-hardening, �( p,T ) is the shear modulus thatdepends on pressure p and temperature T, and �0 is a constant. Based onEquation (1), the change in sample temperature with respect to the plastic strain wascalculated and is presented in Figure 14. The dashed vertical line defines the finalstrain of the impacted samples. It can be seen that the temperature at the end ofdeformation does not reach that required for the initiation of RX, i.e. 500K [9], evenif � is assigned a large value of unity. The strain is not uniformly distributed withinthe sample, thus generating a spatial variation in temperature. In the shear bands, thelocalised strain is as high as 101 for OFHC copper [33]. Therefore, the localised strainaround these amorphised shear bands should also exceed the overall macroscopicplastic strain of 2.3. Moreover, a comparison with the findings of Belyakov et al. [12]and Kobayashi et al. [11] suggests the generation of finer grains with a larger strainimposed, and for the generation of grains with sizes of 0.16mm a cumulative strain ofat least 5 is required.

Noting the nanograins generated in the current study, it is envisaged that thelocalised strain in regions containing nanograins should be much larger.


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Nevertheless, assuming that the localised strain in regions near the shear bands is

only 1.5 times that of the overall final strain (i.e. 1.5� 2.3¼ 3.45), then the respective

final temperatures are 512.4K and 642.4K for �¼ 0.7 and �¼ 1 according to thecurves in Figure 14. These two temperatures exceed the critical temperature for

initiation of RX. However, investigations [9,26] have demonstrated that for metals,

the heat generated in small localised regions after deformation will be rapidlyconducted into their surroundings, so that RX is unable to occur via conventional

nucleation and grain growth, but rather by rotational DRX. Rotational DRX is a

process during which dislocation cells gradually transform into subgrains and then

into high angle grains driven by the minimisation of the interfacial energy; thekinetics for rotational DRX follow a function of temperature and time, as defined by

Equation (4) [16]:

3 tan � � 2 cos �

3� 6 sin �þ2

3�4ffiffiffi3p

9ln2þ

ffiffiffi3p

2�ffiffiffi3p þ

4ffiffiffi3p

9lntan �=2ð Þ � 2�

ffiffiffi3p

tanð�=2Þ � 2þffiffiffi3p

¼4��D0b exp �Qb=RTð Þ

L1kTt, ð4Þ

where �, �, �, D0b, Qb, R, T, L1, k, t represent, respectively, the subgrain

misorientation, grain boundary energy, grain boundary thickness, a constant relatedto grain boundary diffusion, activation energy for grain-boundary diffusion, the gas

constant, temperature, average subgrain size, the Boltzmann constant and time. The

values of �, �, D0b, Qb, R and k can be obtained from the literature [16], whereas

L1¼ 20 nm corresponds to the current study. According to the mechanism ofrotational DRX, a rotation angle of 0.52 radians is required for the formation of

recrystallised grains. Figure 15 shows the variation of grain misorientation with time

for two temperatures, and indicates that the higher the sample temperature, theshorter the time needed for accomplishment of RX. Moreover, for both the

Figure 14. Variation of temperature with strain, predicted using modified SCGL model.


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temperatures in Figure 15, the time for RX is less than that for deformation (33ms).This supports the proposition of rotational DRX accounting for the formation ofnanograins in the current study.

A comparison of properties such as the HV and microstructure of samplesdeformed under different conditions (Table 1) indicates that nanograins are onlygenerated in samples subjected to low temperature (77K) and high-strain-ratedeformation, and occur in regions of large localised strain. The influences of largestrain, high strain rate and low temperature on the process of nanograin formationare interpreted as follows: (1) dislocations are generated by plastic strain; (2) with areduced temperature (77K) and high strain rate, the capacity for dislocation storageis enhanced, compared to that of deformation at lower strain rates and highertemperatures; this leads to smaller dislocation cells bounded by a network ofdislocations, especially in regions of large strains; (3) when the temperature increasewith plastic strain exceeds the critical value for initiation of RX, rotational DRXtakes place, resulting in randomly orientated grains. Figures 12 and 14 indicate thata true strain in excess of 2.3 is necessary for both the generation of a nano-sizedstructure and for sufficient temperature elevation to trigger RX.

4. Summary and conclusions

The microstructure and strength of OFHC copper subjected to uniaxial singlecompression at 298K and 77K were investigated. For quasi-static deformation at298K, the hardness reaches a saturation value of 123.6HV when a cumulative strainof 2.8 is imposed; further deformation by multiple forging causes substructurerefinement. This saturation HV value of the hardness is consistent with that reportedfor samples subjected to ECAP and HPT. Samples subjected to high-strain-rateuniaxial single compression at 298K exhibit a decrease in hardness compared withthose deformed quasi-statically; this is the case for both initially hardened and

Figure 15. Variation of angle of rotation of subgrain boundary with time.


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annealed samples. The microstructure of impacted sample is characterised by theformation of deformation twins either individually, or intersecting one another, aswell as equiaxed micron-sized grains. At an ambient temperature of 77K, thehardness of quasi-statically-deformed samples is slightly higher than the saturationHV value. This is attributed to the suppression of dynamic recovery. Nano-scaletwins are observed, but the number is small compared to that produced by dynamiccompression (103 s�1) at 77K [24]. The hardness of dynamically-deformed samplesat 77K exceeds the saturation HV value by 16%. The resulting microstructureincludes nano- and ultrafine grains, as well as shear bands with a composite structureof amorphous and crystalline phases, whereas twins are scarce. Formation of theshear bands results from the occurrence of very high localised strains, and grainsmeasuring several nanometres in size are commonly found near the bands. Thevariation in gain size between neighbouring bands is associated with the direction ofshear that initiates the bands. The nanograins observed are deduced to have beenevolved through rotational DRX, and a true strain exceeding 2.3 is required forformation of such fine grains.

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on the generation of nanograins in pure copper through uniaxial single compression

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