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Acta Materialia 57 (2009) 761–772

Effect of the Zener–Hollomon parameter on the microstructuresand mechanical properties of Cu subjected to plastic deformation

Y.S. Li, Y. Zhang, N.R. Tao, K. Lu *

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, PR China

Received 18 July 2008; received in revised form 13 October 2008; accepted 13 October 2008Available online 10 December 2008

Abstract

Pure Cu was deformed at different strain rates and temperatures, i.e. with different Zener–Hollomon parameters (Z) ranging withinlnZ = 22–66, to investigate the effect of Z on its microstructures and mechanical properties. It was found that deformation twinningoccurs when lnZ exceeds 30, and the number of twins increases at higher Z. The average twin/matrix lamellar thickness is independentof Z, being around 50 nm. Deformation-induced grain refinement is enhanced at higher Z, and the mean transverse grain size drops from320 to 66 nm when lnZ increases from 22 to 66. The grain refinement is dominated by dislocation activities in low-Z processes, whiledeformation twinning plays a dominant role in high-Z deformation. An obvious increment in yield strength from 390 to 610 MPawas found in deformed Cu with increasing Z, owing to the significant grain refinement as well as the strengthening from nanoscale defor-mation twins.� 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Copper; Plastic deformation; Nanostructures; Zener–Hollomon parameter; Nanoscale deformation twinning

1. Introduction

Plastic deformation with high strains (or so-called severeplastic deformation, SPD) is one of the most importantmethods for producing ultrafine-grained (UFG; grain sized in the submicrometer regime) metallic materials, whichexhibit enhanced strength and hardness relative to theircoarse-grained (CG) counterparts [1]. The microstructuresand mechanical properties of metals and alloys subjectedto SPD, such as by equal channel angular pressing (ECAP)[2] and high-pressure torsion (HPT) [3], have been muchinvestigated over the years. Grain refinement in SPD met-als is in fact not fundamentally different from that in sam-ples deformed by conventional cold-rolling or drawing[4,5], and their mechanical properties are very similar.For example, both the SPD processes and the cold-rollingcan eventually refine grains of pure Cu down to a few

1359-6454/$34.00 � 2008 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2008.10.021

* Corresponding author.E-mail address: lu@imr.ac.cn (K. Lu).

hundred nanometers upon extending straining, with asaturation yield strength of about 400 MPa [6]. Furtherincreasing the plastic strain or changing the deformationapproach does not seem to be effective in further reducingthe grain size or increasing the strength [6,7]. Therefore, thefurther reduction in the grain size of metals by plasticdeformation, or producing bulk nanostructured (NS;d < 100 nm) metals and alloys via plastic deformation,has become a challenging subject.

Plastic strain, strain rate and deformation temperatureare known to be the three primary factors in deformationprocesses. Most SPD processes are performed at an ordin-ary strain rate (<100 s�1) and at ambient temperature[1–3,5–7]. However, previous investigations have shownthat very fine grains (far below 100 nm) have been obtainedin various metals and alloys by means of special plasticdeformation processes, such as ball milling [8], surfacemechanical attrition treatment [9,10] and cryogenic rolling[11,12]. In these processes, either high strain rates or lowtemperatures (or both) are applied. Very recently, we dem-onstrated that bulk NS Cu specimens with much higher

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762 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

strength can be produced by dynamic plastic deformation(DPD, i.e. plastic deformation with high strain rates) atcryogenic temperatures [13–15], even though the appliedstrain is only 2.0, which is much smaller than that usedin ECAP processes. These observations indicate that strainrate and deformation temperature are two dominating fac-tors in grain refinement. Systematic investigations into theeffect of these two parameters on grain refinement mecha-nism are vital for the development of synthesis techniquesfor bulk NS materials.

In the present work, we will systematically study themicrostructure characteristics and mechanical propertiesof bulk pure copper samples deformed at different strainrates (10�3–103 s�1) and different deformation tempera-tures (77–293 K). It is known that an increase in strain rateduring deformation is thought to have an equivalent effectto that of a decrease in deformation temperature and viceversa. The combined effects of strain rate (_e) and deforma-tion temperature (T) are often represented by a singleparameter, the Zener–Hollomon parameter (Z), as definedby [16]

Z ¼ _e expðQ=RTÞ ð1Þwhere R is the gas constant and Q is the related activationenergy for deformation. Hence, in this work, we use theZener–Hollomon parameter in a large range (ln Z = 22–66) to demonstrate the combined effects of strain rateand temperature on the grain refinement process in Cu sub-jected to plastic deformation, as well as on the mechanicalproperties of the deformed Cu samples.

2. Experimental

2.1. Sample

Copper cylinders (9 mm in diameter and 12 mm in thick-ness) with a purity of 99.995 wt.% were used as raw mate-rials for plastic deformation. Prior to deformation, the Cucylinders were annealed in vacuum at 973 K for 2 h toobtain homogeneous CG structures. Grain sizes of theas-annealed sample were within a range of 100–250 lmand annealing twins were found in some grains.

2.2. Plastic deformation treatments

All samples were plastically deformed by uniaxial com-pression, but with different strain rates (10�3–103 s�1) andat different temperatures (77–293 K). The high strain ratedeformation was conducted with a DPD facility [13–15],in which a strain rate of up to 103 s�1 was applied to thesample. Deformation at low strain rates was performedon an MTS servo-hydraulic test machine. An oil-basedmolybdenum disulfide lubricant was used to reduce frictionbetween the specimen and the compression platens toobtain the uniform deformation of compressed sample.The copper samples were quasi-statically compressed withnominal strain rates of 10�3 s�1 (referred to as QSC1)

and 10�1 s�1 (QSC2), respectively. The samples weredeformed at three different temperatures: liquid nitrogentemperature (LNT, 77 K), dry-ice temperature (DIT,195 K) and room temperature (RT, 293 K). The Cu cylin-ders were immersed into a liquid nitrogen bath or dry ice tomaintain the cryogenic temperature during deformation.

The deformation strain is defined as e = ln (L0/Lf),where L0 and Lf are the initial and final thickness of thedeformed sample, respectively. Multiple impacts wereapplied to deform the Cu samples to an eventual strainof e = 2 in the DPD treatments in order to maintain thehigh strain rates, while a single compression was appliedto deform the sample to the given strain in the QSCtreatments.

2.3. Microstructural characterization

The microstructures of the deformed copper sampleswere characterized by means of transmission electronmicroscopy (TEM) on a JEOL 2010 high-resolution trans-mission electron microscope operated at 200 kV. Cross-sec-tional thin foils for TEM observations were prepared bymeans of double-jet electrolytic polishing in an electrolyteconsisting of 25 vol.% alcohol, 25 vol.% phosphorus acidand 50 vol.% deionized water at about �10 �C.

X-ray diffraction (XRD) analysis of the as-deformed Cusamples was performed on a Rigaku DMAX/2400 X-raydiffractometer with the sample plane perpendicular to theloading direction of deformation. Microstrain of the sam-ples was determined by means of XRD peak broadeninganalysis using the Scherrer–Wilson method [17]. Eachdatum point was averaged from three independentmeasurements.

2.4. Thermal analysis

Differential scanning calorimetry (DSC) analysis wascarried out using a Perkin-Elmer DSC-7 system in a tem-perature range of 50–300 �C at a constant heating rate of20 �C min�1. Aluminum pans were used for both samplesand the reference, and high-purity Ar gas was used to pro-tect the sample from oxidation. Every sample was reheatedat the same conditions for determining the baseline, andthe final DSC curve is the difference between the secondand the first run.

2.5. Mechanical property tests

Uniaxial tensile tests were performed on an Instron 5848MicroTester system with a strain rate of 6 � 10�3 s�1 atroom temperature. A contactless MTS LX300 laser exten-someter was used to measure the sample strain upon load-ing. The gauge section of the dogbone-shaped tensile1-mm-thick specimens was 5 mm in length and 1 mm inwidth. More than four tensile tests were performed on eachsample. Microhardness measurements were carried out ona MVK-H300 Vickers hardness testing machine with a load

Y.S. Li et al. / Acta Materialia 57 (2009) 761–772 763

of 50 g and a loading time of 10 s. The hardness valueobtained was averaged from at least 20 indentations foreach sample.

3. Results

In total, eight Cu samples were treated under uniaxialcompressive deformation with different combinations ofstrain rate and temperature, as listed in Table 1, whichincludes deformation variables such as the strain rate, thenominal temperature (TN), the transient temperature riseduring deformation (DT, which is estimated as describedin Section 3.4) and the corresponding Z values determinedfrom Eq. (1) by taking the activation energy for grainboundary (GB) self-diffusion in copper (72.5 kJ mol�1

[18]).

3.1. TEM characterization of deformed Cu samples with

different Z values

It is known from previous investigations that in copperspecimens deformed via either drawing [4] or ECAP [6]e = 2.0 is a critical strain beyond which a saturationhardness or strength is achieved corresponding to a stablecharacteristic structure size. Hence, microstructural obser-vations in the present work focused on the deformed Cusamples with e = 2.0.

Cross-sectional TEM images showed that microstruc-tures of RT-QSC2, RT-DPD and DIT-DPD samples arecharacterized mainly by parallel lamellar boundaries (LBs)with elongated grains or subgrains, as in Fig. 1a1–a3.High-density dislocations were found inside thesesamples.

For sample RT-QSC2, statistical measurement of thespacing between neighboring LBs from plenty of TEMimages indicated that it exhibits a normal logarithmic dis-tribution in the range from 100 to 600 nm, with a meanvalue of about 290 nm (Fig. 1b1). Misorientations acrossthe most LBs range from a few up to 20�, similar to thatobserved in the SPD and the cold-rolled Cu samples. Theaverage aspect ratio of grains or subgrains is about 5–10.

For sample RT-DPD, the mean LB thickness was deter-mined to be about 233 nm (Fig. 1a2 and 1b2), smaller than

Table 1Summary of deformation variables (strain rate, temperature and temper-ature rise during deformation) and the calculated ln Z values for differentCu samples used in the present work.

Sample ID _e (s�1) TN (K) DT (K) InZ

RT-QSC1 Cu (lnZ = 22) 10�3 293 0–20 21.0–22.9RT-QSC2 Cu (lnZ = 25) 10�1 293 0–50 23.1–27.5RT-DPD Cu (lnZ = 33) 103 293 30–60 30.9–34.8DIT-QSC1 Cu (lnZ = 35) 10�3 195 0–25 32.7–37.8DIT-QSC2 Cu (lnZ = 38) 10�1 195 0–50 33.3–42.4DIT-DPD Cu (lnZ = 43) 103 195 35–65 40.4–44.8100K-DPD Cu (lnZ = 59) 103 100 55–75 56.0–63.2LNT-DPD Cu (lnZ = 66) 103 77 60–80 61.7–70.5

that in sample RT-QSC2. Misorientations across the LBsand the average aspect ratio of grains are consistent withthose in the sample RT-QSC2. Deformation twins wereidentified in this sample and formed bundles in thedeformed structure, constituting about 5 vol.%. This isunderstandable as deformation twinning is favored at highstrain rates, as previously addressed [19,20]. Twin/matrix(T/M) lamellar thickness was determined from TEMimages, varying from 10 to 150 nm, with an average of47 nm. The length of deformation twins is in the range ofa few hundred nanometers to several micrometers.

In the DIT-DPD Cu sample (Fig. 1a3 and 1b3), themean LB thickness is 165 nm, clearly smaller than thosein RT-QSC2 and RT-DPD samples. The volume fractionof deformation twin bundles is about 10%, with a similaraverage T/M lamellar thickness to the RT-DPD sample.

The microstructure of LNT-DPD Cu (Fig. 1a4) is com-posed of about 35 vol.% nanoscale deformation twin bun-dles embedded in nano-sized grains. Most nanograins areelongated, with an aspect ratio of 2–3. The crystallographicorientations of the nanograins are nearly random. Thetransverse grain size ranges from a few up to 200 nm, witha mean size of about 66 nm (Fig. 1b4). The average T/Mlamellar thickness determined from TEM images is alsoabout 46 nm.

Morphologies of deformation twins in different Cu sam-ples are quite similar, as shown in Fig. 2a. Plenty of dislo-cations were identified at the TBs, typical of deformationtwins. Fig. 2b–d shows the statistical T/M lamellar thick-ness distribution in these samples, respectively, which var-ies from several to about 150 nm in these three samples.The mean T/M lamellar thickness is rather consistent,being about 50 nm in each sample.

With systematical TEM characterization of otherdeformed samples (RT-QSC1, DIT-QSC1, DIT-QSC2and 100K-DPD [15]) with a strain e = 2.0, several micro-structural characteristic features of the deformed Cu weresummarized as a function of lnZ, as in Fig. 3. One cansee an obvious decreasing transverse grain size (D) athigher Z values. With lnZ increasing from 22 to 66, D

decreases from 320 to 66 nm. The datum points of conven-tional cold-drawn [4], cold-rolled [11], HPT [21] and ECAPCu samples [6,22] are also included for comparison, whichseem to be consistent with the present results.

No deformation twin was found in Cu samples forlnZ < 30. As shown in Fig. 3b, for lnZ > 30, the volumefraction of deformation twin bundles in the deformed Cusamples increases monotonically with Z. It is worth notingthat the mean T/M lamellar thickness, k, being about50 nm in each deformed Cu sample, is independent of Z

within the measurement regime (Fig. 3c). As indicated inour previous work [15], k seems to be independent on defor-mation strain during the DPD process. In addition, similar kvalues were reported in pure Cu samples deformed by shockloading [19] or deformed at liquid helium temperature(4.2 K) [23]. These results indicate that the T/M lamellarthickness is insensitive to the deformation parameters,

b3

b4

b1

b2

0

4

8

12

16

0

4

8

12

16

Transverse grain size (nm)0 100 200 300 400 500 600

0

4

8

12

16

0

4

8

12

16

Volu

me

fract

ion

(%)

Fig. 1. Cross-sectional bright field TEM images for the microstructure morphology and statistic grain size distributions for different deformed Cu sampleswith a strain e = 2.0: (a1, b1) RT-QSC2 (lnZ = 25); (a2 and b2) RT-DPD (lnZ = 33); (a3 and b3) DIT-DPD (lnZ = 43); and (a4 and b4) LNT-DPD(lnZ = 66).

764 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

100 nm100 nm

0

4

8

12

16

20

Volu

me

fract

ion

(%)

0

4

8

12

16

20

0 20 40 60 80 100 120 1400

5

10

15

20

T/M lamellar thickness (nm)

b

a

c

d

Fig. 2. (a) A typical bright field TEM image for deformation twins in the deformed Cu samples. Statistical distributions for the T/M lamellar thickness in(b) RT-DPD (lnZ = 33), (c) DIT-DPD (lnZ = 43) and (d) LNT-DPD (lnZ = 66) Cu samples, respectively.

Y.S. Li et al. / Acta Materialia 57 (2009) 761–772 765

including strain, strain rate and deformation temperature.More in-depth investigations on this phenomenon areneeded to understand the intrinsic twinning mechanism.

With the above-mentioned structure parameters, the GBand twin boundary (TB) densities (area per unit volume)were calculated for each deformed sample, as shown inFig. 4. With lnZ increasing from 22 to 66, the GB density(SGB) increases by a factor of about 4, from 4.01 � 106 m�1

(RT-QSC1) to 17.2 � 106 m�1 (LNT-DPD), while the TBdensity (STB) increases from 2.0 � 106 m�1 (RT-DPD) to7.6 � 106 m�1 (LNT-DPD). Clearly, the total boundarydensity (sum of SGB and STB) is increased by one orderof magnitude from 4.01 � 106 m�1 (RT-QSC1) to2.48 � 107 m�1 (LNT-DPD).

3.2. Microstrain of deformed Cu samples with different Z

values

Microstrain determined from XRD peak broadening rep-resents the concentration of lattice defects (mainly disloca-tions) in the samples. With increasing Z, the measuredmicrostrain increases monotonically from about 0.13%(RT-QSC1 sample) to 0.25% (LNT-DPD sample), as shownin Fig. 5. Previously published data show that the micro-strain in Cu samples processed via different approaches var-ies across a wide range, such as from about 0.1% in ECAP Cu[6], to 0.14% in HPT Cu [24] and 0.2% in ball-milled Cu [25].Our measurements are close to these data. This indicates thatmany more defects (dislocations) are introduced into thesamples plastic-deformed with higher Z parameters, which

is in agreement with the observed decreasing grain sizes athigher Z values (Fig. 3a) and the stored energy measure-ments, as will be shown in next section.

3.3. Stored energies of deformed Cu samples with different Z

values

Upon heating the as-deformed Cu samples, an exother-mic peak corresponding to recrystallization was detected inthe DSC curves (Fig. 6a). For RT-QSC2 Cu, a single broadexothermic peak (onsets at about 205 �C) is seen with astored energy of about 0.8 J g�1. At higher Z values, theexothermic peak shifts to lower temperatures while the heatrelease is larger. For the LNT-DPD Cu, the onset of theexothermic peak is at 120 �C with a stored energy of about1.7 J g�1. As shown in Fig. 6b, with increasing Z, the char-acteristic temperatures (onset and peak) drop obviouslyand the stored energy increases monotonically. The mea-sured stored energy results are reasonably consistent withthe published data for deformed Cu samples [4,11,26–28].Some minor differences can be attributed to the impurityof the processed Cu and the range of measurements inthe DSC experiments.

3.4. Mechanical properties of deformed Cu with different Z

values

Variations in the microhardness of the deformed Cusamples (RT-QSC2, RT-DPD and LNT-DPD) withimposed strain are shown in Fig. 7. The early deformation

0

100

200

300

Present workECAP Cu [6,22]Drawing Cu [4]Rolling Cu [11]HPT Cu [21]

10 20 30 40 50 60 70 800

25

50

75

λ (n

m)

lnZ

0

10

20

30

40

Twin

bund

le v

ol (%

)Tr

ansv

erse

gra

in s

ize

(nm

) a

b

c

Fig. 3. Plots of several characteristic parameters vs. lnZ in Cu samples (e = 2.0) processed via different approaches: (a) average transverse grain size; (b)volume fraction of deformation twin bundles; and (c) average T/M lamellar thickness (k, nm). Data from the literature on grain sizes are included in (a).

10 20 30 40 50 60 70 800

5

10

15

20

25

Den

sity

of G

B/TB

(106

m-1

)

lnZ

SGB

STB

Fig. 4. Variations in GB and TB densities with ln Z for the deformed Cusamples with e = 2.0.

10 20 30 40 50 60 700.08

0.12

0.16

0.20

0.24

0.28 Present workECAP Cu [6]Rolling Cu [26]HPT Cu [24]

Mic

rost

rain

(%)

lnZ

Fig. 5. Variation of measured microstrain from XRD analysis with lnZ

for the deformed Cu samples, in comparison with results of SPD Cusamples from the literature.

766 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

stage of all the samples shows obvious strain hardening,with a rapid increase in hardness with strain. The hardnesstends to level off at a saturation value during subsequentdeformation when the strain exceeds 2.0. The saturationhardness values are about 1.6, 1.3 and 1.2 GPa for theLNT-DPD, RT-QSC2 and RT-DPD samples, respectively.

Similar behavior has also been observed in metals andalloys upon plastic deformation [11,29], which indicates adynamic equilibrium between generation and annihilationof strain-induced defects (dislocations).

Uniaxial tensile tests showed an obvious difference instrength and ductility among the deformed samples with

100 150 200 250 3000.00

0.02

0.04

0.06

0.08

0.10

RT-QSC2 Cu (lnZ=25)

RT-DPD Cu (lnZ=33)

DIT-DPD Cu (lnZ=43)

Hea

t flo

w (W

/g)

Temperature (ºC)

LNT-DPD Cu (lnZ=66)

10 20 30 40 50 60 70

0.8

1.2

1.6

2.0

120

160

200

240

Present workRolling Cu [11]Drawing Cu [4]ECAP Cu [28]

Stor

ed e

nerg

y (J

/g)

lnZ

Peak temperatureOnset temperature

Tem

pera

ture

(ºC

)

Fig. 6. (a) Typical DSC traces for the LNT-DPD (lnZ = 66), DIT-DPD(lnZ = 43), RT-DPD (lnZ = 33) and RT-QSC2 (lnZ = 25) Cu samples.(b) Variations in the onset temperature, peak temperature and storedenergy determined from the DSC experiments with lnZ for the deformedCu samples with e = 2.0. Previously published data on stored energy areincluded in (b).

0.0 0.5 1.0 1.5 2.0 2.5

0.6

0.8

1.0

1.2

1.4

1.6

1.8

LNT-DPD Cu (lnZ = 66)RT-DPD Cu (lnZ = 33)RT-QSC2 Cu (lnZ = 25)

Har

dnes

s (G

Pa)

Strain

Fig. 7. Microhardness vs. strain for the Cu samples deformed via differentapproaches and different Z parameters.

0 5 10 15 200

100

200

300

400

500

6000

100

200

300

400

500

600

Engi

neer

ing

stre

ss (M

Pa)

Engineering strain (%)

LNT-DPD Cu (lnZ=66)DIT-DPD Cu (lnZ=43)

RT-DPD Cu (lnZ=33)RT-QSC2 Cu (lnZ=25)

RT-QSC1 Cu (lnZ=22)

RT-DPD Cu

RT-QSC2 Cu

LNT-DPD Cu100K-DPD Cu (lnZ=59)

DIT-DPD Cu

CG Cu

b

a

ε = 2.0

ε = 1.0

Fig. 8. Typical engineering stress–strain tensile curves for the Cu samplessubjected to plastic deformation via different approaches with strains of(a) e = 1.0 and (b) e = 2.0.

Y.S. Li et al. / Acta Materialia 57 (2009) 761–772 767

different Z values. As in Fig. 8, much enhanced strengthand decreased plasticity (elongation-to-failure) were foundin each deformed sample at strains of e = 1.0 and 2.0, com-pared with the as-annealed CG Cu. Both yield strength andultimate tensile strength of the deformed samples withe = 2.0 are higher than those with e = 1.0, consistent withthe hardness measurements. The deformed samples exhibit

very little uniform elongation (about 1%), analogous to theCu samples deformed via other approaches [4,6,26]. This isdue to an insufficient ability to strain harden in thedeformed metals, causing the onset of early necking [30].However, no obvious change in elongation-to-failure wasnoticed with different strains.

The tensile stress–strain curves clearly demonstrate thatboth yield strength and ultimate tensile strength of thedeformed samples increase with Z value at an equivalentamount of strain (either at e = 1.0 or e = 2.0). The yieldstrength increases from about 390 ± 6 MPa (RT-QSC1)to about 610 ± 14 MPa (LNT-DPD). The elongation-to-failure drops with increasing Z from about 17% (RT-QSC1) to 8% (LNT-DPD). The strength and ductility ofthe RT-QSC1 sample are consistent with those of theECAP and cold-rolled Cu samples reported in the litera-ture [6,26]. As shown in Fig. 9, both hardness and yieldstrength increase almost linearly with lnZ. The Z depen-dence of yield strength determined in the present workagrees well with the literature data from Cu samplesdeformed via different techniques [4,6,12].

The saturation stress of deformed samples withincreased strains can be described by Voce equation [31]

rs � rrs � r0

¼ exp � eec

� �ð2Þ

where r0 is the initial yield strength, rs is the saturationstrength and ec is a characteristic strain that depends uponthe material and the deformation variables. In terms of ten-sile results, one can calculate the corresponding values of rs

and ec. As shown in Fig. 10, the measured yield strength fitsthe Voce equation very well for various samples. The calcu-

800

1000

1200

1400

1600

1800

10 20 30 40 50 60 70 80

0

5

10

15

20300

400

500

600

700

ε = 2.0ε = 1.0

Har

dnes

s (M

Pa)

ε = 2.0Present workECAP Cu [6]

ε = 1.0Present workECAP Cu [6]El

onga

tion-

to-fa

ilure

(%)

lnZ

ε = 2.0Present workECAP Cu [6]Rolling Cu [12]Drawing Cu[4]

ε = 1.0Present workECAP Cu [6]

Yiel

d st

reng

th (M

Pa)

a

b

c

Fig. 9. Plots of several mechanical properties vs. lnZ for the deformed Cu samples with e = 1.0 (open symbols) and e = 2.0 (solid symbols), respectively:(a) microhardness, (b) tensile yield strength and (c) elongation-to-failure. Previously published data on yield strength and elongation-to-failure areincluded in (b) and (c), respectively.

0.0 0.5 1.0 1.5 2.0 2.5 3.00

100

200

300

400

500

600

LNT-DPD Cu (lnZ=66) Voce equ (εc=0.76) DIT-DPD Cu (lnZ=43) Voce equ (εc=0.64) RT-DPD Cu (lnZ=33) Voce equ (εc=0.62) RT-QSC2 Cu (lnZ=25) Voce equ (εc=0.56) RT-QSC1Cu (lnZ=22) Voce equ (εc=0.55)

Yiel

d st

reng

th (M

Pa)

Strain

Fig. 10. Variation of measured yield strength and the fitted yield strengthusing the Voce equation with deformation strain for several deformed Cusamples with different Z parameters.

768 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

lated saturation strengths, rs, from the Voce equation are399, 413, 507, 525 and 652 MPa for RT-QSC1, RT-QSC2, RT-DPD, DIT-DPD and LNT-DPD sample,respectively. The characteristic strain, ec, increases at high-er Z values from 0.55 (RT-QSC1) to 0.76 (LNT-DPD).With these data, the transient temperature rise inducedby plastic deformation can be estimated.

The actual sample temperature (T) can be expressed as

T ¼ T N þ DT ð3Þwhere TN is the nominal deformation temperature and DTis the strain-induced temperature rise. For adiabatic defor-mation (DPD processes can be regarded as adiabatic defor-mation due to the high strain rate and very shortdeformation duration), the temperature rise of deformationsample can be calculated according to [18]

DT ¼ bqC

Z e2

e1

rde ð4Þ

where b = 0.9 (assuming 90% deformation work was con-verted to heat), q is the density of the sample and C is

the specific heat capacity. The mean strain increment 4eis about 0.4 for each impact in the DPD process. For defor-mation at low strains, such as in QSC1, a minor tempera-

Y.S. Li et al. / Acta Materialia 57 (2009) 761–772 769

ture rise is induced (<20 K). With an increasing strain rate,higher temperature rises are produced. Table 1 lists the cal-culated temperature rises under different deformation con-ditions. In Ref. [18] the maximum temperature incrementwas estimated to be 50 K in the ECAP process, which isconsistent with the present results. The highest temperaturerise was estimated to be about 60–80 K for the LNT-DPDsamples.

4. Analysis and discussion

4.1. Z effect on grain refinement mechanism

An obvious Z effect on the microstructure of deformedCu has been demonstrated: finer grains are formed indeformation with higher Z values, which can be under-stood from the grain refinement mechanism induced byplastic deformation.

In plastic deformation of Cu at low strain rates and atambient temperature or above (i.e. with a low Z), refine-ment of coarse grains is dominated by dislocation activitiesby forming various dislocation configurations, includingdislocation cells, walls, geometry necessary boundariesand incidental dislocation boundaries [20,32]. These dislo-cation cells gradually transform into subgrains separatedby boundaries of small misorientations (from dislocationcell walls). With increasing strain, misorientations of thesubgrain boundaries increase, forming high-angle GBs sothat refined grains are randomly oriented. With this mech-anism, the eventual grain size is determined by the disloca-tion cell size. Dislocation cell sizes (Ddc) are dependentupon the shear stress applied (s) according to [33]

Ddc ¼KGbs� s0

� KGbs

ð5Þ

where K is a constant (normally taken as 10), G is the shearmodulus, b is Burgers vector and s0 is friction stress. As theshear stress to initiate dislocation slip increases at higher Z,Ddc and the eventual grain size become smaller withincreasing Z.

With this grain refinement mechanism, it is noted thatthe sizes of cells and grains decrease at a larger appliedshear stress. An extreme case is that when the applied shearstress reaches its upper limit, i.e. the maximum shear stressof the material (smax), Ddc may reach its minimum value,i.e. the size limit of dislocation cells. From Eq. (5) and tak-ing smax = G/30, we obtained a limit of Ddc of about 90 nmfor Cu. This means that grains may not be refined furtherbelow 90 nm via the dislocation mechanism, which isapparently inconsistent with our observations that averagegrain sizes below 90 nm have been achieved in the LNT-DPD and 100K-DPD samples.

In fact, a different grain refinement mechanism mayoperate at high-Z deformation. During high-Z plasticdeformation when dislocation manipulation and rearrange-ment are suppressed, the critical shear stress for deforma-tion twinning is lower than that for slip. Hence, twinning

becomes the preferred deformation mechanism and defor-mation twin bundles are formed inside the original coarsegrains. With increasing deformation twinning, the originalthree-dimensional coarse grains are refined into two-dimensional lamellae by an increasing number of twinboundaries. The T/M lamellae can be refined into thenanometer regime.

Further plastic deformation induces transformation ofthe nanometer-thick T/M lamellae into nano-sized grainsvia two different mechanisms. As described in detail inRef. [15], nano-sized grains could be formed (i) via frag-mentation of nanometer-thick T/M lamellae because ofTB–dislocation interactions or, alternatively, (ii) via for-mation of shear bands within which nano-sized grainsare formed under a large degree of shear deformation.With mechanism (i), the transverse grain size is veryclose to the original T/M lamellae thickness (about50 nm). In mechanism (ii), grain sizes are slightly largerthan the lamellae thickness (about 75 nm) due to graincoarsening induced by high stress and the transient tem-perature rise within shear bands. Statistical measure-ments showed that in the LNT-DPD Cu sample [15]about 30% in volume corresponds to nano-sized grainsfrom fragmentation of nanotwin bundles and about15% to nanograins formed via shear banding. In con-trast, only about 20% is from grain refinement via dislo-cation activities. This means that the majority ofnanograins were refined from nanoscale deformationtwin bundles, from which the average grain size is muchsmaller than that in low-Z samples refined via disloca-tion activities. As shown in Fig. 3b, with increasing Z

value, the tendency of deformation twinning is enlargedwith an increasing number of twin bundles. Hence, anincreasing number of nanograins are refined from nano-scale twin bundles, resulting in a decreased average grainsize.

The transition in grain refinement mechanism withincreasing Z can also be identified from the variation ofGB energy, as described in Section 4.2.

Deformation twinning in face-centered cubic (fcc) met-als is controlled by deformation conditions (such as strain,strain rate and temperature) as well as the nature of mate-rials, including grain size and stacking fault energy. A thor-ough understanding of the twinning behavior and thesubsequent grain refinement process might be facilitatedby systematic investigations using molecular dynamic(MD) simulations. The extremely high strain rates(�107 s�1) and very low temperatures usually applied inMD simulations favor deformation twinning in fcc metals.In fact, previous MD simulations have demonstrateddeformation twinning in nano-sized grains of Al with ahigh stacking fault energy [34]. MD simulations on nucle-ation and growth of deformation twins, as well as the inter-action of twin boundaries with dislocations at the atomisticlevel during high-Z deformation, are needed for identifyingthe controlling parameters in the twinning-related struc-tural refinement mechanism.

10 20 30 40 50 60 700.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Present workECAP Cu [28]Rolling Cu [11]

GB

eneg

y (J

/m2 )

lnZ

Fig. 11. Variation of GB energy determined from DSC experiments withlnZ in the deformed Cu samples. Reported results on GB energy in theliterature are also included for comparison.

770 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

4.2. Z effect on grain boundary energy

In terms of the measured stored energy from DSCexperiments, the GB energy in the deformed samples canbe estimated, which is a signature of the structure and ther-modynamic states of GBs. In ultrafine-grained or nano-grained metals, the majority of stored energy releasedduring recrystallization is attributed to the disappearanceof a high density of GBs and lattice dislocations. The con-tributions from other defects, such as vacancies and theassociated elastic strain energy, are minor [35]. Conse-quently, for the deformed samples without deformationtwins (lnZ < 30, e.g. sample RT-QSC2) the stored energy(E) can be divided into a dislocation term and a GB termby

E ¼ 1

q� Ed � qg þ EGB ð6Þ

where Ed is the energy per unit length of a dislocation andqg is the dislocation density in the grain/cell interiors. TheGB part (EGB) is related to specific GB energy bycGB = q � EGB/S, in which S is the GB area in the unit vol-ume (S � 3/D) and q is the density.

Taking an average value of Ed = 5 � 10�9 J m�1 [35]without making any distinction between edge/screw dislo-cations, complete/partial dislocations and the dislocationdensity within the grain/cell interiors of about2 ± 1 � 1014 m�2 in terms of detailed TEM observationsof the RT-QSC2 sample (which is consistent with data inthe literature [6,7]), we obtained that cGB is 0.54 J m�2

for the RT-QSC2 sample. This is reasonably consistentwith the reported high-angle GB energy in Cu(�0.625 J m�2 [36]) considering the mixture of characteris-tics of low- and high-angle GBs in the deformed samples.Very similar GB energy values were gained in other sam-ples with low Z. GB energies determined in Cu samplesthat had undergone different plastic deformation modesin the literature are in the range of 0.5–0.6 J m�2, in agree-ment with our measurements, as shown in Fig. 11.

For the deformed samples with deformation twin bun-dles, the energy stored at deformation TBs (including theenergy of dislocations accumulated at TBs) should be takeninto account in calculating the GB energy, as described inour previous work [26]. The total stored energy can bedescribed as E = Etwinf nt + Ematrix(1 � f nt), where Etwin ¼1q ð1k cTB þ Ed � qntÞ [37], f nt is the volume fraction of thenanotwin bundles, cTB is the coherent TB energy (takenas half of its stacking fault energy, i.e. 0.039 J m�2), k isthe average T/M lamellar thickness, qnt is the dislocationdensity in the nanoscale twins and Ematrix is the energystored in the matrix (submicro- or nano-sized grains) asexpressed in Eq. (6). In terms of TEM measurements of dis-location density in the nanoscale twins in the LNT-DPDCu sample, which are about 2 ± 1 � 1015 m�2, the storedenergy associated with deformation TBs was determined.Then, the average GB energy can be calculated from thestored energy in the nanograined matrix (Ematrix) in terms

of Eq. (6), being about 0.30 J m�2 for the LNT-DPD sam-ple. Similarly, the GB energy in sample 100K-DPD wasdetermined to be about 0.31 J m�2. From the variation inmeasured GB energy with lnZ as in Fig. 11, one may seethat GB energy is unchanged at about 0.55 J m�2 whenlnZ increases from 22 to 40. As lnZ exceeds 40, an obviousdrop in GB energy appears from 0.55 to 0.3 J m�2.

As described earlier, submicro-sized grains in the sam-ples deformed at low Z are evolved from dislocation struc-tures. However, for the high-Z deformation samples(100K-DPD and LNT-DPD), most nano-sized grains werederived from nanotwin bundles, either from fragmentationof T/M lamellae or from shear banding of the nanotwinbundles. Hence, most GBs in these samples were fromthe original low-energy TBs. TBs possess rather lowenergy, much smaller than that of high-angle GBs (forCu, cTB = 0.02–0.04 J m�2 [36]). The low cGB in these sam-ples (about 0.3 J m�2) implies that a large fraction of GBsare in energy states close to that of the original TBs. Trans-formation of the original nanotwin bundles into nano-sizedgrains will unavoidably generate plenty of GBs that are insimilar low-energy configurations as the original TBs. Thisargument is verified by detailed TEM observations on thenature of GBs in the LNT-DPD samples. Micro-area elec-tron diffraction on individual GBs separating nano-sizedgrains indicated that a considerable number of boundariesexhibit twin orientation relationships or slightly deviatedtwin relationships in the LNT-DPD samples. The GBenergy drop in Fig. 11 corresponds to an evident incrementin the number of deformation twins (Fig. 3c), verifying thechange in grain refinement mechanism.

4.3. Strengthening of grain refinement and nanoscale twins

As shown in Fig. 9, an increasing strength correspondsto higher Z values. This phenomenon can be primarilyattributed to a decreasing grain size accompanied with anincreasing dislocation density with an increasing Z. Forthe deformed samples with refined grains in whichstrengthening is mainly caused by dislocation–dislocation

10 20 30 40 50 60 70

400

450

500

550

600 MeasuredCalculated

Yiel

d st

reng

th (M

Pa)

lnZ

Δσy

Fig. 13. Variations of the measured (solid squares) and the calculatedyield strength (open squares) with lnZ for the deformed Cu samples.

Y.S. Li et al. / Acta Materialia 57 (2009) 761–772 771

interactions, yield strength (ry) can be correlated to the dis-location density (qd) following the Taylor equation [38]:

ry ¼ r0 þ aMGbffiffiffiffiffiqd

pð7Þ

where r0 is the friction stress, a is a constant (taken as�1/3),M is the Taylor factor and G is the shear modulus. The dis-location density is related to the stored energy as determinedfrom thermal analysis, as presented in Section 3.3 and Ref.[26]. The calculated dislocation densities for the deformedsamples with different Z values are shown in Fig. 12,which are consistent with the results in the literature(1.1–1.5 � 1015 m�2 in the SPD Cu samples [18]).

The yield strength values of deformed Cu samples withdifferent Z values can then be obtained in terms of Eq.(7), as shown in Fig. 13. The calculated yield strength isseen to agree reasonably with the measured data for thesamples with lnZ < 40. For the samples with lnZ > 40,increasing differences are seen between the calculated andthe measured data at higher Z. For the LNT-DPD sam-ples, the difference is as large as 65 MPa.

Such strength differences originate from the presence ofnanoscale deformation twin bundles in the deformed sam-ples. As described in previous sections, samples withlnZ > 40 can be recognized as composites of nano-sizedgrains with embedded nanotwin bundles, the strength ofwhich can be treated in terms of the ‘‘rule-of-mixture”:

rDPDy ¼ rng

y ð1� f ntÞ þ rnty f nt ð8Þ

where f nt is the volume fraction of nanotwin bundles, andrng

y and rnty are the yield strength for the nano-sized grains

and nanotwin bundles, respectively. Following the T/Mthickness dependence of yield strength for the nanoscaletwins in Cu as reported in Ref. [26], the yield strength ofthe nanotwin bundles with k = 50 nm is determined, beingabout 810 MPa. Therefore, the additional contributions ofnanotwin bundles to the measured yield strength values inthe LNT-DPD, 100K-DPD and DIT-DPD samples wereestimated to be about 90, 85 and 33 MPa, respectively.These results agree reasonably well with the differences

10 20 30 40 50 60 701.2

1.6

2.0

2.4

2.8

3.2

3.6

Present workECAP Cu [28]Rolling Cu [11]

Dis

loca

tion

dens

ity (1

015

m-2

)

lnZ

Fig. 12. Dislocation density determined from stored energy as a functionof lnZ for the deformed Cu samples. Previously published data onmeasured dislocation density are included for comparison.

between the measured and the calculated yield strength interms of Eq. (7), as shown in Fig. 13.

Consequently, it may be concluded that the deformedCu samples with high-Z values are strengthened not onlyby the significant grain refinement but also by the presenceof a considerable number of nanoscale twin bundles. Thelatter strengthening mechanism does not exist in the Cusamples deformed at low Z values.

5. Conclusions

By using different plastic deformation approaches withdifferent strain rates and temperatures, the effects of theZener–Hollomon parameter on microstructures andmechanical properties in pure Cu were investigated. Exper-imental measurements showed:

(i) Deformation twinning occurs when lnZ is larger than�30, and the number of twins increases with increas-ing Z. The average T/M lamellar thickness is inde-pendent of Z, being around 50 nm in each sample.

(ii) The sizes of grains refined by plastic deformationdecrease at higher Z. With lnZ increasing from 22 to66, the mean transverse grain size decreases from 320to 66 nm. For the low-Z processes where grain refine-ment is dominated by dislocation activities, highershear stresses for slip at higher Z values lead to smallersizes of dislocation cells and of eventual grains. In high-Z deformation, deformation twinning plays a domi-nating role in grain refinement. Fragmentation andshear banding of the nanoscale deformation twin bun-dles result in even smaller grains than those from dislo-cation cells. The transition in the grain refinementmechanism was demonstrated by an obvious drop inGB energy when lnZ exceeds 40.

(iii) With lnZ increasing from 22 to 66, tensile yieldstrength of the deformed Cu increases from 390 to610 MPa. The strength increment can be attributedto significant grain refinement as well as the strength-ening from nanoscale deformation twins.

772 Y.S. Li et al. / Acta Materialia 57 (2009) 761–772

Acknowledgements

Financial support from the National Natural ScienceFoundation of China (Grants Nos. 50431010, 50671106and 50071061), the Shenyang Science & Technology Pro-ject (Grant No. 1071107-1-00) and the Ministry of Scienceand Technology of China (Grants No. 2005CB623604) isacknowledged.

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