Journal of Alloys and Compounds 618 (2015) 139–145

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Journal of Alloys and Compounds

journal homepage: www.elsevier .com/locate / ja lcom

Effect of twin spacing, dislocation density and crystallite sizeon the strength of nanostructured a-brass

http://dx.doi.org/10.1016/j.jallcom.2014.08.1310925-8388/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +91 3222 283284; fax: +91 3222 282280.E-mail address: j.das@metal.iitkgp.ernet.in (J. Das).

N.K. Kumar, B. Roy, J. Das ⇑Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India

a r t i c l e i n f o

Article history:Received 30 May 2014Accepted 16 August 2014Available online 27 August 2014

Keywords:DislocationsX-ray diffractionTransmission electron microscopyCryorollingNanotwinninga-Brass

a b s t r a c t

Nanotwinned a-brass (Cu–30 wt.% Zn) with varying lamellae thickness in the range of 28–170 nm, hasbeen produced by cryorolling (CR). The effect of CR strain (eCR = 0.2–0.95) on the evolution of homogene-ity and refinement in terms of twin lamellae thickness, twin spacing, and their distribution, have beenstudied using high-resolution transmission electron microscopy (HRTEM) and microhardness measure-ments. Analysis of X-ray peak broadening has shown that the crystallite size reduces down to 20 nmat eCR = 0.95, which scales with the subgrain size in preexisting twin lamellae, as revealed under HRTEM.The effect of dislocation density and crystallite size on the strength of nanotwinned brass has beencorrelated using an analytical model.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Reduction of grain size has been a long strategy for improvingthe strength of metals and alloys [1,2]. A large number of studieshave shown that grain refinement from micrometer down to thenanometer range leads to substantial strengthening due to thepresence of abundant grain boundaries (GBs) [3]. Severe plasticdeformation (SPD) processes such as, (i) accumulative roll bond-ing (ARB), (ii) equal channel angular pressing (ECAP), (iii) highpressure torsion (HPT) etc. have been widely used to synthesizebulk materials with nano-/ultrafine grained microstructure[3–6]. Even though, SPD produces a large population of high-angle grain boundaries (HAGBs) during microstructural refine-ment, however, a large variation of SPD strain along cross-sectionof the sample results evolution of inhomogeneous microstructure[7]. Such microstructural fluctuations was investigated usingmicrohardness measurements in differently SPD processedspecimens [8,9].

Recently, cryorolling have been adopted to produce nanocrys-talline Cu and Al-base alloys [7,10,11]. The minimum grain sizewas reported to be 500–600 nm for SPD processed pure Al [12],100–500 nm for Cu [13–15], 70–110 nm for Cu–30 wt.% Zn [16].Furthermore, post SPD recrystallization produces fine microstruc-ture with grain size �7.5 lm for Cu–5 wt.% Zn and 4.5 lm forCu–5 wt.% Al, respectively [7]. It is well established that lattice

dislocations are responsible for plastic strain in coarse-grainedpolycrystalline metals and alloys [17,18]. The population ofHAGBs increases with deformation strain, which restricts theinter-grain dislocation motion. As a result, the cold worked metalbecame harder and further deformation of the specimen requireshigher stress according to Hall–Petch relation [1,2,19]. In addi-tion, dislocation activity can be suppressed during deformationat high strain rate or at cryogenic temperatures [19]. In such acase, twinning is one of the major deformation mechanisms formetals/alloys with low stacking fault energy, i.e., stainless steel(8–45 mJ/m2), silver (25 mJ/m2), and a-brass (14 mJ/m2), etc.[11,19,20]. Since, presence of Zn reduces the stacking fault energy(SFE) of pure Cu from 78 mJ/m2 to 14 mJ/m2 (Cu–30 wt.% Zn),hence, addition of Zn is found to be beneficial in theformation of twins in a-brass. On the other hand, Zn helps inretaining the dislocation density upon deformation at cryogenictemperature, restricts cross-slip, and prevents dynamic recovery[11,20–22].

The present investigation is aimed to study the microstruc-tural and hardness homogeneity in nanostructured a-brass(Cu–30 wt.% Zn) processed by cryorolling. Characterization ofas-rolled nanostructure has been performed in terms ofcrystallite size, twin lamellae thickness (k), twin spacing (dtwin),and their distribution at different extent of cryorolling, to explorethe underlying mechanism of microstructural refinement. Theeffect of strengthening due to dislocation density, twin spacing,and crystallite size on the flow stress of differently CR specimenshave been correlated.

Fig. 2. XRD patterns of rolled specimens on (a) RW and (b) NW planes showingpeak broadening upon cryorolling.

140 N.K. Kumar et al. / Journal of Alloys and Compounds 618 (2015) 139–145

2. Experimental

Long bars (70 � 15 � 5 mm3) were cut from Cu–30 wt.% Zn ingot and were solu-tion treated (ST) at 560 �C for 24 h followed by air cooling. The samples were dippedinto liquid N2 (�100 �C) for 25–30 min before and after each pass of rolling [23–25].The reduction of thickness has been estimated to be �5% after each rolling pass.Samples were collected after achieving a true strain (eCR) of 0.2, 0.4, 0.7, 0.9 and0.95 along thickness direction and were identified as CR02, CR04, CR07, CR09 andCR095, respectively. Structural investigation was performed using X-ray diffraction(XRD, Philips PANalytical PW 3373, Netherlands) with Cu Ka radiation on both therolling-width (RW) and normal-width (NW) planes, as shown schematically inFig. 1(a). Thin slices have been prepared by Ar-ion milling (PIPS-691, Gatan) withliquid N2 cooling facility. Microstructural characterization was performed usingHRTEM (JEM-2100, JEOL, Japan) operated at 200 kV. Vickers’ microhardness mea-surements were carried out using a Bühler MicroMet 5103 hardness tester at50 gf load with 15 s dwell time. Hardness values at each location on NW planeswere estimated by averaging the hardness of four surrounding points positionedat the edge of a 150 lm � 150 lm size square, as shown schematically inFig. 1(b) [8]. Parallelepiped specimens (2 � 2 � 4 mm3) were cut from the solutiontreated (ST) and rolled bars, and were tested using Tinius Olsen H50KS (Germany)universal testing machine at a strain rate of 8 � 10�4/s at room temperature. Theopposite surfaces and both ends of the test specimens were polished carefully tomaintain uniaxiality during compressive loading.

3. Results

3.1. Analysis of X-ray peak broadening

XRD patterns of CR specimens for both NW and RW planes areshown in Fig. 2(a and b). Analysis of all these patterns has revealedthe presence of single fcc phase (a-brass) pointing that no phasetransformation had occurred during CR. However, the width ofall the peaks became broader in CR specimens than that of ST. Usu-ally, the instrumental broadening, crystallite size, and lattice strainare the major factors, which contribute peak broadening [26]. Theinstrumental line broadening has been estimated using a standardSi-disc (PW3132/62) of 2-mm thickness and 32-mm diameter. Thepeak broadening (b) of the specimens has been corrected using thefollowing equation [27]:

b ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðb2

obs � b2SiÞ

qð1Þ

where bobs and bSi are the integral breath of the corresponding (hk l)reflections from the specimen and standard silicon disc, respec-tively. Therefore, the lattice strain and crystallite size have beenestimated using classical and modified Williamson-Hall techniquefrom the XRD peak broadening [27]. The crystallite size of the STspecimen has been estimated to be �162 nm, which was reduceddown to 17–27 nm in CR095 specimen for both NW and RW planes,as shown in Table 1. On the other hand, average lattice strain (he2i

12)

increases from 2.24 � 10�3 (ST) to 5.08 � 10�3 (CR07), and he2i12

reaches up to a value of 5.21 � 10�3 at CR095. The dislocation

Fig. 1. Schematic showing (a) different directions of a cryorolled bar, and (b) the methodo

density (qd) can be estimated from the lattice strain according tothe following equation [28]:

qd ¼2ffiffiffi3phe2i

12

Dbð2Þ

where Burger’s vector, b is 0.26 nm for Cu–30 wt.% Zn. The averagevalue of qd has been found to increase from 3.45 � 1014/m2 (CR02)up to 2.98 � 1015/m2 (CR095) with CR strain. These qd values aretypical for deformed ductile metals [29–31].

3.2. Post-CR microstructural characterization under TEM

The microstructures of the CR specimens were characterizedusing bright (BF) and dark field (DF) imaging mode under TEM.The representative micrographs and selected area electron

logy adopted for microhardness measurements to study the hardness homogeneity.

Table 1Summary of XRD analysis such as crystallite size (D) and lattice strain (he2i

12) as estimated through classical and modified Williamson-Hall method on both RW and NW planes.

Sample Classical Williamson-Hall Modified Williamson-Hall

RW plane NW plane RW plane NW plane

D (nm) he2i12 D (nm) he2i

12 D (nm) he2i

12 D (nm) he2i

12

ST 175 0.00181 133 0.00266 142 0.0027 198 0.0018CR02 122 0.00229 85 0.00304 92 0.00359 142 0.00252CR04 40 0.00410 30 0.00602 35 0.00497 35 0.00331CR07 35 0.00460 24 0.00654 25 0.00536 30 0.00382CR09 33 0.00481 22 0.00658 23 0.00540 29 0.00385CR095 28 0.00483 18 0.00661 20 0.00545 27 0.00395

N.K. Kumar et al. / Journal of Alloys and Compounds 618 (2015) 139–145 141

diffraction (SAED) patterns show the presence of twin in all the CRspecimens, as depicted in Fig. 3(a–f). As an example, the BF imageshows alternate lamellae of twin and matrix in CR02, as depicted inFig. 3(a). The SAED pattern in Fig. 3(e) shows double diffractionsspots along ½�121� zone axis confirming the brighter lamellae tobe twin. TEM (BF) micrograph of CR07 and the correspondinghigh-resolution (HR) image of the selected region are shown inFig. 4(a–c). The presence of curved twin boundaries (TBs) has beenfrequently observed, as marked by white rectangle in Fig. 4(a). Ithas been reported that during severe deformation of Cu andCu-alloys, high density dislocation flux glide and either accumulateat TBs or transmit across TBs [15,32–34]. The dislocated TBs reducetheir excess energy by forming steps leading to the formation ofcurved TBs. These faceted steps is a low energy state, which is ther-modynamically more stable than that of dislocated TBs [32–34].Moreover, a closer investigation of the HRTEM images has revealedthat the microstructure contains �10 nm size subgrain in side thepreexisting twin lamellae, as marked in Fig. 4(b) and (c). On theother hand, high density twins with reduced twin spacing (dtwin)has been observed in severely CR specimens, as shown inFig. 3(c) and (d) for CR07 and CR095, respectively. Moreover,another set of twins have appeared to lie along the perpendiculardirection of the primary twins, which were identified as secondarytwins, as marked by arrows in Fig. 3(d) for CR095.

In order to characterize the microstructure evolution quantita-tively during cryorolling, twin spacing/matrix lamellae thickness(dtwin) and twin lamellae thickness (k) were estimated from a largenumber of DF images, and their distribution are presented inthe histograms in Fig. 5(a)–(h). The average values of k and dtwin

Fig. 3. (a–d) TEM bright field images and (e–h) double diffraction spots in the SAEDfragmentation of twin during CR.

have been estimated to be 66 ± 6 nm and 170 ± 8 nm for CR02;and 28 ± 3 nm and 38 ± 3 nm for CR095, respectively. Fig. 5(a–h)shows that the average values of k and dtwin decrease and theirdistribution become narrow with the increase of CR strain.

3.3. Microhardness measurements

The evolution of microstructural homogeneity upon CR hasbeen evaluated by Vickers’ microhardness measurements alongthe width direction on NW plane, and the results are shown inFig. 6. A few trends have been observed as follows: (i) the averagehardness for each specimen increases gradually with the increaseof CR strain, and (ii) uneven fluctuations of microhardness hasbeen observed over a length of �1–2 mm. Furthermore, the extentof fluctuations increases with increase of CR strain and has beenfound to reach to a maximum value of 156.4 ± 6.2 Hv in CR07 com-pare to that of ST (81.9 ± 2.7 Hv). However, the fluctuationsdecreases with further increase of CR strain. As an example, theaverage microhardness of CR09 and CR095, were estimated to be168.0 ± 4.4 Hv and 173.2 ± 4.3 Hv, respectively. The decrease inthe error range of the microhardness values indicates the evolutionof homogeneity in CR09 and CR095 as observed in Fig. 6.

3.4. Compression test results

The stress–strain curves of ST and CR specimens are shown inFig. 7. The yield strength (ry) of ST specimen (110.3 MPa) is lowerthan that of CR specimens. Moreover, ry increases considerablywith increase of CR strain and reaches up to ry = 603 MPa in

patterns of CR02, CR04, CR07, CR095, respectively, showing the formation and

Fig. 4. (a) TEM bright field images of CR07 showing curved twin boundary, and (b–c) corresponding HR images showing the presence �10 nm size subgrains withinpreexisting twin lamellae.

Fig. 5. Histograms showing distribution of (a–d) twin lamellae thickness (k), and (e–h) matrix lamellae thickness (dtwin), as measured from the TEM DF images of rolledspecimens (n = number of measurements).

142 N.K. Kumar et al. / Journal of Alloys and Compounds 618 (2015) 139–145

CR07, which is closer to that of CR09 (620 MPa) and CR095(647 MPa). Besides large plasticity (ep = �61%) in ST, thecompressive plastic strain decreases with increase of CR strain, asevidenced in Fig. 7. As an example, ep decreases from 42.0%(CR02) to 1.2% (CR095). Therefore, the flow stress of CR specimensincreases with increase of CR strain followed by a loss of compres-sive plasticity.

4. Discussion

4.1. Microstructural refinement during cryorolling

Annihilation of defects due to dynamic recovery limits the grainrefinement process during SPD at room temperature [20,27].Whereas, deformation at cryogenic temperature minimizes the

Fig. 6. Average value of Vickers’ microhardness (Hv), plotted against the distancefrom the center of the ST and rolled specimens along width direction on NW planeshowing the evolution of hardness homogeneity at eCR P 0.9.

Fig. 7. Compressive stress–strain curve of ST and CR specimens at room temper-ature at an initial strain rate of 8 � 10�4/s, showing an increase of flow stressfollowed by a loss of compressive plasticity at higher CR strain (eCR P 0.7).

N.K. Kumar et al. / Journal of Alloys and Compounds 618 (2015) 139–145 143

dynamic recovery lowers the possibility of detwinning reactions inthe matrix, and thus helps in retaining the defect structure [20,30].It is inferred from XRD analysis that the crystallite size decreasesfrom �162 nm (ST) to �17–27 nm (CR095) during CR. The micro-structural refinement depends on qd, qtwin and a slow recovery pro-cess during plastic deformation [28].

In the case of low-SFE fcc metals, [211] dislocations are disso-ciated into partials ([110] and [121]) forming a wide SF ribbons,which restrict cross-slip/climb of dislocations [11,19,28]. There-fore, deformation twinning becomes a preferred mode of deforma-tion and expected to form in a-brass upon CR due to its low SFE(14 mJ/m2) as evident in Fig. 3. In the present study dissociationof the microstructure proceeds by the formation of twinned andmatrix regions during the initial stage of CR. Further refinementin the microstructure involves formation of newer twins in thematrix, which reduces the thickness of k and dtwin resulting a nar-row T/M distribution as shown in Fig. 5(b)–(d). Local relaxation ofmechanical twinning results in the formation of secondary twininside primary twin along width direction [11], which refines themicrostructure by reducing the length of primary twin lamellae,as observed in Fig. 3(d).

XRD analysis has shown that qd increases from 3.45 � 1014/m2

(CR02) to a maximum value of 2.98 � 1015/m2 at eCR = 0.95. It isinferred that a large dislocation flux flow through the grains duringCR to increase the stored sessile dislocation density. Since TBs actas a dislocation barrier, dislocations must have accumulated at

TBs resulting a curved feature, as evidenced in the white rectanglein Fig. 4(a). It is believed that the dislocation piles up at TBs inter-sect the twin lamellae at higher stress level and have fragmentedthem into equiaxed structure. Accumulation of dislocations atTBs results the formation of LAGBs and �10 nm size subgrains, asshown in Fig. 4(c).

4.2. Evolution of microscopic and macroscopic homogeneity

The results of microhardness measurement revealed two majortrends in differently CR specimens. The first important observationis that, the average microhardness values increases with theincrease of CR strain. TEM studies revealed that dtwin decrease withincrease in CR strain and increase the fraction of TB area, which actas a barrier to dislocation motion. Therefore, the hardness (H) ofthe CR specimens increases with the reduction of dtwin accordingto Hall–Petch type relation as H ¼ Ho þ kHd

�12

twin, where Ho and kH

are constants [35].Second, the fluctuation of microhardness values along width

direction increases with increase of CR strain up to eCR = 0.7 asshown in Fig. 6. A homogeneous hardness distribution along thecross section has been observed in case of ST (81.9 ± 2.7 Hv) andCR095 (173.2 ± 4.3 Hv) specimens. The microstructure of the STconsists of equiaxed grain of �500 lm size [11], and is responsiblefor the homogeneous hardness distribution with small error value.Furthermore, the microstructure is dissociated into twin andmatrix upon CR, as observed in Fig. 3. A large difference in the val-ues of k, and dtwin has been observed at the initial stage of CR(eCR < 0.7). Since k < dtwin, therefore, the hardness recorded intwin-rich regions will be higher than that of matrix region. As aresult, the fluctuation in the microhardness profile has beenobserved for CR02, CR04 and CR07 specimens. On the other hand,both k, and dtwin decreases and k values approaches to dtwin result-ing a narrow distribution of both twin and matrix lamellae athigher CR strain (eCR P 0.9) as shown in Fig. 5(d and h). Therefore,a homogeneous nanostructure has been evolved at CR09 andCR095 resulting homogeneous hardness distribution.

4.3. Correlation between structural defects and flow stress

TEM study revealed that formation of twins during CR refinesthe microstructure and should contribute to the strength of thespecimens according to the Hall–Petch type relationship, asreported earlier [15]:

ry ¼ ro þ k1

dtwin

� �12

ð3Þ

where ro and k are constants. ry has been plotted against inversesquare-root of twin spacing (

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=dtwin

p) as shown in Fig. 8(a). A poor

linear fit between ry andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=dtwin

pyields a R2 value of 0.8470.

Therefore, it is intuitive that other substructure(s) coexisting withTBs, are responsible for altering the flow stress of the differentlyCR specimens. The microstructural parameters such as, subgrainsize (dsub), qd, and dtwin will interact with dislocations, which influ-ence the flow stress of CR specimens in the present study(0.2 6 eCR 6 0.95) [31]. In addition, we have also considered theabove mentioned parameters for the specimens from our earlierwork (0.98 6 eCR 6 2.0) [11]. Since the XRD analysis revealed thatthe change in the lattice strain as well as qd is very low for speci-mens above eCR > 0.4, hence, qd for CR specimens (0.98 6 eCR 6 2.0)of our earlier work has been considered to be 2.98 � 1015/m2. Aquantitative estimation has been made to calculate the strengthcontribution arises due to various microstructural parameters uponCR for a wide range of strain (0 6 eCR 6 2.0) according to the follow-ing equation [36,37]:

Fig. 8. Plots between the flow stress (ry or ry � aGbffiffiffiffiffiffiqdp

) andffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=dtwin

por

ffiffiffiffiffiffiffiffiffiffiffi1=dfp

pof

differently CR specimens; R2 values for plot (a) and (b) are 0.8470 and 0.9524,respectively; data points of the filled bubbles are taken from reference [11].

144 N.K. Kumar et al. / Journal of Alloys and Compounds 618 (2015) 139–145

ry ¼ ro þ k1

dfp

� �12

þ aGbffiffiffiffiffiffiqdp ð4Þ

where dfp is the mean free path for dislocations, a is a constantwhich varies from 0.2 to 0.6, and G is the shear modulus. However,dfp depends on the grain size and presence of any twins/subgrains inthe microstructure. Therefore, the coexistence of TB and subgrainduring nanostructuring has been considered in the present studyand therefore, dfp can be estimated as [38]:

1dfp¼ 1

dtwinþ 1

dsubð5Þ

Hence, Eq. (4) can be rewritten as:

ry ¼ ro þ k1

dtwinþ 1

dsub

� �12

þ aGbffiffiffiffiffiffiqdp ð6Þ

The shear modulus of a-brass is �39 GPa, Burger’s vector is 0.26 nmfor fcc (111) [112], slip system and a is taken as 0.2. The values ofdsub has been considered to be the average value of crystallite size(D) for NW and RW planes as calculated by classical and modifiedWilliamson-Hall method. A good linear fit has been obtainedbetween ðry � aGb

ffiffiffiffiffiffiqdp Þ and

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=dtwin þ 1=D

pwith R2 = 0.9524 to

predict the strength of the nanotwinned brass as shown in Fig. 8(b).It is obvious that formation of twin inside a grain reduces dfp

and contribute to the strengthening mechanism. Whereas, the dis-crepancies of the experimental results in Fig. 8(a) indicates the lim-itation of Eq. (3) to predict the strength of nanotwinned brass.Examination of HRTEM micrographs in Fig. 4(b) and (c) revealedthe formation of subgrains inside the preexisting twin lamellae,which reduces dfp further. Therefore, we have considered the aver-age crystallite size (D) as subgrain size in Eq. (6) to estimate dfp.Furthermore, X-ray analysis has shown that qd increase over oneorder magnitude during CR. As a result, aGb

ffiffiffiffiffiffiqdp

increases from37.7 MPa (CR02) to 110.9 MPa (CR095), which considerably con-tributes to increase the overall strength of the specimen. Thus,the contribution of D and qd along with dtwin is essential to explainthe observed strength of the nano-twinned brass. It has beenobserved that the value of dfp is mostly dominated by dtwin at theearly stage of CR (eCR 6 0.4), whereas, the values of D dominatesat the later stage.

5. Conclusions

The following conclusions have been drawn from the presentinvestigation:

� The microstructure of Cu–30 wt.% Zn with 500 lm grain sizehas been refined down to nanometer range (�20 nm inCR095) by adopting CR technique as estimated by XRD andTEM analyses. The microstructural refinement process duringCR involves formation of primary/secondary twins, dissociationof the microstructure into twinned and matrix regions, frag-mentation of T/M lamellae by high-density dislocation flux thatpile-up at TBs, and formation of �10 nm size subgrains withinthe preexisting twin lamellae.� Even though, the average hardness and compressive strength

values increase about 2–2.5 times upon CR but, the local microh-ardness fluctuations have occurred over a length scale of�1–2 mm, which decreases at larger CR strain (eCR P 0.9).Formation of newer twins in the matrix causes reduction of dtwin,which approaches to k value with increase of CR strain. Presenceof equal thickness of k and dtwin, and their uniform distribution ateCR P 0.9 help on the evolution of homogeneous nanostructureresulting an increase in the hardness homogeneity.� The reduction of dfp and the increase of qd during CR have raised

the flow stress follows by a loss of compressive plasticity. Theflow stress is mostly dominated by dtwin at the initial stage ofCR. Whereas, formation of subgrains inside the preexistingT/M lamellae reduces the effective dfp and controls the flowstress at CR strain (eCR P 0.4). Model calculations show thatqd, D and dtwin are the important parameters for predictingthe strength of the nanotwinned brass.

Acknowledgements

The authors thank P. Das, K. Sahoo, R. Basu, and S. Bhattacharyafor technical assistance. Financial support provided by DST, SERB,Govt. of India for the project entitled ‘‘Processing and characteriza-tion of bulk nanostructured brass’’ (Grant number: D.O. SR/FTP/ETA-88/2010) is gratefully acknowledged.

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