MECHANICAL BEHAVIOR OF BULK ULTRAFINE ...mp.ipme.ru/e-journals/RAMS/no_2604/zhang/zhang.pdfof ultrafine-grained and nanocrystalline materials may be enhanced by the following ways

53Mechanical behavior of bulk ultrafine-grained and nanocrystalline Zn

Corresponding author: X. Zhang, email: [email protected]

Rev.Adv.Mater.Sci. 6 (2004) 53-93

© 2004 Advanced Study Center Co. Ltd.

MECHANICAL BEHAVIOR OF BULK ULTRAFINE-GRAINEDAND NANOCRYSTALLINE Zn

X. Zhang1, H. Wang1 and C. C. Koch2

1 Materials Science and Technology Division, Mail Stop G755, Los Alamos National Laboratory, Los Alamos,NM 87545, USA

2 North Carolina State University, Department of Materials Science and Engineering, Raleigh, NC, 27695-7907,USA

Received: February 15, 2004

Abstract. Mechanical properties of bulk ultrafine-grained and nanocrystalline Zn produced bymechanical milling are reviewed. Dynamic recrystallization plays an important role in themicrostructural evolution of cryomilled Zn during early milling times. The modulated oscillation ofhardness during cryomilling is a combinational effect of dynamic recrystallization, average grainsize, grain size distribution and dislocation density variations. Bulk ultrafine-grained andnanocrystalline Zn, synthesized by in situ consolidation during milling, possess high tensileductility. Deformation mechanisms in larger grains (submicron) are different from that in nanoscalegrains. Microstructure, ductility and deformation mechanisms in Zn and other ultrafine-grainedand nanocrystalline elemental metals are compared. These comparisons indicate that the ductilityof ultrafine-grained and nanocrystalline materials may be enhanced by the following ways (i)increasing strain hardening (ii) increasing strain rate sensitivity (iii) activating other deformationmechanisms such as twinning or stacking faults (iv) accommodating grain boundary sliding topostpone the generation of pores along the grain boundaries or triple junctions. The engineeringdesign of materials with high strength and high tensile ductility can be achieved by optimizing themicrostructures of ultrafine-grained and nanocrystalline materials.

Table of Contents

1. Introduction 542. Background 542.1. Evolution of microstructure during

mechanical milling 542.1.1. Nanocrystallite formation mechanisms 542.1.2. Evolution of grain size 552.1.3. Lattice strain and stored enthalpy 562.1.4. Recovery and recrystallization 562.2. Techniques that can synthesize bulk

ufg and nc materials 572.3. Deformation mechanisms 582.3.1. Size effect on plasticity 582.3.2. Ductility 593. Microstructure evolution in cryomilled Zn 603.1. Nanocrystallite formation by dynamicrecrystallization 60

3.2. Lattice strain and stored enthalpy 634. Mechanical behavior of cryomilled bulk nc Zn 674.1. Effect of dynamic recrystallization on the

mechanical behavior of compacted bulkCM Zn 67

4.2. Ductility of compacted bulk CM Zn 705. The synthesis of bulk nc Zn by in situ

consolidation of powders 726. Mechanical properties of in situ

consolidated bulk nc Zn 746.1. Strength and ductility of nc Zn studied

by microhardness and MDBT tests 776.2. Ductility and deformation mechanisms

of BM Zn studied by uniaxial tensile tests 747. Comparisons of the microstructure and

mechanical properties of bulk nc Znprepared by cryomilling and roomtemperature milling 81

54 X. Zhang, H. Wang and C. C. Koch

7.1. Grain size and its distributions asa function of temperature 81

7.2. Mechanical properties 827.3. Optimizing mechanical properties of

bulk nc Zn by combination of the twotechniques 82

8. Comparisons of deformation mechanismsin bulk ufg and nc elemental metals 84

9. Summary 90

1. INTRODUCTION

Recently there has been a great deal of interest instudying the mechanical behavior of bulk ultrafine-grained (ufg, grain size in the range of 100 nm –1000nm) and nanocrystalline (nc, grain size in therange of less than 100 nm) metals and alloys. Thedriving forces behind these studies come from thehope that ufg and nc materials may possess bothenhanced strength and ductility. The knowledge ofdeformation mechanisms of ufg and nc materials iscritical for engineering design of these materials withhigh strength and high ductility. Such informationcan be obtained from rigorous tensile testing tech-niques, such as uniaxial tensile tests, by using largeenough bulk specimens. There have been many tech-niques that can synthesize nc materials in the formof powders or thin films, eg. inert gas condensation[1], rapid solidification [2], electrodeposition [3], crys-tallization of amorphous phases by annealing [4],chemical processing [5], sputtering [6] and pulsedlaser deposition [7]. Mechanical attrition-the ballmilling of single or multicomponent powders- hasalso been widely used to synthesize nanostructuredmaterials [8]. However, the techniques that can syn-thesize fully dense bulk nc materials are very lim-ited. Consolidation of powders with nanoscale grainsize is one of the most commonly used techniques.Porosity on the nm or µm level usually remains af-ter compaction and proves to be detrimental to theductility of nc materials. The difficulty of obtainingporosity-free bulk nc materials has stimulated ex-tensive research on improving existing processingtechniques as well as exploring new approaches,such as equal channel angular pressing [9,10], coldrolling [11], electrodeposition [12-14] and stackingof multilayers by magnetron sputtering [15]. Detailson some of these techniques will be given in Sec-tion 2.2. In addition, Section 2 provides backgroundinformation that may put the work of the paper incontext. This section explains important basic con-cepts and summarizes up-to-date progress and chal-lenges in close relevance to the article. The follow-ing subjects will be reviewed in section 2:(1) evolution of microstructure during mechanical

milling;

(2) techniques that can synthesize bulk ufg and ncmaterials; and

(3) deformation mechanisms.

In this article, we will review the microstructuralevolution and mechanical properties of porosity freebulk ufg and nc Zn synthesized via several ap-proaches: (i) cryomilling (mechanical milling per-formed at 77K) followed by powder compaction, (ii)in situ consolidation of powders during room-tem-perature mechanical milling (iii) a combination ofcryomilling and in situ consolidation technique. Morespecifically, the article will focus on the followingsubjects:(1) evolution of microstructure (grain size and its

distribution) in cryomilled (CM) Zn with empha-sis on the dynamic recrystallization (DRX) phe-nomenon and the correlation of stored enthalpyand microstrain induced during milling (Sec. 3);

(2) effects of DRX, grain size distribution and dislo-cation density variations on the mechanical prop-erties of compacted CM Zn powders (Sec. 4);

(3) synthesizing bulk ufg and nc Zn by in situ con-solidation of nc Zn powders during mechanicalmilling at room temperature (BM) (Sec. 5);

(4) mechanical properties and deformation mecha-nisms of in situ consolidated bulk nc Zn studiedby tensile tests (Sec. 6);

(5) comparisons of the microstructure and mechani-cal properties of bulk ufg and nc Zn prepared bycryomilling and room temperature ball milling(Sec. 7);

(6) comparisons of deformation mechanisms in ufgand nc Zn with other metals and strategies toimprove ductility of ufg and nc metals (Sec. 8).

Zn with ufg or nc structures will serve as themodel material to illustrate basic concepts, under-stand the plastic deformation mechanisms and ex-plore the possibilities of optimizing strength andductility in ufg and nc metals from a broader point ofview.

2. BACKGROUND

2.1. Evolution of microstructureduring mechanical milling

2.1.1. Nanocrystallite formation mechanismsDuring mechanical milling, materials will often ex-perience heavy cyclic deformation. It is believed thatmechanical milling produces its nanostructures bythe structural decomposition of coarser-grained (cg)structures as the result of severe plastic deforma-tion. The current understanding of the developmentof nc microstructures in single-phase materials by


mechanical milling has been reviewed before [8,16].Initial information in this regard comes from trans-mission electron microscopy (TEM) studies of ball-milled Ru and AlRu microstructures as a function ofmilling time [17,18]. These early studies proposethe formation of subgrains followed by their rotationsuch that small nc grains possessing high anglegrain boundaries are created [16]. This mechanismworks reasonably well for many single-phase met-als milled at room temperature. A common featureindicated by this mechanism is that nc grains withhigh angle grain boundaries, on the order of 10 nmor less, will be produced after a long period of mill-ing time. However, this may not be the only operat-ing mechanism when milling is carried out underliquid nitrogen temperature (77K), cryomilling. Dy-namic recrystallization has been proposed to ex-plain the formation of nc Zn and other materials dur-ing early stages of cryomilling or cold working [17-19]. Details on the new mechanisms for the forma-tion of nc Zn during cryomilling will be presented inSec. 3.2.

2.1.2. Evolution of grain sizeUsing X-ray line broadening to measure average grainsize it is commonly observed that the average grainsize decreases with milling time. The minimum av-erage grain size (d

min) obtainable by milling has been

attributed to a balance between the defect/disloca-tion structure introduced by the plastic deformationof milling and its recovery by thermal processes [20].It was also found that d

min scales inversely with melt-

ing temperature for selected face centered cubic(fcc) metals as shown in Fig. 1 [21] (data takenfrom [20, 22-26]). However, the d

min for body cen-

tered cubic (bcc) and hexagonal close packed (hcp)metals, and for fcc metals with higher melting tem-peratures, exhibit essentially constant values withmelting temperature. The value of d

min is about 14

nm for hcp metals, 8 nm for bcc metals and 6nm forhigh melting point fcc metals. It had been proposedfor pure metals that the limiting grain size is deter-mined by the minimum grain size that can sustaina dislocation pile-up within a grain and by the rateof recovery [20]. It was shown that there was anapproximate linear relationship between the finalgrain diameter and the critical equilibrium distancebetween two edge dislocations in a pile-up, L

c. The

latter distance was calculated from the expression[27]:

��

��

=−

�

�π ν� �� (1)

Fig. 1. Minimum grain size for nc elements vs. theirmelting temperatures (open symbols (20, 22); filledcircles (26); Si (23, 24); C (25)).

where G is the shear modulus, b is the magnitudeof the Burgers vector, ν is Poisson’s ratio, h is hard-ness of the material. Therefore hardening results inreduced values for L

c.

There are several factors that can influence thevalue of d

min attained by ball milling. These include

the energy of mill [28], ball to powder ratio (BPR)[29], solid solution hardening [30] and milling tem-perature [28]. Typically, higher mill energy, largerBPR values and lower processing temperature willlead to a finer grain size. It should be noted, how-ever, that in certain cases grain size was found toincrease to a certain extent during ball milling andthen decreased for further milling instead of decreas-ing continuously with increasing milling time [31,32].Most previous studies focus on the evolution of av-erage grain size during milling. Recently attentionhas been paid to the evolution of grain size distribu-tion as this parameter is important for understand-ing mechanical behavior of nc materials [17,33,34].

2.1.3. Lattice strain and stored enthalpyStudies on lattice strain and stored enthalpy willprovide additional information on nc formation mecha-nisms. Lattice strain is usually introduced into thematerials due to severe plastic deformation duringmilling. The effects of lattice strain and grain sizescan be separated from each other by careful analy-sis of the X-ray peak shapes [35,36]. The latticestrain results from the literature were summarizedand plotted vs. reciprocal grain size (1/d) by Koch[21]. Interestingly, in his plot of lattice strain vs. 1/d,it has been found that for some systems, Ti [37],Pd [20], the lattice strain increased continuouslywith decreasing grain size and reached a maximumvalue at the smallest grain size. For some other


systems such as Ru [22], Al, Ni, Fe and W [26],however, the lattice strain first increases, reaches amaximum and then decreases, i.e., there is also amaximum in lattice strain with the decreasing grainsize. An example of the plot of strain vs. 1/d for W(solid points) is given in Fig. 2. The stored enthalpy(or stored energy) in W, represented by open datapoints in the same plot, followed the same trendcompared with that of lattice strain. To explain themaxima in stored enthalpy with 1/d, some suggestedthat the stored enthalpy comes mainly from grainboundaries and grain boundary strains [26]. Stressrelaxation or recover may be responsible for themaxima [26]. However, the fact that the two maximado not occur at the same grain size raises someconcern for this explanation. Maxima of lattice strainand stored enthalpy were also observed in cryomillednc Zn. Details on these results are presented inSec. 3.2.

2.1.4. Recovery and recrystallization

Recovery. As mentioned in Sec. 2.1.2. and 2.1.3.,recovery is related to the d

min obtainable during the

milling process and the maxima of lattice strain incertain systems. Recovery refers to changes in theproperties of deformed materials which occur priorto recrystallization; these changes are such as topartially restore the properties to their values beforedeformation [38]. Recovery can occur in plasticallydeformed materials and in crystals that possess ahigh density of defects, point defects and/or linedefects, and reduce the defect density or strain asa result. The recovery process can be described in

several steps: the formation of dislocation cell wallsin highly dislocated materials, annihilation of dislo-cations within the cells, the formation of subgrainsand subgrain growth by either subgrain boundarymigration or subgrain rotation and coalescence [38].Complete recovery occurs when polycrystallinemetals have been lightly deformed [39]. If the crys-tals are heavily deformed to a certain extent, how-ever, recrystallization usually occurs [40]. As therecovery process usually happens at higher anneal-ing temperatures, one can depress recovery by re-ducing the deformation temperature.

Recrystallization. Recovery is a relatively homo-geneous process that progresses gradually withoutidentifiable beginning or end of the process.Whereas recrystallization involves the formation ofnew grains, free from strains, in certain parts of thespecimen and the subsequent growth of these grainsto consume the deformed or recovered microstruc-ture [38]. Both processes are driven by and conse-quently consume the stored energy in the deformedmaterials. Recovery, if it occurs first, could consumea large fraction of stored energy and therefore sup-press the occurrence of recrystallization and viceversa. Recrystallization will prevail over recoveryduring a high strain rate, low temperature deforma-tion process [38,41]. Mechanical milling can createvery high strain and strain rate in the ball milledmaterials compared to that from the traditional coldrolling method, and thus create inhomogeneouslydistributed dislocations and defects where someregions may have a high dislocation density. Thesehighly disordered areas may store enough energyto induce or facilitate a recrystallization process.

Dynamic recrystallization. Recrystallization canbe categorized by comparing the sequence of re-crystallization with the plastic deformation. In manycases, recrystallization occurs during post-deforma-tion annealing processes, which is called static re-crystallization. If the recrystallization occurs duringdeformation, however, it is called dynamic recrys-tallization (DRX). The nucleation mechanisms forstatic recrystallization include strain induced grainboundary migration [38,42] and preexisting nucleisuch as dislocation cells or subgrains [43,44]. Dur-ing DRX, nucleation as well as growth (grain bound-ary migration) takes place while the strain is beingapplied [45]. New grains originate at the old grainboundaries. As the materials continues to deform,the dislocation density of the new grains increases,thus reducing the driving force for further grain growth,and the recrystallized grains eventually cease togrow [40].

Fig. 2. Stored enthalpy and lattice strain vs. recip-rocal grain size for W [26].


The nucleation mechanism for DRX is assumedto be similar to that for static recrystallization, straininduced grain boundary migration. Bulging of grainboundaries is frequently observed as a prelude toDRX. The critical nucleus diameter, x

c, for DRX is

given by

��

�

=� �ρ

ε�� (2)

where M is the grain boundary mobility, L is the meanslip distance of the dislocations, G is shear modu-lus, b is Burger vector, ρ

m is the dislocation density,

�ε is the strain rate. Details on derivation for this for-mula can be found in references 38, 46 and 47.

Under the assumption that nucleation occurs bya bulge mechanism, then the condition for the for-mation of a critical nucleus with diameter x

c, is

�

�

�

>�γ

� (3)

where E is the stored energy and γb is the specific

boundary energy. E is given by E = KρmGb2, K is a

constant. Hence the condition for nucleation is

ρ

ε

γ �

��

�

� �

�

�

�> (4)

The terms on the right hand side are approximatelyconstant at a particular temperature. Thus the con-dition for the nucleation of DRX is that a critical valueof ρ

m/ �ε must be achieved. In materials with low

stacking fault energy, recovery is slow and the dis-location density could be increased to the criticalvalue necessary for DRX to occur. Decreasing thedeformation temperature can also suppress the dis-location recovery and therefore facilitate DRX.

Different types of DRX have been identified ac-cording to their characteristics during the process.In the case of geometric DRX, grain boundaries de-velop serrations during dynamic recovery, and thewavelength of these serrations is similar to thesubgrain size [48-50]. Although a large number ofthe boundaries are usually low angle grain bound-aries, the fraction of high angle grain boundarieswill increase with increasing strain [48]. GeometricDRX often occurs in a variety of higher stacking faultenergy alloys where pronounced dynamic recoveryoccurs [45]. In other cases, DRX is characterizedby progressive lattice rotation. New grains with highangle boundaries may be formed by the progres-sive rotation of subgrains with little accompanyinggrain boundary migration [51]. The mechanism by

which this progressive subgrain rotation occurs isnot very clear. It is possible that grain boundary slid-ing is also involved in this process. DRX has beenidentified in CM Zn and is believed to be respon-sible for the formation of nanoscale grains with highangle grain boundaries during the early stages ofcryomilling [17]. Details of DRX phenomenon incryomilled Zn will be presented in Sec. 3.1. This phe-nomenon will be revisited when discussing the evolu-tion of mechanical behavior of CM nc Zn in Sec. 4.

2. 2. Techniques that can synthesizebulk ufg and nc materials

Bulk ufg and nc materials can be synthesized via atwo-step processing technique, production of pow-ders with nc grains followed by compaction toachieve full density in the materials, for examplethe synthesis of bulk nc Cu, Pd [52] by combina-tions of inert gas condensation and compaction. Thetwo-step techniques have the advantage of obtain-ing nc metals with a wide range of grain sizes vary-ing from submicron to ~ 10 nm in a wide variety ofmaterials. However, the compacted materials maynot reach full density. A certain amount of contro-versial research, such as negative Hall-Petch rela-tions (where below certain grain size, the hardnessof materials decreases with decreasing grain size)and extremely limited tensile ductility could be re-lated to the residual porosity in these compactednc materials [53]. Some attempts have been madeto increase the density of compacted materials. Animprovement in ductility of compacted materials hasbeen achieved [52,54].

Compared with the above-mentioned two-stepprocessing techniques, several one-step process-ing techniques have been developed.(1) Severe plastic deformation (SPD). SPD has been

shown to be an effective way to produce bulk ufgand nc materials. Details have been reviewed byValiev et al. [55]. Typical SPD techniques includehigh pressure torsion (HPT), equal channel an-gular pressing (ECAP) and repetitive corrugationand straightening (RCS). These techniques pro-duce nc or ufg by severely deforming bulk mate-rials. Therefore as-prepared materials typicallyhave the same density as raw materials, avoid-ing the generation of porosity.

(2) Electrodeposition. Electrodeposition has beensuccessfully used to produce bulk ufg and ncmetals, such as Cu [56], Ni [57], Zn [13] and Co[14]. This technique provides several advantages:(i) synthesizing artifact-free bulk materials (ii)easy to control grain sizes from 10 nm to sub-


micron (iii) usually narrow grain size distribution.Special attention should be paid to the incorpo-ration of certain impurities (S, O and H, etc.)into the materials, as some of these elementsmay embrittle the materials.

(3) Flux melting and casting. Recently Shen andSchwarz successfully synthesized bulk Cu/Agnc alloys via flux melting techniques [58,59].First, they synthesize alloys by mechanical al-loying. Then melt the alloyed powders in fusedsilica tube and purify the melt with a flux. Byquenching the molten alloys, bulk nc metals oreven amorphous alloys can be synthesized. Theydemonstrate that the microstructure, such asgrain size, can be controlled by carefully purify-ing the melt with flux and choosing appropriatequenching rate [59]. Bulk nc Cu/Ag eutectic al-loys synthesized via this technique possess highstrength and low resistivity, making it an attrac-tive candidate as strong structural materials forhigh magnetic field applications. He et al. [60]use casting method to obtain a nanocompositewhere dendrites of a ductile Ti-rich solution wereformed in situ within nc matrix. These nanocom-posites have high strength and potentially goodductility.

(4) Synthesizing sheet metals by roll-bonding andsputtering. Roll-bonding process has been usedto synthesize bulk nc composites by cyclic roll-ing and stacking dissimilar metals [61]. To achievegood bonding between adjacent materials, care-ful surface cleaning and a high degree of defor-mation (50% rolling) are usually required [62].Composites with nc grain size and in certain casesamorphous alloys can be attained [62, 63]. Misraet al. [15, 64] have recently performed system-atic studies on Cu based multilayer films synthe-sized via magnetron sputtering techniques. Theunique feature of this technique is that the indi-vidual layer thickness of multilayer compositescan be controlled, varying from a few nm to sub-micron, while keeping the total thickness in tensor even hundreds of micron range. These bulk nccomposites have unusually high strength [15] andconsiderable ductility as evidenced by rolling andtensile tests [64,65].

One-step processing techniques have the ad-vantage of obtaining porosity-free bulk ufg or nc ma-terials. The ductility of thus-prepared materials isusually higher than those prepared via two-step pro-cessing techniques. Some of these techniques havepotential to mass-produce bulk ufg and nc materi-als and therefore stimulate the hope of commercial-izing bulk ufg and nc materials.

2. 3. Deformation mechanisms

Current understanding of the deformation mecha-nisms of nanostructured materials is very limitedpartially due to the porosity in compacted materi-als. Another major barrier is that it is usually diffi-cult to produce specimens large enough for deci-sive tensile tests. Based on current research ondeformation mechanisms in UFG and nc materials,we will review some of the following aspects.

2.3.1. Size effect on plasticityIn single-phase bulk nc materials, it is likely that forthe larger end of the nanoscale grain sizes, about50 to 100 nm, dislocation activity dominates for testtemperatures < 0.5 T

m, where T

m stands for melting

temperature of the material. As grain size decreases(still larger than 10 nm), dislocation activity decreasesdue to the reduction of dislocation density in smallnc grains. In other word, intragrain deformation, evi-denced mainly by dislocation activity, dominates atthese stages (10-100 nm). At the smallest grainsizes regimes, 10 nm or less, a new deformationmechanism might dominate, intergrain deformation,which may involve grain boundary sliding or grainrotation accompanied by short-range diffusion as-sisted healing events. Grain boundary sliding waspredicted by molecular dynamics (MD) simulations[66-68] and observed experimentally [69,70]. More-over, MD simulations have shown that grain bound-ary sliding might be triggered by atomic shufflingand to a minor extent, stress assisted free volumemigration [68]. Atomic shuffling involves short rangeatomic motion in which an atom shifts from a posi-tion associated with one grain orientation to a posi-tion associated with another neighboring grain ori-entation or an intermediate one [68]. This is a non-diffusional process, as it does not involve long-rangemass transport. Chen et al. [71] determined the criti-cal shear stress to initiate plasticity in nc Cu (aver-age grain size is around 14 nm) with nanoindentationtechnique. The measured critical shear stress,around 8 GPa, is identical to that required for thenucleation of lattice dislocations in cg Cu, close tothe theoretical strength in dislocation free singlecrystal Cu. Their studies, consistent with MD simu-lations [72], indicate that the onset of plasticity ofthe nc Cu is associated with initiation of dislocationactivities at grain boundaries.

The grain size effect on plasticity is also reflectedfrom the strength of these materials. In the typicalHall-Petch plot, hardness vs. 1/d -1/2 (d is the aver-age grain size), the hardness usually increases lin-early with 1/d -1/2 for grain size larger than 100 nm.Dislocation pile- up model can explain the strength-


ening behavior in this regime. This linear strength-ening relation is deviated, with hardness falling be-low the value predicted by the extension of linearrelation, at smaller grain sizes, 10 ~ 100 nm. Dislo-cation pile-ups become less likely in this range. In-stead, dislocation bowing mechanism, Orowanmodel, may start to operate [73,74]. The hardnesstypically reaches its maximum at around 10 nm,where dislocation activities mainly originate fromgrain boundaries. Misra et al. [75,76] propose asingle dislocation model to explain the strengthen-ing in multilayer composites when the layer thick-ness is in the nanoscale, 100 nm or less. The modelpredicts an increase in strength of the multilayerwith decreasing layer thickness of each individuallayer, consistent with experimental observations.

2.3.2. DuctilityAlthough nc metals have significantly higher strengththan cg materials, their ductility is often limited.Ductility can be measured via many techniques.Uniaxial tensile tests are most frequently used formeasuring ductility in conventional materials as theyprovide rich information about deformation mecha-nisms of the materials, such as strain hardeningand strain rate sensitivity.

Strain hardening. During plastic deformation of con-ventional metals and alloys, the flow stress requiredto produce slip continuously increases with increas-ing strain. This effect, known as strain hardening orwork hardening, is usually caused by dislocationsinteracting with each other or with barriers whichimpede their motion through the crystal lattice.Strain hardening is an important behavior often ob-served in ductile deformation. An ideal plastic ma-terial, where there is no strain hardening, wouldbecome unstable and start necking as soon as yield-ing occurs. The condition of tensile instability is de-scribed as: (dσ/dε) < σ, where σ and ε stands forflow stress and strain during deformation.

Research on strain hardening behavior in ufg andnc materials is somewhat controversial. In somecases, ufg and nc materials are found to show strongstrain hardening behaviors [11,14,78,79], whereas inother cases, they show little strain hardening [80-83]. Careful examinations of these studies are nec-essary as the difference in these studies lie in manyfactors such as processing techniques, microstruc-ture, density and testing techniques.

Strain rate sensitivity. Strain rate, �ε is defined asdε/dt and is expressed in units of s-1. Strain ratehas an important effect on the flow stress. At con-stant strain and temperature, a general relationshipbetween flow stress and strain rate is:

σ ε= �

�� (5)

where C is a constant and m is known as the strainrate sensitivity. m can be calculated by:

= =��

��

∂ σ

∂ ε

σ σ

ε ε

�

��

��

��

� �

� �� (6)

Therefore, the exponent m can be obtained from aplot of logσ vs. log �ε . The value of m conveys infor-mation of deformation mechanisms related to dislo-cation activity and/or grain boundary sliding [84].Strain rate sensitivity of metals is usually low (m <0.2) at room temperature but m increases with test-ing temperature. A more sensitive way to obtain m,is a rate change test or jump test, in which m isdetermined by measuring the change in flow stressbrought about by a change in �ε at a constant strainand temperature.

Mechanical properties of certain ufg and nc ma-terials are found to be more sensitive to strain ratethan their cg counterparts [57,81,85]. High strainrate sensitivity, typically > 0.33, is a characteristicof superplastic metals and alloys. Superplasticityrefers to extreme extensibility with elongations usu-ally between 100 and 1000 percent [84]. There aresome examples where ufg or nc elemental metalspossess superplastic behavior [86], but it has char-acteristics different from those of micron grain sizematerials.

By systematic studies of plastic deformation ofufg and nc materials as a function of testing tem-perature, strain rate, and grain size in artifact freesamples, it is possible to obtain an improved under-standing of the deformation and fracture mecha-nisms in these materials. This understanding can

Fig. 3. X-ray result of grain size vs. cryomillingtime for CM Zn.


be greatly assisted by careful examination of mi-crostructures before and after tests such as grainboundary structure, dislocation density, grain sizeand its distributions.

3. MICROSTRUCTURE EVOLUTIONIN CRYOMILLED Zn

3.1. Nanocrystallite formation bydynamic recrystallization

Evolution of average grain size and grain sizedistributions. The average grain size of CM Zn es-timated by using (0002) type X-ray diffraction line

Fig. 4. (a) TEM dark field image for CM0.5h Zn. (b)TEM dark field image for CM12h Zn.

Fig. 5. The number fraction and volume fraction ofgrains vs. grain sizes at different cryomilling time.5A-5E stands for number fraction and 5a-5e standsfor volume fraction for CM0.5h, CM1h, CM3h, CM6h,and CM12h.


broadening [35,36], gave values which decreasedrapidly during the first hours of milling and then slowlydecreased to a nearly constant value for longer mill-ing times as shown in Fig. 3. The grain size clearlysaturates to the minimum value of about 20nm afterabout 12 h of milling. All the Zn samples aftercryomilling were still in the powder form. The evolu-tion of average grain size with milling time is some-what typical for many other ball milled metals.

Transmission electron microscopy (TEM) stud-ies of CM Zn provide more insight into the evolution

Fig. 5. Continued.

of grain size distribution during milling. Fig. 4a showsthe TEM dark field images of the CM0.5h Zn. Largegrains of about 250 nm exist together with smallgrains of less than 10 nm. Fig. 4b shows the TEMdark field images of the CM12h Zn specimen. It isclear that the grain size is much more uniformlydistributed. Fig. 5 shows the results of number frac-tion (5A-5E) and volume fraction (5a-5e) of grainsizes of the CM Zn calculated from TEM studies. Itis surprising to see a large fraction of nc grains,less than 5 nm with a number fraction of about 30%,


Table 1. A comparison of grain sizes calculatedfrom TEM and X-ray studies.

Grain size (nm)TEM result X-ray result

CM 0.5 h 37±1 36±2CM 1h 30±1 31±2CM 3h 23±1 24±2CM 6h 23±1 21±1CM 12h 17±1 19±1

Fig. 6. (a) High resolution transmission electronmicroscopy (HRTEM) image of CM0.5h Zn. (b)HRTEM image of CM12h Zn.

even in an early stage (0.5h) of cryomilling as shownin Fig. 5a. The corresponding volume distribution ofthe grain size shows that these small grains do notcontribute to the total volume as much as they doto the number fraction distribution. Large grains (>50nm) comprised more than 75% of the total volumeof the grains. The grain size distribution (volume frac-tion) tends to be bimodal in Figs. 5a – 5c, whereone peak exists in the small grain size regime andthe other broad and higher peak lies in in the largegrain size regime. This tendency is reduced after 6 hmilling, i.e., after 6 h cryomilling, there is only onepeak, though still broad, in the volume fraction grainsize distribution as presented in Fig. 5d. After 12 hcryomilling, only one narrower peak exists in boththe number fraction and volume fraction curves asseen in Fig. 5e. This shows that the grain size hasbeen reduced to a uniformly small and saturationvalue, i.e. the average minimum grain size has beenreached after 12 h cryomilling. At this stage, about98% of the grains were less than 60 nm in diameter.

Table 1 gives the values of average grain sizecalculated from X-ray and TEM (from the volumefraction result). It shows that the average grain sizescalculated from these two methods are consistentwith each other, even if the close agreement maybe fortuitous given the approximate nature of theXRD line broadening method. The d

min of Zn induced

by cryomilling was about 17 nm (according to theTEM results for CM12h Zn). It is in a similar range,although slightly larger, compared to other hcp met-als (about 14 nm for Co, Hf and Ru) [21]. This maybe understood since Zn has a fairly low melting point(T

m = 692.6K), which might lead to relatively higher

dmin

than other hcp metals that have been studiedwith much higher T

m. According to Eq. (1), the criti-

cal equilibrium distance (Lc) between two edge dis-

locations in a pile-up was calculated to be about 15nm for Zn. This is consistent with the minimum av-erage grain size of Zn.

The microscopic characteristics of small ncgrains obtained during the early cryomilling stage,CM0.5h, are quite similar to those of nc grains ob-tained after a much longer milling time, CM12h. Asshown in Fig. 6a studied by high resolution trans-mission electron microscopy (HRTEM), smallgrains, about 4 nm in diameter, induced by 0.5 h ofcryomilling also possess high angle grain bound-aries, which is the typical characteristic of nc grainsin CM 12h Zn.

The mechanism proposed by Fecht [16] mayexplain the gradual decrease of the volume fractionof the large grains (~ 100 nm). This mechanism,however, has some difficulties in explaining the gen-eration of a large number of small grains (around 5nm) in the early cryomilling stages. At this millingstage, according to the Fecht mechanism, subgrainsaround 20 nm with low angle grain boundaries couldbe formed [16].


The formation of small nc grains in CM Zn bydynamic recrystallization. Mechanical milling willusually create a high strain and high dislocationdensity similar to some traditional cold working tech-niques. The energy induced by cold working is usu-ally stored in the high dislocation density regions orregions with high strain levels. The stored energywill be greater for large strains. At low to mediumstrain levels (generally < 1.0), and at normal strainrates, metals deform by slip or twinning and at some-what higher strain levels instabilities develop andshear bands form [87]. Shear bands of all typesprovide favored sites for the nucleation of recrystal-lized grains. Ridha and Hutchinson [88] have shownthat after annealing, nuclei having a wide range oforientations develop in the shear bands. Shear bandshave been found in Zn which was induced by severecold rolling [89]. DRX happened within the shearbands at room temperature. Compared to cold roll-ing, cryomilling may induce much higher strain intothe deformed metals, thus creating some highlystrained regions. These highly strained areas mayhave stored enough energy to promote the nucle-ation of nc Zn grains during the cryomilling process.

A critical requirement for nucleation is that thesurface of the recrystallized grain nucleus must bea mobile grain boundary, i.e. high angle grain bound-ary [90]. Several possible nucleation mechanismshave been proposed [38,45]. Though different fromeach other, they all suggest that the nucleation hap-pens in certain locations of the deformed microstruc-ture, in particular in deformation inhomogeneitieslike shear bands or microbands, where there is ahigh dislocation density. The critical nucleation di-ameter for DRX has also been closely related to thedislocation density and strain rate as shown in Eq.(2) in Sec. 2.1.4. It follows that the ratio of disloca-tion density (power 3) over strain rate has to achievea certain value in order to form the critical nucleusdiameter, see Eq. (4) in Sec. 2.1.4. However, in somematerials deformed at room temperature, dynamicrecovery usually happens simultaneously with de-fect creation so the dislocation density cannot reachthis value. But in the current case, the dynamic re-covery rate may be well depressed by the low mill-ing temperature, thus decreasing the dislocationrecombination rate allowing the achievement of thecritical nucleus radius. However, the critical nucleusradius may be only a few nm for the formation of ncgrains, which therefore may not need as high a dis-location density to promote nucleation as traditionalmaterials do.

The DRX mechanism can also be understoodfrom the thermodynamic point of view. During the

ball milling process, the plastic damage in the formof dislocations is generated via high strain rate im-pacts from the balls. As the milling time increases,the dislocation density continues to increase. Thiscritical value of dislocation density ρ

c is given by

NEc/E

d, where N is the atomic density, E

c is the

recrystallization energy and Ed is the total disloca-

tion energy per unit length including the core en-ergy of the dislocation. For micro-erosion, a roughestimate in silicon, shows that for around 6.1011

cm-2 dislocation density, the average energy storedin dislocations reaches about 0.1ev/atom, which isclose to the amorphous-to-crystalline crystallizationenergy [91]. It is envisaged that at these levels ofdislocation density, small energy fluctuations result-ing from impacts during the milling process can trig-ger a DRX event. This DRX event leads to formationof nc grains with orientations different from the origi-nal grain orientation.

Based on the DRX mechanism, the bimodal grainsize distribution in the early stage of milling may beunderstood. We assume that the peak in the smallgrain size distribution in Figs. 5a – 5c has beeninduced by DRX. That is, the small grains around5nm as shown in the Fig. 6a and Fig. 6b are grainscreated by DRX. Such small grains will not growsignificantly (usually to less than 20 nm) becauseof nucleation of additional grains at the migratingboundaries [38]. On the other hand, the decompo-sition of the very large grains may follow a mecha-nism similar to that described by Fecht [16]. Withinthe large grains the subgrains are usually on thescale of 20 nm. The broad grain size distribution atearly cryomilling stages (< 6h) suggests that thesetwo mechanisms may operate simultaneously. Af-ter certain cryomilling times [20] the broad grainsize distribution becomes a single narrow peak,which implies a dynamic equilibrium has beenreached.

3. 2. Lattice strain and stored enthalpy

The lattice strains of three different types of planes,(0002) (10�0) (10�1), calculated by the approachof Williamson and Hall [35], are plotted vs. millingtime in Fig. 7. It is seen that the lattice strains riserapidly to about 0.15% for (10�0) and (10�1) typeplanes after 1 h of milling. Thereafter, they drop rap-idly and approach zero for longer milling time. Thelattice strain for (0002) type planes continues to in-crease with milling time, reaches a maximum valueof 0.48% after 6 h of milling and then decreases,almost linearly, with milling time to a small value ofabout 0.05% at 12 h. The fact that the larger values


of lattice strain are observed for the (0002) type re-flections suggests that the lattice strain comesmainly from the basal plane. This is reasonable,since the predominant slip system for Zn is {0001}<11�0> [92]. For Zn, the c/a ratio is 1.856, whichis much larger than the ideal value of 1.633 for thehcp structure. Thus basal plane slip is favored. Dis-locations are confined to the closely packed basalplane and do not move freely from it [38]. The mag-nitude of lattice strain is a good indication of dislo-cation density within the materials. Thus the varia-tion of lattice strain with cryomilling time indicatesthe change of dislocation density in the system.

Thermal stability of the CM Zn was studied bydifferential scanning calorimeter (DSC). Figs. 8a-8dshow the DSC heat flow vs. temperature plots (at aconstant heating rate of 40 °C/min) for Zn cryomilledfor 1, 3, 6, and 9 h respectively. For 1 h milling time(Fig. 8a), two broad exothermic peaks (a low tem-perature peak and a high temperature peak) areevident at about 195 °C and 295 °C with anotherpeak (middle peak) following the low temperaturepeak closely at 245 °C. After 3h of milling (Fig. 8b)the peaks at 195 °C and 245 °C appear to mergeinto a single broad peak at about 210 °C. The sec-ond DSC peak drops in temperature somewhat toabout 285 °C. Continued milling to 6 h gives whatappears to be a single broad peak at about 200 °C(Fig. 8c) and little evidence for the second peak,which can be revealed only at higher DSC heatingrates (≥60 °C/min). No obvious peaks are evidentover the temperature range up to 350 °C after 9 h ofmilling (Fig. 8d). The thermal stability studies of CMZn will focus on the low temperature peak, referredto as the LT peak. Details on high temperature peakcan be found in ref. [93].

Fig. 7. Lattice strain vs. cryomilling time for threetypes of lattice planes, (0002) (10�0) (10�1).

Fig. 8. DSC thermograms for Zn cryomilled at 77Kfor (a)1 h, (b) 3 h, (c) 7 h, and (d) 9h.


The exothermic heat associated with the LT peak(around 200 °C) was calculated from the area underthe peak. This stored enthalpy so released (mea-sured at a constant heating rate of 40 °C/min) isplotted vs. milling time in Fig. 9. The stored enthalpyincreases to a maximum of 0.14kJ/mol after 6 h ofmilling and then decreases rapidly to zero at 9 h ofmilling. The relatively high stored enthalpy aftercryomilling for 2 h may be due to the overlapping ofthe LT peak and the middle peak.

In order to assess the source of the exothermicpeaks observed in the DSC scans, annealing wascarried out in the DSC by heating the selectedsamples to the certain temperatures with the sameheating rate of 40 °C/min and then cooling downimmediately. The evolution of lattice strain and av-erage grain size was studied by XRD for three setsof planes. As shown in Fig. 10, in all cases, there ishardly detectable grain growth from below 245 °C,which is the finishing temperature for the LT DSCpeak. The lattice strain in the (0002) type planes,however, dropped by about a factor of two after the

Fig. 9. Stored enthalpy of LT DSC exothermic peakvs. cryomilling time.

Fig. 10. Lattice strain and grain size vs. annealingtemperature for (a) (0002) type planes, (b) (10�0)type planes, (c) (10�1) type planes for CM3hsample.

Table 2. A comparison of grain size calculated fromTEM (average grain size estimated from the volumefraction distribution) and X-ray (0002) type planesfor CM3h sample annealed at different temperatures.

Annealing Grain size (nm)temperature TEM result X-ray result(°C)

as milled (23) 23±2 24±2142 24±3 24±2245 27±2 26±2

annealing period of LT DSC peak. Whereas the re-duction of lattice strain on the (10�0) and (10�1)planes during the same annealing period is not assignificant as that in the (0002) plane. TEM studiesof the annealed CM3h Zn specimens, as shown inFig. 11, confirmed that there is very little variation ofthe average grain size, (the average grain size dataare compared with that calculated from XRD in Table2) for annealing below 245 °C.

The above studies indicate that the contributionof grain growth to stored enthalpy measured in LTDSC peak is negligible. The reduction of lattice strain


Fig. 11. TEM dark field images of grain size afterannealing at different temperatures for CM3h Zn. (a)23 °C, (b) 142 °C, (c) 245 °C.

on (0002) type planes during annealing indicatesthe decrease of dislocation density. Plastic defor-mation induced by the cryomilling process can cre-ate a very high dislocation density. The stored en-ergy due to dislocations is proportional to the dislo-cation density (ρ) as shown in the following equa-tions [94]:

��

= ρ � (7)

��

��

= ��

�

�

� � �

ν

π

α (8)

where ED is the total strain energy of the disloca-

tion, Edis

is the strain energy of the dislocation perunit length, G is the shear modulus, b is the magni-tude of the Burgers vector, f(ν) is a function ofPoisson’s ratio, f(ν) =(1-ν/2)/(1-ν) with consider-ations of both screw dislocations and edge disloca-tions, R is the separation between the dislocations,a is the core energy factor close to unity [95].

For nc Zn, assume that the maximum disloca-tion density (ρ) reachable is of the order of 1015/m2,which is a reasonable assumption compared withdislocation densities reached in other pure metalsdeformed at 77K [96]. Taking G = 49.3 GPa, b =0.267nm, ν = 0.3, ρ = 10 15/m2, R = ρ-1/2, α =1, E

D is

calculated to be about 120 J/mol, which is very closeto the measured maximum stored enthalpy of 110J/mol for the CM3h Zn. This suggests that the ma-jority of the stored enthalpy may originate from thehigh density of dislocations induced by high-energycryomilling.

Variation of the stored enthalpy (for the first peak)and lattice strain on the basal plane were plotted

Fig. 12. Stored enthalpy (lower temperature peak)and lattice strain on the basal plane vs. 1/d, whered is the grain size.


together vs. the reciprocal of the average grain size(1/d) in Fig. 12. In contrast to some other observa-tions on other elements [26], Fig. 12 clearly showsthat maxima in both stored enthalpy and latticestrain occur at the same grain size. The consis-tency between the two maxima confirms that thechange of stored enthalpy is dominated by variationof dislocation density during milling. Thus it sug-gests that the dislocation density increases duringthe initial cryomilling stage, reaches a maximum ataround 6 h, and then decreases almost linearly withcontinuous cryomilling. It is generally believed thatnc materials with grain sizes less than a certainvalue are dislocation free [69,70]. Therefore the re-duction of dislocation density might be due to theincrease of these dislocation-free nc grains.

The inconsistency between the maxima of storedenthalpy and lattice strain in certain systems [26]may be related to the cancellation of strains duringmilling. The strain field of dislocations could be can-celled out if dislocations with positive Burgers vec-tor and others with negative Burgers vector are nextto each other. The total lattice strains may be re-duced due to this cancellation effect. But the dislo-cation energy is proportional to the square of themagnitude of Burgers vector according to Eq. (8).Thus the dislocations with either positive or nega-tive Burgers vector will contribute to the stored en-thalpy. For fcc and bcc metals, slip can occur onmultiple (typically more than five) slip systems. Thecancellation of strain field due to adjacent disloca-tions with positive and negative Burgers vector onmultiple slip systems can be significant. This mightexplain the discrepancy of maximum of lattice strainand stored enthalpy occurring at different millingtimes observed in the bcc and fcc structured met-als [19]. In the case of hcp metals, such as Zn, slipis mostly confined to the basal planes, the latticestrain may add up without a significant cancellationeffect. Therefore, for Zn, the variation of lattice strainis consistent with the observed change of storedenthalpy, that is the lattice strain and stored en-thalpy reach maxima at the same grain size.

Positions of the LT peak temperatures were seento shift to higher temperatures with increased heat-ing rates in the DSC. Heating rates were selectedwith a variation from 20 °C/min to 80 °C/min. Thisallowed for the Kissinger method [97] to be used toestimate activation energy values for the processesresponsible for the exothermic peaks. The activa-tion energy for samples cryomilled for different timesis listed in Table 3. The activation energy for the LTpeak is around 80 kJ/mol. This is in between theactivation energy for grain boundary self diffusion in

Zn of 59 kJ/mol [98], and lattice self diffusion in Znof 96 kJ/mol [99]. The dislocations are distributedboth within the larger nc grains and at the grainboundaries. During the annealing process, the an-nihilation and movement of these dislocations mayhave different activation energies. Dislocations lo-cated at the grain boundaries need less activationenergy to annihilate with each other, while thoselocated within grains may need higher activationenergy to move. Therefore the annealing processesin this temperature range might be correlated withboth grain boundary diffusion and lattice diffusionprocesses.

4. MECHANICAL BEHAVIOR OFCRYOMILLED BULK NC Zn

4.1. Effect of dynamic recrystallizationon the mechanical behavior ofcompacted bulk CM Zn

Evolution of hardness with milling time.Cryomilled nc Zn powders were compacted at roomtemperature in an attempt to test their mechanicalproperties, such as strength and ductility. The mea-sured density and hardness values for CMZn areplotted in Fig. 13 as a function of milling time. Arelative density greater than 98% (0.98) of theoreti-cal density was obtained for all of the CMZn samples.Fig. 13 shows that the CMZn hardness undergoesmarked oscillations as a function of milling time.The magnitude of the hardness peaks decreaseswith milling time, thus exhibiting a modulated cy-clic hardening manifest as damped oscillations ofthe hardness. At longer milling times the hardnessreaches a steady-state value about twice that ofunmilled Zn. Impurity concentration as a function ofmilling time, given in Table 4, did not exhibit cyclicbehavior. The oxygen concentration was found toincrease steadily from about 0.11 at.% for as-re-ceived Zn to 0.956 at.% after 12 h. The (negligible)

Table 3. Activation energy calculated from the peaktemperature by Kissinger plot for the LT peak, E

LT.

Milling time (h) ELT

(KJ/mol)

1 842 753 814 796 727 828 85


Table 4. Quantitative chemical analysis of oxygenand iron impurities in the as-received and somecryomilled Zn samples.

Sample Oxygen (at.%) Iron (at.%)

as-received Zn 0.115 N/ACM 2h 0.238 0.012CM 6h 0.614 0.015CM12h 0.956 0.028

Fig. 13. Hardness vs. milling time for CM Zn (solidcircles) The relative density for CMZn samples isshown by the open squares.Fe impurity concentration likewise increased mono-

tonically from 0.012 at.% at 2 h milling to 0.028at.% at 12 h. Therefore it is unlikely that the hard-ness oscillation is related with the impurities pickedup during milling.

Evolution of microstructure (dislocation density,grain size and its distribution) with milling time.TEM bright field micrographs are shown in Fig. 14for samples milled between 0.25 and 3 hours. Ahigh dislocation density was observed in larger sizegrains (Figs. 14a and 14d), typically with grain sizes> 50 nm. In contrast, few dislocations could be ob-served for grain sizes < 50 nm (Fig. 14b), and dislo-cations were clearly absent in the smallest grains.These observations indicate that a grain size of 50nm is a reasonable demarcation value above whichstrain hardening can produce high dislocation den-sities during milling and below which dislocationgeneration and strain hardening are not effective.Estimates made from HRTEM micrographs showedthat the maximum dislocation density that could beachieved for grain sizes > 50 nm was on the orderof 1016 m-2. Fig. 14c shows a significant feature thatwas observed for those milling times where the hard-ness drops to its minimum values during the cyclichardness variations. A profuse distribution of verysmall, dislocation-free grains has been formed withina single large grain after a milling time of 2 h. Thiscorresponds to a hardness minimum for CMZn inFig. 13, and the occurrence of a DRX effect is clearlysuggested.

Detailed measurements of the grain-size distri-butions as a function of milling time can be found inFig. 5. The volume fraction of grains with sizes largerthan 50 nm is plotted against milling time in Fig.15. It should be noted that intermittent drops wereobserved (arrows at open points) which coincide withthe hardness oscillation minimum points for the firsttwo peaks in Fig. 13. The volume fraction is tempo-rarily reduced at these points because of the forma-

tion of a transient population of very small disloca-tion-free grains like those shown in Fig.14c. Thesesmall grains subsequently grow and the overall de-crease in the volume fraction of grains with a size >50 nm is represented by the dashed trend line inFig. 15.

Theoretical simulation of hardness oscillationbased on DRX model. The DRX model follows thereaction-rate model proposed by Sluiter and Kawazoe[100]. The reaction-rate model was proposed to ex-plain amorphous-to-crystalline phase transforma-tions observed during ball milling [100]. In theirmodel, it is assumed that ball milling increases thestored energy of the reactant phase due to defectaccumulation. Once the activation energy for reac-tion (crystallization from amorphous phase) is sur-passed, a reaction ‘event’ will occur with a sharplyaccelerating transformation rate. In the DRX model,we assume that dislocations produced by strainhardening in larger grains are the primary contribu-tion to the stored energy in the DRX model. Basedon the TEM observations, it is assumed that DRXoccurs due to the accumulation of dislocations ingrains with grain sizes larger than 50 nm (disloca-tions do not accumulate in smaller grains). Severalimportant aspects have been captured by the DRXmodel:(i) the evolution of dislocation density. The stored

dislocations will strengthen the materials bystrain hardening.

(ii) average grain size and grain size distributions.The gradual increase in hardening is related toaverage grain-size reduction during milling, i.e.Hall-Petch type hardening. Based on the as-sumption that dislocations will accumulate mainlyin grains larger than 50 nm, the volume fraction


Fig. 14. TEM bright field images of CM Zn milled for different times: (a) 0.25 h, (b) 0.5 h (c) 2 h, (d) 3 h.

of grains larger than 50 nm will determine theextent of dislocation-induced strain hardening.

(3) DRX events in the strain-hardened material pro-duce modulated oscillations in hardness.

The strengthening in CM Zn eventually damp out asthe volume fraction of grains with a size > 50 nm isreduced at longer milling times. The details of DRXmodel can be found in ref. 101.

Fig. 16 shows the hardness data in Fig. 13 forCMZn plotted along with the results from the DRXmodel. The agreement is surprisingly good consid-ering the simplifying assumptions needed to develop

the DRX model. The model overestimates some-what the period (width) of the second peak and, es-pecially, the third peak. This is due in large part tothe lack of data points available to estimate the ini-tial slopes and the hardening rate. Nonetheless, thefact that the hardness peak widths decrease as theinitial slopes increase is clearly confirmed by themodel. It is also noteworthy that the peak dampingpredicted by the model using as the scaling factorthe volume fraction of grains with a size > 50 nm isconsistent with the CM Zn data.

The model presented here does not address themechanisms that govern the actual DRX process in


CMZn. However, the model does indicate that a criti-cal strain-hardening dislocation density on the or-der of ρ

c ≅ 1016 m-2 (a critical parameter obtained by

fitting experimental hardness data) will trigger DRXevents in the larger grains. This upper limit for dislo-cation density is consistent with HRTEM estimatesof the maximum dislocation density that could beobserved in CM Zn samples [102].

Another important parameter that can be ob-tained from this model is the activation energy forkinetic reaction (or DRX). The best-fit value obtainedfor the reaction-rate parameter, K, was 2.10-4 s-1. Arough estimate of the activation energy (enthalpy)Q

o can be obtained from the value of K [101],

K e eS k Q kT= ν 0 0/ /, (9)

where ν is the attempt frequency, S0 is the activa-

tion entropy, k is the Boltzmann’s constant. Afterrearranging this equation, one can derive that

� ��

�

�

�

��

= −�

��

�

��

�

ν (10)

The attempt frequency for atom motion is on theorder of the atomic jump frequency ν ≅ 1013 s-1. As-suming activation entropy to be on the order of S

o =

Fig. 15. Volume fraction of grain sizes > 50 nm vs.milling time for CMZn. Arrows (open points) indi-cate the positions of the hardness minimums forthe first two peaks as shown in Fig. 13.

Fig. 16. Comparison of the DRX model results (dotedlines) with the experimental results of hardness vs.milling time for CM Zn (solid circles). The grain-boundary hardening (GS effect) is given by the dash-dot line.

10 – 20k, and using K = 2.10-4 s-1 with T = 100 K forcryomilling, Eq. (10) gives Q

o = 40–50 kJ.mol-1. The

activation energy for grain-boundary diffusion in pureZn is reported to be 59 kJ.mol-1 [98]. The activationenergy for the DRX process during cryomilling thusappears consistent with grain-boundary diffusioncontrolled atom mobility. This in turn would be con-sistent with grain-boundary migration processes,and these are expected to play an important role inDRX [45].

4. 2. Ductility of compacted bulk CM Zn

Strength and ductility of CM Zn were tested by min-iaturized disk bend tests (MDBT). The details of thistechnique are given in the literature [103-106]. MDBTtechnique was originally developed to study the ef-fects of fast neutron irradiation on the mechanicalbehavior of small specimens of reactor alloys [103-106]. Recently this technique has been improvedand used for quantitative analysis of the mechani-cal behavior of nc materials [107, 108]. This tech-nique has the advantage of testing in tension smallsamples produced by, for example, compaction ofnc powders. Compared with conventional uniaxialtensile tests, MDBT is an equibiaxial tensile testtechnique. Therefore the strain measured from MDBTis equibiaxial tensile strain.


Fig. 17 shows the force vs. normalized displace-ment curves for selected samples. Normalized dis-placement (η) is expressed by w/t, where w is thedisplacement of specimen, t is the specimen thick-ness. Theoretical analysis shows that η is propor-tional to strain given all specimens have similar thick-nesses [109]. Therefore the magnitude of η couldprovide an indication of the ductility of the speci-men. As shown in Fig. 17a, CM 3h Zn has verylimited η (about 18%) when the maximum force isreached. Whereas the CM4h Zn has a dramatic in-crease of η (about 40%) at the maximum of appliedforce, as presented in Fig. 17b. Both samples showplastic deformation. CM4h Zn has much more strainhardening than CM3h Zn specimen. The variationsof yield stress, σ

y, and ε (calculated from force and

displacement [109]) are plotted vs. cryomilling timein Fig. 18. It can be seen that both ε and σ

y show a

modulated cyclic behavior with cryomilling time. Twomaxima for σ

y are at CM0.5h and CM3h respectively,

while two minima occur at CM2h and CM4h. ε var-ies in an opposite way with cryomilling time. Thatis, the peak of e

occurs where there is a minimum

of σy. The low value of ε for all tested specimens

may indicate the existence of two-dimensional flawsdue to incomplete bonding between the powder par-ticles. The fracture mechanism could be partly con-trolled by interparticle decohesion or powder-pow-der debonding. Given that all specimens have simi-lar relative density, the number of two-dimensionalflaws is, presumably, similar for all specimens.Therefore the variation of ε can still be used as aprobe to compare the ductility of as-compacted Znspecimens. The results of microhardness, H

v and

3σy, when plotted together vs. cryomilling time as

Fig. 17. Force vs. normalized displacement (w/t) for selected samples tested by MDBT. (a) CM3h (b)CM4h. The symbol, σ

y, stands for yield stress, while E stands for Young’s modulus.

Fig. 18. Variations of yield stress (σy)

and strain (ε)

vs. cryomilling time for CM Zn.

Fig. 19. Comparison of 3σy and microhardness (H

v)

vs. cryomilling time for CM Zn.

given in Fig. 19, exhibit a coincident phenomenonboth in the trend and magnitude of the variations. Itis generally accepted that 3 times the yield strengthis roughly the value of microhardness for the samematerials. This empirical rule seems to work for Znmeasured from MDBT.


The morphology of the fracture surface of CM0.5hZn and CM2h Zn samples after MDBT, studied byfield emission scanning electron microscopy(FESEM), are shown in Fig. 20. The fracture sur-face of CM0.5h sample, as shown in Fig. 20a, showscertain brittle fracture features, with approximatelya 10 µm cleavage feature size. However, some duc-tile features, such as local tearing ridges, are alsoobserved, indicating that these small regions mayfracture by plastic flow. Tearing is frequently observedwhen small unbroken areas remain behind the maincrack front. This suggests a mechanism of localfracture that is often found at a discontinuity in thecrack advance by another fracture mechanism [110].The fracture surface of CM2h Zn samples showscomplex features on a rough surface as shown inFig. 20b. Dimples, tearing ridges, as well as a num-ber of quasicleavage features (shallow dimples) areobserved on a macroscopic scale. These complexfracture features suggest that CM 2h Zn is muchmore ductile than CM0.5h Zn specimens. These

Fig. 20. FESEM observation of fracture surface of(a) CM0.5h Zn and (b) CM2h Zn after MDBT.

observations are consistent with the MDBT result,where the value of e

of CM 2h Zn is about 3 times

that of CM0.5h Zn.It is observed from TEM that a broad bimodal

grain size distribution exists for Zn cryomilled forless than 6h [17]. Grain size distribution, presum-ably, may also contribute to the deformation mecha-nisms and ductility of nc Zn. The phenomenologicalequation for grain boundary sliding controlled by grainboundary diffusion is given by [111, 112]

� �εσ

≈ ��

��

�

�

�

��

(11)

where σ is the stress, Dgb

is the grain boundary dif-fusion coefficient, b is the Burgers vector and d isthe grain size. Eq. (11) suggests that for a very finenanoscale grain size, grain boundary sliding maybe a significant deformation mode even at relativelylow temperatures. Therefore a broad grain size dis-tribution indicates a complex mixture of deforma-tion modes controlled by different grain sizes. Thiscomplexity will be reduced as the broad grain sizedistribution is replaced by a narrow single-peak grainsize distribution for longer milling time.

5. THE SYNTHESIS OF BULK NC ZnBY IN SITU CONSOLIDATION OFPOWDERS

Recently, bulk ufg and nc Zn were prepared by insitu consolidation of powders during milling at roomtemperature [113]. Pure Zn powders have been ballmilled from 1 h up to 25 h at room temperature un-der ultra high purity argon. Only the original samplesand the sample ball milled for 1 h (BM1h) are in theform of powders. All other samples ball milled forlonger times are in form of ≥ 1mm size spheres.Fig. 21 shows the Zn spheres induced by ball mill-ing at different times. After 5 h of ball milling thesphere sizes varied from 2 mm to 5 mm. The spheresizes increased to about 4 ~10 mm after 25 h ofball milling. The average size and the largest size ofthe spheres all increased with the increase of ballmilling time. The appearance of these balls becomesmore regular and uniform for longer milling times. Itis well known that ball milling producesnanostructured materials by a severe plastic defor-mation process. During this process, the powderparticles undergo a repetitive cold welding and frac-ture mechanism [8]. The fact that spherical ballsare formed for Zn, Al and their alloys after ball mill-ing at room temperature suggests that cold weldingis predominant in these systems at room tempera-


Fig. 21. Formation of spheres of pure Zn after mill-ing for different times (a) 5 h, (b) 18 h, (c) 25 h.

ture. Spheres of nc copper have been synthesizedby similar techniques and cold welding is believedto be predominant in this case as well [114,115].

The oxygen contamination of these Zn bulksamples is relatively small. As shown in Table 5, amaximum oxygen concentration of around 1 at.%was introduced after 25 h of ball milling. This is amodest amount of contamination compared with

other materials ball milled by high energy ball mill-ing techniques [21]. The contamination from ironduring the ball milling process is essentially negli-gible. Due to the ductile nature of these powders, athin layer of powders formed on the surface of thestainless steel milling balls, thus reducing the pos-sibility of further contamination from iron.

The evolution of grain size for BM Zn was stud-ied with TEM. Some examples are given in Fig. 22for Zn ball milled for 1h, 3h, 18h, and 25h. The evo-lution of volume fraction for these specimens, cal-culated from TEM micrographs, is presented in Fig.23. A broad grain size distribution is observed inBM Zn in the early milling stages. The grain size ofBM3h Zn varies from 5 to 500 nm. A bimodal grainsize distribution is observed for BM1h Zn. Graingrowth with continued milling is clearly seen fromthe comparison of the grain size distributions ofBM1h and BM3h Zn. The grain size distribution be-comes much narrower at longer milling time. After25 h of ball milling, the grain size varies from 5 to 80nm with an average value of 23 nm. The grain growthphenomenon in early milling stages has also beenobserved in several other materials [20,32]. In thecase of BM Zn, it is possible that during the earlymilling stage, around 1 h, defect/dislocation gen-eration dominates and therefore grain size is con-tinuously refined. Between 1 and 3 h dynamic re-covery dominates and grain growth is facilitatedduring this stage.

Zn spherical balls obtained by in situ consolida-tion can be compressed uniaxially at room tempera-ture into a disk with a diameter of around 10 mmand thickness of about 1mm. The density of thesedisks was measured using the Archimedes prin-ciple method. In all cases, a relative density higherthan 98% of theoretical density has been achieved.The bulk samples made from this technique are largeenough (~ 10 mm in diameter) to perform many dif-ferent kinds of mechanical tests, including the ten-sile test.

Table 5. Oxygen contamination in as-received andball milled Zn samples.

Sample Oxygen (at.%)

As-received (powder) 0.115BM3h (sphere) 0.258BM 5h (sphere) 0.296BM 25h (sphere) 1.025


Fig. 22. TEM dark field images of Zn ball milled for different times. (a) 1 h (b), 3 h, (c) 18 h, (d) 25 h.

6. MECHANICAL PROPERTIES OF INSITU CONSOLIDATED BULK NCZn

In this section, we will discuss the mechanical prop-erties of bulk nc Zn studied by microhardness,MDBT and uniaxial tensile tests in an attempt toexplore the deformation mechanisms in nc Zn.

6.1. Strength and ductility of nc Znstudied by microhardness andMDBT tests

The microhardness of BM Zn is plotted vs. d -1/2 inFig. 24. In general, a linear relationship is observed

with a positive Hall-Petch slope. The hardness ofcg Zn [110] falls on the same line with that of BMZn. Hardness for BM Zn with the smallest grain size,23 nm, deviates from this linear relation, i.e. it isbelow the hardness as predicted from the linear re-lation. The variation of hardness vs. d -1/2 in BM Zn istypical compared to strengthening in many othernc metals, where the hardness of materials is con-trolled mainly by their average grain size. The hard-ness of BM Zn is comparable to that of nc Zn ob-tained from other techniques, such as inert gascondensation [116] and pulsed laser deposition[117]. The hardness of electrodeposited nc Zn, how-ever, is remarkably higher compared with all otherstudies [13]. This phenomenon, still under investi-


Fig. 23. Volume fraction distribution of different grain sizes for Zn milled for different times. (a) BM1h, (b)BM3h, (c) BM18, (d) BM25h.

Fig. 24. Microhardness vs. d-1/2 for BM Zn andcoarse-grained Zn [110].

gation, could be related to the texture of electrode-posited nc Zn [13].

Some of the MDBT results of BM Zn are shownin Fig. 25 in the form of force-displacement curvesobtained directly from MDBT tests. Plastic defor-mation is observed in all the BM Zn samples. Thestrain calculated from the maximum displacementreached a maximum value of around 5.5% after 3 hof ball milling. The design of the MDBT apparatusrequired the tests to be stopped at a biaxial tensilestrain level of about 5% [107]. Hence the maximumstrain observed from MDBT does not represent thereal failure strain of the samples. Three times theyield stress, 3σ

y, calculated from MDBT is plotted

vs. milling time together with hardness results, asshown in Fig. 26. The magnitude and the variationof yield stress with milling time are very consistentwith that obtained from microhardness tests. Thedramatic drop in hardness/strength between 1 and3 h at milling is consistent with the large increasein average grain size from 80 nm to 240 nm.

The force-displacement curves can be catego-rized into five regions (boundaries between region3, 4 and 5 are not clearly marked for the purpose of

simplicity) for Zn ball milled for less than or equal to18 h, as shown in Figs. 25a and 25b. The observa-tion of these five regions is typical for ductile mate-rials and is described by Manahan et al. [118] asfollows:


Fig. 25. Force vs. displacement calculated fromMDBT results for some BM Zn specimens. (a) BM3h, (b) BM 18h, (c) BM 25h.

Fig. 26. Comparison of 3σy (result from MDBT) and

hardness vs. milling time.

Region 1: Elastic deformation governed by Young’smodulus, yield stress and the initial hardeningrate. Force and displacement has a linear rela-tionship;

Region 2: Departure from linearity due to throughthickness and propagation of yield surface fromregion of contact in the disk radially outward overa large portion of the disk;

Region 3: Transition region indicating that the tran-sition of stress mode from bending to membranestretching occurs in most regions of the disk;

Region 4 and Region 5: Membrane stretching isdominant in most regions of the disk. Thesestresses eventually lead to fracture in Region 5.

The boundary between the region 1 and region 2defines the yield stress where the deviation fromlinearity of force-displacement curves begins. Theforce was translated into yield stress according tothe equation in refs. [119-121]. In the transition re-gion (region 3) for Zn ball milled for ≤ 18h, the slopeof the force-displacement curve is increased by afactor of about 2 after the displacement reaches acertain value. Two tangent dashed lines in Fig. 25aand 25b illustrate the two slopes of the plastic de-formation curves. The crossover point of these twotangent lines defines a ‘transition strain’, which isexpressed by ε

T. This strain, ε

T, is calculated from

the displacement at the transition point accordingto the method used by Huang et al. [103]. The strain,ε

T, is roughly at the middle of the transition region

(region 3). It is noticed that for BM25h Zn, the tran-sition region (region 3) is not observed, as shown inFig. 25c. MDBT results of BM1h Zn have a linearelastic region 1 and a small amount of plastic defor-mation in region 2 before fracture. The variations oftransition strain, ε

T, with milling time are shown in

Fig. 27. The value of εT shows a steady increase

with the increase of milling time. It reaches about2.4% after 18 h of ball milling. The fact that the tran-sition strain, ε

T, is increased at longer milling time

is coincident with the observation that the hardnessof BM Zn generally increases with increasing mill-ing time (except the case of BM 1h Zn). A harder,i.e. higher yield stress, sample may lead to a higherε

T which is required to transform from bending to the

membrane stretching region [122].


The surface morphology of BM Zn after MDBTtests is unique. A typical example for BM 18h Zn,studied by scanning electron microscopy, is givenin Fig. 28. The specimen, with an average grain sizeof around 60 nm, has a hat shaped morphology af-ter MDBT. The side view of a BM 18h Zn specimenreveals significant plastic deformation without sur-face cracks. As mentioned before, MDBT can onlydetect a maximum strain of about 5% in the mate-rials, whereas the ductility of BM Zn is obviouslyabove the limit of MDBT technique. In the next sub-section, we will discuss the ductility and deforma-tion mechanisms in BM Zn studied by uniaxial ten-sile tests.

6.2. Ductility and deformationmechanisms of BM Zn studied byuniaxial tensile tests

Tensile specimens with a 1 mm gage length x 1mm width were electro discharge machined fromZn disks. Details on the tensile test machine andtechniques can be found in references 102 and 123.BM Zn specimens with different grain sizes are alltested. We will first begin with BM3h Zn with anaverage grain size of 240 nm, focusing on its ductil-ity and deformation mechanisms. We will then com-pare ductility of BM Zn with different average grainsizes.Deformation mechanism in BM3h Zn with anaverage grain size of 240 nm. Typical true stress-true strain (called stress–strain hereafter for sim-plicity) curves at different strain rates are shown inFig. 29, illustrating a strain rate sensitivity for BM3hZn. Strain hardening (the increase of stress with

Fig. 27. Variation of transition strain (εT) with mill-

ing time for BM Zn.Fig. 28. A typical outlook of BM18h Zn specimenafter MDBT test.

Fig. 29. A comparison of tensile tests performed atdifferent strain rate for Zn with 240 nm grain size(BM3h) at room temperature.

strain) is observed for a strain rate of 4.10-3 s-1

whereas a steady state flow with very little strainhardening was seen at lower strain rates. An elon-gation of 105% is clearly identified for BM3h Zntested at the optimum strain rate of 10-3 s-1, as shownin Fig. 30.

To further explore the strain rate sensitivity ofBM3h Zn, jump tests (changing the strain rate by afactor of usually 2 during tensile tests) were per-formed at 20 °C, 40 °C and 60 °C. Fig. 31 gives twoexamples of the results. The tensile elongation ofBM 3h Zn reached a remarkable value of 110% afterthe jump test at 20 °C. A typical TEM bright fieldimage in the region near the fracture surface of theBM3h Zn after 110% tensile elongation is shown inFig. 32, showing equiaxed grains remain despitesuch large strain. The interior of these equiaxed


Fig. 30. An elongation of 105% is achieved for BM3hZn tested at room temperature with a strain rate of10-3 s-1.

Fig. 31. A comparison of jump tests performed onBM3h Zn at 20oC and 60 °C.

grains has fewer dislocations than were seen in thegrains before the tensile test. There are no visiblechanges in the average grain size before and aftertensile tests for all specimens.

At constant strain (ε) and temperature (T), thestrain rate sensitivity, m, can be calculated accord-ing to Eq. (6) given in Sec. 2.3.2. Experimentally,the changes of flow stress as a result of a suddenincrease of strain rate are recorded during a jumptest. The values of m are then calculated from theslope in the plot of lnσ vs. ln �ε as shown in Fig. 33.The m value is 0.15 for BM3h Zn tested at 20 °Cand 40 °C and about 0.17 for Zn tested at 60 °C.High strain rate sensitivity, usually m > 0.33, is acharacteristic of superplastic metals and alloys [84].Therefore there is basically no superplasticity in ufgZn tested at room temperature, although a 110%elongation is observed.

A simple assumption for creep is that creep canbe considered as a singly activated process which

Fig. 32. TEM bright field image showing the micro-structure of BM3h Zn after the jump tensile test at atemperature of 20 °C.

Fig. 33. Strain rate dependence of stress obtainedfrom jump tests performed on BM3h Zn at 20 °C, 40°C and 60 °C respectively.

can be expressed by an Arrhenius-type rate equa-tion [124]

� �� ε σ= −��

��

��

��

�

� (12)

where A0 is the preexponential complex constant,

containing the frequency of vibration of the flow unit,the entropy change and a factor that depends onthe structure of the material, n is the stress expo-nent, Q is the activation energy for the rate control-ling process, and R is the universal gas constant,in the units of J.mol-1.K-1. If we assume a constantn at different test temperatures and under a con-stant stress, Eq. (12) can be expressed by


� �� ε = −��

��

��

�� (13)

where A1 is a constant in this case.By drawing a horizontal line in Fig. 33 at σ = 132

MPa, three strain rates are obtained at the cross-over points. In a plot of ln �ε vs. 1/T, Fig. 34, Q iscalculated to be 60±10 kJ/mol. From Eq. (12), thestress exponent, n, can be obtained as the slope inthe plot of [ �ε exp(Q/RT)] vs. lnσ. The value of n isestimated to be around 6.6 as shown in Fig. 35.The activation energy for plastic deformation in BM3hZn, around 60 kJ/mol, is very close to the activationenergy for grain boundary self diffusion in pure Zn,which is about 59 kJ/mol [98]. The value of stressexponent, n = 6.6, calculated based on the activa-tion energy is exactly the inverse of strain rate sen-sitivity (m= 0.15), which was calculated initially. Ann value of 6.6 suggests that the deformation mecha-nism is controlled by dislocation creep. This pro-cess could be assisted by grain boundary diffusion.However, dislocation activity in small grains (< 50nm) is, presumably, very limited, therefore, the dis-location creep mechanism could mainly control theplastic deformation within larger grains. The largergrains (> 50 nm) in BM3h Zn have a volume fractionof greater than 80% [122]. The volume fraction oflarger grains kept on decreasing during milling andreduced to around 30% at the longest milling time,25 h [122].

Grain size effect on deformation mechanismsand ductility in BM Zn. Jump tests were also per-formed on BM5h Zn (with an average grain size of

Fig. 34. An activation energy of Q = 60 ± 10 kJ/molis calculated from the plot of ln �ε vs. 1/T for BM3hZn.

Fig. 35. Plot of the normalized strain rate vs. steadystate stress over the temperature range of 20-60 °Cfor BM3h Zn. A stress exponent of n = 6.6 is calcu-lated from this plot.

about 180 nm) to study the strain rate effect on itsmechanical properties. An example is shown in Fig.36a for a jump test performed at 40 °C. A strain ofaround 60%, which corresponds to an elongation ofaround 82%, was observed. The m value is about0.15 as calculated from Fig. 36b. This m value isthe same as that for BM 3h Zn indicating a similardeformation mechanism, dislocation creep, in thelarger grains in both cases.

To study the average grain size effect on me-chanical properties, stress-strain curves for Zn withdifferent average grain sizes are plotted together inFig. 37. The strain rate is 10-3 s-1 for 238 nm and 59nm Zn, 5.10-3 s-1 for 178 nm Zn and 10-4 s-1 for 23nm Zn. Although the strain rates are a little differentfrom one another, the average grain size effect onmechanical behavior is clear. Yield stress increases,while elongation decreases with the decrease of theaverage grain size. It should be noted that the mag-nitude of yield stress calculated from uniaxial ten-sile tests is very close to that calculated from MDBTstudies [122]. The variation of elongation with aver-age grain size is shown in Fig. 38 for UFG and ncZn as well as Zn with conventional grain sizes (datataken from references 125 and 126). For Zn withconventional grain sizes (> 20 µm), elongation in-creases almost continuously with decreasing grainsize. However, for ufg and nc Zn, elongation de-creases with the refinement of grain size. The maxi-mum achievable elongation in ufg Zn (BM3h Zn) isabout 2-3 times higher than that for cg Zn, while thehardness of ufg Zn is at least a factor of two greaterthan its cg counterpart.


Fig. 36. (a) Jump tests performed on BM5h Zn at40 °C. (b) Strain rate sensitivity of 0.15 is calcu-lated from lnσ vs. ln �ε plot.

Fig. 37. Stress-strain curves for BM3h, BM5h,BM18h and BM25h Zn (with an average grain sizeof 240 nm, 180 nm, 60 nm and 23 nm respectively)tested at a constant strain rate of 10-4 s-1- 10-3 s-1 atroom temperature.

Fig. 38. Variation of elongation with average grainsize for Zn. BM Zn tested at 20 °C, squares; coarseZn tested at 20 °C, circles replotted from ref. 125,triangles replotted from ref. 126. All results are ob-tained under the similar strain rate varied around10-4 s-1- 10-3 s-1.

To understand the enhanced ductility in ufg andnc Zn, the following aspects should be considered.First, ‘in situ’ consolidation of powder during ballmilling is a one-step method compared with the tra-ditional two-step methods (nc powder production +compaction). Bulk Zn specimens all have full den-sity after this one-step technique. Eliminating po-rosity improved the ductility of these materials. Sec-ond, most ufg and/or nc Zn specimens have broadgrain size distributions, varying from a few nm to afew hundred nm. Both small grains and large grainsmay accommodate strain during plastic deforma-tion. However, they may deform in a quite differentway. On one hand, the traditional ductile fracturemechanism – nucleation of voids and crack growthby void coalescence - might be avoided or delayedby grain boundary sliding of small grains (5-10 nm).Molecular dynamic simulation of nc Cu and Ni hasshown that grain boundary sliding can accommo-date a large amount of plastic deformation by in-ducing viscous sliding of grains with respect to eachother without crack or cavity formation [68,127].

Migrations of the grain boundaries are usually ob-served during grain boundary sliding events. The factthat grains remain equiaxed after 110% elongationin BM3h Zn is indirect evidence that grain boundarymigration is occurring. On the other hand, the stressexponent of n = 6.6 measured from the jump testfor BM3h and BM5h Zn suggests a climb controlleddislocation creep deformation mechanism within thelarger grains (presumably > 50nm) can also accom-modate a fraction of the total strain. The superior duc-tility observed in ufg and nc Zn could therefore be aresult of accommodating the strains by a mixture ofthe two major deformation mechanisms: namely grain


boundary sliding among small nanograins and dislo-cation creep within the larger grains.

The reduction of elongation with decreasing grainsize in ufg and nc Zn is similar to the observation inmany other nc elemental metals [53]. Therefore theprediction that ductility will be increased with thedecrease of grain size [128] seems to be valid onlywhen the average grain size is beyond a certain limit.During the grain refinement process, the decreaseof larger grains will obviously reduce the amount ofstrains that can be accommodated by them. Theincrease of small nc grains during refinement, how-ever, should increase the amount of strains accom-modated by grain boundary sliding mechanisms. Thefact that ductility decreases with the decrease ofaverage grain size could therefore indicate that largergrains posses a higher capacity in accommodatingthe strain during plastic deformation. Furthermore,BM25h Zn with an average grain size of 23 nm stillpossesses an elongation of about 20%. This is muchlarger than values that have been seen in many othernc elemental metals, where only 1-2% elongation isobserved [53]. As strain in nc BM25h Zn could bemainly accommodated by grain boundary sliding, theobserved ductility, about 20%, in BM25h Zn may in-dicate an upper limit of ductility for these small ncgrains. As shown in Fig. 38, there is, presumably, amaximum elongation somewhere in between the cur-rent studies of ufg Zn and those of coarse-grained Zn.A transition of the dependence of ductility on averagegrain size in Zn may occur in between the two cases.

7. COMPARISONS OF THEMICROSTRUCTURE ANDMECHANICAL PROPERTIES OFBULK NC Zn PREPARED BYCRYOMILLING AND ROOMTEMPERATURE MILLING

In this section, we will compare the microstructure(sec. 7. 1) and mechanical properties (7. 2) of bulkCM Zn and BM Zn. These two techniques providedifferent routes to synthesize bulk ufg and/or ncmaterials. The advantage and disadvantage of eachtechnique are evident after these comparisons. Thisleads to the idea of optimizing the mechanical prop-erties of bulk ufg and nc Zn by combining thestrengths of the two techniques (7. 3).

7.1. Grain size and its distributions asa function of temperature

Fig. 39 illustrates the evolution of the average grainsizes with milling time for BM Zn ball milled at room

Fig. 39. The evolution of the average grain size withmilling time for BM Zn milled at room temperature(300K) and CM Zn milled at liquid nitrogen tempera-ture (77K).

temperature (300K) and CMZn ball milled at 77K.The following differences of microstructure evolutionexist for the two techniques. First of all, the averagegrain size of CM Zn is always smaller than that ofBM Zn after the same amount of milling time. Sec-ond, the average grain size of CM Zn decreasesdramatically to around 50 nm after very shortcryomilling time, less than 1 h. The grain size re-finement rate is reduced thereafter. Whereas theaverage grain size of BM Zn decreased significantlyto around 80 nm after 1h of ball milling, then it in-creased to around 240 nm after 3 h of ball milling.The grain refinement rate thereafter is much higherthan that of CM Zn during similar milling periods.The value of d

min of Zn could be about 17 nm as evi-

denced by the saturation of grain size evolution curvein CM Zn. BM Zn may achieve this d

min as well at,

however, a much longer milling time. Finally, aftercomparing the grain size distributions of the two casesFig. 5 for CM Zn and Fig. 23 for BM Zn, it is clear thatCM Zn usually has a narrower grain size distributionthan BM Zn milled for the same time.

During the ball milling process, the powder par-ticles undergo a repetitive cold welding and fracturemechanism. Grain size is usually refined fasterwhen fracturing dominates the ball milling process.Dynamic recovery and cold welding are, presum-ably, significantly reduced by lowering the tempera-ture during milling, such as cryomilling. Thus thegrains are refined much faster and they can reach asmaller d

min for CM Zn. The milling temperature ef-

fect on grain size refinement is consistent with pre-vious studies on the TiNi intermetallic compound[28]. The grain refinement process in BM Zn could


be mainly controlled by the Fecht mechanism [16],whereas DRX plays an important role in refininggrains during early milling times in CM Zn [17].

7.2. Mechanical properties

The evolution of microhardness of CM Zn and BMZn is compared in Fig. 40. The maximum hardnessof CM Zn can reach about 0.8 GPa. At the finalstage of cryomilling, the microhardness reaches asaturation value of about 0.6 GPa. Themicrohardness of BM Zn increases gradually withincreasing milling time. A hardness value of about0.54 GPa is reached after 25h of ball milling, with-out a clear indication of saturation. The high hard-ness observed in CM Zn and the hardness evolu-tions are combinational results of DRX, dislocationdensity variation and grain size evolutions. Detailshave been given in Sec. 4.1. The gradual increaseof hardness in BM Zn is mainly controlled by itsaverage grain size as detailed in Sec. 6.1. Cryomillingseems to be an efficient method to increase thehardness of Zn by accumulating dislocations moreefficiently. However, the ductility of CM Zn is verylimited presumably due to the retaining of artifactsduring compaction. Whereas BM Zn shows very highductility varying from 20% for an average grain sizeof 23 nm to over 100% for an average grain size of240 nm. At this stage, it is clear that cryomillinghas the advantage of refining the grains and there-fore increasing the strength in a very short time,while in situ consolidation during room temperaturemilling can produce porosity free bulk materials withhigh ductility. These comparisons lead to the thought

Fig. 40. Comparisons of the evolution ofmicrohardness during milling for CM Zn and BM Zn.

that high strength and high ductility ufg or nc Zncould be produced by a combination of cryomillingfollowed by in situ consolidation during room tem-perature milling.

7.3. Optimizing mechanical propertiesof bulk nc Zn by combination ofthe two techniques

Microstructural evolution. Cryomilling was car-ried out at 77K for times from 0.5 to 3 h in order tosynthesize Zn powders with nc microstructures.These powders were then ball milled for 6 h at roomtemperature. The microstructures of the samplescryomilled and consolidated by room temperaturemilling were determined by TEM. Examples of thebright field TEM images of samples cryomilled foreither 0.5 h or 1 h followed by room temperaturemilling for 6 h (CM0.5h/BM6h and CM1h/BM6h) areillustrated in Figs. 41a and 41b respectively. Thegrain size distributions were determined from darkfield micrographs. The volume fraction of grains vs.grain size is presented in Fig. 42 for (A) CM0.5h,(a) CM0.5h/BM6h and (B) CM1h, (b) CM1h/BM6h.Similar results were obtained for CM2h/BM6h andCM2h/BM6h Zn. The broad grain size distribution ofthe cryomilled samples is narrowed by the appar-ent disappearance of both the very largest and verysmallest grains after room temperature milling. Assummarized in Table 6, the room temperature ballmilling resulted in the average grain sizes for thesamples cryomilled for either 0.5 h or 3 h being es-sentially unchanged, even though the grain size dis-tributions were very different. After room tempera-ture milling, the average grain sizes for the samplescryomilled for 1 and 2 h were approximately doubled.Fewer grains in the range < 50 nm are seen in thesesamples. However, in all cases the average grainsizes remain below 100 nm after room temperaturemilling. That is, the microstructure remainsnanoscale.

The process of combining cryomilling to providea nanoscale microstructure with room temperaturemilling to compact the powders into fully densespheres has been shown to be successful [129].The microstructure so developed is significantly finerthan can be obtained by simply milling at room tem-perature for the same time. That is, milling Zn for 6h at room temperature gives an average grain sizeof about 150 nm with grains in the distribution over400 nm in size [122]. The microstructure of CM Znhas been discussed in detail in Sec. 3.1. Brieflyspeaking, CM0.5h and CM3h Zn have higher dislo-cation densities, whereas the CM1h and CM2h Zn


Table 6. Comparison of average grain size betweensamples produced by cryomilling (CM) andcryomilling followed by ball milling for 6 h (CM/BM6h).

Average grain size (nm)CM CM/BM6h

CM0.5h 37±1 31±3CM1h 30±1 62±5CM2h 22±3 68±4CM3h 23±1 21±2

Table 7. Summary of uniaxial tensile test resultsfor samples cryomilled from 0.5 to 3 h and thenmilled for 6 h at room temperature and BM5h Znspecimen.

Milling time Yield strength Elongation(h) (MPa) (%)

CM0.5h/BM6h 140 40CM1h/BM6h 113 70CM2h/BM6h 107 75CM3h/BM6h 160 60BM5h 101 78

have many small nc grains as a result of DRX. It islikely that the high dislocation densities resultingfrom cryomilling can be reduced by room tempera-ture recovery processes during milling. The fact thatthe average grain sizes of the samples cryomilled 1and 2 h increase after room temperature milling isapparently due to the reduction in the number of thesmaller grain sizes to bias the distribution to a largeraverage value. This may be due to the higher mobil-ity of the newly dynamically recrystallized grains inthese samples and therefore the more rapid graingrowth kinetics that might result. In fact, in the pre-vious study of modulated hardening behavior [101]it was demonstrated that the grains newly formedby dynamic recrystallization grew rapidly.

Mechanical properties. The mechanical proper-ties of the samples ball milled at room temperaturewere determined by hardness measurements,MDBT measurements for the yield strength, anduniaxial tensile tests. Examples of the stress-straincurves for CM/BM samples are given in Fig. 43 forthe samples CM0.5h/BM6h and CM3h/BM6h. Table7 gives values of the yield strength and fracture strainfor all the CM/BM and BM5h Zn specimens. Allspecimens prepared by the CM/BM technique main-tain high strength and considerable ductility. Val-ues of 3 times the yield strength (3σ

y) and hardness

are plotted in Fig. 44 for the samples aftercryomilling, open symbols, and after cryomilling fol-lowed by room temperature milling, closed symbols.There is reasonable agreement among the 3σ

y val-

ues determined by the various tests. The strengthof the samples consolidated by room temperaturemilling is significantly reduced from that for thecryomilled condition, although the same trend withcryomilling time is maintained. The reduction of yieldFig. 41. Bright field TEM micrographs of nc Zn

samples. (a) CM0.5h/BM6h, (b) CM1h/BM6h.


Fig. 42. Volume fraction of grains vs. grain size processed at various times via different techniques. (A)CM0.5h, (B) CM1h, (a) CM0.5h/BM6h, (b) CM1h/BM6h.

Fig. 43. Selected true stress-true strain curves forCM0.5h/BM6h and CM3h/BM6h Zn samples.

strength in CM0.5h/BM6h and CM3h/BM6h Znspecimen compared to CM Zn could be a result ofdecreasing dislocation density due to dynamic re-covery. In the case of CM1h/BM6h and CM2h/BM6hZn, the decreasing strength is consistent with thefact that grain size increases after room tempera-ture ball milling. The CM3h/BM6h Zn specimen hasthe best combination of strength and ductility. Thisis in contrast to the results of MDBT estimated duc-tility which was low for this high strength condition[109]. Thus, the 6h milling at room temperature hasmodified the microstructure to provide good ductil-ity. The lowering of the dislocation density may beimportant in this case.

8. COMPARISONS OF DEFORMATIONMECHANISMS IN BULK UFG ANDNC ELEMENTAL METALS

Effect of grain size and its distribution on yieldstrength and tensile ductility. It is clear now thatthe yield strength of metallic materials can be in-creased by decreasing their average grain sizes.

The dislocation pile-ups in submicron or larger grainsare the main strengthening mechanisms. While thegrain size decreases to tens of nm level, disloca-tion pile-up becomes more and more difficult. Atthis regime, materials may deform by the single dis-location bowing (Orowan model) mechanism [75,76].This is typically the case for metallic multilayers


Tab

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. Mic

rost

ruct

ures

and

tens

ile d

uctil

ity o

f ufg

and

nc

elem

enta

l met

als

test

ed a

t roo

m te

mpe

ratu

re.

Mat

eria

lP

roce

ssin

gA

vera

ge g

rain

Gra

in s

ize

Elo

ngat

ion

Wor

kS

trai

n ra

teR

efer

ence

tech

niqu

e s

ize

(nm

)di

strib

utio

n(%

) / s

trai

nha

rden

ing

sens

itivi

tyra

te (s

-1)

(m)

Cu

ED

174-

251

Yes

Ebr

ahim

i20

2-24

6et

al.

[56]

273-

323

5.1-

6.7

Cu

Rol

l13

3V

ery

little

Ebr

ahim

iR

oll/1

00o C

152

et a

l. [5

6]R

oll/4

25o C

>100

036

.6C

uE

CA

P30

0Ye

sW

ang

EC

AP

/rol

l20

0et

al.

[77]

EC

AP

/rol

l/19

015

100o C

Cu

Rol

l20

010

Yes

Wan

gR

oll/2

00o C

200-

3000

65et

al.

[77]

Cu

EC

AP

100

51 (1

.0. 1

0-3)

0.09

-0.1

4Va

liev

et a

l. [1

30]

Cu

Spu

tter

5617

(8.9

. 10-4

)M

erz

7721

(8.9

. 10-4

)et

al.

[131

]

Ni

ED

60.

7 (4

. 10-4

)Ye

sW

ang

403.

1 (4

. 10-4

)et

al.

[57]

Ni

ED

43-4

5Ye

sE

brah

imi

38-5

6et

al.

[132

]73

-79

283-

342

3.3

12N

iE

D21

13-2

93-

4 (2

.0. 1

0-4)

Yes

0.01

-0.0

3D

alla

Tor

re e

t al.

[133

]Ti

EC

AP

260

10 (1

.0-4

.0. 1

0-4)

0.00

9Ji

a et

al.

[80]

TiH

PT

120

Ver

y lit

tleS

ergu

eeva

HP

T/25

0o C12

0Ye

set

al.

[83]

HP

T/30

0o C15

030

Yes

Co

ED

128-

186-

7 (1

.0-

Yes

Kar

impo

or5

0.10

-4)

n =

009

-02

et a

l [1

4]


[]

Rol

l/425

o C>1

000

36.6

Cu

EC

AP

300

Yes

Wan

gE

CA

P/r

oll

200

et a

l. [7

7]E

CA

P/r

oll/

190

1510

0o CC

uR

oll

200

10Ye

sW

ang

Rol

l/200

o C20

0-30

0065

et a

l. [7

7]C

uE

CA

P10

051

(1.0

. 10-3

)0.

09-0

.14

Valie

vet

al.

[130

]

Cu

Spu

tter

5617

(8.9

. 10-4

)M

erz

7721

(8.9

. 10-4

)et

al.

[131

]

Ni

ED

60.

7 (4

. 10-4

)Ye

sW

ang

403.

1 (4

. 10-4

)et

al.

[57]

Ni

ED

43-4

5Ye

sE

brah

imi

38-5

6et

al.

[132

]73

-79

283-

342

3.3

12N

iE

D21

13-2

93-

4 (2

.0. 1

0-4)

Yes

0.01

-0.0

3D

alla

Tor

re e

t al.

[133

]Ti

EC

AP

260

10 (1

.0-4

.0. 1

0-4)

0.00

9Ji

a et

al.

[80]

TiH

PT

120

Ver

y lit

tleS

ergu

eeva

HP

T/25

0o C12

0Ye

set

al.

[83]

HP

T/30

0o C15

030

Yes

Co

ED

128-

186-

7 (1

.0-

Yes

Kar

impo

or5.

0.10

-4)

n =

0.0

9-0.

2et

al.

[14]

Znin

situ

235-

8024

(4. 1

0-4)

Ver

y lit

tleN

/AZ

hang

et

cons

olid

atio

n59

5-32

048

(4. 1

0-4)

N/A

al. [

34, 1

22]

178

5-50

078

(4. 1

0-4-4

. 10-3

)0.

1523

85-

500

110

(4. 1

0-4-8

. 10-3

)0.

15

Not

e: E

D-E

lect

rode

posi

tion,

SP

D-s

ever

e pl

astic

def

orm

atio

n, E

CA

P-e

qual

cha

nnel

ang

ular

pre

ssin

g, H

PT

- hi

gh p

ress

ure

tors

ion.

Table 8. Continued.


with layer thickness on the order of tens of nm. Whenthe grain size becomes very small, a few nm, dislo-cation activity within the grains becomes less likelyand the materials may deform by grain boundarysliding. A broader grain size distribution, especiallywith an increased volume fraction of coarser grains,tends to significantly reduce the yield stress of thematerials [33].

A decrease in ductility is typically observed withthe increase of strength when grain sizes are de-creased to the nanoscale regime. This phenom-enon, a potential hurdle to the application of ncmaterials has been summarized by Koch et al. [53].Complexity is introduced when comparing tensiletest data in the literature for different materials. Thefollowing aspects should be considered when com-paring these data: (i) the porosity induced by com-paction of nc powders usually deteriorates the duc-tility of nc materials (ii) the starting microstructureof the tested materials could vary greatly in termsof grain size distributions, dislocation densities andtextures (iii) tensile ductility is usually lower thancompressive ductility (iv) testing conditions may vary,for example strain rate and temperature. Microstruc-tural changes (such as recovery, recrystallizationor grain growth) may occur during testing at elevatedtemperatures.

To make the comparison less complicated, wecollect the literature data on ductility with the fol-lowing characteristics:

Fig. 44. Comparisons of mechanical properties forCM Zn and CM/BM6h Zn as a function of cryomillingtime. Open circles, hardness of CMZn; Opensquares, 3σ

y of CMZn from MDBT; Solid circles, 3σ

y

of CM/BM6h Zn from uniaxial tensile tests; Solidsquares, 3σ

y of CM/BM6h Zn from MDBT tests.

(1) ufg and nc elemental metals without the consid-eration of alloys

(2) ufg or nc elemental metals produced by certainprocessing techniques, where porosity is oftennot a critical issue, such as severe plastic de-formation (rolling, ECAP, high pressure torsion(HPT), in situ consolidation), sputtering and elec-trodeposition.

(3) ductility data obtained from uniaxial tensile testsat room temperature

As shown in Table 8, the average grain sizes aswell as grain size distribution of nc elemental met-als are listed. The characteristics of tensile test data,including elongation to failure, strain hardening andstrain rate sensitivity are given in the table. Com-parisons of strain hardening and strain rate sensi-tivity will be discussed in the next two subtopicsrespectively. The temperatures given in the tableindicate the annealing temperature before the ten-sile tests.

Elongation to failure vs. grain size is given inFig. 45 for different elemental metals. Data on Cuare compared in Fig. 45a. Several things are no-ticed from this plot: (i) For a specific processingtechnique, the ductility of Cu decreased with de-creasing grain sizes (ii) The ductility of nc Cu is stillreasonably high, about 20% elongation for sputterednc Cu. Strikingly high ductility is observed in ufg Cuproduced by ECAP [130] and cold rolling followedby controlled annealing [11]. The enhanced ductil-ity in rolled Cu [11] originated mainly from the ac-commodation of strain hardening within the largergrains. Although Cu and Ni have similar lattice pa-rameters and the same crystal structure, fcc, theductility of electrodeposited ufg or nc Ni at roomtemperature is much lower than that of Cu with simi-lar grain sizes as shown in Fig. 45b. However, ufgor nc Ni tested at elevated temperature possessessuperplasticity [86] where abnormal grain growthoccurs during tensile tests. It is too early to con-clude that ufg or nc Ni possesses poor ductility atroom temperature, as there are little tensile test datafor ufg or Ni produced by other techniques, such asSPD. Ductility of elemental hcp metals (Ti, Co andZn) is compared in Fig. 45c. The ductility of Zn andTi decreases with decreasing average grain sizes.The high ductility in ufg Zn is mainly contributedfrom the larger grains, a few hundred nm. As thevolume fraction of larger Zn grains goes down, theductility also decreases. Zn and Co with nc grainsizes still retain significant ductility.

These comparisons rule out the effect of poros-ity on ductility induced by processing techniques.


Metals with nanoscale grain size possess reason-ably good ductility, much higher than previouslycompared data [53] as a result of improved process-ing techniques. However, the fact that ductility de-creases with decreasing grain size indicates thatnc elemental metals may have inherently lower duc-tility than their ufg counterparts. It is known thatdislocation activity is diminishing within nc grains.Strain hardening, important for good ductility, istherefore reduced. In addition the strain that can beaccommodated by grain boundary sliding of ncgrains is also limited. At higher strains, grain bound-ary sliding will open up pores and initiate cracksfrom these pores as demonstrated vividly by Kumaret al. [85]. Therefore a composite structure, largergrains embedded in a matrix of small grains, is ben-eficial in obtaining high strength from the strength-ening in the nc matrix and high tensile ductility dueto strain hardening in the larger grains. Besides thesuccessful example of highly ductile ufg Cu by Wanget al. [11], McFadden et al. [86] demonstrated su-perplasticity in Ni where large grains coexist withnc matrix.Strain hardening. The flow curve of many metalsand alloys in the region of uniform plastic deforma-tion can be expressed by power curve relation:

σ ε= �� (14)

where K is the strength coefficient, n is the strainhardening exponent. By a plot of lnσ vs. lnε, the nvalue can be determined. According to theConsid�re’s criteria for tensile instability, dσ/dε<σ,the value of n is equal to the true uniform strain[134]. Strain hardening behavior in ufg and nc met-als could be very different dependent upon their mi-crostructure prior to tensile deformation. Data in thisrespect is summarized in Table 8. There are veryfew studies that provide n values for ufg and ncmetals. In the limited example of electrodepositednc Co [14], the n value is lower than that of itscoarse-grained counterparts, indicating the uniformstrain is smaller in nc metals. This could also be aresult of limited strain hardening in small nc grainssince strain hardening is important for achievinguniform plastic deformation in materials.

As mentioned in Sec. 2.3.2., research on strainhardening behavior in ufg and nc materials is some-what controversial. In some cases, ufg and nc ma-terials are found to show strong strain hardeningbehavior [11,14,78,79], whereas in other cases, theyshow little strain hardening [80-83]. These contro-versial observations do not necessarily exclude eachother. In fact, they may somehow be consistent with

Fig. 45. Comparisons of elongation to failure vs.grain size for different elemental metals. (a) Cu (datataken from ref. [11, 56, 77, 130]). The rectangularbars indicate the range of grain sizes for Cu pre-pared by rolling and annealing [11], the maximumgrain size is around 3 µm. (b) electrodeposited Ni(data taken from ref. [57, 131, 132]. The error barsfor grain sizes indicate the range of grain sizes. (c)hcp metals, Ti, Co and Zn (data taken from ref. [14,34, 80, 83, 122]). The rectangular bars stands forthe range of grain sizes in Zn, while the black spheri-cal dots on the bars indicate the average grain sizesof the specimens.


each other when considering the origins of strainhardening in the materials. Strain hardening incoarse-grained materials comes typically from theaccumulation and interaction of dislocations, or in-terception of slip systems which in turn lead to dis-location jogs or tangles [134]. The flow stress ofstrain hardened materials is typically proportionalto the square root of dislocation density, σ ∝ ρ1/2.Strain hardening in ufg or nc metals produced bySPD is usually not significant during tensile testssince these materials are already strain-hardenedduring processing. However, annealing can usuallyremove dislocations in these materials and there-fore restore their ability to work harden by accumu-lating more dislocations. If the annealing tempera-ture is chosen such that there is not much increaseof average grain size, then high strength and highductility materials can be produced, such as thecases of ufg Cu [11,82] and Ti [83]. The fact thatstrain hardening is usually very small in ufg and ncZn could be an effect of dynamic recovery duringtensile tests. Since room temperature is about 40%of the melting temperature for ufg and nc Zn, dy-namic recovery could occur during tensile tests andannihilate the dislocations generated by plastic de-formation. Strain hardening is observed in ufg Zntested at higher strain rates, Fig. 29. This evidencemay support the fact that dynamic recovery ratecan not keep up with the strain hardening rate dur-ing higher strain rate tensile tests.

Strain rate sensitivity. The plastic instability dur-ing a tensile test is quite often related to both strainhardening and strain rate sensitivity. In this case,the plastic instability can be described by Hart’scriteria [135]:

γ + ≤ �� (15)

where γ is a dimensionless strain hardening coeffi-cient, γ = (1/σ)(dσ/dε) and m is the strain rate sen-sitivity, defined by Eq. (6) in Sec. 2.3.2. The equa-tion clearly states that both strain hardening andstrain-rate hardening contribute to suppressing theonset of plastic instability. Therefore, high strain ratesensitivity may enhance the ductility of materialsand is a desirable property.

In the model proposed by Kim et al. [136], thestrain rate sensitivity for ufg and nc Cu is calculatedto increase with decreasing grain size. However, ex-perimentally, the m values for ufg and nc Cu areusually very low, as shown in Table 8. The m valueis in general very low for ufg and nc materials. It ismoderately higher for ufg and nc Zn [34, 123] andmuch higher for superplastic ufg and nc Ni [86, 137].

It is not clear why strain rate sensitivity is low inmany cases, while it is higher in a few other cases.

Twinning and stacking faults. The enhanced duc-tility in ufg Cu is partially attributed to deformationtwining by Wang et al. [11]. They believe that twinboundaries can act as barriers to dislocation move-ment and therefore add extra strain hardening ca-pability into ufg Cu [11]. In fact twin boundaries canbe very strong barriers to dislocation crossing andtherefore enhance the strength of materials as evi-denced and modeled for twinning in sputtered 330stainless steel films [138,139]. In coarse-grainedmaterials the critical stress to activate slip is usu-ally smaller than that to activation twinning or stack-ing faults. However, when the grain sizes enternanoscale regime, the above mentioned phenom-ena reverse, i.e. twinning is preferred over slip whenthe grain size is below a certain value, typically tensof nanometers. Deformation twinning can thereforeoccur in nc metals even with high stacking faultenergies [140,141]. The twinning enhanced ductil-ity in ufg and nc metals is therefore based on theenhanced strain hardening due to twin interfaces.The higher ductility observed in nc Cu than that innc Ni shown in Fig. 45 a and b could be related withthe ability to initiate twinning in these materials, asNi has a much higher stacking fault energy thanthat in Cu. Sputter deposited nc Cu with a high den-sity of twinning also possesses high tensile ductil-ity [131]. Enhanced ductility in nc Co has been at-tributed to the high density of stacking faults andtwins [14].

In cg materials, ductility enhancement by twin-ning alone is usually very limited. However, the ori-entation change resulting from twinning may placenew slip systems in a favorable orientation with re-spect to the stress axis so that additional slip cantake place [134]. Furthermore, we speculate thattwinning induced orientation change may facilitatethe sliding of nanoscale grains and therefore post-pone the generation of pores followed by crack ini-tiation as is the case for many nc metals, such asNi [85,142]. Molecular dynamics simulations as wellas in situ TEM studies in this respect may help tofurther explore this possibility.

Optimizing strength and ductility. The above dis-cussions have already suggested how to improvethe ductility of ufg and nc metals while maintainingtheir high strength. Basically, enhanced ductility canbe achieved by (i) increasing strain hardening (ii)increasing strain rate sensitivity (iii) activating otherdeformation mechanisms such as twinning or stack-ing faults (iv) facilitating grain boundary sliding to


postpone the generation of pores along the grainboundaries or triple junctions. As suggested by Ma[143] and Koch [144], a broad grain size distribu-tion may be beneficial to maintain both high strengthin the nc matrix and high ductility due to strain hard-ening in the larger grains. Another way to restorestrain hardening ability is to remove dislocations inufg or nc metals by annealing or recovery. The ma-terials processed in this way may possess loweryield strength, but they can maintain considerableultimate tensile strength and greatly enhanced duc-tility. In materials with lower stacking fault energiesit is easier to activate enough deformation twinningor stacking faults to maintain some ductility in ncmetals. Many issues critical to improve the ductil-ity of ufg and nc metals remain unclear, such ashow to improve their strain rate sensitivity and howto avoid or delay the creation of pores by grain bound-ary sliding during plastic deformation at certain lev-els of strain.

SUMMARY

In this article, we attempt to explore the deforma-tion mechanisms in ufg and nc metals by using Znas an example. The major observations are sum-marized as follows:(1) the evolution of microstructure (grain size and

its distribution) in cryomilled nc Zn is controlledby a combination of dynamic recrystallizationand the Fecht mechanism.

(2) the modulated oscillation of hardness duringcryomilling is a combinational effect of dynamicrecrystallization, average grain size, grain sizedistribution and dislocation density variations.

(3) bulk ufg and nc Zn synthesized by in situ con-solidation during milling posses high tensile duc-tility and reasonably high strength. The high ten-sile ductility may have originated from strainsaccommodated within the larger grains (submi-cron) and grain boundary sliding of nanoscalegrains.

(4) Several possibilities of improving the tensile duc-tility of nc metals are described, such as increas-ing strain hardening and strain rate sensitivity,activating other deformation mechanisms suchas twinning or stacking faults and accommodat-ing grain boundary sliding to postpone the gen-eration of pores along the grain boundaries ortriple junctions.

ACKNOWLEDGEMENT

The authors would like to thank Profs. RonaldScattergood and Jagdish Narayan for helpful dis-cussions. C. C. Koch acknowledges financial sup-port from NSF under grant no. DMR-0201474 andDOE under grant no. DE-FG02-02ER46003. X. Zhangand H. Wang acknowledge support by DirectorFunded Postdoctoral Fellowship at Los AlamosNational Laboratory.

REFERENCE

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MECHANICAL BEHAVIOR OF BULK ULTRAFINE ...mp.ipme.ru/e-journals/RAMS/no_2604/zhang/zhang.pdfof ultrafine-grained and nanocrystalline materials may be enhanced by the following ways