Mechanical behavior of nanocrystalline metals and … · Mechanical behavior of nanocrystalline...

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Acta Materialia 51 (2003) 5743–5774 www.actamat-journals.com Mechanical behavior of nanocrystalline metals and alloys K.S. Kumar a,, H. Van Swygenhoven b , S. Suresh c a Division of Engineering, Brown University, Providence, RI 02912, USA b Paul Scherrer Institute, Villigen-PSI, CH-5232, Switzerland c Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Accepted 31 August 2003 Abstract Nanocrystalline metals and alloys, with average and range of grain sizes typically smaller than 100 nm, have been the subject of considerable research in recent years. Such interest has been spurred by progress in the processing of materials and by advances in computational materials science. It has also been kindled by the recognition that these materials possess some appealing mechanical properties, such as high strength, increased resistance to tribological and environmentally-assisted damage, increasing strength and/or ductility with increasing strain rate, and potential for enhanced superplastic deformation at lower temperatures and faster strain rates. From a scientific standpoint, advances in nanomechanical probes capable of measuring forces and displacements at resolutions of fractions of a picoNewton and nanometer, respectively, and developments in structural characterization have provided unprecedented opportunities to probe the mechanisms underlying mechanical response. In this paper, we present an overview of the mechanical properties of nanocrystalline metals and alloys with the objective of assessing recent advances in the experimental and computational studies of deformation, damage evolution, fracture and fatigue, and highlighting opportunities for further research. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanocrystalline materials; Mechanical properties; Grain boundaries; Grain refining; Modeling 1. Introduction The processing, structure and properties of met- allic materials with grain size in the tens to several Corresponding author. Tel.: +1-401-863-2862; fax: +1- 401-863-7677. E-mail address: sharvanF[email protected] (K.S. Kumar). The Golden Jubilee Issue—Selected topics in Materials Science and Engineering: Past, Present and Future, edited by S. Suresh 1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.08.032 hundreds of nanometer range are research areas in which there has been a considerable increase in interest over the past few years. The application of grain refinement as a powerful tool to design microstructures with superior properties and per- formance has long been the focus of metallurgical research; numerous papers with this theme have been published in Acta Metallurgica/Materialia over the past fifty years. However, several major drivers have contributed to the rapid increase in research into nanocrystalline metals and alloys in recent years. Advances in the processing of alloys

Transcript of Mechanical behavior of nanocrystalline metals and … · Mechanical behavior of nanocrystalline...

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Acta Materialia 51 (2003) 5743–5774www.actamat-journals.com

Mechanical behavior of nanocrystalline metals and alloys�

K.S. Kumara,∗, H. Van Swygenhovenb, S. Sureshc

a Division of Engineering, Brown University, Providence, RI 02912, USAb Paul Scherrer Institute, Villigen-PSI, CH-5232, Switzerland

c Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Accepted 31 August 2003

Abstract

Nanocrystalline metals and alloys, with average and range of grain sizes typically smaller than 100 nm, have beenthe subject of considerable research in recent years. Such interest has been spurred by progress in the processing ofmaterials and by advances in computational materials science. It has also been kindled by the recognition that thesematerials possess some appealing mechanical properties, such as high strength, increased resistance to tribological andenvironmentally-assisted damage, increasing strength and/or ductility with increasing strain rate, and potential forenhanced superplastic deformation at lower temperatures and faster strain rates. From a scientific standpoint, advancesin nanomechanical probes capable of measuring forces and displacements at resolutions of fractions of a picoNewtonand nanometer, respectively, and developments in structural characterization have provided unprecedented opportunitiesto probe the mechanisms underlying mechanical response. In this paper, we present an overview of the mechanicalproperties of nanocrystalline metals and alloys with the objective of assessing recent advances in the experimentaland computational studies of deformation, damage evolution, fracture and fatigue, and highlighting opportunities forfurther research. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Nanocrystalline materials; Mechanical properties; Grain boundaries; Grain refining; Modeling

1. Introduction

The processing, structure and properties of met-allic materials with grain size in the tens to several

∗ Corresponding author. Tel.:+1-401-863-2862; fax:+1-401-863-7677.

E-mail address: [email protected] (K.S.Kumar).

� The Golden Jubilee Issue—Selected topics in MaterialsScience and Engineering: Past, Present and Future, edited byS. Suresh

1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.actamat.2003.08.032

hundreds of nanometer range are research areas inwhich there has been a considerable increase ininterest over the past few years. The applicationof grain refinement as a powerful tool to designmicrostructures with superior properties and per-formance has long been the focus of metallurgicalresearch; numerous papers with this theme havebeen published in Acta Metallurgica/Materialiaover the past fifty years. However, several majordrivers have contributed to the rapid increase inresearch into nanocrystalline metals and alloys inrecent years. Advances in the processing of alloys

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along with the precipitous rise in the sophisticationof routine, commonly available tools capable ofcharacterizing materials with force, displacementand spatial resolutions as small as picoNewton (pN= 10�12 N), nanometer (nm = 10�9 m) and Ang-strom (0.1 nm), respectively, have provided unpre-cedented opportunities to probe the structure andmechanical response of alloys in the nanoscaleregime. In addition, major improvements in com-puter hardware and software have facilitated simul-ations of the structure and deformation of materialswith a degree of sophistication and refinementunimaginable as recently as a decade ago. Thesefactors, along with major national initiatives in thebroad area of nanotechnology in the United States,Europe and Japan, have further accelerated interestin the study of nanocrystalline metals and alloysfor a wide variety of structural and functionalapplications. In the Millennium Special Issue ofActa Materialia, published in 2000, Gleiter [1]presented a comprehensive overview of nanostruc-tured materials, with a specific emphasis on theconnections between structure and functionalproperties. A critical appraisal of the current stateof understanding and of possible avenues forfurther exploration in the broad field of mechanicalproperties of nanoscrystalline metals and alloys,particularly in the context of processing-structure-property connections, seems appropriate at thistime.

For the purpose of discussion throughout thispaper, we define nanocrystalline (nc) metals andalloys as those with an average grain size andrange of grain sizes smaller than 100 nm. Ultrafinecrystalline (ufc) metals and alloys are taken to bethose with an average grain size in the 100–1000nm range, whereas their microcrystalline (mc)counterparts have average grain dimension of amicrometer or larger. It is important to note in thiscontext that the mechanisms of deformation andthe properties of the nc material not only dependon the average grain size, but are also stronglyinfluenced by the grain size distribution and thegrain boundary structure (e.g., low-angle versushigh-angle grain boundaries).

Some appealing characteristics of nc metals andalloys with potential significance for engineeringapplications include ultra-high yield and fracture

strengths, decreased elongation and toughness,superior wear resistance, and the promise ofenhanced superplastic formability at lower tem-peratures and faster strain rates compared to theirmc counterparts. Consider, for example, the vari-ation of flow stress as a function of grain size fromthe mc to the nc regime, which is schematicallyshown in Fig. 1. In many mc and ufc metals andalloys with average grain size of 100 nm or larger,strengthening with grain refinement has tradition-ally been rationalized on the basis of the so-calledHall-Petch mechanism [2–4]. Here pile-up of dislo-cations at grain boundaries is envisioned as a keymechanistic process underlying an enhanced resist-ance to plastic flow from grain refinement. As themicrostructure is refined from the mc and ufcregime into the nc regime, this process invariablybreaks down and the flow stress versus grain sizerelationship departs markedly from that seen athigher grain sizes. With further grain refinement,the yield stress peaks in many cases at an averagegrain size value on the order of 10 nm or so.Further decrease in grain size can cause weakeningof the metal. Although there is a growing body ofexperimental evidence pointing to such unusualdeformation responses in nc materials, the underly-ing mechanisms are not well understood. Conse-quently, there is a concerted global effort underwayusing a combination of novel processing routes,experiments and large-scale computations to

Fig. 1. Schematic representation of the variation of yieldstress as a function of grain size in mc, ufc and nc metalsand alloys.

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develop deeper insights into the various aspects ofthese phenomena.

In this overview, we focus attention on themechanical behavior of nc metals and alloys. Themajority of available experimental and compu-tational results on this topic pertain to face-cent-ered cubic (fcc) structure, and hence the resultshighlighted primarily deal with this class of metals;however, references to other crystal structures areincluded, wherever available. The paper is broadlydivided into five major sections: (1) processing, (2)grain boundary structure, (3) mechanical proper-ties, (4) deformation mechanisms, and (5) fracturemechanisms. An attempt is made to compare thebehavior of nc metals with those of ufc and mcmetals, and to assess computational predictions inlight of experimental observations, wherever poss-ible. It is worth noting that the topic of grainrefinement also constitutes an important aspect ofthe broad area of superplasticity in metals andalloys. However, available results in this area prim-arily deal with ufc materials and consequently, itis not taken up for discussion in this overview.Examples of recent activity in the area of super-plasticity of ufc materials can be found in [5–11].

2. Processing of nanocrystalline metals andalloys

Several laboratory-scale processing techniquesare currently available to produce nc and ufcmaterials. They can be generally classified into thefollowing four groups: mechanical alloying(including cryomilling) and compaction [12–15],severe plastic deformation [16], gas-phase conden-sation of particulates and consolidation [17–19],and electrodeposition [20–22]. Whereas the firsttwo methods typically tend to yield material withultra-fine grain sizes, the latter two techniques arecapable of producing material with mean grainsizes in the tens of nm. A fifth technique whichcan, in principle, facilitate the production of a ncalloy entails controlled crystallization of a materialcapable of forming an initially fully amorphousmetallic glass, particularly if the metallic glass canbe produced in bulk form. This approach is attract-ive for producing controlled two-phase microstruc-

tures [23,24], but due to the nature of the process,the technique is limited to glass-forming compo-sitions. With this approach, nanocrystallites can beformed either by controlled thermal annealing (e.g.in [25–27] and/or by severe mechanical defor-mation at the bulk [28] or local [29] level.

Mechanical alloying, and specifically cryomil-ling in a liquid nitrogen medium, has been used toproduce ultra-fine-grained materials in reasonablequantities and the resulting powder has beenwarm/hot consolidated to full/nearly-full densitywith insignificant grain growth. The method hasbeen particularly successful with aluminum alloys[14,15] and the presence of fine oxides/nitrides thatresult from the milling process is key to main-taining the fine grain size during consolidation.While the advantage of the process lies in itsability to produce reasonable size billets ofmaterial, its principal disadvantages include theinability to control material purity and obtainingfull density. Some of the shortcomings associatedwith material purity can be offset by using theapproach of severe deformation of bulk material(as, for example, via torsion, multiple extrusion ormultiple forging) where material purity is limitedonly by that of the starting material, but the typicalgrain sizes obtained still remain in the 150–300 nmregime or more. Metals and alloys have been suc-cessfully processed by this route and include Alalloy 01420, Cu, Ni and Ti and its alloys (suchas Ti-6Al-4V), steels and intermetallic compounds.Due to extensive and repeated deformation pro-cessing, the grain boundaries are highly dislocated.The microstructure is usually characterized bylarger grains (having high-angle grain boundaries)with an internal sub-grain boundary structure. Acomprehensive review by Valiev et al. [16] dis-cusses the various metallurgical aspects ofmaterials produced by severe plastic deformation.

Gas-phase condensation or inert gas conden-sation [17–19] has been used in a limited way toproduce nc metals such as Cu, Ni and Pd. Here,powder particles with grain size in the 5–50 nmregime are produced by condensing from the vaporphase, and the particles are then consolidated in adie using high pressures and, in some cases, withadditional thermal energy. The process has severallimitations including specimen volume and yield,

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purity issues particularly in the vicinity of the par-ticle boundaries, incomplete densification/porosity(resulting in specimens with densities lower then99% of the theoretical density), and difficultiesassociated with retaining the fine grain size duringconsolidation. Improvements to the process havebeen reported [18], but considerable furtheradvances in process optimization are needed beforethis method can find commercialization. The pro-cess, however, is capable of providing a micro-structure that is usually texture-free and consistingof equiaxed grains. Recently it has been shown thatthe density of the specimens can be increased bycold rolling, while retaining the equiaxed, texture-free microstructure without a change in grainsize [30].

Electrodeposition (direct current and pulsed) hasbeen used to produce sheets of nc metals (such asNi, Co, Cu) and binary alloys (such as Ni-Fe; Ni-W) [20–22,31–34]. Grain size can be controlledand sheets with thickness of 100 µm or more andgrain size of 20–40 nm are routinely produced[34]. A bright field image (Fig. 2(a)) shows thetypical microstructure of electrodeposited nc Niwith an average grain size of about 30–40 nm.Alloying with W has enabled further reductions ingrain size down to 10 nm or less [33], and a rep-resentative bright field micrograph of the structureof a Ni-W alloy is shown in Fig. 2(b). Grain sizedistribution in these materials often tends to be nar-row with the maximum grain size not exceeding80 nm for a material with a mean grain size of 20–30 nm [35]. The use of saccharin in the platingbath to produce nc grains often results in carbonand sulfur as impurities in the material [36,37]; fur-thermore, hydrogen levels in the deposits can besubstantial and it is not uncommon to find hydro-gen-filled nano-bubbles in the microstructure eventhough full-density is measured within the errorsof the Archimedes technique. Process control dic-tates the presence or absence of a columnar struc-ture, and the presence of clusters of grains withminimal misorientation between each other hasbeen reported [35]. Likewise, process parametersinfluence the texture of the deposit, and in the caseof Ni produced by pulsed electrodeposition, El-Sherik and Erb [37] report a change in texture withdecreasing grain size, an observation also made by

Fig. 2. Bright field TEM images of electrodeposited (a) nc-Niwith an average grain size around 30 nm, and b) nc-Ni-W withan average grain size of ~10 nm.

Ebrahimi and coworkers [36]. Electrodepositionhas also successfully been used to produce nc met-allic coatings on complex shapes [34].

In recent years, more effort has been devoted toimproving the synthesis of nc-metals byelectrodeposition rather than by inert gascondensation/compaction, primarily because of theproblems associated with attaining full density viathe latter approach. Reports on the mechanical

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properties and deformation response of nc metalsand alloys in earlier papers were often influenced,in many cases, by the presence of porosity(samples densities were frequently lower then98%) and impurities. Furthermore, even at present,the microstructure of a metal produced by a parti-cular technique appears to vary from batch to batchand frequently, microstructures have not beencharacterized to the level necessary for rigorousinterpretation of the observed results. For example,very small pores of tens of nm size scale, com-monly referred to as nanovoids, are often presentin the material, and they can have a significantinfluence on the measured mechanical properties.These nanovoids are below the detection limits ofdensity measurements and can only be inferred bypositron annihilation [38,39]. Not accounting prop-erly for the possible direct effects of suchprocessing-induced defects on the mechanicalresponse has led to numerous contradictory resultsin the published literature (examples of which arediscussed in [40,41]). These factors have made itdifficult to identify, in many cases, the intrinsicdeformation characteristics of materials with grainsizes in the nanometer size scale and therefore, toobtain a clear mechanistic understanding of theirmechanical response.

3. Grain Boundaries (GB) in nanocrystallinemetals and alloys

Relative to mc metals and alloys (i.e. materialswith grain size in the micrometer range), ncmaterials contain a higher fraction of grain bound-ary volume (for example, for a grain size of 10 nm,between 14 and 27% of all atoms reside in a regionwithin 0.5–1.0 nm of a grain boundary); therefore,grain boundaries are thought to play a significantrole in the deformation of these materials. Theseboundaries act as sources and sinks for dislocationsand facilitate such stress-relief mechanisms asgrain boundary sliding. Given this trend, there aresurprisingly few experimental studies that havesought to examine the structure of grain boundariesin nc metals and alloys. Earlier postulates that thereexists an amorphous layer (or variously called an“extended disordered region” or “ randomly

arranged atoms” ) at grain boundaries of nc metalsand alloys [17,42–46] have been questioned basedon experimental observations [41,47,48] and com-putations (a more detailed discussion followsbelow and also in [49]). High-resolution images ofgrain boundaries in electrodeposited Ni with anaverage grain size of 30–40 nm (Fig. 3(a),(b)) andin vapor-phase condensed and consolidated nc Cu(Fig. 3(c),(d)) confirm that crystallinity is main-tained right up to the boundary. Gleiter [17] pointsto the need for caution in correlating grain bound-ary structures observed by high resolution TEM tostructures in bulk nc materials due to possibleinfluence of relaxation; this has, however, beenshown not to be an issue by Siegel and Thomas[47] and by the calculations of Mills and Daw [50].For Ni-W nanocrystalline alloys, Schuh et al. [33]report the existence of a finite non-crystallineregion at grain boundaries that were examined byhigh-resolution microscopy but enough evidencewas not presented there for its prevalence at allboundaries. Moreover, it is not clear whether thisis a chemical effect arising from the W in the alloyor if it is a direct consequence of the extremelyfine grain size (typically � 10 nm). Chemical seg-regation of impurities or alloying additions to grainboundaries and its effects on structure (or lackthereof), deformation and fracture have not beenexamined. It is also not known if such effects pro-vide a preferred crack path at the very high strengthlevels typical of such fine-grained materials. Grainboundaries in the as-deposited material (in the caseof electrodeposition), and in as-deformed material(in the case of ufc alloys produced by severe plas-tic deformation) can be in a non-equilibrium stateand in the latter case, can also have a high densityof dislocations. Such structures are difficult tocharacterize in the transmission electron micro-scope and their metastable nature and spatial non-uniformity often make clear interpretation of obser-vations difficult. Simulations [51] of thedeformation response of nc-Ni containing grainboundaries with various levels of disorder (i.e.equilibrium versus non-equilibrium) that mimic theas-deposited and annealed conditions, have shownthat grain boundary relaxation by a process suchas annealing leads to a decrease in plasticity andincrease in strength. While the experimental results

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Fig. 3. High resolution TEM images of grain boundaries in (a,b) electrodeposited nc-Ni, and (c,d) nc-Cu produced by gas-phasecondensation. In all cases, crystallinity is maintained right up to the boundary and no second phase is observed.

on inert gas condensed nc-Cu [52] support thesimulation results, the results of Ebrahimi et al.[22] on electrodeposited Cu (grain size 175–250nm) suggest otherwise. It is possible that at theselarger grain sizes (as opposed to at 10–20 nm grainsize), the structure of the grain boundary is alreadyclose to equilibrium. Further experimental data areneeded to verify the suggestions from computersimulations [51].

The use of large-scale molecular dynamics(MD) to obtain atomic level structural informationon the grain boundaries in nc fcc metals [46,49]has significantly enhanced the understanding real-ized from experiments. Most simulations have

been performed on fcc pure metals with dislo-cation-free grains; Keblinski et al. [53] have alsostudied nc Si. A fully three-dimensional (3D) ncgrain boundary (GB) network may be constructedin one of several ways: simulations of materialsynthesis can be accomplished (a) by clusterassembly followed by compaction [54,55], (b) bycooling from the melt with pre-defined crystalliz-ation seeds [46,56], or (c) by using space fillingtechniques based on Voronoi construction [57]with randomly generated seeds and orientations inorder to prepare samples with mainly high anglegrain boundaries [49,58,59] or with restrictions oncrystallographic orientations in order to obtain tex-

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tured samples [60]. The maximum grain size thathas been simulated in full 3D GB networks is30nm [58] for a sample containing 15 grains. Allsimulations apply periodic boundary conditions, areplica technique that mimics bulk conditions. Inorder to increase the grain size in simulations,samples with a two-dimensional (2D) columnarGB network containing four hexagonal-shaped fcccolumnar-grains textured around the [110] axishave been constructed in which the periodicboundary conditions are applied on ten atomicplanes in the columnar direction. In these samplesthe GBs are perpendicular to the tensile directionand contain only twist-free misorientations [61,62]and therefore cannot mimic a general nc GB net-work. The GBs made by cooling from the meltusing pre-existing fcc crystal seeds would beexpected to have a different non-equilibrium staterelative to those derived from a space-filling tech-nique. Furthermore, even within one technique, thefinal GB structure will depend on the relaxationtime and temperature, as has been shown forVoronoi constructed samples [51].

Simulations show that different patterns anddegrees of order with different length scales areobtained when different criteria are used for GBatoms [63]. This is demonstrated in Fig. 4a-d. Thethree upper images (Fig. 4(a)–(c)) show a sectionof the GB viewed perpendicular to the GB plane,whereas Fig. 4(d) shows a section viewed alongthe GB plane where a general GB with an irreduc-ible 50° misorientation around a (110) axis of thelower grain is shown. In Fig. 4(a), the GB isdefined by those atoms, which according to themedium range order (MRO) analysis [49,64] donot have the fcc structure. In Fig. 4(b), the GB isdefined by those atoms that are positional dis-ordered (PD) i.e. atoms which cannot be assignedto a particular lattice site of the neighboring fccgrains [65]. In Fig. 4(c), the GB is defined by theatoms having an excess energy higher than the lat-ent heat of melting. The view along the GB planein Fig. 4(d) shows the coherence among (111)crystallographic planes of the lower grain and(100) crystallographic planes of the upper grain,with a regular pattern of misfit areas. From Fig. 4,it is clear that claiming the existence of amorphousGBs on the basis of a single criterion, such as

excess energy [46,53], is not justified. Using theabove-mentioned criteria, it has been demonstratedthat pure metallic samples resulting from aVoronoi construction have grain boundaries thatare fundamentally the same as their coarse-grainedcounterparts [49]. For all types of misfit, a largedegree of structural coherence is observed and mis-fit accommodation occurs in somewhat regular pat-terns, with the misfit areas containing a largerdegree of disorder.

Further important information on grain bound-aries in nc materials can be obtained by the directcalculation of the variation of the internal stress[66,67] and the free volume in GBs [68]. The localpressure variations, made up of adjacent regions ofhigh compression and dilatation (the colour coderanges from red for 2 GPa to blue for –2 GPa), areshown in Fig. 5(a) for the GB discussed in Fig. 4(Fig. 5(b) shows the stress distribution after 0.5nsec of tensile deformation—the details pertainingto Fig. 5(b) are presented in the DeformationMechanism section). The stress concentrationsobserved in such a GB would be expected to pro-duce inhomogeneous strain inside the grains, aparameter that is experimentally obtained frompeak broadening in X-ray diffraction. The amountof free volume and its distribution also influenceatomic mobility in GBs. It is also possible to calcu-late positron life times in simulated samples whichcan then be compared to experimental data [39,68].Such calculations for samples synthesized in thecomputer by a space-filling technique [68] showthat they have densities similar to the experimentalvalues (99.26% for a 20 nm sample), but containno nano-scale voids. Instead, they contain smallamounts of free volume of sizes in-between thatfor a single vacancy and of the perfect crystal.However, in nearly all experimental samples,nano-scale voids containing 5 to 20 vacancies havebeen identified in positron lifetime measurements–even when the samples are fully dense as determ-ined by the Archimedes principle [38,39,68]. Thisimportant difference in free volume distributionbetween simulated and experimental samplesshould be addressed in order to render thecomputational models more representative ofexperiments.

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Fig. 4. Perpendicular view of a general GB using different criteria for the definition of GB atoms a) medium range order b) positionaldisorder c) excess energy; d) View along the GB plane showing coherence across the GB (grey: fcc atoms, green: other-12 coordinatedatoms, blue: non-12 coordinated atoms).

Fig. 5. View normal to the same GB plane as in Fig. 4 show-ing the local pressure variations (colour code ranges from red= 2 GPa and blue = �2 GPa) a) before deformation b) after0.5 nsec tensile deformation corresponding to 3% total strain.

4. Mechanical properties of nanocrystallinemetals and alloys

4.1. Yield strength and tensile elongation

The mechanical properties of fully-dense fccmetals (Cu, Ni and Pd) with grain size less than100 nm have been primarily derived from uniaxialtension/compression tests and micro- or nano-indentation [19,22,31,35,36,40,69,70]. Typically,these nanocrystalline metals exhibit significantlyhigher yield strength, and reduced tensile elong-ation relative to their microcrystalline counterparts.Furthermore, hardness and yield strength havebeen found to increase with decreasing grain sizein this regime (� 100 nm) down to at least 15 nm.The reasons for this behavior are still under debateas dislocation sources within grains are notexpected to operate at these grain sizes. In addition,there is no documented evidence of dislocation

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pile-ups in deformed specimens, and any dislo-cation activity is primarily believed to originateand terminate at grain boundaries. Furthermoreexperimental evidence [32,33,71–73] indicates thatbelow a grain size of ~10 nm, strength decreaseswith further grain refinement (the so-called“ inverse Hall-Petch-type” relationship). In thisregime, grain boundary sliding and/or Coble creepapparently constitute the dominant deformationmodes [72,73]; yet, there appears to be no directexperimental confirmation in the published litera-ture of the operation of these processes.

Results of uniaxial tensile tests reveal severalunusual features specific to the deformation of nc-metals with fcc structures. For instance, the tensileelongation at fracture of nc metals is low relative totheir conventional mc counterparts [19,35,36,69].This behavior is often attributed to plastic insta-bility originating from the lack of an effectivehardening mechanism and/or internal flaws; thisinstability manifests itself as either shear bands orthrough “early” necking, as discussed by Ma [74].Ebrahimi et al. [22] compared 100-µm thick cold-rolled mc copper with electrodeposited nc-Cu, andconcluded that the low tensile elongation to frac-ture in these thin sheet specimens was a conse-quence of the early onset of plastic instability caus-ing localized deformation. The observation ofmacroscopic chisel-tip fracture in electrodepositednc-Ni and nc-Cu [22,36] tensile tests with little ten-sile elongation to fracture supports the localizeddeformation hypothesis. In this context, Jia et al.[75] have shown the formation of localized shearbands during compression deformation of nc bodycentered cubic (bcc) Fe at quasi-static strain ratesat room temperature; they further noted that thewidth of the band increased with increasing strainand increasing grain size. Shear bands have alsobeen reported in nc Fe-10%Cu alloy in com-pression and in tension [76], in nc Pd in com-pression [77] and in nc Cu in fatigue [78]. Earlynecking was observed in nc-electrodeposited Ni[35] and it was shown that the shape of the tensilestress-strain curve and tensile elongation wereaffected by specimen size, with uniform defor-mation along the gauge section observed in smallspecimens but not in larger specimens. Theobserved differences were attributed to microstruc-

tural inhomogeneity. Since a number of experi-mental studies have focused on electrodeposited ncNi, it is pertinent to recall the results of Robertsonand Birnbaum [79] on the effects of hydrogen ondeformation and fracture of conventional polycrys-talline Ni. They demonstrated that hydrogendecreases the stress required for crack advance andlocalizes deformation.

In the early stages of permanent deformation,independent of the technique used to produce thenc-Ni or nc-Cu, a strong “work hardening”response is always observed [19,22,31,35,36,69]and in some cases, it appears to be stronger thanthat seen in mc metals [19,22]. Mechanisms forhigh work hardening in fcc metals include theformation of dislocation locks such as the Lomer-Cottrell locks, formation of dipoles and significantpinning due to dislocation intersections [80,81],none of which has been experimentally demon-strated for nc metals. The inability to observe thesefeatures has raised questions regarding the originof the non-linear portion of the stress-strain curvesobtained for nc metals.

The above discussion has focused on fcc metalsand alloy. However, mechanical properties of ncbody centered cubic (bcc) and hexagonal closepacked (hcp) metals and alloys have also beenobtained [75,76,82–85]. Electrodeposited nc-Co,for example, with an average grain size of 12 nmshows tensile elongation comparable to that of mc-Co [84]; the limited amount of information avail-able on such systems precludes the extraction ofgeneral trends.

4.2. Strain rate effects in tension, compressionand indentation

Experimental studies have shown that nc metalsexhibit highly strain-rate sensitive mechanicalresponse under different loading conditions. Theseinvestigations also reveal that an increase in theloading rate generally leads to an increase in tensilestrength, whereas the observed dependence of duc-tility on loading rate appears to depend strongly onprocessing, composition and testing methodemployed to probe rate sensitivity. In an earlystudy published on this topic, Wang et al. [86]found electrodeposited nc Ni to be highly strain

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rate sensitive at room temperature. Lu et al. [6,31]reported that electrodeposited nc copper, with anaverage grain size of about 30 nm, showed only amoderate increase in flow stress, from about 85–150 MPa at 1% plastic strain, as the strain rate wasraised from 6 × 10�5 to 1.8 × 103 s�1. However,the strain to failure was observed to increase mark-edly with increasing strain rate. This trend is dis-tinctly different from that of conventional mc cop-per where the fracture strain is known to dropslightly with strain rate. Dalla Torre et al. [35], onthe other hand, observed that the ductility of elec-trodeposited nc Ni decreased as the strain rate wasraised from 5.5 × 10�5 to 5.5 × 10�2 s�1. Theyalso found that the tensile strength was essentiallyindependent of strain rate over this range, whereasit increased significantly as the strain rate wasraised from 101 to 103 s�1. Mukai et al. [87] inves-tigated the response under quasi-static tension andhigh-strain-rate dynamic tension (using the split-Hopkinson bar) of several Al-Fe alloys (in the Fecomposition range 1.15–1.71 at.%) produced by e-beam deposition. These alloys comprisedmicrocrystallites with high angle boundaries andnc subgrains. The flow stress was found to behigher for the strain rate of 1.1 × 103 s�1 than thatfor 10�3 s�1, although the elastic limit and tensilestrain to failure were essentially unaffected bystrain rate. Mukai et al. [87] observed that whilethe high angle boundaries had the effect of enhanc-ing ductility, the smaller grains imparted a higherstrength.

A number of complications arise in establishinga clean comparison of the foregoing experimentaldata. Firstly, the materials with which strain rateeffects were studied were produced by differentprocessing routes. Consequently, their structure,purity and distribution of grain sizes were different,and in many cases, the materials were not thor-oughly characterized by recourse to high-resolutionelectron microscopy. Secondly, experimentalmethods used to impose different strain rates on thespecimen often involved widely different loadingmethods, even in the same study. For example,direct quasi-static tension test results for slowstrain rates are often compared with high-strain-rate experiments performed using dynamic loadswhere the specimen geometry and stress state are

considerably different. As a result, it is often diffi-cult to isolate the effects of experimental artifactsfrom intrinsic rate sensitivity of material response.Thirdly, the volume of material sampled by differ-ent experimental techniques is usually different,and given the small specimen dimensions com-monly used to probe many nc metals, it is essentialto isolate any possible effects of specimen sizefrom intrinsic material properties. With these con-siderations in mind, Schwaiger et al. [88] perfor-med systematic experiments to investigate the ratesensitivity of deformation of a well characterized,fully dense, nc pure Ni produced by electrodepos-ition with a grain size of approximately 40 nm(whose structure is revealed at high resolution inFig. 3(a) and (b)) using two different experimentaltechniques: depth-sensing instrumented indentationand direct tensile testing. In order to assess theeffects of grain size on rate sensitivity, they alsoperformed parallel experiments on a similarly pro-duced electrodeposited ufc Ni.

Fig. 6(a) shows results of constant strain rateindentation tests on the nc Ni at three differentstrain rates, whereas Fig. 6(b) shows results of fourdifferent constant load rates on the indentationresponse of the same material [88]. It is evidentthat, over the range of values examined, anincrease in strain/loading rate causes a small, butexperimentally reproducible, increase in the inden-tation stiffness which is reflected in the measuredhardness values. Identical experiments performedon the electrodeposited, ufc Ni, with an averagegrain size about 300 nm, did not reveal any ratesensitivity of indentation response or hardness[88]. Considerably larger experimental scatter wasobserved in the case of the ufc Ni, possibly as aconsequence of the significantly larger variation inthe distribution of grain sizes. The results summar-ized in Fig. 6, along with the related data presentedin [88], clearly show that nc pure metals exhibit anoticeably more pronounced strain rate sensitivitycompared to their larger-grained counterparts.

Fig. 7(a) is a plot of the effect of strain rate, inthe range 3 × 10�3 to 3 × 10�1 s�1, for the nc Nisubjected to direct tension loading [88]. It is evi-dent from this plot that the overall trends seen inthe indentation tests are also observed in the tensiletests. The flow stress of nc Ni increases noticeably

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Fig. 6. Depth-sensing instrumented nanoindentation responseof electrodeposited nanocrystalline Ni subjected to (a) constantstrain rate indentation and (b) constant loading rate indentation.Each curve in (a) and (b) represents an average of 5 differentexperiments along with an error bar. From Schwaiger et al. [88].

with strain rate although no clear trends could beestablished on the effects of strain rate on tensilestrain to failure.

The mechanisms underlying the unusual rate-sensitivity of deformation of nc metals and alloysare not fully understood at this time. However,potentially useful insights into such mechanismscan be gained from computational simulations thatseek to explore the effects of different structuralfactors. While such simulations inevitably call formethods that appropriately account for the atom-istics of deformation (see later section), continuumformulations of the overall deformation responsealso provide additional information on rate-sensi-

Fig. 7. (a) Results of tensile tests at three different strain rateson electrodeposited nanocrystalline Ni with an average grainsize of 40 nm, and (b) Finite element computational simulationsof the tensile stress-strain response of nanocrystalline Ni (grainsize, 30–40 nm) at three different strain rates, assuming aGBAZ volume fraction of 25%. The symbol “x’ refers to tensilestrength. From Schwaiger et al. [88].

tivity at realistic time scales which cannot beobtained solely from experiments or atomisticsimulations. One such analysis was presented bySchwaiger et al. [88] who employed finite elementmodeling within the context of unit cell formu-lations with periodic boundary conditions in anattempt address the following questions. (1) If onepostulates the existence of a region neighboring thegrain boundary (so called “grain boundary affectedzone” or GBAZ) of a nc metal wherein the crystal-line lattice is locally strained differently than theinterior of the grain, can possible differencesbetween the rate sensitivity of deformation (as esti-

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mated, for example, by a pure power law, rate-dependent constitutive response) of GBAZ andgrain interior be used to rationalize the overallstrain-rate sensitivity of the nanocrystalline metal?(2) How does the volume fraction of such a postu-lated GBAZ affect deformation? (3) By invokinga criterion for tensile failure within the context ofa finite element model, can the overall tensile duc-tility of the nc metal be estimated as a function ofimposed strain rate?

Schwaiger et al. [88] considered hexagonalgrains with a plastically softer GBAZ whose defor-mation was rate-sensitive and a plastically hardergrain interior, with the effects of their relative vol-ume fractions on strength and ductility examinedfor different nc metals. A simple strain-based cri-terion for failure was postulated: materialdamage/failure initiates when the local plasticstrain reaches a critical value, and the materialstrength declines linearly with plastic strain to zeroover a certain plastic strain increment. This modelwas used to rationalize stress-strain characteristicsand tensile strain to failure as a function of severaldifferent strain rates. Fig. 7(b) shows the compu-tationally predicted tensile stress-strain responseand tensile strain to failure values for nc Ni (grainsize 30–40 nm) at three different strain rates [88],assuming 25 vol.% for GBAZ. While the simplefinite element analysis based on the GBAZ unit cellmodel is at present based on a hypothetical struc-ture which has not been backed by direct experi-mental verification, it is evident from Fig. 7(b) thatit provides one possible rationale for the influenceof strain rate on tensile strength and ductility.

Fig. 8 provides a summary of experimentalresults available in the literature on the effects ofstrain rate, from 10�5 to 104 s�1, on the yieldstrength of a wide variety of mc, ufc and nc metalsand alloys [87]. It is evident from this figure thatnc metals show a significantly more pronouncedstrain-rate sensitivity than coarser grainedmaterials over a wide range of strain rates.

4.3. Fracture and fatigue response

Developing an understanding of the damage tol-erance of nc metals and alloys is essential for eval-uating their overall usefulness as structural

Fig. 8. A summary of experimental data available in the litera-ture on the variation of dynamic yield strength (normalized bythe corresponding static yield strength at the slowest strain rate)for a wide variety of microcrystalline, ultrafine crystalline andnanocrystalline metals and alloys. Results taken from literaturesurvey by Mukai et al. [87] (where further information on theoriginal sources can be found), with additional results fromSchwaiger et al. [88].

materials or coatings in engineering components.Such understanding should inevitably include com-prehensive knowledge of the resistance to fractureinitiation and growth under quasi-static anddynamic loading conditions, and of stress- andstrain-based total fatigue life and subcritical crackgrowth under fluctuating loads at different meanstress, cyclic frequency and environment. Manyattractive features of nc metals, such as highstrength, high hardness, and improved resistance towear and corrosion damage (as compared to con-ventional metals), would likely be rendered non-viable if the damage tolerance of these materialsdoes not meet certain minimum acceptable levelsfor particular applications.

Despite such need, very little published infor-mation is presently available on the damage toler-ance characteristics of nc metals and alloys. Thispaucity of information can be attributed to the factthat processing methods, such as electrodepositionor e-beam deposition, which are used to producefully dense nc materials with uniform purity anduniformly small grain sizes (typically smaller than100 nm or so) typically yield only thin foils thatare at most only several hundred micrometers inthickness. Although these methods can provide

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material with large in-plane dimensions, typicallyin excess of 100 × 100 mm, the small specimenthickness poses considerable experimental diffi-culties in performing a “valid” test to extract frac-ture toughness, resistance-curve or fatigue proper-ties. Such difficulties include severe constraints ingripping the test specimen or imposing controlledloads and stress states without experimental arti-facts such as out-of-plane bending or buckling ofthe specimen. Specifically, special precautionsshould be taken to ensure that the thin foils arenot subjected to any bending moments during theapplication of static or cyclic tensile loads; thesemeasures invariably restrict the range of loads,stress intensity factors, mean stress levels, cyclicfrequencies or test environments imposed on thespecimen. Similarly, the possibility of buckling ofthe thin specimen restricts cyclic loading testsprimarily to direct tension loading or three or fourpoint bending tests. In addition, a significant rangeof the subcritical crack growth experiments perfor-med under quasi-static or cyclic loading representplane stress states because the plastic zone size atthe tip of the crack is comparable to or larger thanthe specimen thickness.

The limited through-thickness dimension of thespecimens is an impediment to extracting “valid”damage tolerance properties of nc materials pro-duced by some processing methods. In other cases,it is possible to circumvent these barriers by adopt-ing processing methods, such as the mechanicalalloying/consolidation or the equal-channel anglepressing techniques described earlier in Section 2.These methods provide materials of sufficient vol-ume to perform conventional fracture and fatiguetests on nc materials which conform to the stan-dards specified by the American Society for Test-ing and Materials and which can also be directlycompared with results available in the literature onmc materials. A significant drawback of such pro-cessing methods, however, is that they producehighly inhomogenous microstructures with pro-nounced variations in grain size, grain structure,and defect density, and that they contain highinitial defect densities as well as relatively largegrain dimensions (typically on the order of up toseveral hundred nm). These complexities constituteserious obstacles in using such materials for study-

ing fundamental mechanisms of crack initiationand propagation and for examining, in a systematicmanner, the connections between structure anddamage tolerance.

Mirshams et al. [89] studied the quasi-staticfracture toughness of thin sheets of nc nickel pro-duced by electrodeposition by investigating theirR-curve response. In this approach, the stressintensity factor or strain energy release rate is plot-ted against the increment in crack length with theobjective of assessing the resistance of the materialto quasi-static crack growth in a subcritical man-ner, usually for specimens in a state of plane stress.Mirshams et al. [89] studied subcritical growthresistance by monitoring R-curves with small com-pact tension specimens where a clip gage was usedto monitor crack extension along with opticalmicroscopy. Their results revealed a strong influ-ence of annealing temperature and carbon dopingon the resistance-curve behavior of nickel with anaverage grain size which varied in the range of 19–48 nm. For undoped and 500-ppm carbon-dopednc Ni with an average grain size of approximately20 nm, they reported plane stress steady-statequasi-static fracture toughness values of about 120and 20 MPa√m, respectively, for specimen thick-nesses of 0.22 and 0.35 mm, respectively (with in-plane dimensions being 32 × 40 mm in both cases).By contrast, the corresponding fracture toughnessfor a pure polycrystalline Ni with an average grainsize of 21 µm was found to be approximately 60MPa√m. Thermal annealing and carbon dopingwere found to deteriorate crack growth resistance.These experiments [89] provide useful insights intothe damage tolerance response of the nc Ni. How-ever, they also raise interesting questions and con-cerns that require substantial further inquiry. (a)The structure of the materials studied had not beeninvestigated in detail using electron microscopy.(b) It appears that small-scale yielding conditionsdid not prevail over the full range of stress inten-sity factor values for which damage tolerancevalues were reported. As a result, the validity in theuse of stress intensity factor to characterize fractureresponse becomes somewhat questionable,especially at the higher stress intensity levels. (c)The reported fracture properties have not been sub-stantiated by independent experimental results

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employing different specimen geometry or loadingmethods. (d) No mechanistic investigations of theorigins of differences between different test con-ditions were undertaken. (e) Typical scatter in theexperimental data and issues associated with repro-ducibility of results for the testing conditions aswell as for crack growth monitoring were notreported.

Independent experimental studies of fractureresistance in fatigue-pre-cracked 100 µm-thickpure Ni sheets with a narrow range of grain size(20–40 nm), also produced by electrodeposition,reveal that the plane stress fracture toughness inlaboratory air is at least about 25 MPa√m [90].Thus, the limited extent of experimental infor-mation available to date, primarily on electrodepo-sited nc Ni, appears to indicate that the materialhas a reasonable fracture toughness considering itsrelatively high strength and low ductility comparedto mc Ni. However, further experimental studiesof fracture toughness in nc metals and alloys arecritically needed so as to develop a fundamentalframework with which their fracture mechanismscan be systematically assessed.

It is widely recognized from the wealth ofexperimental information available in the literature(e.g., [91]) on conventional metals and alloys thatgrain refinement markedly influences the resistanceto fatigue crack initiation and propagation. In mcmaterials, a reduction in grain size generally resultsin an elevation in strength which engenders anincrease in fatigue endurance limit during stress-controlled cyclic loading of initially smooth-surfaced laboratory specimens. Since the totalfatigue life under such conditions is dominated bycrack nucleation and since fatigue cracks generallynucleate at the free surface (in initially flaw-freemetals), grain refinement here is considered toresult in improvements in fatigue life as well asendurance limit, with all other structural factors setaside. On the other hand, a coarser grain structurewith lower strength and enhanced ductility gener-ally plays a more beneficial role in the strain-con-trolled fatigue response of metals and alloys. Herethe low cycle fatigue properties generally improvewith grain coarsening, with all other structural fac-tors set aside. The situation is somewhat differentwhen the effects of grain size on fatigue crack

growth behavior are examined in mc metals andalloys. In the near-threshold regime of fatiguecrack growth, where the extent of fatigue crackgrowth per stress cycle is on the order of a latticespacing, finer grained materials usually exhibit arelatively faster rate of crack propagation and alower fatigue threshold stress intensity factor range[91,92]. This trend is at least partially ascribed tothe reduced level of fracture surface roughnessseen in the finer-grained metal, as the deflections incrack path promoted during crystallographic crackadvance are reduced with grain refinement [93]. Inaddition, any lowering of effective stress intensityfactor range due to premature contact between mat-ing crack surface asperities would also be expectedto be reduced due to grain refinement [91,93]. Itshould be noted, however, that it is often difficultto isolate the sole effects of grain size on fatigueresponse since other structural factors such as pre-cipitate content, size and spatial distribution, stack-ing fault energy and the attendant equilibriumspacing of partial dislocations, and crystallographictexture, are also known to have an important effecton the fatigue characteristics of mc metals [91].

Although considerable experimental informationis available on the fatigue response of metals andalloys with grain size typically larger than 1 µm,little is known about the fatigue characteristics ofufc and nc metals. Several studies have examinedthe total fatigue life of ultra-fine crystalline metalsproduced by equal channel angular pressing, wheresevere plastic deformation was used for grainrefinement [94–96]. In these experiments involvingmetals with average grain sizes of more than a hun-dred nm, repeated cyclic loading resulted in pro-nounced cyclic softening and a weakening of theresistance to low cycle fatigue. These trends, how-ever, have also been seen in microcrystalline met-als and alloys where, as demonstrated by Feltnerand Laird [97], initially soft microstructures (suchas those produced after annealing) cyclicallyharden, and initially hard microstructures (such asthose produced by severe cold working) soften asa consequence of the realignment of dislocationnetworks to a common saturated state of optimalstored elastic strain energy. Similar behavior isseen when the stacking fault energy of the metalis altered by alloying, although lowering of the

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stacking fault energy leads to a cyclically hardenedstate for the initially soft metal than the softenedsaturated state attained for the initially hardermetal. This effect of stacking fault energy has beenattributed by Feltner and Laird [97] to the possi-bility of restricted cross-slip of screw dislocationswhose dissociated partials have a larger equilib-rium separation because of the lower stacking faultenergy. In this case, the reduced propensity forcross slip leads to different final states in the twocases by constraining the ability of dislocations toreorganize into a common final state. The cyclicdeformation results presented in [94–96] for ufcmetals thus exhibit trends which are consistentwith those well established for conventional mcmetals. These studies [94–96] have also shown thatthe total fatigue life of ufc metals is generallyenhanced compared to that of their mc counter-parts, as reflected in their relatively high fatigueendurance limit values.

To the authors’ knowledge, there appears to beonly one published report [98] of the fatigue lifeand fatigue crack growth characteristics of a well-characterized nc metal with a narrow grain sizerange below the 100 nm level and with full densityand high purity. Hanlon et al. [98] compared thestress-life (S-N) fatigue response of a fully dense,electrodeposited nc Ni (grain size in the range 20–40 nm) with that of a similarly produced ufc Ni(grain size in the 300 nm range) and of a conven-tional mc Ni. They performed fatigue experimentsat zero-tension-zero loading (i.e., load ratio, R =ratio of the minimum load to the maximum loadof the fatigue cycle = 0) at a cyclic frequency, n= 1 Hz (sinusoidal waveform) in the nominal lab-oratory air environment. Fig. 9 shows that grainrefinement has a significant effect on the S-Nfatigue response of pure Ni. Nanocrystalline Ni hasa slightly higher, but reproducible, increase in thetensile stress range needed to achieve a fixed lifeand in the endurance limit (defined at 2 millionfatigue cycles) compared to the ufc Ni. Both nc andufc conditions have a significantly higher fatigueendurance limit than the mc metal. Hanlon et al.[98] also conducted fatigue crack growth experi-ments on nc Ni using edge notched specimens thatwere subjected to cyclic tension at different Rratios. Fig. 10(a) shows the increase in fatigue

Fig. 9. S-N fatigue response of electrodeposited, fully densenanocrystalline Ni (grain size 20–40 nm) compared to that ofa similarly produced ultrafine crystalline Ni (grain size approxi-mately 300 nm) at R = 0 and frequency of 1 Hz in laboratoryair environment. Also shown for comparison are the literaturevalues of the range of endurance limit for microcrystalline pureNi. From Hanlon et al. [98].

crack length as a function of number of constantamplitude fatigue cycles at a common initial stressintensity factor range, �K = 11.5 MPa√m, at R =0.3 and n = 10 Hz (sinusoidal waveform) in labora-tory air for the nc, ufc and mc pure Ni. It is evidentthat the rate of fatigue crack growth is significantlyincreased with decreasing grain size in this inter-mediate regime of fatigue fracture. Fig. 10(b)shows the constant amplitude fatigue crack growthdata for pure Ni as a function of grain size fromthe mc to nc. Again, a marked reduction in grainsize from the micrometer to the nanometer scale isseen to result in up to an order of magnitudeincrease in fatigue crack growth rates in the inter-mediate regime of fatigue fracture. Such trends arefully consistent with the mechanistic expectationsof fatigue fracture based on results available formc alloys that were mentioned earlier in this sec-tion. These results reveal that strategies for grainboundary engineering that lead to an improvementin the total fatigue life may have a concurrent detri-mental effect in that they can deteriorate the resist-ance to subcritical crack growth under constantamplitude fatigue.

The foregoing trends seen in pure nc Ni alsoappear to carry over to the more complex situation

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Fig. 10. A comparison of the fatigue crack growth character-istics of pure Ni as a function of grain size spanning the micro-to the nano-scales. (a) Increase in crack length with fatiguecycles for the nc, ufc and mc Ni at a common initial �K =11.5 MPa√m1/2, at R = 0.3 and n = 10 Hz. (b) Constant ampli-tude fatigue crack growth response under the same test con-ditions. From Hanlon et al. [98].

involving commercially produced ufc alloys whereconventional fatigue fracture studies could beundertaken using standard experimental techniqueswidely used for mc metals because of the largevolume of material available for investigation. Fig.11 shows the constant amplitude fatigue crackgrowth response of a cryomilled Al-7.5 wt% Mgalloy with an equiaxed grain size of approximately300 nm [99]. Note that, when compared to the

Fig. 11. Comparison of the constant amplitude fatigue crackgrowth characteristics of a mechanically alloyed Al-7.5 wt%Mg alloy with an average grain size of approximately 300 nm,produced by cryomilling and consolidation, with that of a com-mercial Al-5083 alloy with microcrystallites. From Hanlon etal. [98].

fatigue crack growth response of a commercialaluminum alloy 5083 with similar composition butwith mc structure, the cryomilled alloy shows rela-tively faster crack growth rates which are morethan an order of magnitude higher in the intermedi-ate regime of fatigue crack growth. The finergrained alloy also has a lower fatigue crack growththreshold stress intensity factor range [99].

5. Deformation mechanisms

It was noted in earlier sections that nc metalsand alloys exhibit a number of apparent anomaliesin their deformation and failure processes as com-pared to microcrystalline alloys. (1) At grain sizestypically smaller than 100 nm, nc metals seldomfollow “Hall-Petch” type strengthening with grainrefinement. Such behavior is not fully surprising inthat the mechanism commonly associated withHall-Petch type strengthening, i.e. dislocation pile-up at grain boundaries, has not been experimen-tally documented in nc metals. Furthermore, belowa certain transition grain size, typically on the orderof 5–15 nm in fcc metals, there appears to exist aregion in which strength and hardness decrease

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with decreasing grain size. (2) As shown in Figs.6–8, the dependence of yield strength on strain rateis distinctly different for nc metals and alloys com-pared to their mc counterparts. Furthermore, thestrain to failure in nc metals appears to vary withstrain rate in a manner opposite to that seen mcmetals and alloys (see Fig. 7). In this section wereview current understanding of deformation of ncmetals and alloys, starting with the insightsafforded by atomistic computer simulations whichare supplemented with experimental observations.The discussion of experimental observations is div-ided into two subsections: the first dealing withcontrolled, model experiments, and the secondinvolving microscopy.

5.1. Atomistic simulations

The use of large scale molecular dynamics (MD)simulations has provided insight into the atomicscale processes that may occur during plasticdeformation. Such computer simulations are usu-ally performed in uniaxial tension, with high loadschosen to produce a measurable strain within thesub-nanosecond MD time scale. The restrictedtime-scale, nanoseconds compared to hundreds ofseconds in real experiments, may exclude certaintime-dependent processes. Simulations shouldtherefore be regarded only as a source ofinspiration and quantitative guidance and not as ameans to validate or disprove the existence of amechanism.

Two approaches have been taken in the simula-tions of deformation: the first where a constant loadis applied and the evolution of deformation overtime is followed [61,62,100–108], and the second,where deformation is applied by constant strainsteps, followed by a short relaxation time, mimick-ing constant strain rate deformation [59,109]. Inboth types of simulation, the samples deform atvery high strain rates and care should be taken toensure that the stress waves travel at speeds severalorders of magnitude below that of the speed ofsound in the sample. This can be avoided by keep-ing the strain rate on the order of 107/sec. Simula-tions have been performed at room temperatureand at higher temperatures [102,110], the latter inorder to enhance diffusional activities.

At room temperature and in fully 3D GB net-works with a mean grain size below 30 nm in Niand Cu, the simulation demonstrates the ability ofthe nano-sized GB network to accommodate anexternal applied stress by means of GB sliding andemission of partial dislocations involving localstructural changes in the network [59,101–103,109]. The interplay between the two mech-anisms constitutes the origin of the formation oflocal shear planes which facilitates further plasticdeformation [105]. It has also been observed thatalong the shear plane, grains with small misorien-tations can coalesce to form a larger grain. Thepartial dislocation activity seems to be more effec-tive in grains with a mean grain size that exceeds10 nm, the size being dependent on the stackingfault energy of the material [100]. When a constantstrain rate is applied to nc Cu, the yield stress isfound to decrease with decreasing grain size, ther-eby suggesting a reverse Hall-Petch type relation-ship [59,109]. This softening has been ascribed tothe increased content in GB atoms that facilitatesliding, but no direct link with dislocation activityhas been made. Simulations on samples containing125 grains allowing cooperative grain mechanismhave shown that partial dislocations emitted fromGBs are also observed in 6 nm sized grains as ameans for transferring slip along a mesoscopicshear plane [105].

Both grain boundary and the dislocation plas-ticity appear to be triggered by atomic shufflingand, to a minor extent, by stress-assisted free vol-ume migration. The result is a local change in thestructure of the GB which causes redistribution ofpeak values of shear stress and compressive hydro-static pressure in neighbouring parts of the GB net-work. Atomic shuffling involves short-rangeatomic motion in which an atom shifts from a pos-ition associated with one grain orientation to a pos-ition associated with another neighbouring grainorientation or an intermediate one [111]. This pro-cess does not involve long-range mass transportand is therefore not diffusion-based. The free vol-ume migration is often observed in connection withpartial dislocation emission from the GBs[102,103]. No preferred direction has beenobserved in the free volume migration as would beexpected from a Coble creep mechanism at room

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temperature. The changes in local stress distri-butions during sliding are shown in Fig. 5 wherea view perpendicular to the GB plane is given fora GB with a misorientation of 50° around the [110]axis of one of the grains (as was described earlierin the section on grain boundary structure). Fig.5(a) shows the stress distribution prior to defor-mation and Fig. 5(b) after 0.5 ns of tensile defor-mation. This GB has been observed to migrate dur-ing sliding (which as shown in Section 5.2, alsohas some experimental support from bubble raftmodel studies) and involves atomic activity and,to a minor extent, free volume migration. In otherwords, the simulations underscore the benefit ofthe presence of GBs that can reduce their stressstate during the deformation.

Fig. 12 represents the atomic configuration of asection of grains 12 and 13 (denoted G12 and G13)in a 12 nm Ni sample, both before (a) and after(b) the emission of a partial dislocation at about0.3 ns of deformation. The GB and the two neigh-bouring triple junctions are represented by theblue-green atoms, the hexagonal close packed(hcp) atoms in the stacking fault behind the partial

Fig. 12. Section of the GB between grain 12 (G12) and grain13 (G13) before (a) and after (b) the emission of a partial dislo-cation. The GB planes where GB dislocations can be observedare numbered. The inset shows a detailed view on the atomicmotion towards the nucleation site.

are colored red. The view is along a [1–10] direc-tion of grain 13, where for this grain the unit cellhas been highlighted by the yellow rectangle. Thegrain boundary plane is close to a (1–113) planeof grain 13 and the tilt angle between the observed(111) planes in grain 13 and 12 is approximately24°. The twist angle was found to be approxi-mately 18°. The GB structure accommodates theabove-mentioned misfit through a GB dislocation(GBD) network. The planes where GBD areobserved are numbered in Fig. 12(a) and two ofthem are marked by a yellow circle. Just after theemission of the partial, a free volume unit of thesize of a vacancy migrated from GBD3 towardsGBD2, followed by a rearrangement of the otherGBDs. The migration of atoms towards thenucleation site (free volume away from nucleationsite) is shown in the inset in Fig. 12(b). For a moredetailed description of the emission process, thereader is referred to [102,103].

Simulations of tensile deformation have alsobeen performed at room temperature on Al with2D-columnar GB networks. The four columnar-grains have special orientations, so that only threetypes of grain boundaries are represented[61,62,112]. For a 20 nm columnar diameter sam-ple, it was shown that by increasing the load from2–2.3 GPa, the strain rate increases by more thantwo orders of magnitude resulting in strain rates of~108–109/s, and that the deformation processchanges from one involving GB processes to onedominated by partial dislocations with a strain ratethat depends inversely on the grain size. The pres-ence of two length scales, one the grain size andthe other represented by the dislocation splittingdistance under stress, was recognized [62] as beingimportant to the onset of slip-deformation pro-cesses in nc Al. This analysis led to the generationof a “dislocation-nucleation phase diagram” thatcaptured the interplay between these two lengthscales. Twinning was shown to occur afterapproximately 12% plastic strain and a stress levelof 2.5 GPa for a grain size of 45 nm, with twinsoriginating at grain boundaries as well as in thegrain interior from the interactions of stackingfaults [112]. The inverse dependence of the strainrate on the grain size has however been recognizedas a geometrical consequence of the simulation

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setup and the nc-structure. This is so because thestrain arising from the nucleation and propagationof a dislocation has a limiting length scale equalto that of the grain size [104]. The observation ofa dislocation-dominated regime characterized bymechanical twinning and unit dislocations (at thelarger grain sizes) was attributed to the relativelyhigh intrinsic stacking fault (SF) energy for Alpotential used in the simulations. The value of theSF energy used in their potential is, however, lowerthan value for the potential used in the simulationsfor Ni [63], and therefore the observation of fulldislocations cannot be assigned to the stackingfault energy alone.

In a detailed temporal and spatial analysis of thecontributions to the excess energy during emissionand propagation of a partial dislocation in a 3D ncnetwork, the effective SF energy of the sub-systemis found to be reduced by up to 50% via stressrelief within the entire grain and structural relax-ation of the surrounding GB [63,67]. For a trailingpartial to follow its leading partial, and thus fora full dislocation to be observed, the sequence ofnucleation and propagation associated with GBstructural activity must be repeated. It has beenobserved that nucleation and emission of a partialcorresponds to the removal of a GBD from the GBnucleation site and a reorganization of the remain-ing GBDs [102,103], suggesting that the barrier fora full dislocation event may be considerable. Theatomic activity that underlies the structural relax-ation is, to a great extent, inhibited in 2D columnarnetworks due to the constraints coming from per-iodic boundary conditions and the process ofnucleation and emission is expected to be different[63,67], possibly leading to the observation of fulldislocations at smaller grain sizes. That this atomicactivity in 3D GB networks is playing a key rolein the emission process has also been demonstratedduring simulations of nanoindentation of nc-Au[113]. Indeed, by keeping the force constant underthe indenter and inhibiting accommodation bymeans of atomic activity, full dislocations are emit-ted under the indenter, propagating through thegrain until they are absorbed at opposite GBs. It isimportant to realize that due to the sub nano-second time restrictions of an MD simulation(usually less then 0.5 ns), the emission of a second

partial on the same or on an adjacent plane, andtherefore the removal of a stacking fault defect orthe creation of a twin might not be seen. Muchlonger simulations times might be required for thisphenomenon to be actually observed [63,67].

Deformation studies at higher temperatures(0.7–0.9 Tm) suggest a Coble creep mechanismwith GB sliding as an accommodation mechanism,known as Lifshitz sliding [46,110]. The conclusionis drawn from calculation of an activation energyextracted from the first 100 ps of strain-time curvesperformed at different temperatures all above 70%of the absolute melting temperature. Althoughextrapolations of Coble creep mechanism to roomtemperature have been proposed [46,110], theredoes not appear to be justification for such anextrapolation. This is because there is no funda-mental basis to assume that the rate-limiting pro-cess at a temperature close to the melting tempera-ture, where grain boundaries are no longer stable atthe timescale of seconds, can be also the dominantprocess at room temperature.

Calculations of activation energies from con-stant load experiments [110] where the strain ratesare taken from the very initial stages of defor-mation can be misleading. Fig. 13 shows a strain-time curve for a nc Ni sample with a mean grainsize of 12 nm where the sample is deformed during1.5 ns. The initial strain rates of 107/s steadilydecrease by an order of magnitude over the nsrange [51]. This effect is expected to increase forincreasing deformation temperatures, especially

Fig. 13. Strain versus time for a computer simulated nc-Nisample with mean grain size of 12 nm showing the decrease instrain rate as simulation time continues.

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when temperatures are high enough for graingrowth. The plot shows that the calculation of acti-vation energies from Arrhenius-type curves willgive time-dependent results since a steady state isnot reached [101] and that it is therefore inappro-priate to draw conclusion from this type of analysison the type of constitutive law that fits the defor-mation mechanism, such as establishing a Coblecreep dependence. Therefore, the only meaningfulinformation that can be extracted from MD simula-tions is from a careful classification of the atomicprocesses taking place during deformation and ver-ifying the occurrence of these processes at thelonger nano-second timescale.

Computational models at the atomic level havealso been developed in recent years to address thefundamental issue of nucleation and kinetics ofdefects in response to mechanical loading. In orderto make direct correlations with experiments in aquantitative manner, many of these studies [113–118, for example] have focused on defectnucleation under conditions of nanoindentation ofsurfaces, which is a convenient experimental toolfor quantifying local deformation. Using controlledmodel experiments involving a raft of initiallydefect-free soap bubbles as a basis to exploredefect nucleation and motion in a systematic man-ner (see the discussion in the next subsection), Liet al. [119] and Van Vliet et al. [120] presented ananalytical formulation of the elastic limit which iscapable of predicting the location and slip charac-ter of a homogeneously nucleated defect in crystal-line lattices. By postulating an energy-based localelastic stability criterion, they have extended theformulation to the atomic scale. They have alsodemonstrated that this approach can be incorpor-ated efficiently into commonly used computationalmethods such as molecular dynamics and finiteelement models. They have further validated andcalibrated the criterion for defect nucleation in thesingle crystalline, initially defect-free latticethrough nanoindentation experiments on fcc crys-tals and on the bubble raft model. Quantitativeunderstanding of defect nucleation and motionwould be significantly enhanced if such criteria canbe extended to include defect nucleation at grainboundaries in nc metals.

5.2. Bubble raft model experiments

As noted in the context of Fig. 1, experimentalstudies on a number of nc metals have indicatedthe possibility of a decrease in strength and hard-ness with decreasing grain size, below a certaintransition grain size, which is approximately 10nm. Mechanistic origins of such an inverse Hall-Petch type effect are not well understood at thistime, partly because of the limitations of availableexperimental tools to image and record, duringdeformation, the deformation processes at nano-meter resolution. In order to overcome such limi-tations, attempts have recently been made to vis-ualize defect nucleation at the atomic level in ncmetals using the Bragg-Nye soap bubble raft model[121], which is a two-dimensional (2-D) analog tofcc metals [122,123]. As reviewed in [123], thismethod entails the creation of a single crystallineor polycrystalline 2-D raft of up to several hundredthousand uniformly sized soap bubbles by forcingpressurized air through a micropipette in a soapsolution. The interactions among the 1-mm diam-eter bubbles are analogous to the interatomic inter-actions of fcc metals, with the bubble size havinga geometric scaling with the atomic diameter ofapproximately 0.3 nm. Van Vliet et al [123] pro-duced such polycrystalline rafts with an averagegrain size that had a value between 4 and 37 nm(based on the above scaling analogy) and a vari-ation in grain size of 20% or less. New rafts wereproduced for each grain size. Localized defor-mation was introduced by nanoindentation, anddefect nucleation was monitored using video pho-tography. The polycrystalline raft was used toassess whether the deformation mechanisms variedwith grain size. The maximum pressure under theindent was then estimated corresponding to theonset of defect activity and was associated withthe magnitude of the critical resolved shear stressrequired to induce defect activity. Fig. 14 showsthe variation of the flow stress (normalized by thevalue of the critical flow stress at the maximumstrength at the transition grain size) for defectactivity, which approximately correlates with yieldstrength, as a function of the grain size. Defectactivity was identified to be initiated by two differ-ent mechanisms: (i) nucleation of discrete dislo-

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Fig. 14. Normalized critical stress as a function of grain sized. Red triangles indicate critical stress to initiate plasticity inbubble raft nanoindentation experiments [123]. Filled and openblue circles indicate experimental data for electrodeposited Nifrom several references cited in [123] and molecular dynamicssimulations for Cu [59], respectively.

cations at grain boundaries and triple junctions and(ii) motion of grain boundary regions by migrationand/or sliding. Crystalline rafts with an averagegrain size typically larger than 7 nm primarilyexhibited the former process whereas the lattermechanism was dominant below an average grainsize of about 7 nm. Despite the obvious limitationsof the 2-D bubble raft in providing realistic fea-tures of defect nucleation in a 3-D nc metal, theresults of Fig. 14 provide an experimental justifi-cation and a unique in-situ visualization of thepossible occurrence of a transition from strength-ening with grain refinement to weakening withgrain refinement. Remarkably, the transition grainsize of approximately 7 nm found in the bubbleraft experiments is the range of values found fromhardness measurements of nanocrystalline Ni,which are also plotted in Fig. 14. It is also interest-ing to note that the observations of weakening withdecreasing grain size below 7 nm in the bubbleraft experiments are qualitatively similar to thosepredicted by Shiøtz et al. [59] in their atomisticcomputational simulations of nanocrystalline Cu;these predictions are also indicated in Fig. 14.

5.3. Transmission electron microscopyobservations

5.3.1. Dislocation plasticityIt is generally accepted that conventional dislo-

cation sources such as the Frank-Read source ceaseto operate in nc metals, and that grain boundariesbecome potential dislocation sources and sinks.Post-deformation observations of nc specimens inthe transmission electron microscope have failedto reveal dislocation debris characteristicallyobserved in deformed mc specimens [41,69].Alternate deformation mechanisms such as grainboundary sliding, Coble creep and grain rotationhave been suggested in simulations and proposedin analytical models [72,73,101,109,124,125].However, convincing experimental evidence hasnot been provided thus far to support the notionthat these mechanisms are operative. Limited creepstudies that have been performed to date provideconflicting information: GB sliding is suggested asthe deformation mechanism in electrodeposited Cuduring tensile creep tests performed at 20–50°C[126], but similar experiments on nc-Cu and nc-Pdshow creep rates much lower than that predictedfor diffusional creep at low-to-moderate tempera-tures [127]. Grain boundary sliding has been pro-posed as a dominant deformation mechanism innanocrystalline Zn [85] but experiments were con-ducted at or above room temperature, which is asignificant fraction of the homologous temperatureof zinc.

The absence of dislocation debris in deformedspecimens has led to several in-situ deformationstudies in an attempt to observe possible dislo-cation activity during deformation [41,128–131].While the in-situ deformation technique is instru-mental in revealing deformation processes at thecrack tip, the problem associated with the influenceof the pair of free surfaces present in the electron-transparent region of the thin foil on inferred defor-mation modes [132] raises questions about theapplicability of these observations to bulk materialdeformation. However, the observations areintriguing, since in nearly all cases, dislocationactivity is observed in the vicinity of the crack tip.

In-situ deformation of a tensile specimen in thetransmission electron microscope [41] has revealed

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that, in nc Ni with grain size in the 30–40 nmregime, copious dislocation emission is triggeredat the crack tip, and that there is some evidence ofthis process extending over several grains ahead ofthe tip. Furthermore, it appears that these dislo-cations are generated at grain boundaries, and thatthey proceed to the adjacent/opposite boundarywhere they are absorbed. Nano-scale voids evolveat grain boundaries and triple junctions ahead ofthe crack tip and they eventually grow and coalesceto form larger dimples. Similar observations havealso been made by Youngdahl et al. [129] in ncCu produced by inert gas condensation followedby compaction. The material was reported as being97% dense and having a broad grain size distri-bution range from 20–500 nm, although “ themajority” was between 50–80 nm. More recently,in-situ studies have been performed on uniform100 nm thick Ni films synthesized either by pulsedlaser deposition or by DC magnetron sputtering[131]. Both films had grain sizes below 50 nm andwere transparent to electrons so that thinning pro-cedures could be avoided. A starter crack wasintroduced before deformation. The authors report“pervasive dislocation nucleation and motion” ingrains as small as 10 nm and indirect evidence forminimal contribution from GB sliding. A differentbehavior in failure mechanism was observedbetween the two films, and this was attributed tothe presence of GB porosity.

In-situ electron microscopy studies to date havebeen able to confirm dislocation activity in theneighborhood of a crack tip during tensile testing.There is no evidence of extended partial dislo-cation activity during the in-situ experiments (assuggested by simulations), but this might be dueto several reasons: i) the difference in time scalesbetween the in-situ experiments and the simula-tions as suggested in previous paragraphs, and ii)experimental difficulties relating to the dynamicnature of the in-situ experiments combined withthe need to conduct them in the bright field mode athigh magnification in order to view the individualgrains and dislocations within them. Recent atom-istic simulations of crack propagation in nc-Nisamples similar to those reported previously haveshown evidence for extensive dislocation activityat the crack tip, including full dislocations and

twinning in grains as small as 10 nm [133]. Theseresults indicate that the dislocation activityobserved in in-situ tensile testing in the microscopehas to be related to the propagation of the crackand that extrapolation to bulk tensile deformationmay be tenuous.

Recently, it was inferred from X-ray diffractionexperiments that cold rolling of 10–30 nm grainsize Pd (produced by gas-phase condensation)caused an increase in stacking fault density,although the grain shape remained equiaxed andthere was no preferred texture [30]. Further, in thisstudy [30], transmission electron microscopy evi-dence was provided for the first time for the exist-ence of a mesoscopic glide plane.

5.3.2. TwinningTwinning is an alternate mode of plastic

deformation and it has been observed in conven-tional fcc metals and alloys with low stacking faultenergy (e.g. austenitic stainless steel [134]; Cu-Alalloys [135]); Twins have also been observed infcc metals and alloys with relatively high stackingfault energy when extreme deformation conditionsare imposed (cryogenic temperatures, shock-loading, and/or large strains). For example, defor-mation twinning was noted in an Al-4.8% Mg alloyduring cryogenic shock loading [136]. Embury etal. [135] postulate two necessary conditions for theformation of deformation twins in fcc metals: (1)a change in the dominant slip system must occur,and (2) a critical stress level needs to be reachedlocally at the site of the twins. Recently, Kumar etal. [41] reported the observation of twins duringthe deformation of electrodeposited nc Ni in thetransmission electron microscope, (Video imagesof the formation of twins can be found in thesupplementary material provided in [41] at thewebsite: http://ninas.mit.edu/Submission/SupInfo/index2.html). Computer simulations of defor-mation of nc Al with a grain size of 45 nm [112]have also shown that twinning occurs afterapproximately 12% plastic strain and a stress levelof 2.5 GPa, with twins originating at grain bound-aries as well as in the grain interior, the latterresulting from the interactions of stacking faults.Chen et al. [137] have reported deformation twin-

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ning in vapor-deposited nc aluminum that was sev-erely deformed by micro-indentation and grinding.

Several key issues should be considered beforethe possible role of twinning in influencing thedeformation characteristics of nc metals and alloyscan be ascertained. Growth twins are frequentlyobserved in electrodeposited Ni independent ofgrain size (Fig. 15(a),(b)), in nc Cu produced bygas-phase condensation (Fig. 11(c)), in ufc vapor-deposited Au (Fig. 15(d)) and in vapor-depositednc Al [137]. Care must be exercised to differentiatedeformation twins from these growth twins. Fur-thermore, little is known about the role of growthtwin boundaries in assisting or hindering plasticdeformation in nc metals, and about the interactionof emitted dislocations with the growth twin

Fig. 15. Growth twins (a) in electrodeposited mc-Ni, (b) in electrodeposited nc-Ni, (c) in nc-Cu produced by gas-phase condensation,and (d) in ufc Au produced by electron beam deposition. Insets in (b) and (c) are bright field images, as are (a) and (d). (b) and (c)are high resolution images.

boundaries. Computations have thus far notincluded such growth twins in the starting micro-structure and since grown-in twins are observedexperimentally in very small grains, simulationsshould address this issue. In the case of conven-tional mc Ni which is prone to twinning duringstrain annealing, it has been shown that the pres-ence of twin boundaries enhances corrosion resist-ance and reduces the propensity for intergranularfracture [138,139]. Hydrogen and other interstitialimpurities are often present in electrodepositedmaterials and these can also influence the twinningstress of the material. For example, it is knownthat nitrogen lowers the stacking fault energy instainless steels and encourages twinning [140].There also remain questions regarding: i) the

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nucleation mechanism of such deformation twins,ii) the stage of deformation at which they evolve,and the dependence of onset of twinning on grainsize, and iii) the role they play in affecting theoverall deformation characteristics of the nc metal.Currently available experimental evidence fortwinning in nc metals is predicated upon obser-vations made under special circumstances. Forexample, twinnig in nc Al was observed in a speci-men which was subjected to significant plasticdeformation by indentation and extensive grinding[137], whereas observations of twinning in nc-Niwere reported during deformation in the trans-mission electron microscope in the last ligament ofa thin foil [41].

In summary, atomistic simulations seem to havea potential for providing insight into the defor-mation mechanism at the atomic scale. However,many aspects of the proposed mechanisms remainto be explored and the comparison between simu-lated samples and experimental samples should beconsidered with the necessary criticism. Forinstance, simulated samples always have grainswithout any defects, which is probably justified forsome kind of defects in grain sizes below 20 nm,but less probable in 70 nm sized grains, as has beensimulated in 2D columnar networks. The incorpor-ation of defects in the larger grains could activatedislocation sources other then GBs and thereforealter the global deformation response. Moreoverthe simulated samples have densities comparableto full dense nc-materials obtained by elec-trodeposition or severe plastic deformation, but theexperimental samples contain nanovoids, as evi-denced by positron lifetime annihilations. Thesimulated samples contain only free volume unitsof the size of a vacancy or less.

6. Fracture mechanism(s)

The evolution of damage and final fracture in ncmetals and alloys is only beginning to be under-stood. Few systematic experiments have been con-ducted to elucidate how these processes proceed.In what follows, we summarize the main experi-mental findings and their interpretation throughsimulation and modeling, followed by a criticalview of microstructural issues.

The absence of substantial macroscopic tensileductility in nanocrystalline fcc metals together withthe observation of dimpled rupture on fracture sur-faces (for example in Ni in [35,41,106]) leads tothe hypothesis that deformation is localized.Whereas localized deformation is clearly mani-fested through the appearance of shear bands ondeformed specimen surfaces in nc bcc Fe and Fealloys even at quasi-static strain rates [75,76], thisdoes not appear to be the case in their fcc counter-parts, where shear bands have been reported tooccur in nc-Ni only after high strain rate defor-mation [35]. It is worth noting that with the excep-tion of [35], compression specimens have beentypically used to observe shear bands in ncmaterials and they can be often be deformed tolarger strains than possible in uniaxial tension. Therestriction to thin sheet geometry for electrodepos-ited material has precluded compression tests andencouraged widespread use of tension tests for thenc metals produced by this process. In bcc nc-Fe,TEM images taken from within the shear bandsshow grains that are elongated in the shear direc-tion whereas the grains remain equiaxed outside ofthe band, a further testament to deformation local-ization [75]. However, since these tests were donein compression, fracture surface were not availablefor observation. How the deformation structureevolves inside a shear band requires further experi-mental investigation.

In-situ TEM studies conducted for the purposeof detecting possible dislocation activity duringdeformation of nc metals and alloys also providesome insights on the damage evolution processahead of the crack tip. In electrodeposited nc Ni[41], voids at grain boundaries and triple junctionsahead of the main crack grow with progressiveloading. A sequence of observations from [41] isreproduced in Fig. 16(a)–(c) that illustrates damageevolution during deformation. While there isuncertainty about the validity of extending suchobservations to bulk behavior, MD simulationsalso suggest the formation of voids at grain bound-aries and triple junctions ahead of the main propa-gating crack which then link up [141] producingintergranular fracture.

In-situ tensile study on DC magnetron sputterednc-Ni and pulsed laser deposited nc-Ni [131] films

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Fig. 16. A region ahead of a crack tip in a thin foil of nc-Niwith 30–40 nm grain size that was subjected to in-situ defor-mation in the TEM by the application of displacement pulses.In (a), the region is shown in a “reference state” (0 pulse) eventhough the specimen is under load; in (b) a single additionaldisplacement pulse opens the voids at grain boundaries and triplepoints; and in (c) the application of 3 additional pulses furtheropens these voids and promotes cracking along boundaries.

of uniform thickness, both having mean grain sizesof 15–20 nm, revealed the importance of the pres-ence of nano-scale voids in the structure prior todeformation. The magnetron sputtered Ni, contain-ing some grain boundary porosity, failed in a brittlemanner via rapid coalescence of intergranularcracks whereas the crack propagated slowly,accompanied by continuous film thinning, in thelaser deposited film that contained no porosity

Fracture surfaces resulting from tensile testshave frequently shown dimpled rupture in elec-trodeposited nc-Ni, nc Al-Fe and nc-Cu[22,35,36,41,87]. Further, it has been shown thatthe dimple size is significantly larger than the aver-age grain size; in addition, in [41], a pair of matingfracture surfaces was shown that clearly illustratedthe presence of significant stretching of the liga-ments between the dimples that was taken to beindicative of appreciable local plasticity. Anexample of a fracture surface obtained from a ten-sile specimen of electrodeposited nc Ni with agrain size of around 25–30 nm is shown in Fig.17(a). It reveals dimpled rupture with the dimplediameter and dimple depth (~300–400 nm) beingan order of magnitude larger than the grain size(Fig. 17(a)). Furthermore, the dimple size is uni-form and extends across most of the specimencross-section (Fig. 17(b)).

When the grain size is reduced to ~10 nm orless, as in the case of an electrodeposited Ni-Walloy (Fig. 2b), the resulting fracture surface froma tensile specimen still continues to show whatappears to be dimpled rupture (Fig. 18(a)) with theimportant difference that the dimple diameter onan average is finer in size (but still much largerthan the grain size) relative to those seen in Fig.17(a). Whether this is a direct consequence of areduction in grain size or is influenced by the pres-ence of W in the alloy is unclear. Further, the dim-ples in Fig. 18(a) are shallower than those in Fig.17(a), and they exhibit a wide size distribution. Asignificant portion of the tensile specimen fracturesurface exhibited this mode of failure (Fig. 18(b)).In-situ cracking of tensile specimens in the TEMconfirmed that the crack propagates in an unstablemanner in the nc Ni-W alloy as compared to the30-nm grain size electrodeposited Ni.

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Fig. 17. Fracture surface of a 30 nm grain size electrodepos-ited Ni tensile specimen that was deformed in-situ in the TEMbut was fractured outside the microscope: (a) dimpled rupturewith dimples that are significantly larger in diameter (200–400nm) than the grain size, and (b) a lower magnification imageshowing the prevalence of the fracture mode.

As stated above, atomistic simulations of crackpropagation in full dense nc-Ni with mean grainsizes of 6 nm and 12 nm [141] have shown that apreformed crack propagates intergranularly withthe formation of nano-scale voids ahead of thecrack. In the simulation, plasticity is only observedin the vicinity of the crack tip and therefore collec-tive events such as those that may occur duringtensile deformation are excluded. On the otherhand, molecular dynamics simulation of tensiledeformation where plasticity is observed in theentire specimen containing 125 grains with a meangrain size of 6 nm shows the formation of meso-scopic shear planes as a result of GB sliding and

Fig. 18. Fracture surface of a ~10 nm grain size electrodepos-ited Ni-W tensile specimen that was deformed in-situ in theTEM but was fractured outside the microscope: (a) dimpledrupture with a range of dimple sizes that are larger in diameter(100–200 nm) than the grain size, and (b) a lower magnificationimage showing large areas of the fracture surface exhibiting thismode of fracture.

partial dislocation activity. Additionally it has beendemonstrated that due to the presence of specialGBs that resist GB sliding, local shear planes canbe formed, creating a cluster of grains embeddedin a sliding environment [106]. Thus, a plasticitylength scale of the order of several grain sizesemerges that may correspond to the dimensions ofthe dimple structures seen on the fracture surfacesresulting from experiments. In the simulations[106], the applied technique does not allow theobservation of fracture, both, due to the timerestriction and due to the applied periodic bound-ary conditions. The formation of such a local net-work of shear planes could lead to the formationof nano-cavities via unaccommodated GB sliding,

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and eventually macroscopic fracture that could beadditionally enhanced by the presence of preexist-ing voids.

Based on the observations of dimpled rupture,dislocation activity at the crack tip, and the forma-tion of voids at grain boundaries and triple junc-tions in the regions ahead of the advancing crack,Kumar et al. [41] proposed a model for damageevolution and fracture which is captured in thesequence of events schematically depicted in Fig.19. In the early stages of deformation, dislocationsare emitted from grain boundaries under the influ-ence of an applied stress, when intragranular slipis coupled with unaccommodated grain boundarysliding to facilitate void formation at the grainboundaries. Such voids do not necessarily form atevery boundary. Triple junction voids and wedgecracks can also result from grain boundary slidingif resulting displacements at the boundary are notaccommodated by diffusional or power law creep.These grain boundary and triple junction voidsthen act as sites for nucleation of the dimpleswhich are significantly larger than the individualgrains and the rim of these dimples on the fracturesurface do not necessarily coincide with grainboundaries. Thus, at a local level, the nc-Ni dem-onstrates considerable plasticity (and could rep-resent localized deformation within a shear band).Its deformation and fracture processes are closelyrelated to the coupling of dislocation-mediatedplasticity and formation and growth of voids.

The fundamental difference between the twoapproaches is that the atomistic simulations revealintergranular crack propagation, where the GBsthat are chosen by the crack path are determined byplastic deformation processes, whereas the modelillustrated in Fig. 19 proposes the formation oflocal ligaments with free surfaces as the voidsevolve, stretching in concert and finally leading totransgranular fracture. Whatever the fracture mech-anism, it is evident that the fracture will be heavilyinfluenced by microstructural features which haveup to now been mostly neglected such as the pres-ence of nano-scale voids or even bubbles and thepresence of grown-in twins. It is well known thatbubbles filled with hydrogen (hydrogen bubbles)are often present in electrodeposited metals andthese could serve as nucleation sites for the dim-

ples without the need to nucleate additional voidsduring deformation [31,142]. These bubbles can bepresent at GBs as well as in the grain interior.Additionally, positron annihilation has shown thepresence of nanovoids of 10–20 vacancies innearly all nc samples [35,39], and they are con-sidered to populate grain boundaries and triplejunctions. However, their location has not beenexperimentally verified. The presence of twins hasbeen suggested as an interface control mechanismin coarse-grained metals [139] and may representa relevant microstructural feature that influencesfracture, since many of the nc metals containgrown-in twins. The role played by twin bound-aries (or boundaries close to twin misorientation) indiscouraging GB sliding and thereby determining aplasticity scale that is comparable to experimen-tally observed dimple size has been suggested insimulations [106].

7. Concluding remarks

Research into the structure, deformation andfailure of nanocrystalline metals and alloys hasprovided a wealth of experimental information dur-ing the past decade. Such knowledge forms a criti-cal foundation for the development of newer gener-ations of structural materials whose mechanicalproperties can be modulated through the judiciousdesign of grain boundaries. Advances in charac-terization tools and computational simulations havefurther aided progress in this area, and have pro-vided unprecedented opportunities for interpretingthe mechanical deformation mechanisms at thenanoscopic size scales.

In considering the structure of nc metals andalloys and its impact on deformation behavior, therole of grain boundaries is clearly paramount.Experiments and computations have demonstratedthat these grain boundaries are substantially similarto those in mc metals and alloys and that there isno “grain boundary region” that is highly dis-ordered or amorphous as originally proposed.However, this is where experimental characteriz-ation has stopped. Computations have taken this tothe next level of detail and shown the effects ofatomic structure at the boundaries (boundary type

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Fig. 19. A schematic illustration depicting how deformation evolves in nanocrystalline nickel based on experimental observationsi) during in-situ deformation in the TEM, and ii) of resulting fracture surfaces in the SEM. Dislocation motion, void formation/growthat grain boundaries and triple junctions, the formation of partially unconstrained ligaments that deform plastically, and the interactionof these various features to produce the eventual fracture morphology are all synthesized in this figure.

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and boundary stresses—equilibrium versus non-equilibrium) on grain boundary sliding and thecapacity of a GB to emit dislocations into a grainand absorb dislocations. While these descriptionsseem plausible, there is currently little direct orindirect experimental evidence to support the com-putational finding even for simple tensile defor-mation. Clearly, the field would benefit immenselyfrom dedicated experimental efforts on grainboundary structures in nc metals and their responseto applied stress. Furthermore, experimental vali-dation of computations is required at a more funda-mental level rather than at the level of macroscopicmechanical properties such as hardness, strengthand ductility because factors that affect theseproperties (for example, impurity content, nano-scale porosity, etc) cannot be conveniently incor-porated into computations.

Microstructural characterization has also notbeen systematic and as a direct consequence, theconnection between structure and mechanicalproperties has not been well established in manync metals and alloys. Even the relatively simple-to-determine characteristics such as texture, grainsize distribution, grain shape through the cross-section, and population of growth twins are oftennot well defined. However, in order to createmaximum synergy between simulation and experi-ment, detailed information on the microstructure isnecessary such as a distribution of the lattice mis-orientation and the GB plane misorientation, para-meters that are accessible for coarse-grainedmaterial by means of sequential sectioning in ascanning electron microscope [143] or by analysiswith a 3D-X-ray microscope [144]. Information ofsuch type would facilitate a one-to-one copy of thesample in the computational model. Unfortunately,these techniques presently do not have the spatialresolution needed for nc metals.

Another common problem is the inability toreproduce microstructures even within a singleprocessing route. Frequently, there is a wide distri-bution of grain sizes that varies from batch-to-batch and it is not obvious which segment of thedistribution dominates the response to an appliedstress. Furthermore, limitation in material avail-ability has placed significant constraints on thenumber of mechanical tests performed in an inves-

tigation, raising additional questions on thereliability of the reported data.

This is an emerging field where findings fromcomputations (primarily using large-scale molecu-lar dynamics simulations) have far outpacedexperimental observations. As a consequence, sev-eral fundamental theories and models remain to bevalidated with careful experiments. The compu-tational models are only beginning to incorporationof realistic structural features including impurityand defect populations. A limitation of the compu-tations is that molecular dynamics can only coverthe very initial stages of the deformation. Thus,while structural information (e.g. grain boundarystructure) and information pertaining to the veryearly stages of deformation (e.g. emission of a fewdislocations from a boundary or motion of a fewatoms at a boundary) may be considered reliable,evolution of damage and final fracture are all sub-stantially affected by the starting microstructureand its consequence on microstructural evolution.

Comprehension of the deformation and fractureof nanocrystalline metallic materials at tempera-tures of the order of 0.1–0.2 of the melting tem-perature (e.g Cu, Ni, Co and Fe and their alloys)must accommodate i) the macroscopic observationof minimal tensile ductility in these materials, ii)the observation of intense localized deformationbands (shear bands), more prominent in the bccmetals and alloys (not reported thus far at quasi-static strain rates in nanocrystalline Ni or Cu), iii)the general acceptance of dislocation-mediateddeformation at grain sizes of 30–40 nm and iv)the observation of dimpled rupture on the fracturesurfaces, with the scale of dimples being signifi-cantly larger than the grain size but yet scalingwith grain size.

A limited amount of systematic experimentalinformation [98] has revealed that considerableopportunities exist for the design of highly dam-age-tolerant structural components through thejudicious use of nc metals and alloys. For example,the results shown in Figs. 9 and 10 indicate thatgrain refinement with nc metals can impartimproved resistance to fatigue crack nucleationunder predominantly high cycle fatigue loading.However, such grain refinement strategies can leadto a detrimental effect on subcritical crack growth.

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It is conceivable that layered and/or graded micro-structures with nc grains at critical sites of cracknucleation, such as at free surfaces and in theimmediate vicinity of stress concentrations, maylead to better overall damage tolerance in compo-nents made primarily of lower strength, higher duc-tility mc alloys.

Recent experimental work [145] has also shownthat some nc metals offer improved resistance todamage evolution in monotonic and repeated slid-ing compared to ufc metals. Furthermore, it is alsoknown that the addition of W to nc Ni can impartimprovements in the tribological resistance [33].Capitalizing on this potential for improving thescratch resistance and tribological properties ofengineering structures by the proper design of sur-face layers with nc metals and alloys thus consti-tutes an interesting area that is rich in scientific andtechnological opportunities.

Acknowledgements

SS and KSK gratefully acknowledge supportfrom the Defense University Research Initiative onNanoTechnology (DURINT) on “Damage- andFailure-Resistant Nanostructured and InterfacialMaterials” which is funded at the MassachusettsInstitute of Technology (MIT) by the Office ofNaval Research under grant N00014-01-1-0808.The authors also acknowledge additional supportfrom the Division of Materials Sciences and Engin-eering, Office of Basic Energy Sciences, U.S.Department of Energy under contract DE-AC05-00OR22725 with UT-Battelle, LLC. HVSacknowledges the support provided by severalgrants of the Swiss National Science Foundationand the CTI-program TOPNANO21. We thankDrs. M. F. Chisholm and J.A. Horton of Oak RidgeNational Laboratory for their assistance with thetransmission electron microscopy.

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