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FailureofmetalsIII.FractureandfatigueofnanostructuredmetallicmaterialsARTICLEAUGUST2015DOI:10.1016/j.actamat.2015.07.049

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AndrePineauMINESParisTech301PUBLICATIONS5,299CITATIONS

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A.A.BenzergaTexasA&MUniversity67PUBLICATIONS1,388CITATIONS

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ThomasPardoenUniversitcatholiquedeLouvain242PUBLICATIONS4,080CITATIONS

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Availablefrom:AndrePineauRetrievedon:02January2016

obDepartment of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USAcDepartment of Materials Science and Engineering, Texad Institute of Mechanics, Materials and Civil Engineering

a r t i c l e i n f o

Article history:Received 20 March 2015Revised 18 July 2015

perspectives regarding the physics and mechanics of fracture inmetallic materials with nano-scale internal or external dimen-sions. Several reviews have been dealing in recent years withthe mechanical behavior of these systems, e.g. [38], with a focus

limited attentiony reported/or low flved in o

deals with bulk 3D macroscopic metals involving submicroncharacteristic internal microstructure features as well as metallicstructures involving at least one submicron dimension, i.e. both2D lms or coatings and 1D wires, rods and beams whichinvolve submicron characteristic internal microstructure sizes aswell. The fracture of 1D and 2D structures is more complex in asense, as both the microstructural and component characteristiclengths generally affect it. Incidentally, covering all three types

Corresponding authors.E-mail addresses: [email protected] (A. Pineau), thomas.pardoen@

uclouvain.be (T. Pardoen).

Acta Materialia xxx (2015) xxxxxx

Contents lists availab

Acta Mat

elsmicrons range as used in traditional macroscopic components,the present overview addresses the state of the art and future

open the range of possible viable applications of nanostructuredmetallic materials. Fig. 1 describes the coverage of the paper; itWhile the companion overviews [1,2] deal with recentresearch advances in the fracture of industrial metallic alloysinvolving typical microstructure dimensions within the tens of

strengths that can be attained, but often withto fracture. The resistance to fracture is usuallweak, as quantied by a limited ductility andtoughness. This is a key issue that must be sohttp://dx.doi.org/10.1016/j.actamat.2015.07.0491359-6454/ 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dx.doi.org/10.1016/j.actamat.2015.07.049to beracturerder tosions are based on experimental, theoretical and simulation results from the recent literature, and focusis laid on linking microstructure and physical mechanisms to the overall mechanical behavior.

2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction on the deformation mechanisms controlling the extremeAccepted 18 July 2015Available online xxxx

Keywords:DuctilityFractureFatigueMetalsNanocrystallineThin lmsNeckingDamages A&M University, College Station, TX 77843, USA, Universit Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

a b s t r a c t

Pushing the internal or external dimensions of metallic alloys down to the nanometer scale gives rise tostrong materials, though most often at the expense of a low ductility and a low resistance to cracking,with negative impact on the transfer to engineering applications. These characteristics are observed, withsome exceptions, in bulk ultra-ne grained and nanocrystalline metals, nano-twinned metals, thin metal-lic coatings on substrates and freestanding thin metallic lms and nanowires. This overview encompassesall these systems to reveal commonalities in the origins of the lack of ductility and fracture resistance, infactors governing fatigue resistance, and in ways to improve properties. After surveying the various pro-cessing methods and key deformation mechanisms, we systematically address the current state of the artin terms of plastic localization, damage, static and fatigue cracking, for three classes of systems: (1) bulkultra-ne grained and nanocrystalline metals, (2) thin metallic lms on substrates, and (3) 1D and 2Dfreestanding micro and nanoscale systems. In doing so, we aim to favour cross-fertilization between pro-gress made in the elds of mechanics of thin lms, nanomechanics, fundamental researches in bulknanocrystalline metals and metallurgy to impart enhanced resistance to fracture and fatigue inhigh-strength nanostructured systems. This involves exploiting intrinsic mechanisms, e.g. to enhancehardening and rate-sensitivity so as to delay necking, or improve grain-boundary cohesion to resist inter-granular cracks or voids. Extrinsic methods can also be utilized such as by hybridizing the metal withanother material to delocalize the deformation as practiced in stretchable electronics. Fatigue crack ini-tiation is in principle improved by a ne structure, but at the expense of larger fatigue crack growth rates.Extrinsic toughening through hybridization allows arresting or bridging cracks. The content and discus-Andr Pineau , A. Amine Benzerga , Thomas PardoenaMines ParisTech, Centre des Matriaux, CNRS UMR 7633, BP 87, 91003 Evry, FranceOverview No.

Failure of metals III. Fracture and fatiguematerials

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teriof material systems enables links to be made between the com-munity that develops bulk nanostructured alloys for potentialstructural applications and that working on nano- and thin-lmmechanics for electronics, coatings and nanotechnology. In orderto limit the scope, only room temperature static fracture and fati-

nano-crystalline (NC) will be reserved for grain sizes below

of derivatives of these processes. Depending on the details of the

teriamanufacturing. In microelectronic devices, large strains in thininterconnects result from thermal cycling and associated internalstress evolution. In all these applications, permanent plasticdeformation is not necessarily prohibited, but should developwithout or with limited micro-cracking to preserve the expectedfunction. The same problem as for bulk nanostructured systemsof Section 3 emerges: most metallic lms exhibit limited ductility[11], even though recent counterexamples have been described inthe literature with thin freestanding metallic lms deforming bymore than 10%, e.g. [12,13]. For the sake of clarity, the fracture ofmetallic coatings while lying on a substrate is addressed inSection 4, and the fracture of freestanding lms or wires inSection 5. Even though the intrinsic failure mechanisms are usuallysimilar, the experimental challenges and failure scenarios can bequite different. In particular, the exible electronics communityhas developed a series of innovative extrinsic ductilization strate-gies, involving similarities with the hybrid approaches applied tobulk nanostructured metals. In the case of freestanding lms, wereview recent progress about in situ characterization of failuremechanisms with a realm of new observations and improvedunderstanding.

In these three core Sections 35, we will address failure interms of the properties that are used to quantify the resistanceto fracture:

(1) the uniform elongation, in terms of the engineering strain Ag(%) or true strain eu (/), which is the strain at the onset of dif-fuse necking;

(2) the true fracture strain ef (/) which is the effective plasticstrain attained in the broken region as measured from thearea reduction of section;

(3) the total elongation eengf (/) which is extracted from a uniaxialtensile test as the total displacement at fracture divided byinitial length. This quantity is often reported in the literaturebut can lead to confusion as it is gauge length dependent andvery much dominated by the magnitude of Ag;

(4) the true fracture stress rf (MPa) which may be more mean-ingful than the true fracture strain when the behavior is brit-tle or quasi-brittle;

(5) the fracture toughness expressed by the critical stress inten-sity factor KIc (MPa

pm), critical energy release rate GIc

(J/m2), critical value of the J integral JIc (J/m2), or the criticalCrack Tip Opening Displacement (CTOD) dIc (lm) (limitedhere to mode I crack opening conditions) which requires,to be valid, samples with a sharp pre-crack and sufcientlylarge dimensions to represent an intrinsic, geometry-independent material fracture resistance index. These valuesare usually dened at cracking initiation except if indicatedotherwise. The meaning and relevance of these concepts inthe context of submicron components will be criticallydiscussed;

(6) the resistance to fatigue expressed by the endurance limit rend(MPa) which is the stress amplitude above which fracture byfatigue does not occur below a given high number of cycles(usually 106107 cycles), or by the Da/DN (lm) versus DK(MPa

pm) response which gives the increment of crack

growth Da per loading cycle DN under a given amplitudeof stress intensity factor DK.

Even though a material is not physically broken when plasticlocalization occurs (as quantied with Ag or eu), the integrity ofthe structure is compromised and, from an engineering viewpoint,one may consider that failure has been attained. The prediction ofthe integrity of a structural component or the formability of a

A. Pineau et al. / Acta Mamaterial part must be based on a series of failure criteria involvingboth fracture from preexisting defect or not and plastic localization

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dprocess, the grain size can be rened to a mean dimension below1 lm, and sometimes below 100 nm by a mechanism of grain frag-mentation through dislocation cells formation, see an example inFig. 2a of a very ne grained Cu microstructure obtained by ECAP[17]. SPD methods have been successfully applied on most pureand alloyed metals.

In terms of hybrid nanostructured metals, if the initial grain sizeobtained by SPD is sufciently small as in Fig. 2a, a bimodal struc-ture can be produced by heat treatments with the size of the largegrains in the micron range, see the example of Cu in Fig. 2b [17].The ARB process has been successfully applied to produce lami-nates of alternating Cu and Nb layers owing to repeated roll bond-ing, cutting, stacking and further rolling, e.g. [18,19]. The layerthicknesses range from 10 to 1000 nm with up to meter scalein-plane dimensions. A variant of the ARB process named re-peated press and rolling has been used to process nano-layeredcomposites with alternating Cu/Fe, Cu/Ag, Fe/Ag and Cu/Nb com-100 nm and ultra-ne grained (UFG) for grain sizes between100 nm and 1 lm. Classical metallic polycrystals will bereferred as coarse grained (CG). A lm is considered as thin whenthe thickness is below 1 lm and a nanowire is dened as having amore or less equiaxed section with a characteristic dimensionbelow 1 lm.

2.1.1. Bulk ultrane grained and nanocrystalline metalsThe most common method to produce UFG and NC metallic

alloys is through Severe Plastic Deformation (SPD), under highhydrostatic pressure to avoid failure problems, sometimes at highstrain rates. Many reviews have been dedicated to this topic, e.g.[1416]. There is a large number of possible routes to apply ultradeformation involving [16] equal-channel angular pressing(ECAP), high pressure torsion (HPT), accumulative roll bonding(ARB), multi-axial forging, twist extrusion, swaging and all sorts(and buckling, though not discussed here). We will discuss howthese properties play out in the systems described above, how theyconnect with the microstructure and with the various characteris-tic lengths involved. On the one hand, the small size makes thetesting and characterization more complicated for some aspects,such as for quantitative load measurement, manipulation andalignment, but, on the other hand, direct observation withTEM on the full scale specimen can be performed and volumessimilar to those analysed experimentally can be treated with ato-mistic simulations or dislocation dynamics codes. For this, relevantrecent literature on experimental, computational and theoreticalresearches will be reviewed involving open questions. Even thoughthe literature on fracture and fatigue of these systems is much lessextensive than the literature dealing with deformation andstrength aspects, it is still wide enough and we do not claim a com-prehensive treatment. Instead, we propose some possible lines ofarticulation for the underlying questions and recent ndings.

2. Basics on processing, microstructures and deformationmechanisms

2.1. Processing of nanostructured metals

This sub-section involves information both on the processingmethods and main characteristics of the micro- and nanostruc-tures, with an emphasis on the elements that are needed to under-stand the different topics addressed in the paper. The term

lia xxx (2015) xxxxxx 3positions, e.g. [2022]. Accumulative extrusion, drawing andbundling can generate nano-laments of Nb within a channeling,highly textured Cu matrix with a controlled hierarchical structure

x.doi.org/10.1016/j.actamat.2015.07.049

teri4 A. Pineau et al. / Acta Masee e.g. [23]. Shot peening can be also considered as a SPD processas it heavily deforms under high strain rates the near surfaceregions of metals, leading to a hybrid structure with very ne grainsizes at the surface and a gradient towards to core with largergrains [24,25].

Recently, new routes involving advanced thermo-mechanicaltreatments have been proposed to produce nanostructured metals,especially steels, with processing routes compatible with industrialpractice. In particular, there is a growing interest in the develop-ment of new advanced high strength steels (AHSS) with enhancedcombination of strength and ductility. UFG dual phase (UFG DP)steels can be produced using two types of concept: the Q&P andthe inter-critical heat treatments. In both cases, metastable

Fig. 2. Set of UFG, NC and thin lm metallic microstructures; (a) NC Cu produced by ECAshown in (a); (c) TEM micrographs of the submicron thick lm type retained austenite inausteniteferrite (

teriatemperature with the purpose of promoting C (and other c stabiliz-ing elements, such as Ni and Mn) transfer from martensite into theaustenite. This austenite is thus stabilized and retained at roomtemperature. The RA phase is often under the form of very thinlms (

forest hardening behavior. At moderate strains, more dislocationsare produced than recovered, leading to the stage III strain hard-

teriening mechanism [62]. Depending on the recovery capacity,hence on the stacking fault energy, CG metals exhibit a value ofn varying between 0.05 and 0.5. Dislocations tend to organize intocells with high dislocation density into cell walls. At very largestrains, the so-called stage IV strain hardening regime sets in witha constant, low hardening rate. The strength ry is a combinationof the initial resistance to dislocation glide in the originalmicrostructure r0 plus the strain hardening contribution. Whenrening the microstructure by decreasing the grain size d, r0varies as KHP/da (see later for more details) with a often around0.5 as expressed by the HallPetch law [63,64] and KHP aconstant, see Fig. 3a. Usually, the rate sensitivity m is low in CGone of the sides of the material. As an alternative to these top downapproaches to produce nano-scale structures, nano-wires ornano-ribbons can be directly grown using bottom up processingmethods. For instance metallic nanowires can be producedby physical vapor deposition, often at elevated temperatureand under ultra-high vacuum conditions, e.g. [60,61]. Thesenano-whiskers can be tens of micrometers long with diametersranging from tens to hundreds of nanometers, involving a veryclean and defect free single crystal structure. They offer model sys-tem to address plasticity in ideal defect free conditions.Nano-manipulation is needed to transport these structures to thetest apparatus (see Section 5).

2.2. Basics on deformation mechanisms in metals with nano-scaledimensions

Prior to failing, most metals deform plastically and nanostruc-tured metals are no exception. However, compared withconventional metallic systems in which plasticity is essentiallydominated by forest type dislocation activity, nanostructured met-als exhibit a variety of deformation mechanisms involving ther-mally activated dislocation nucleation from GBs, grain growthwith GB migration, room temperature diffusion and exhaustionhardening (or dislocation starvation). These mechanisms eithercooperate or compete with one another leading to complicatedphysical scenarii which set the magnitude of the stress levels thatare attained, the rate sensitivity and the stability of the microstruc-ture. Sub-divided into the various types of systems addressed sub-sequently, this section surveys the minimum needed to appreciatethe role of plasticity in fracture. Comprehensive review papers onnanostructured materials develop these topics in more detail, e.g.[38].

The two key parameters that quantify the connection betweenstrength and plastic deformation are the strain hardening expo-nent n and strain rate sensitivity m dened in general terms asn @ lnry=@ ln ep and m @ lnry=@ ln _ep, respectively, where ry isthe current yield stress, ep is the accumulated plastic strain, and_ep is the effective plastic strain rate.

The reference for further comparisons and discussions is pro-vided by Conventional CG polycrystals whose main characteristicsregarding plastic deformation are reminded hereafter. CG poly-crystals deform at room temperature by dislocation-mediatedmechanisms, involving sometimes deformation twins.Dislocations are produced from different types of sources, glide,interact with other dislocations and with other microstructurefeatures (solute atoms, precipitates, grain and phase boundaries),get pinned and depinned, which may require the generation ofadditional dislocations to pursue the deformation, leading to the

6 A. Pineau et al. / Acta Mafcc (below 0.01) and moderately low in bcc and hcp materialsat room temperature (not more than 0.030.05 except for verylow melting point metals).

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://d2.2.1. Deformation mechanisms in single phase UFG and NC metalsIn UFG metals, qualitatively the same mechanisms as in CG

metals occur except that no dislocation cells are observed.Furthermore, Geometrically Necessary Dislocations (GNDs) accu-mulate near GBs to accommodate possible deformation incom-patibility among neighboring grains. Presumably, accumulationtakes place in boundary layers whose width is comparable withthe grain size. The so-called core and mantle [4] descriptionof the deformation of grains with a wide central part (the core)and a thin boundary layer (the mantle) involving a high disloca-tion density loses its signicance. Hence, the increase of strengthwith decreasing grain size still follows a KHP/da trend but with avalue a or a proportionality constant KHP that can differ, seeFig. 3b with an example for IF steels [65], while other examplescan be found for Al [66] or Ti [67]. Sinclair et al. [68] followedby [69], developed a closed form description of the dislocationaccumulation near GBs. With the introduction of a saturation ofthe GB dislocation density, involving the relaxation of the impen-etrable character of the GB, as well as a back stress evolution lawinvoking a progressive shielding by the dislocations on the oppo-site side of the GB, these authors captured not only the evolutionof the yield stress but also the decrease of strain hardening capac-ity for small grain size. The high density of GNDs compared tostatistically stored dislocations (SSDs) leads to high kinematichardening levels.

All these effects can be described using advanced continuumplasticity models that take into account barriers to plastic owand the impact of GNDs on hardening usually through higher orderboundary conditions and higher order stress quantities theso-called strain gradient plasticity (SGP) theories , e.g. [70] orthrough back stress based formulations related to the plastic slipincompatibility [71], both theories being mathematically equiva-lent under some prescriptions [72]. In these theories, the accumu-lation of GNDs at GBs is accounted for in a smeared way, leading tothe introduction of one or several phenomenological internallengths qualitatively connected to dislocation mechanisms, seee.g. discussion in [73,74]. Recently, these strain gradient plasticitytheories have been enhanced to better represent the behavior ofGBs involving the partial or full transparency to dislocation motionunder stress, e.g. [65,7477], which allowed, for instance, bettercapturing experimental trends at the smallest grain size in IFsteels, see Fig. 3b [65]. Discrete dislocation dynamics (DDD) simu-lations of polycrystals have also allowed looking at this range ofgrain sizes in 2D [78]. The HallPetch relationship is fairly wellcaptured by these simulations but the drop of strain hardeningwith decreasing grain size is not, because specic rules for theGB response are missing. In [78], the authors explicitly indicatedthe need for transmission rules at GBs to better reect the physics,which was included in recent SGP theories as explained above.Interestingly, incorporating enhanced physics that accounts fordislocation junctions and forest hardening following [79,80] doesnot affect the macroscopic response, including HallPetch scalingand hardening rates, although it does affect the dislocation densityevolution [81] with possible consequences on energy storage thatcould eventually drive recrystallization and grain renement.Thus, a better understanding of relaxation mechanisms at GBs isstill needed.

The deformation mechanisms in NC metals are even more com-plex. In this range of sizes, dislocation mechanisms compete orcooperate with other deformation mechanisms associated withthe mobility of GBs. Internal dislocation sources are scarce as thegrain size decreases. Several authors have suggested, based onmolecular dynamics simulations, that GB dislocation sources are

alia xxx (2015) xxxxxxactivated in nano-grains [82] from ledges or other local stress con-centration owing to the very large strength levels. The GBs act asdislocations sinks in which their stress eld can spread [83]. But


teriaA. Pineau et al. / Acta Madislocations, owing to the high stress levels, can also traverse theGBs while leaving some debris. This transition from regulardislocation activity from pre-existing intra-granular dislocationsources to GB dislocation nucleation dominated plasticity is notabrupt. It depends on the magnitude and distribution of the initialdislocation density from grains to grains and on the distribution ofgrain size. Now, as the grain size decreases, GB mediated deforma-tion mechanisms involving GB sliding [84], GB rotation [85] and GBmigration [86] start competing with dislocation-mediated plastic-ity. A number of studies have indeed reported stress-assistedgrain growth as an efcient mechanism in small-grained materials[8791]. The detailed mechanisms of GB sliding or shear coupledGB migration, by atom shufing or GB dislocations, depend onthe misorientation, on the orientation of the GB plane withrespect to the tensile axis and on the presence or not of GB soluteelements.

(a)

(b)Fig. 3. (a) Schematic representation of the variation of the yield strength as a function ofbetween experimental data and FE simulations based on an advanced strain gradient pl

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dlia xxx (2015) xxxxxx 7In real NC polycrystals, the grain size distribution is such thatthe smallest grains can be extremely resistant to plasticity whileother grains, better oriented or larger, can deform by more classicaldislocation mechanisms or relax the stress by GB sliding or migra-tion, leading to huge levels of internal stress and long elasto-plastictransitions, see e.g. [92,93]. The concept of yield stress is thus notwell dened anymore and must be given at a representative levelof plastic strain [93]. The extreme strengths are attained for condi-tions of grain sizes and GB nature such that dislocation nucleationdominated deformation is pushed to the upper stress limit atwhich the GB mediated mechanisms start relaxing the load. Thistypically occurs at average grain sizes around 1050 nm with r0sometimes equal to several GPa. In [94], it was shown that theyield stress could peak at 10 nm grain size in NC Cu. In the mean-time, the difculty to store dislocations increases the difculty forfurther plastic ow and leads to very limited strain hardening

grain size, with several possible scenarii; (b) example for IF steels with comparisonasticity formulation, reproduced from [65].


capacity n near 0. All mechanisms described above involve thecooperative activity of only a small number of atoms which canbe triggered by thermal activation owing to a small activation area.An essential characteristics of NC metals is thus to exhibit a highrate sensitivity m as depicted in Fig. 4 which has been constructedbased on a wide compilation of data provided in [95]. In fcc, mmonotonously increases with decreasing grain size; but for bcc,m rst decreases with decreasing grain size while it re-increasesonly at sizes around 3050 nm. Furthermore, the long elastoplastictransition resulting from the heterogeneities in the microstructureand the different natures of the deformation mechanismslead to very large back stress levels. The combination of high backstress and high rate sensitivity can result in the surprisingobservation of reverse (creep-)plasticity under small load levels,e.g. [96]. In summary, single phase NC metals involve highstrengths, high rate sensitivity, high levels of back stress and lowisotropic strain hardening capacity. Finally, in NC metals withgrain size below 1020 nm, GB deformation mechanismsdominate. Aspects of the behavior bear resemblance to that of

stated, the interaction between twins, and (iii) the stability of these

8 A. Pineau et al. / Acta Materitwins during deformation. These issues are also addressed in thereview by Zhu et al. [102].

Fig. 4. Schematic variation of the rate sensitivity exponent m as a function of grainamorphous materials and this goes beyond the scope of the presentreview.

2.2.2. Deformation mechanisms in NT metalsThe twinning tendency of a Face-Centered-Cubic (fcc) metal is

largely determined by its stacking fault energy (SFE). For examplecoarse-grained (CG) fcc metals with high SFE such as Al and Ni nor-mally deform by slip of perfect dislocations, while fcc metals withlow SFE such as Ag primarily deform by twinning which is pro-duced by the propagation of partial dislocations. High strain ratesand low deformation temperatures also promote deformationtwinning: see [99] for a review on deformation twinning in CGmetals. An essential element for further discussion in this paperis that the formation of mechanical twins produces an increaseof the work-hardening rate quantied here by n through a progres-sive HallPetch type mechanism, e.g. [100,101]. The focus in thissection is on deformation twinning in NC fcc metals or on the plas-ticity mechanisms in NT fcc metals (in which the grain size is notnecessarily very small). Three main issues are addressed: (i) thecondition to nucleate mechanical twins in NC metals, (ii) the effectof twins on the mechanical behavior of NT metals or, otherwisesize for fcc, bcc and hcp metals inspired from the compilation of data provided in[95].

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dContrary to CG metals which become more difcult to twinwith decreasing grain size, NC (fcc) metals twin more easily withdecreasing grain size, reaching a maximum twinning probability,and then become more difcult to twin when the grain sizedecreases further, i.e. exhibiting an inverse grain-size effect ontwinning [102104]. Molecular dynamics simulations (MD) haverevealed several important deformation mechanisms of NC materi-als, see [102]. Emission of Shockley partials from GBs has beenextensively observed. Three mechanisms for twin nucleation andgrowth were suggested by Yamakov et al. [105] and discussed byZhu et al. [102] (see in their Fig. 11). In UFG Cu (with grain sizein the range 400600 nm), pronounced enhancement of the strainhardening rate occurs when the twin spacing is smaller than15 nm. It has been suggested that at larger twin spacing, thestrength of such NT Cu is dominated by the twin boundary (TB)resistance to dislocation slip activities, e.g. [103]. As the twin spac-ing is reduced to less than 15 nm, nucleation of twinning partials atTBGB intersections could lead to a reduction of yield strength anda modication of strain hardening capacity [9,103]. Moreover, thepresence of dense nanoscale twins signicantly inuences the evo-lution of the activation volume for plastic ow which is threeorders of magnitude smaller than the one known in CG Cu [106].This explains why a large number of experimental studies andmodelling has been devoted to NC metals and alloys containing alarge fraction (2050%) of NT (twin spacing, k < 100 nm). At thetwin spacing transition, the yield strength is almost 10 times theyield strength of pure Cu. Moreover the critical twin spacing varieslinearly with grain size [102]. The transition in twinning behaviorfrom CG to NC metals is caused by the change in deformationmechanism as indicated earlier. An analytical model based onobserved deformation micro-mechanisms in NC metals, i.e. emis-sion of dislocations from twins in NC fcc metals has been proposed[102,107,108]. The interactions between pre-existing twins andpartial dislocations have also been studied using moleculardynamics simulation [109,110] and by high resolution TEM[52,111]. These studies have conrmed that these interactions tendto promote a strengthening effect related to slip arrest in the formof LomerCottrell locks [112].

The NTs are not always stable. De-twinning effect is oftenobserved. This phenomenon is not specic to NC metals sincede-twinning can also occur in CG metals. This process is causedby the interaction between matrix perfect and partial dislocations(PDs) and TBs, see e.g. [113115] for recent reviews. De-twinningcan be partly responsible for the deformation of NC metals, in par-ticular for their work softening. In-situ TEM experiments on NT Curevealed systematic activation of Shockley twin PDs from TBGBtriple junctions and their motion parallel to TBs causing TB migra-tion [116]. This migration may annihilate entirely thin twin lamel-lae producing de-twinning, especially when the twin thickness k isvery small (k < 30 nm) [117]. Wang et al. [115] described a mech-anism operating in incoherent TB (ITB). These ITBs propagate as adisconnection or a step (see [118] for a description of disconnec-tions) that is a multiple {111} atomic planes thick resulting fromthe collective glide of multiple TPs which may possess identicalor different Burger vectors, satisfying the mechanism needed forde-twinning. Wang et al. [115] have suggested when modellingthe migration of ITBs that de-twinning becomes the dominantdeformation mechanism for growth twins of the order of a fewnanometers thick. De-twinning explains also the annihilation ofTBs in rolled, highly textured NT Cu lms and the softening effectobserved in UFG NT Cu. It can also be noted that the motion of TBscontrolled by a local shear stress generating the displacement oftwin partial dislocations produces an elongation in a direction per-

alia xxx (2015) xxxxxxpendicular to the plane of the TB, as described in [119], and mod-elled in [120,121].


PVD does not. This intriguing result has been recently explainedby a detailed analysis of the crystallography of the interfaces: thefaceted {112}Cu||{112}Nb type interfaces in ARB multilayersfavour the production of deformation twins in Cu while the{111}Cu||{110}Nb atomistically at interfaces of PVD multilayersfavour symmetric slip [18,130,131]. The control of the crystallo-graphic texture is another key issue texture [132]. Cu/Ni/Nb tri-layer based systems processed by PVD can provide more strainhardening capacity by favouring the operation of so-called superthreaded dislocations, which leave some dislocation content atthe fccbcc interfaces [133]. Note nally that metallic multilayerswith alternating crystalline and amorphous layers reveal interest-ing properties [134,135] but these systems go out of the scope ofthis review.

2.2.4. Deformation mechanisms in metallic lms, pillars andnanowires

Systems with at least one submicron external dimensioninvolve a very ne microstructure dictated by the outer dimen-sions but also by the typical deposition processes which are oftenfar from equilibrium and which lead to a high density of defects in

terialia xxx (2015) xxxxxx 92.2.3. Deformation mechanisms in NC and UFG multiphased metalsIn bimodal grain distribution structures, the deformation is

heterogeneous with the continuous network of small grainsproviding the high strength while the large grains bring about anisotropic strain hardening contribution. Furthermore, a largekinematic hardening contribution results from the strength mis-match between small and large grains [122]. The importance ofthe back stress generated by a bimodal distribution has been cap-tured by FE cell simulations of representative grain aggregate usingSGP type models allowing the introduction of higher order bound-ary conditions that mimic the constraint of GBs on plastic ow[65,123].

Deformation mechanisms in multi-phase microstructures implystrong obstacles to dislocation motion due to the interfacesbetween different phases. These interfaces are often stronger thanGBs regarding dislocation transmission. Strong back stress is gen-erated due to the different strength of the different phases, leadingto the accumulation of high densities of GNDs. Another size effect,in addition to the grain size of the rst matrix phase, comes fromthe dimension of the second phase. Recently developed hybrid sys-tems exhibit even more complex mechanisms. For instance, theeffect of thin lms of austenite located along lath or grain bound-aries in ferrous lath martensite (Fig 2c) must be distinguished fromthe dual phase effect observed in duplex UFG steels. The recentstudies by Mine et al. [124] and Maresca et al. [28] provide adetailed analysis of the deformation modes of the tiny austenitelms. Slip transfer from one phase to the other one depends onthe crystallography and the orientation relationship. In dual phasematerials the effect of the second phase is more massive, in par-ticular when this phase can be deformed by mechanical twinningor by martensitic phase transformations (e (hcp); a0 (bcc)), see[30]. Quantitative study of these phase transformations wouldrequire the knowledge of the local stresses and the local composi-tion which controls in particular the stacking fault energy, SFE.Some observations [30] indicate that the a0 transformation isstress-induced, contrarily to what is observed in many coarsegrain low SFE steels. In these steels, a0 preferentially nucleates atthe intersection of twins and/or e platelets while in the high Mnsteel with a duplex UFG microstructure a0 is preferentially nucle-ated at grain boundaries leading to the assumption that a0 wasstress induced. If this was the case, one should expect that thiseffect and its consequences like the TRIP effect should be ampliedwhen the test temperature is decreased. The nature ofwork-hardening in multi-phased materials due to a TRIP effect isvery much dictated by SGP effects connected to the submicron sizeof the transforming domains [125,126].

In thick multilayer metallic systems, the resistance to sliptransmission across the interphase boundaries constitutes thedominant factor that dictates the maximum strength of the multi-layer. In Cu/Nb laminates produced by magnetron sputtering, semicoherent energetically favourable interfaces form respecting theKurdjumovSachs orientation relationship typical of fccbcc sys-tems. The strength increases with decreasing layer thicknessthrough a HallPetch type mechanism down typically to 50 nm,e.g. [56,127]. Below 50 nm thickness, the strength keeps increasingwith decreasing layer thickness through the so-called connedlayer slip. When the thickness gets about a few nm, the disloca-tions are then able to glide across the interfaces and the peakstrength is attained [127,128]. The overall picture is thus not muchdifferent than in Fig. 3a, although the relaxation mechanism thatdictates the position of the peak is different. The shear strengthof the semi coherent interfaces in Cu/Nb multilayers is not verylarge [129]. In general, the isotropic strain hardening of Cu/Nb

A. Pineau et al. / Acta Mamultilayers is very small in the small layer thickness regime. TheCu/Nb produced by ARB exhibit deformation twins when the indi-vidual layer thickness is below 50 nm while Cu/Nb produced by

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dterms of twins, GBs, vacancies, stacking faults etc (nanowhiskersconstitute one notable exception). The main mechanical character-istic of these nano-objects is that the ow strength increases withdecreasing dimensions. This is illustrated by the data compiled in[6] and schematically reproduced in Fig. 5. The data has essentiallybeen obtained using pillar compression. Note that the behavior inpillars exhibits stochastic aspects so that the increase in strength isaccompanied with an increase in scatter. The same trends areobtained when pulling thin metallic lms in tension, e.g. see[136]. This smaller is stronger effect parallels the HallPetchbehavior described in Section 2.2.1. The origin of this effect ispartly similar as the grain size usually scales downwith the dimen-sions of the lm, see Section 2.1.2, but not entirely. Indeed, theplasticity mechanisms discussed in Section 2.2.1 are still valid forthin lms and nanowires but with at least ve important pointsof attention:

(1) Dislocations in thin lms constrained by an underlying sub-strate often move through a mechanism of channeling: socalled threading dislocations advance or recede by glidingon well oriented planes, with the dislocation line extending

Fig. 5. Schematic variation of the shear ow stress on relevant slip or twinning

system normalized by the elastic shear modulus as a function of pillar diameternormalized by the norm of Burgers vector for fcc, bcc, and hcp systems, inspiredfrom the large set of data compiled in [6].


plasticity mechanisms. Mompiou et al. [147] have recently

10 A. Pineau et al. / Acta Materifrom the free surface to the interface [137,138]. This mech-anism gets more and more difcult to operate with thedecrease of the congurational force as the thicknessdecreases [137], providing one origin of the increasingstrength at small thicknesses.

(2) When there are only one or a few grains over the thickness/-diameter, which is the usual conguration in thin lms/-nanowires, the presence of free surfaces can signicantlyimpact plasticity by allowing dislocations to escape, pre-venting their accumulation inside the metal. The imbalancebetween the rates of escape and generation of fresh disloca-tions leads to exhaustion hardening [139,140]. This phe-nomenon is also sometimes referred to as dislocationstarvation. In addition, the behavior in small volumes isoften source limited. When dimensions are small (i) theprobability of nding dislocation sources is low and theyare harder to operate because of reduced activation lengths[141], and (ii) the operation of the few available ones is hin-dered by the proximity of free surfaces leading to hardeningby source truncation [142]. Dislocations can also nucleatefrom GBs and then escape the grain with no capacity of stor-age. This explains the very low strain hardening capacitybeyond a transient of extreme hardening. This and relatedphenomenology have recently been addressed byEl-Awady [143] through a comprehensive set of DDD simu-lations on single micro- and nano-crystals. One key parame-ter is the product Dq with D the crystal size and q the initialdislocation density. El-Awady identies four mechanisms:(i) if Dq is very small, pure dislocation starvation is activewith no capacity for storing dislocations; (ii) at larger Dq,the so-called single source strengthening dominates, asgoverned by a single source or a few sparse sources thathardly interact with other dislocations again a very smallstrain hardening capacity is expected; (iii) the third mecha-nism is identied as the exhaustion hardening with a rel-atively high number of dislocation sources, but the mobiledislocations exhaust from mutual interaction and the corre-sponding density is insufcient to sustain ow with increas-ing the applied stress a larger (albeit transient) strainhardening capacity is expected here; also see [144]; (iv)the fourth mechanism is the classical forest hardening. Allsimulation results for different conditions merge into a sin-gle master evolution when plotted as sy

D

p=l versus Dq,

where sy is the yield stress in shear and l is the shear mod-ulus. The overall behavior of a real thin lm or nanowire isthe collective response of micro- or nanocrystals involvingGB and free surface and falling in one of these categoriesdepending on the distribution of sizes and initial dislocationdensity. Factors such as the grain shape, the presence ofoxide at the surface and the resistance of this oxide will alsoplay a role in the dislocation starvation capacity, see e.g.[145,146].

(3) When the structure is columnar for thin lms andbamboo-types for nanowires with a single grain in the smalldimension, the lack of constraint in one or two of the dimen-sions facilitates the operation of GB sliding and migrationmechanisms. The grain rotation or GB sliding can be easilyaccommodated in the transverse direction. Many exampleshave indeed been provided in studies on thin metallic lms,e.g. [86,147,148]. This has been conrmed by MD simula-tions of tensile tests on Ni nanowires with 10 nm grain size[149]: the contribution to the overall deformation from GBmediated mechanisms is dominant in wires with diameter

on the order of the grain size, while larger wires with several

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dshown that the GB grooves in 200 nm thick Al lms initiatea process of GB dislocation glide, leading to GB sliding andgrain rotation. Only after a few % of deformation,intra-granular dislocation activity is observed, probablydue to the generation of local stress concentration, with evi-dences of grain growth mechanisms as well (see also [148]).Furthermore, the free surfaces constitute a preferentialregion for atomic diffusion, which favours creep mecha-nisms in thin lms, e.g. [155].

(5) Strain gradient plasticity can play an additional role in set-ting the resistance to deformation of small objects if thedeformation mechanism is dominated by dislocationglide and storage, i.e. if the product of grain size or specimensize with dislocation density (dq or Dq) is not too small.When thin lms are bent [156], or micro- or nanowires aresubjected to torsion [157], the gradient of plastic strain overthe thickness or diameter can be extreme and must beaccommodated by a high density of GNDs. This leads to anextra source of strengthening, similar to the effects dis-cussed in Section 2.2.1. It is emphasized that the notion ofGNDs is scale-dependent and that more complexinteractions between SSDs and GNDs occur inevitably. Inparticular, GNDs are not only induced by externally imposedgradients, as in bending [158,159] or indentation [160], butalso result from deformation-induced strain gradients [161].A plasticity size effect can thus emerge in microcrystals inthe absence of macroscopic gradients. Such behavior maynot be ubiquitous but has been reported experimentally[162].

Note nally that extremely large Bauschinger effects have beenobserved in thin metallic lms upon unloading, e.g. [163], givingrise to signicant recovery mechanisms. Saif and coworkers havefound that thin Al and Au lms with grain sizes around 50 nmdeformed in the plastic domain and unloaded can recover a largefraction (50100%) of the plastic strain under zero applied stress[164,165].

3. Fracture of bulk UFG and nanostructured metals

The signicant increase in strength ry with decreasingmicrostructure size shown in Fig. 3a is usually accompanied by adrop in ductility. Fig. 6a shows the schematic variation of ry versuselongation to failure (or total elongation) eengf reported in the liter-ature with the so-called banana curve, e.g. [7,35,166]. The sche-matic Fig. 6a is supplemented by Fig. 6b and c compiling real datafrom the literature. Fig. 6b provides an example for Ni systems pre-pared by different methods [35]. Fig. 6c is a compilation by Speeret al. [166] of a wide range of data for steels. We have added inFig. 6c the results on UFG-DP steels obtained in [30] for twograins in the diameter exhibit also GB activity initially butwith the development of high internal constraints at triplejunctions that further lead to dislocation activity. The pre-dominance of GB mediated plasticity mechanisms whichare thermally activated with small associated activation vol-umes often leads to very large rate sensitivity exponents, seee.g. m = 0.050.15 for Al [12,150], 0.030.15 for Au [151],0.020.1 for Pd lms depending on ageing time and on thepresence or not of a thin protective surface layer [152154].

(4) The free surface can have other indirect consequences. Inparticular, the presence of GB grooves or a signicantroughness acts as stress concentrators for initiating the

alia xxx (2015) xxxxxxannealing temperatures and the results on medium C steel [29],


teria(a)

A. Pineau et al. / Acta Masee descriptions in Section 2.1.1 The BQ&P treatment applied to themedium C steel and the short anneal applied at 610 C on the low Csteel lead to extremely attractive properties. Fig. 6d provides arecent compilation by Sharon et al. [167] of elongation at fractureversus microstructure length scale showing the same expectedtrend for a range of metals. It is essential to realize that the useof the elongation to failure eengf as a ductility index mixes boththe resistance to necking, eu, and the resistance to damage accumu-lation, which is better quantied by the true fracture strain ef; seeSection 1. A low value of eengf in a material capable of neckingalways implies a low eu, but not necessarily a low ef. This is whywe separate the two aspects. Section 3.1 deals with the resistanceto plastic localization in bulk nanostructured metals addressingpossible ways to improve it. Section 3.2 focuses on the resistanceto damage and fracture.

The intricate mechanisms of plasticity in nanostructured metalsultimately impart a rate-dependent hardening behavior. Models ofdamage and fracture that are rooted in a bottom-up approachbased on explicit rendering of dislocation slip and twinning arenot mature enough to enable a broad interpretation of availableexperiments. In the local approach to fracture, a phenomenologicalhardening law is typically introduced which will allow discussingamong others the resistance to necking with quantitativeparameters:

ry r0 k1epn1 k2 _epm 1

where ry and r0 are current and initial yield stress, respectively, ep

is the accumulated plastic strain, _ep is the effective plastic strain

(c)

Fig. 6. Variation of the ductility as a function of strength (or characteristics microstructuryield stress, showing the possible options to move out of the banana syndrome; (b) col(c) compilation of elongation versus tensile strength data for high strength steels produce550 and B-610; (d) compiled variations of elongation versus characteristic microstrexperiments and reported by Sharon et al. [167]. The references for (b), (c) and (d) are gthese gures pertain to these papers.

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://d(b)

lia xxx (2015) xxxxxx 11rate, n and m are, respectively, the constant strain hardening andstrain rate sensitivity exponents associated with this specic formof hardening law, and k1 and k2 are two hardening parameters.More physical hardening laws are available, e.g. [62], but Eq. (1) issufcient for the present context.

3.1. Plastic localization in UFG and bulk NC metals

The essentials regarding plastic localization are summarized inFig. 7 assuming the following phenomenological hardening law (1).Fig. 7 contains eight curves:

(1) Represented by curve 1 is the engineering stress reng versusengineering strain eeng response of a reference CG metal withyield stress r0a, strain hardening capacity n1 = 0.1 and strainrate sensitivity m? 0. The onset of necking occurs at themaximum load with strain eFmax = eu n1 = 0.1 as predictedby applying the Considre criterion dr/de = r on Eq. (1)(assuming that r0 is sufciently small compared to thestrain hardening term in Eq. (1)).

(2) If the strain hardening capacity of the material is, by anypossible means (e.g. lower stacking fault energy), increasedto n2 = 0.2 such as in curve 2 the resistance to neckingincreases proportionally.

(3) Usually, m is lower than 0.01 in fcc materials (Fig. 4) anddoes not play any signicant role in plastic localization.But, if m is not negligible as for curve 3 because of higherhomologous temperature or intrinsic rate sensitivity, suchas in several bcc and hcp alloys (Fig. 4) a signicant

(d)

e length scale); (a) schematic evolution of uniform elongation/strain at necking withlection of data for a variety of bulk Ni systems produced by different methods [35];d by many different techniques, see [166] see text for the notations BQ&P, BQ&T, B-uctural length scale taken from published quasi-static (106103 s1) tensileiven in the reference cited in this caption, and the numbering system appearing in


m tan1a1dcd

p=2 1tan1a1

p=2 1

0@

1Am1 m1 m1; 3

where r00 is the contribution to yield stress independent ofgrain size (friction stress and other sources of hardeningthrough solid solution or precipitates), KHP1 is the HallPetchconstant, the limitm1 corresponds to the large grain size limit,m1 corresponds to the small grain size limit, and a1 is a tuningparameter controlling the spread of the transition region. Atemperature effect could be taken into account by changingthe values ofm1 andm1. Values reported in Section 2.2 moti-vate the following possible choice of parameters for typical fccmetals: m1 = 0.009, m1 = 0.1, dc = 250 and a1 = 10 (this last

12 terialia xxx (2015) xxxxxximprovement in the resistance to necking is observed. Theinstability does not occur at the peak load anymore but later.The rate sensitivity stabilizes the incipient necking process.This effect can be quantitatively modelled by an imperfec-tion type analysis (e.g. [168170]) and not anymore by asimple Considre type analysis.

(4) If the material contains imperfections in the form of smallmachining defects (e.g. small reduction of section) or anaggregate of grains with soft orientation, the impact on theresistance to necking can be signicant as exhibited withcurve 4 again for n = 0.2. A 1% section reduction typicallyleads to a 20% decrease of eu [170].

(5) Curve 5 corresponds to a hypothetical UFG or NC metalwith exactly the same characteristics as the referencematerial in terms of strain hardening and no rate sensitiv-ity, but a much higher yield strength r0b r0a. The corre-sponding eu is now much lower than 0.1. It is often notsufciently realized that application of the Considre crite-rion leads to a decrease of eu with strength even at constantstrain hardening capacity.

Fig. 7. Schematic engineering stress/engineering strain uniaxial tension curves ofmetallic materials involving different levels of yield stress, strain hardeningcapacity, rate sensitivity and imperfection see text for a description of each curve.(6)

(7)

PleaseA. Pineau et al. / Acta MaIn reality, the strain hardening capacity n of NC or UFGmetals is, as explained in Section 2.2.1, lower than the ref-erence CG case, see curve 6, [5]. The main reason for thislack of strain hardening capacity results from the impossi-bility to activate forest hardening mechanisms (involvingdislocation dipoles, locks and pinning) during which obsta-cles multiply due to an increasing dislocation density.As explained in Section 2.2.1, fcc NC metals exhibit m valueshigher than in their CG counterpart, see [95,34,7] and Fig. 4,while, bcc metals do not show a monotonic increase of mwith decreasing grain size, but still high m values at verysmall grain dimensions. If m increases, the resistance tonecking can be signicantly improved as shown with curve7. The improvement of the ductility, while maintaining ahigh strength, has been demonstrated in several studies asin [17] in the case of Cu deformed at low strain rates.Detailed theoretical calculations have recently been per-formed by Pardoen [171] using an imperfection-based anal-ysis for nite length specimens. There, it was assumed thatthe yield stress and strain rate sensitivity were related tograin size through, respectively, the following phenomeno-logical laws

r0 r00 KHP1=d

p; 2

tativeaboveto impthe insensit

Fig. 8.effect ochange

cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dx.doi.ot review, in particular because the literature is still very lim-egarding in depth studies on this topic for NC materials.theless, all messages carried away from Fig. 7 remain quali-ly valid when dealing with localized bands. Based on thediscussion, we can synthetize the different means availablerove the resistance to necking, see Fig. 6a, by distinguishingcrease of the strain hardening and the increase of the rateivity.

0

0.1

0.2

0.3

0.4

0.01 0.1 1 10 100 1000

inst

d = h (m)

m constant = 0.009strength varies

m varies from 0.009 to 0.1strength variesparameter allowing a smooth transition at d dc) whichmatch experimental data for Pd, [172] and are reasonable forAl as well [173]. Fig. 8 shows the predicted strain at plasticinstability against grain size [171]. Ifm is constant, the ductil-ity drops continuously just because of the increase of strengthas discussed for curve 5 in Fig. 7. But, ifm varies with grain sizefollowing (3), the drop can be suppressedwith even a possibleimprovement of the strain at necking.

(8) Curve 8 is described in the context of Section 5 as it onlyapplies to micro- or nano-scale specimens.

The plastic localization mechanism discussed up to now refersessentially to diffuse necking under uniaxial tension. But, plasticlocalization also occurs under more general loading conditions.Furthermore, diffuse necking only develops if the deformation eldis sufciently homogeneous, otherwise, only localized necking canform. Localized necking develops at larger strains compared withdiffuse necking (except under plane strain tension conditionswhere they coincide), sometimes inside diffuse necks [170].Forming limit diagrams are used to represent the locus of localiza-tion strains under biaxial loading conditions (both for localized anddiffuse necking). The prediction of localized necking is more com-plicated and typically requires the use of bifurcation theory, see theseminal papers [174,175], as well as to account for complex issuesrelated to corners on the yield surface, softening mechanisms, crys-tal plasticity and texture effects. This goes beyond the scope of thepresenited rNeverVariation of the strain at necking as a function of the grain size d showing thef the increase of rate sensitivity with decreasing grain size compared to noof rate sensitivity.

rg/10.1016/j.actamat.2015.07.049

teriaIncrease the strain hardening capacity:

(1) Accumulation of dislocations in metals with grains as smallas 1030 nm has been recently demonstrated in different fccalloys [176178]. These data were obtained on thin lms(see Section 5) but there is no reason that this should notbe observed in bulk NC. One possible reason for this accumu-lation of dislocations is because of a pre-existing populationof defects inside the grains, as a result of the processing, pro-viding obstacles to pin the dislocations nucleated from theGBs and avoiding thus that all dislocations sink in the oppo-site GBs. This goes along with the importance of consideringthe initial dislocation density q through the product Dq asexplained in Section 2.2.4.

(2) The processing of a bimodal grain size distribution is highlybenecial to resist necking as a source of strain hardening bydislocation storage in the large grains and as a source of backstress. Nevertheless, a necklace structure of nanograins inwhich isolated larger grains are embedded must be main-tained in order to preserve the high strength [122].

(3) As explained in Section 2.2.2, nanotwins, whatever their ori-gin (growth, annealing or deformation), constitute a sourceof strain hardening [38,179,180] with a work hardeningcapacity increasing with decreasing twin spacing down toan optimum size. First, TBs constitute regions for dislocationstorage leading to an isotropic hardening contribution. Also,a TB probably gets more and more impenetrable with defor-mation due to an increasing incoherency [111,181,182].Pre-existing twins constitute also a source of back stress,leading to a kinematic contribution to strain hardening.Now, de-twinning is a source of softening with a negativeimpact on the resistance to plastic localization motion [183].

(4) Deformation twins or so-called TWIP effect [184] is a verystrong source of strain hardening if properly mobilized.The introduction of new TBs brings new obstacles to disloca-tions during the deformation which adds to the othersources of strain hardening mentioned just before associatedto TBs present before deformation. This continuous source ofnew interfaces leads to a continuous increase of the backstress.

(5) A TRIP effect very signicantly enhances strain hardening. ATRIP effect acts positively on the resistance to necking only ifit occurs sufciently late to bring the extra hardening atstrains approaching the localization condition [185187]. Atoo fast or too slow TRIP effect is not interesting, as provedon coarse grain TRIP steels [187]. The explanation is similarto the aforementioned TWIP effect and related to the intro-duction of new interfaces in the course of deformation (aswell as of a new hard phase). Many recent studies devotedto Q&P steels described in Section 2 with very ne grains,see [188193], have shown that it is possible to signicantlyimprove both the strength and the ductility of UFG steelsowing to a TRIP effect [194,195].

(6) Composite effect can also be engineered such as to bring asource of strain hardening, essentially through a back stresscontribution that can signicantly delay necking. Goodexamples can be found in the literature. In multi-phasedhybrid steels, the austenite plays a predominant role inblocking the slip transfer from the ferrite phase and inincreasing the work hardening rate. This largely contributesto the excellent ductility measured in these high strengthsteels, also found in earlier works on DP-UFG steels [196].In multilayers, the capacity to generate super threading dis-

A. Pineau et al. / Acta Malocations which deposit dislocation debris along the inter-faces in tri-layers Cu/Nb/Ni show superior strain hardeningcapacity compared to Cu/Nb [130]. A nal sophisticated

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dFinally, graded structures, like NC graded Cu, can lead also to excel-lent strength ductility performances through a capacity of forcingplasticity to be heterogeneous and gradual, which leads to straindelocalization [24]. This process allows deforming, without earlyfailure, the surface outer nano-grains, which then undergo GBmigration mechanisms. In addition to strain hardening and ratesensitivity effect, this millimetre scale architecturing leads to adelocalization process which resembles the approach followed inexible electronics described in Section 4. All these unconventionalexample is given by nanostructured high strength Mo alloyto which signicant ductility was conferred through a hier-archical structure made of submicron grains and nanometricoxide particles [197].

(7) Deforming metals at low temperatures limits the action ofrecovery mechanisms, maintains the work hardening tohigher values and positively contributes to plastic localiza-tion (except if the lower temperature signicantly decreasesthe rate sensitivity capacity see next paragraph)

Increase the rate sensitivity:The importance of increasing the rate sensitivity has been

explained above. The rate sensitivity can be increased by triggeringall possible sources of thermally activatedmechanisms: dislocationnucleation dominated plasticity regime or GB mediated deforma-tion all involve the activation of a limited number of atoms to gen-erate a local conguration change with an associated discrete strainevents. Now, the balance between the generation of thermallyactivated mechanisms and the possible lack of strain hardeningassociated with these mechanisms must be carefully evaluated tond the optimum condition. For NT systems, the problem is simple:NTs not only act positively on strain hardening but also bringenhanced rate sensitivity due to the thermally activated nature ofthe dislocation/TB reactions [106,108]. But, in other cases, the factthat GB mediated mechanisms can take the lead overintra-granular dislocation activity can generate a drop of n that isnot compensated, in terms of ductility, by the increase in m; and,in some circumstances, can possibly lead to softening and dramaticlocal structural instabilities. These aspects regarding the control ofthe rate sensitivity will be discussed in more details in Section 5.2when dealing with thin lms, for which there are many data avail-able and where the mechanisms leading to rate sensitive effects areoften amplied.

Obviously, many combinations of the different mechanisms dis-cussed above, involving bimodal grain size distribution, NT, TWIPand TRIP effects should cooperate to bring even higher resistanceto plastic localization. A good example is given by 316L austeniticstainless steel microstructures produced rst by a dynamic plasticdeformation under high strain rate (102103 s1) at ambient tem-perature followed by an annealing at 730800 C. The microstruc-ture made of micron size grains, nano-size grains and NT bundlesof micron size involves different sources of strain hardening thatcan operate at different steps of the deformation and probablysome amount of rate sensitivity, leading to an excellentstrength-ductility balance [198]. The competition between raisingm at the expense of n is certainly an important point of analysisthat has not been systematically identied for NC systems, and cer-tainly not addressed from the viewpoint of optimizing thestrength-ductility compromise. On this topic, it would be interest-ing to follow ideas similar to the one recently developed for macro-scopic metal matrix composites [199]. Another key aspect that hasnot received systematic attention is the controlled engineering ofmultiscale micro- and nanostructure with the target of maintain-ing enough kinematic hardening effects even at large strains.

lia xxx (2015) xxxxxx 13approaches to increasing ductility suffer from a lack of models tohelp guide microstructure optimization in problems involvingnumerous parameters.


probably the one that must accommodate the largest GB sliding

terimismatch from the connected grains. The mechanism of voidnucleation at triple junctions associated to GB sliding has been the-oretically investigated by Ovidko et al. [204] using a GB disclina-tion type conguration. Some voids might also result frompre-existing nano-voids due to hydrogen loading during the pro-cess. When a void nucleates, relaxation takes place on neighboringGBs. The voids grow until nal impingement with the plastic owlocalized in the intervoid ligament, reminiscent of the void coales-cence process observed in CG metals, but here at the scale of a sin-gle crystalline ligament. The true fracture strain resulting from thismechanism can be quite large as recently shown by Sharon et al.[167] for thick electrodeposited NiFe alloy layers exhibiting 75%area reduction at fracture and clear dimples. These lms can beconsidered as being bulk NC systems as the grain size was around30 nm involving thus hundreds of grains over the thickness.

This mechanism of failure related to intergranular voids com-petes with a brittle mode of rupture, either inter- ortrans-granular. This cleavage type mechanism is triggered whenthe local stresses, set by the ow strength, exceeds the fracturestress, see e.g. [205]. Most investigations show that this brittle fail-ure mechanism is intergranular. We will come back in Section 5.3to these mechanisms, on the competition of failure modes as wellas on the issue of modelling damage.

Regarding now the resistance to crack initiation and propaga-3.2. Static damage and fracture in UFG and NC metallic systems

In the reviewbyKumar et al. [5], itwas stated that . . . the damagetolerance of these materials does not meet certainminimum acceptablelevels for particular application. Despite such need, very little publishedinformation is presently available on the damage tolerance characteris-tics of NC metals and alloys. This state of affairs is still true 10 yearslater. If a much better understanding of the resistance to plasticlocalization has been attained, as summarized in the former section,studies regarding the damage mechanisms controlling the fractureresistance, under various loading conditions, remain scarce for bulknanostructured materials. One of the main reasons is probably thatthe methods used for CG metals, based on classical polishingcross-sections of the deformed samples [200] or more modernX-ray microtomography [1,201,202], are not applicable to NC bulksamples due to the small nature of the damage. Another reason isthe limited size of the samples that can be processed in order to per-form conventional mechanical tests, such as on notched cylindricalspecimens. A lot of progress in the understanding has been madefrom testing thin metallic lms in situ and characterizing the dam-agemechanisms. Thiswill be covered in Section 5.3 but the questionof the transfer of these observations obtained on small scale systemsto bulk nanostructured metals, although qualitatively valid, mightnot be always direct.

3.2.1. Single phaseConsidering materials with no pre-crack and no marked pro-

cessing defects, one of the most convincing study of damage evolu-tion in bulk nanostructured metal is the one by Kumar et al. [38] onelectro-deposited Ni with grain size around 30 nm, which datesback to 2003, and was already summarized in Ref. [7]. The mainconclusion of this work was that the dimple size on the fracturesurface was signicantly larger that the grain size, in agreementwith other results [67,203]. The observed damage process isschematized in Fig. 9 (from [5]). Void nucleation occurs at GBand more preferentially at triple junction, but not necessarily alongall GBs. The selected triple junctions that give rise to voids are

14 A. Pineau et al. / Acta Mation from a pre-existing crack, ideally one would analyze it in thecontext of fracture mechanics. The fracture test methods are simi-lar to those used for CG bulk macroscopic samples. However, a

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dwide range of nanostructured materials produced by SPD,electro-deposition or mechanical alloying exhibit relatively smalldimensions. The small scale yielding assumption, which requiresthe plastic zone size to be a very small fraction of the crack length,is often not veried meaning that the concepts of non-linear frac-ture mechanics theory, such the J integral or the CTOD, d, must beused. Even with these non-linear concepts, the loss of constraintdue to the small dimension of the sample, [1], might be such thatthe extracted fracture toughness JIc or dc will be specimen-sizedependent, which is not sufciently realized in the literature.Furthermore, the plastic zone size can often be larger than thethickness. For instance, Mirshams et al. [208] measured onelectro-deposited 20 nm grain size NC Ni foils KIc = 120 and20 MPa

pm for 0.22 and 0.35 mm foils, respectively. These values

can hardly be compared to CG Ni (KIc = 60 MPapm) due to the

plane stress/plane strain conditions. The fracture toughnessdepends then on the thickness in a complex way with a regimeof toughness increasing with thickness due to crack tip neckingeffects [206,207], followed by a decrease towards the plane strainregime. Even at the same thickness, we claim that thefracture toughness of two different foil materials cannot necessar-ily be compared due to the change of regime between plane stressand plane strain occurring at different loads, as a function of thestrength of the foil (which affects the plastic zone extension).This issue of thickness dependence will come back in Section 5.3.

Now, there have been a few recent reports of fracture tests per-formed on the thickest possible SPD samples that can be made,from the group of Pippan, see review [209]. Specimens of Cu, Ni,Fe and pearlitic steels with a diameter of 30 mm and thicknessaround 7.5 mm have been processed by HPT [210212]. Theseauthors carefully looked at the validity of the measurements andworked with elasto-plastic fracture mechanics concepts. Theirmain conclusion is that, even though the failure mechanism isclearly ductile, the critical CTOD dc is always relatively small andthe higher yield strength does not compensate for attaining JIc val-ues typical of the CG corresponding materials [210]. Our opinion isthat the lower fracture toughness of UFGNC metals compared tobulk counterparts is not surprizing based on the basic rationalefor the mechanisms setting the resistance to ductile tearing, seee.g. [1,213,214]. Indeed, dimensional analysis shows that, see[215] for more details,

JIcr0X0

F r0E

;n; f 0;rnr0

;other microstructural features

4

where X0 is the mean void spacing, E is the Youngs modulus, f0 isthe initial void volume fraction (pre-existing voids added to thevoids nucleated during deformation), rn is an average critical stressfor void nucleation and F is a function that typically varies between1 and 10. The fracture toughness is thus directly proportional to the

distance X0 that separate cavities. Assuming that r0 KHP1=d

pand

that X0 scales proportional to d, then JIc should decrease propor-

tional tod

pif all other parameters are kept constant.

Furthermore, as explained in [1,215], the strain hardening exponentn has a large inuence on the function F with F signicantlydecreasing when n decreases, which is the rule in UFGNC metals.In addition, due to the large stress levels developing in UFGNCmetals, void nucleation ahead of the crack tip starts at smallerstrains. All these aspects go also in the direction of a lower JIc.Now, the assumption that X0 scales with grain size is based onthe idea that the nucleation sites are located at GBs (e.g. particlessitting on GBs or triple junctions) and that they are all activated.As explained above [38,67,203], the fact that X0 has been repeti-

alia xxx (2015) xxxxxxtively found to be signicantly larger than d, see Fig. 9, is favourablefor JIc, even though not yet fundamentally understood. It is often notsufciently realized that, if the nucleation results from second


teriaA. Pineau et al. / Acta Maphase particles, coarser particles are, at constant volume fraction ofnucleation sites, preferable because it allows for larger fracture pro-cess zones to develop (larger X0) hence larger energy spent per unitarea. Another point is that Eq. (4) applies to metals exhibiting rateindependent conventional plasticity. To what extent rate sensitivitycan impact the magnitude of F remains to be systematically inves-tigated. Finally, if the voids are in the submicron range, the voidgrowth rate can be much smaller than with micron sizes and thiscould also lead to an increase of F. We will come back to this nalquestion in Section 5.3.

In terms of mechanisms, atomistic simulations of crack propa-gation in Ni with 10 nm grain sizes [216,217] have also demon-strated that fracture is intergranular as a result of thecoalescence of voids nucleated along well oriented grain

Fig. 9. Schematic illustration of the damage evolution mechanisms in NC bulk metals bythat the void spacing has been observed to be signicantly larger than the grain size, re

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dlia xxx (2015) xxxxxx 15boundaries, in agreement with the mechanisms discussed forun-cracked specimens. MD simulations by Xu and Demkowicz[218] have recently demonstrated that migrating GBs tend, onaverage, to heal nano-cracks by decreasing the local stress inten-sity factor, hence providing an interesting toughening mechanismthat remains to be demonstrated experimentally. The competitionbetween a brittle and ductile mode of cracking has been addressedin a series of theoretical analyses by Ovidko and Sheinerman, e.g.[219,220].

3.2.2. Multiphase/hybrids/nanotwinned bulk metalsThe effect of twin density on the crack initiation fracture tough-

ness of NT Cu has been investigated by Qin et al. [221] and by Singh

void nucleation at GBs and triple junctions and subsequent void growth, indicatingproduced from [5].


teriet al. [222]. The fracture toughness values determined on 40 lmthick specimens were found to be larger in high density NT Cu(17.2 MPa m1/2) than in lower density NT Cu (14.8 MPa m1/2).However, these results obtained on thin specimens which do notsatisfy the plane strain conditions cannot be considered as trueindicators of an intrinsic fracture toughness.

The benecial effect of dual-phase microstructures (here:matrix + twins) on the ductility and fracture toughness seems tobe a general property. This has been illustrated by some recentwork on Zr [223]. An excellent combination of yield strength(600 MPa) and fracture toughness (120 MPa m1/2) was obtainedon thin (0.5 mm) cryo-rolled (e 2.87) sheets of Zr which weresubsequently annealed at 450 C for 1 h. This thermo-mechanicalheat-treatment produced a nanostructure composed of 22%nano-scale sub-grains and grains (1 lm) embedded in a nano-scale and UFGmatrix. The fracture surface of the tested specimens was coveredwith ductile dimples with a size much larger than the size of thenanograins, as already observed in single phase materials. The for-mation of these deep dimples requires large deformations whichcontribute to the increase of the dissipated energy at fracture.

Nanostructures have been recently produced from realmulti-phase materials, such as bainitic steels by Haddad et al.[224]. These authors modied from ferritic-pearlitic to an UFG bai-nitic the initial microstructure of a 0.45% C steel using HPT (5 rota-tions under 6 GPa pressure) at 350 C. A unique NC microstructureconsisting of equiaxed and elongated ferrite grains with a meansize < 150 nm was generated. In situ tensile tests in a SEM showedvery high tensile strength of the order of 2100 MPa with a totalelongation of 4.5%. These characteristics are comparable to thoseobtained on high strength, high alloyed steels [225]. The failureconsists in the initiation of small localization bands at the edgesof the specimens before any observable diffuse necking. Thesesmall localization bands give rise to micro-cracks that propagatefrom the edges through the entire specimen. The mechanism isfully ductile with submicron dimples involving two classes of sizes.

UFG DP steels consisting of austenite (fcc) along martensite(bcc) laths is one of the best illustration of the interest of nanos-tructures. The thin lms of the fcc phase have two benecialeffects: (i) they can act as cleavage crack arrestors when the mate-rial is tested at sufciently low temperature below the DBTT, (ii)they strongly modify the conditions of slip transfer at the interface.Recent studies by Mine [124] and Maresca and Geers [28] havestarted to throw some light on the relative role of each effect.

It can be added that the ballistic fracture performances of NCand NT stainless steels have also been studied using gas gun ringof projectiles on 2 mm thick sheets [226]. The comparison with CGcounterparts shows lower energy absorption and lower ballisticlimit related to a shear plugging mechanism. Cu/Nb has also beenstudied under ballistic conditions [227] showing a ductile damagemechanism by void nucleation and growth in the middle of the Culayers and not by interface decohesion. Nevertheless, at low defor-mation rates the few studies reporting fracture data on Cu/Nbshow only limited ductility around 3% due to the limited strainhardening capacity [228]. In [22], ductility near 10% was attainedfor samples rolled multiple times and with a low fraction of Nb.The ductility of Cu/Ni/Nb trilayer based systems [133] is expectedto be higher owing to the increased strain hardening capacity asmentioned in Section 2.

The graded NC material [24] already mentioned in Section 3.1for its extremely good capacity to delay necking, also exhibitsremarkable post necking elongation with fracture strains over100%. Quite surprisingly, damage nucleates rst in the highly

16 A. Pineau et al. / Acta Madeformed CG areas. A bimodal grain distribution is also effectivein retarding damage propagation with coarse grains playing therole of ductile patches that can bridge the cracks originating from

Please cite this article in press as: A. Pineau et al., Acta Mater. (2015), http://dthe more brittle nanostructured areas [32]. This proves that a duc-tile core interacting with hard NC regions, either in terms ofgradient or bimodal structures leads to synergetic effects on thedamage and crack shielding. Other sorts of synergetic effects thatcan retard cracking or make it non-percolating will be addressedin Section 4.

3.3. Fatigue in NC and UFG metallic systems

The cyclic behavior of NC and UFG metals is examined in a rstsub-section before considering the fatigue life. Since NC metals areusually not available as readily in bulk form suitable for conven-tional fatigue tests as the UFGmaterials, most of the studies to datehave been performed on UFG materials prepared by various SPDmethods (see Section 2.1). UFG Cu and Ni have been investigatedin more detail than other metals. Some of the results obtained sofar apply also to NC materials.

3.3.1. Cyclic behavior of NC and UFG metalsThe cyclic deformation and fatigue properties of UFG metals

and alloys have been reviewed in some detail by Mughrabi [229],Mughrabi and Hppel [230] and more recently by Hppel andGken [231], Kunz [232], and Padilla and Boyce [233], see also[234236]. From these reviews, it arises that the cyclic and fatiguebehavior strongly depend on parameters of the SPD procedure, onthe purity of the material and on the type of fatigue loading. This isthe reason why special care must be taken when comparing resultsfrom various sources. All these studies have shown that UFG mate-rials exhibit, as already mentioned in Section 2.2, signicantBauschinger effect as compared to conventional polycrystals, seee.g. Fig. 10a and b for Cu taken from [237] and from [238]. ABauschinger parameter bE can be dened as

bE 2rpDep

HrdeH

rde5

where rp is the maximum tensile stress in the loop of width Dep. InFig. 10a, two tests were run on as prepared material (1 and 2). TheBauschinger effect is much larger in specimens 1 and 2 when com-pared to two other specimens annealed at 473 K (3) and 773 K (4).This behavior is also observed in NT Cu, see Fig. 10b. TheBauschinger effect is due to the presence of intense internal stresseswhich are directly related to the microstructure. A simple calcula-tion by Mughrabi and Hppel [230] showed that the stabilized dis-location cell size in polycrystalline metals at the stress saturationstage (or at mid-life) was larger than the grain size of UFG metals.The dislocations thus move inside the small grains without theformation of cells, as illustrated in Fig. 11 [239], and GBs directlyparticipate to the mechanical response of these UFG materials. Astrong grain size effect on the cyclic behavior is observed contrarilyto CG counterparts where the cyclic behavior is almost independentof grain size: the cyclic stress response of UFG metals exhibits agrain-size dependence of a form similar to the HallPetch relation-ship, as found for instance in Ni by Mughrabi [229].

UFG metals exhibit more or less severe cyclic softening in par-ticular when tested under strain controlled conditions, corre-sponding to the low cycle fatigue (LCF) regime, see Fig 12 for thedenitions of the two regimes and the relative position of CGand UFG metals, whereas there is almost no cyclic softening instress controlled tests corresponding to HCF conditions for whichthe plastic deformation is extremely small.

Evidences showing that SPD metals are intrinsically unstableupon cyclic conditions do exist. This instability associated with a

alia xxx (2015) xxxxxxmore or less pronounced softening effect may also be related tothe formation of macroscopic shear bands extending over dis-tances much larger than the grain size. Since UFG materials


Fig. 10. (a) UFG copper in the as-prepared and after heat treatment; (i) hysteresis loops in the stabilized stage (cumulative plastic strain = 500%); (ii) Bauschinger energyparameter as a function of cumulative plastic strain [237]; (b) UFG nano-twinned copper; (i) Hysteresis loops under strain-controlled pullpush conditions with Dep/2 = 1.78 103; (ii) Changes of steady-state hysteresis loops of NT-Cu fatigued at different constant plastic strain amplitudes [238].

Fig. 11. TEMmicrographs of dislocation microstructure in fatigued nickel specimens of different grain sizes; (a) Dislocation substructure inside the grains of a specimen withlarger grain size; (b) Lack of fatigue-induced dislocation structure inside the grains in specimen with very small grains. Original micrographs by Klemm [239], after Mughrabi[229].

A. Pineau et al. / Acta Materialia xxx (2015) xxxxxx 17

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3.3.2. Fatigue life of some NC and UFG metals

Fig. 12. Illustration of fatigue lives of strong UFG and more ductile and sof

18 A. Pineau et al. / Acta MateriThe fatigue life of UFG metals is generally much larger than thatin CG counterparts when aWhler representation is terms of stressis adopted (see e.g. Fig. 13 for Ti [236]). The opposite is oftenobserved in the LCF regime as schematically represented inFig. 12. This conclusion applies to various materials including NCCu which has been investigated in particular by the Brno group,see [232]. The fatigue response of electro-deposited NC Ni andcryo-milled UFG AlMg alloy has been studied by Hanlon et al.[241,242]. The stress life fatigue behavior and fatigue crack growthcharacteristics of pure Ni were studied as a function of grain size,spanning a wide range from tens of nm to tens of lm. It was foundthat grain renement in the true NC regime generally leads to aproduced by SPD are heavily pre-deformed, the occurrence ofmicrostructural instabilities which lead to grain coarsening andshear banding is not too surprising. Fatigue cracks are initiatedfrom these shear bands (see e.g. [112]). In the case of UFG copper,it should be noted that grain coarsening was observed at roomtemperature (RT), i.e. at a homologous temperature as low as 0.2Tm (where Tm is the melting temperature) after mild cyclicstrain-controlled deformation conditions (2 104 < Dep/2

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