Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect

A material strength depends on its microstructure, which in turn, is controlled by an engineering process. Strengthening mechanisms like work hardening, precipitate, and grain boundary strengthening can alter the strength of a material in a predictive, quantitative manner and are readily linked to the deformation mechanism. This quantification strongly depends on the characteristic length scale of a particular microstructure, thereby dictating bulk material’s strength as a function of, for example, grain or precipitate size, twin boundary spacing, or dislocation density. This microstructural, or intrinsic, size governs the mechanical properties and post-elastic material deformation at all sample dimensions, as the classical definition of “ultimate tensile strength” deems it to be “an intensive property, therefore its value does not depend on the size of the test specimen.” Yet in the last 5 years, the vast majority of uniaxial deformation experiments and computations on small-scale metallic structures unambiguously demonstrated that at the micron and sub-micron scales, this definition no longer holds true. In fact, it has been shown that in single crystals the ultimate tensile strength and the yield strength scale with external sample size in a power law fashion, sometimes attaining a significant fraction of material’s theoretical strength, and exhibiting the now-commonly-known phenomenon “smaller is stronger.” Understanding of this “extrinsic size effect” at small scales is not yet mature and is currently a topic of rigorous investigations. As both the intrinsic (i.e. microstructural) and extrinsic (i.e. sample size) dimensions play a non-trivial role in the mechanical properties and material deformation mechanisms, it is critical to develop an understanding of their interplay and mutual effects on the mechanical properties and material deformation, especially in small-scale structures. This review focuses on providing an overview of metal-based material classes whose properties as a function of external size have been investigated and provides a critical discussion on the combined effects of intrinsic and extrinsic sizes on the material deformation behavior.

[1]  C. Schuh,et al.  Superelasticity and Shape Memory in Micro‐ and Nanometer‐scale Pillars , 2008 .

[2]  G. Dehm,et al.  On the importance of sample compliance in uniaxial microtesting , 2009 .

[3]  P. Yan,et al.  Tensile ductility and necking of metallic glass. , 2007, Nature materials.

[4]  C. Thompson.  The yield stress of polycrystalline thin films , 1993 .

[5]  Christopher A. Schuh,et al.  Strength, plasticity and brittleness of bulk metallic glasses under compression: statistical and geometric effects , 2008 .

[6]  N. Thadhani,et al.  Mechanical properties of bulk metallic glasses , 2010 .

[7]  Julia R. Greer,et al.  Size effects in strength and plasticity of single-crystalline titanium micropillars with prismatic slip orientation , 2011 .

[8]  C. Motz,et al.  Micro-compression testing: A critical discussion of experimental constraints , 2009 .

[9]  K. Samwer,et al.  Length scale effects on relaxations in metallic glasses , 2010 .

[10]  H. V. Swygenhoven,et al.  Atomic mechanism for dislocation emission from nanosized grain boundaries , 2002 .

[11]  Ting Zhu,et al.  Temperature and strain-rate dependence of surface dislocation nucleation. , 2008, Physical review letters.

[12]  S. Zapperi,et al.  Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale , 2007, Science.

[13]  W. Johnson,et al.  A universal criterion for plastic yielding of metallic glasses with a (T/Tg) 2/3 temperature dependence. , 2005, Physical review letters.

[14]  G. Pharr,et al.  Small-scale mechanical behavior of intermetallics and their composites , 2008 .

[15]  C. Schuh,et al.  Nanoscale shape-memory alloys for ultrahigh mechanical damping. , 2009, Nature nanotechnology.

[16]  Chung,et al.  Fracture of disordered three-dimensional spring networks: A computer simulation methodology. , 1996, Physical review. B, Condensed matter.

[17]  A. Kunz,et al.  Size effects in Al nanopillars: Single crystalline vs. bicrystalline , 2011 .

[18]  A. Minor,et al.  Direct observation of the NiTi martensitic phase transformation in nanoscale volumes , 2010 .

[19]  E. Arzt,et al.  Loss of pseudoelasticity in nickel-titanium sub-micron compression pillars , 2007 .

[20]  Blythe G. Clark,et al.  On the plasticity of small-scale nickel–titanium shape memory alloys , 2010 .

[21]  T. Nieh,et al.  Sample size effect and microcompression of Mg65Cu25Gd10 metallic glass , 2007 .

[22]  D. Dimiduk,et al.  Dislocation structures and their relationship to strength in deformed nickel microcrystals , 2008 .

[23]  A. Minor,et al.  In situ TEM compression testing of Mg and Mg–0.2 wt.% Ce single crystals , 2011 .

[24]  A. Ngan,et al.  Effects of trapping dislocations within small crystals on their deformation behavior , 2009 .

[25]  K. T. Ramesh,et al.  Size-independent strength and deformation mode in compression of a Pd-based metallic glass , 2008 .

[26]  M. Demetriou,et al.  Anelastic to plastic transition in metallic glass-forming liquids. , 2007, Physical review letters.

[27]  Julia R. Greer,et al.  Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale , 2010 .

[28]  L. Battezzati,et al.  Mechanical properties of Al based amorphous and devitrified alloys containing different rare earth elements , 2004 .

[29]  O. Kraft,et al.  Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition. , 2009, Nano letters.

[30]  T. Nieh,et al.  Homogeneous deformation of Au-based metallic glass micropillars in compression at elevated temperatures , 2009 .

[31]  D. Gianola,et al.  In situ TEM observations of fast grain-boundary motion in stressed nanocrystalline aluminum films , 2008 .

[32]  Yoshihisa Watanabe,et al.  Scanning tunneling microscope observations of metallic glass fracture surfaces , 1993 .

[33]  D. Dimiduk,et al.  Estimating the strength of single-ended dislocation sources in micron-sized single crystals , 2007 .

[34]  F. Pinkerton,et al.  Deformation-induced nanocrystallization in an Al-based amorphous alloy at a subambient temperature , 2003 .

[35]  Xuemei Cheng,et al.  Stress‐Driven Surface Topography Evolution in Nanocrystalline Al Thin Films , 2008 .

[36]  W. W. Milligan,et al.  Observation and measurement of grain rotation and plastic strain in nanostructured metal thin films , 1995 .

[37]  J. R. Patel,et al.  A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction , 2008 .

[38]  S. Phillpot,et al.  Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation , 2002 .

[39]  J. Molinari,et al.  Increased strain rate sensitivity due to stress-coupled grain growth in nanocrystalline Al , 2006 .

[40]  Dong Wang,et al.  Bulk metallic glass formation in the binary Cu–Zr system , 2004 .

[41]  Meijie Tang,et al.  Athermal mechanisms of size-dependent crystal flow gleaned from three-dimensional discrete dislocation simulations , 2008 .

[42]  Duxbury,et al.  Fracture of heterogeneous materials with continuous distributions of local breaking strengths. , 1994, Physical review. B, Condensed matter.

[43]  Wei Zhang,et al.  Shear delocalization and crack blunting of a metallic glass containing nanoparticles: In situ deformation in TEM analysis , 2006 .

[44]  D. Dimiduk,et al.  Sample Dimensions Influence Strength and Crystal Plasticity , 2004, Science.

[45]  D. Gianola,et al.  Grain-size stabilization by impurities and effect on stress-coupled grain growth in nanocrystalline Al thin films , 2008 .

[46]  Amit Misra,et al.  Deformability of ultrahigh strength 5 nm Cu/Nb nanolayered composites , 2008 .

[47]  J. Dora,et al.  NUCLEATION OF KINK PAIRS AND THE PEIERLS' MECHANISM OF PLASTIC DEFORMATION , 1963 .

[48]  A. Inoue.  Stabilization of metallic supercooled liquid and bulk amorphous alloys , 2000 .

[49]  D. Dimiduk,et al.  Scale-Free Intermittent Flow in Crystal Plasticity , 2006, Science.

[50]  En Ma,et al.  Controlling plastic instability , 2003, Nature materials.

[51]  S S Brenner,et al.  Growth and Properties of "Whiskers": Further research is needed to show why crystal filaments are many times as strong as large crystals. , 1958, Science.

[52]  J. D. De Hosson,et al.  Strength of submicrometer diameter pillars of metallic glasses investigated with in situ transmission electron microscopy , 2009 .

[53]  Marc Legros,et al.  Stress-assisted discontinuous grain growth and its effect on the deformation behavior of nanocrystalline aluminum thin films , 2006 .

[54]  J. Hosson,et al.  Effects of network morphology on the failure stress of highly porous media , 2002 .

[55]  J. Langer,et al.  Dynamics of viscoplastic deformation in amorphous solids , 1997, cond-mat/9712114.

[56]  A. Ngan,et al.  Breakdown of Schmid’s law in micropillars , 2008 .

[57]  M. Telford.  The case for bulk metallic glass , 2004 .

[58]  K. Gall,et al.  The influence of aging on critical transformation stress levels and martensite start temperatures , 1999 .

[59]  M. Denda,et al.  Dynamic evolution of nanoscale shear bands in a bulk-metallic glass , 2005 .

[60]  Julia R Greer,et al.  Fabrication and microstructure control of nanoscale mechanical testing specimens via electron beam lithography and electroplating. , 2010, Nano letters.

[61]  Peter Gumbsch,et al.  Dislocation sources and the flow stress of polycrystalline thin metal films , 2003 .

[62]  Michael D. Uchic,et al.  Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples , 2007 .

[63]  A. Hamza,et al.  Ductile crystalline–amorphous nanolaminates , 2007, Proceedings of the National Academy of Sciences.

[64]  K. Han,et al.  Deformation and evolution of shear bands under compressive loading in bulk metallic glasses , 2006 .

[65]  Jin Gao,et al.  Size effects on the compressive deformation behaviour of a brittle Fe-based bulk metallic glass , 2010 .

[66]  J. Eckert,et al.  Mechanical properties of bulk metallic glasses and composites , 2007 .

[67]  Antonio Rinaldi,et al.  Sample-size effects in the yield behavior of nanocrystalline nickel , 2008 .

[68]  K. Dahmen,et al.  Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. , 2009, Physical review letters.

[69]  Michael D. Uchic,et al.  Size-affected single-slip behavior of pure nickel microcrystals , 2005 .

[70]  S. Lee,et al.  Compression testing of metallic glass at small length scales: Effects on deformation mode and stability , 2010 .

[71]  Jian Xu,et al.  Critical size and strength of the best bulk metallic glass former in the Mg-Cu-Gd ternary system , 2007 .

[72]  J. Greer,et al.  Size-induced weakening and grain boundary-assisted deformation in 60 nm grained Ni nanopillars , 2011 .

[73]  Jing Li,et al.  Controlling shear band behavior in metallic glasses through microstructural design , 2002 .

[74]  Global melting of Zr57Ti5Ni8Cu20Al10 bulk metallic glass under microcompression , 2007 .

[75]  Gang Wang,et al.  Super Plastic Bulk Metallic Glasses at Room Temperature , 2007, Science.

[76]  J. Hosson,et al.  Effects of solute Mg on grain boundary and dislocation dynamics during nanoindentation of Al–Mg thin films , 2004 .

[77]  Julia R. Greer,et al.  Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale , 2009 .

[78]  J. Monk,et al.  Strain-driven grain boundary motion in nanocrystalline materials , 2008 .

[79]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[80]  C. Volkert,et al.  Effect of sample size on deformation in amorphous metals , 2008 .

[81]  Julia R. Greer,et al.  Effects of size on the strength and deformation mechanism in Zr-based metallic glasses , 2011 .

[82]  J. Lewandowski,et al.  Compressive plasticity and toughness of a Ti-based bulk metallic glass , 2010 .

[83]  Christopher A. Schuh,et al.  The Hall–Petch breakdown in nanocrystalline metals: A crossover to glass-like deformation , 2007 .

[84]  J. Rault,et al.  Origin of the Vogel-Fulcher-Tammann law in glass-forming materials : the α-β bifurcation , 2000 .

[85]  J. Hosson,et al.  Advances in Transmission Electron Microscopy: In Situ Straining and In Situ Compression Experiments on Metallic Glasses , 2009 .

[86]  Blythe G. Clark,et al.  Size Independent Shape Memory Behavior of Nickel–Titanium , 2010 .

[87]  S. S. Brenner,et al.  Tensile Strength of Whiskers , 1956 .

[88]  Bernd Schmitt,et al.  A new criterion for elasto-plastic transition in nanomaterials: Application to size and composite effects on Cu–Nb nanocomposite wires , 2009 .

[89]  Shouheng Sun,et al.  Cold welding of ultrathin gold nanowires. , 2010, Nature nanotechnology.

[90]  A. Benzerga.  An analysis of exhaustion hardening in micron-scale plasticity , 2008 .

[91]  A. Minor,et al.  Plastic flow and failure resistance of metallic glass: Insight from in situ compression of nanopillars , 2008 .

[92]  D. Miracle,et al.  Effect of the atomic size distribution on glass forming ability of amorphous metallic alloys , 2001 .

[93]  Christopher A. Schuh,et al.  Size effects in shape memory alloy microwires , 2011 .

[94]  J. Hosson,et al.  Tribological and mechanical properties of high power laser surface-treated metallic glasses , 2007 .

[95]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[96]  G. Dehm.  Miniaturized single-crystalline fcc metals deformed in tension: New insights in size-dependent plasticity , 2009 .

[97]  J. Greer,et al.  Nanolaminates Utilizing Size‐Dependent Homogeneous Plasticity of Metallic Glasses , 2011 .

[98]  N. Petch,et al.  The Cleavage Strength of Polycrystals , 1953 .

[99]  E. Arzt,et al.  Correlation between critical temperature and strength of small-scale bcc pillars. , 2009, Physical review letters.

[100]  A microscopic approach to the statistical fracture analysis of disordered brittle solids , 1985 .

[101]  R. Raghavan,et al.  Micropillar compression studies on a bulk metallic glass in different structural states , 2009 .

[102]  P. Bronsveld,et al.  An electron microscopy appraisal of tensile fracture in metallic glasses , 2008 .

[103]  Y. Hou,et al.  Dual specimen-size dependences of plastic deformation behavior of a traditional Zr-based bulk metallic glass in compression , 2009 .

[104]  G. Pharr,et al.  Effects of focused ion beam milling on the nanomechanical behavior of a molybdenum-alloy single crystal , 2007 .

[105]  Douglas C. Hofmann,et al.  Designing metallic glass matrix composites with high toughness and tensile ductility , 2008, Nature.

[106]  M. Véron,et al.  High-strength materials: in-situ investigations of dislocation behaviour in Cu-Nb multifilamentary nanostructured composites , 2002 .

[107]  Julia R. Greer,et al.  Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale , 2009 .

[108]  A. Argon,et al.  Development of visco-plastic deformation in metallic glasses , 1983 .

[109]  A. Minor,et al.  A new view of the onset of plasticity during the nanoindentation of aluminium , 2006, Nature materials.

[110]  J. Greer,et al.  Fundamental differences in mechanical behavior between two types of crystals at the nanoscale. , 2008, Physical review letters.

[111]  W. Wang,et al.  Prevalence of shear banding in compression of Zr41Ti14Cu12.5Ni10Be22.5 pillars as small as 150 nm in diameter , 2009 .

[112]  A. Ngan,et al.  Transition from deterministic to stochastic deformation , 2010 .

[113]  Peter M. Derlet,et al.  Grain-boundary sliding in nanocrystalline fcc metals , 2001 .

[114]  Ahmed S. M. Agena.  A study of flow characteristics of nanostructured Al-6082 alloy produced by ECAP under upsetting test , 2009 .

[115]  P. Liaw,et al.  Extraction of bulk metallic-glass yield strengths using tapered micropillars in micro-compression experiments , 2010 .

[116]  S. Whang,et al.  The creep and fracture in nanostructured metals and alloys , 2005 .

[117]  W. Johnson,et al.  Effect of Oxygen Impurity on Crystallization of an Undercooled Bulk Glass Forming Zr–Ti–Cu–Ni–Al Alloy , 1997 .

[118]  C. Schuh,et al.  Atomistic basis for the plastic yield criterion of metallic glass , 2003, Nature materials.

[119]  R. Mccabe,et al.  A micro-compression study of shape-memory deformation in U-13 at.% Nb , 2009 .

[120]  J. Greer,et al.  Nanoscale gold pillars strengthened through dislocation starvation , 2006 .

[121]  M. Gao,et al.  Deformation-Induced Nanocrystal Precipitation in Al-Base Metallic Glasses , 2001 .

[122]  Wei Zhang,et al.  Unusual room temperature ductility of glassy copper-zirconium caused by nanoparticle dispersions that grow during shear , 2007 .

[123]  Robert Danzer,et al.  Fracture statistics of ceramics – Weibull statistics and deviations from Weibull statistics , 2007 .

[124]  F. Spaepen,et al.  Suppression of the shear band instability during plastic flow of nanometer-scale confined metallic glasses , 2007 .

[125]  van der Erik Giessen,et al.  Scaling of the failure stress of homophase and heterophase three-dimensional spring networks , 2002 .

[126]  P. Duwez,et al.  Non-crystalline Structure in Solidified Gold–Silicon Alloys , 1960, Nature.

[127]  Y. Pei,et al.  Effects of size on the mechanical response of metallic glasses investigated through in situ TEM bending and compression experiments , 2010 .

[128]  C. Koch,et al.  The Inverse Hall-Petch Effect—Fact or Artifact? , 2000 .

[129]  Ludwig Schultz,et al.  Novel Ti-base nanostructure–dendrite composite with enhanced plasticity , 2003, Nature materials.

[130]  Duxbury,et al.  Failure probability and average strength of disordered systems. , 1994, Physical review letters.

[131]  C. M. Wayman,et al.  Shape-Memory Materials , 2018 .

[132]  Jun Sun,et al.  Strong crystal size effect on deformation twinning , 2010, Nature.

[133]  Christopher A. Schuh,et al.  Initiation of shear bands near a stress concentration in metallic glass , 2007 .

[134]  Bairu Li,et al.  Deformation-induced grain rotation and growth in nanocrystalline Ni , 2008 .

[135]  J. Lewandowski,et al.  Local temperature rises during mechanical testing of metallic glasses , 2007 .

[136]  Andrew M. Minor,et al.  Nanomechanical Testing of Gum Metal , 2010 .

[137]  Blythe G. Clark,et al.  Effect of orientation and loading rate on compression behavior of small-scale Mo pillars , 2009 .

[138]  C. A. Volkert,et al.  Size effects in the deformation of sub-micron Au columns , 2006 .

[139]  W. Johnson,et al.  Unusual glass-forming ability of bulk amorphous alloys based on ordinary metal copper. , 2004, Physical review letters.

[140]  D. Kim,et al.  The effect of Sn addition on the glass-forming ability of Cu–Ti–Zr–Ni–Si metallic glass alloys , 2002 .

[141]  Parmanand Sharma,et al.  Nanoscale patterning of Zr-Al-Cu-Ni metallic glass thin films deposited by magnetron sputtering. , 2005, Journal of nanoscience and nanotechnology.

[142]  S. Han,et al.  Size effects on strength and plasticity of vanadium nanopillars , 2010 .

[143]  D. Dimiduk,et al.  Effects of Focused Ion Beam Induced Damage on the Plasticity of Micropillars , 2009 .

[144]  E. Gumbel.  The return period of order statistics , 1961 .

[145]  F. Spaepen.  Metallic glasses: Must shear bands be hot? , 2006 .

[146]  B. Derby,et al.  A universal scaling law for the strength of metal micropillars and nanowires , 2009 .

[147]  A. Sergueeva,et al.  Shear band formation and ductility of metallic glasses , 2004 .

[148]  S. Xie,et al.  Size-dependent plasticity and fracture of a metallic glass in compression , 2008 .

[149]  A. Misra,et al.  Structural metals at extremes , 2010 .

[150]  E. Ma.  Watching the Nanograins Roll , 2004, Science.

[151]  V. Vitek,et al.  Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈1 1 1〉 screw dislocations at 0 K , 2008 .

[152]  G. Pharr,et al.  Effects of pre-strain on the compressive stress-strain response of Mo-alloy single-crystal micropillars , 2008 .

[153]  Hays,et al.  Microstructure controlled shear band pattern formation and enhanced plasticity of bulk metallic glasses containing in situ formed ductile phase dendrite dispersions , 2000, Physical review letters.

[154]  D. Dimiduk,et al.  Plasticity of Micrometer-Scale Single-Crystals in Compression: A Critical Review (PREPRINT) , 2008 .

[155]  M. Yan,et al.  The relations between ΔTx and the glass forming ability of bulk amorphous Zr–Cu–Ni–Al–Hf–Ti and Zr52.5Cu17.9Ni14.6Al10Ti5 alloys , 2004 .

[156]  Jaafar A. El-Awady,et al.  The role of the weakest-link mechanism in controlling the plasticity of micropillars , 2009 .

[157]  J. Greer,et al.  Influence of homogeneous interfaces on the strength of 500 nm diameter Cu nanopillars. , 2011, Nano letters.

[158]  E. Hall,et al.  The Deformation and Ageing of Mild Steel: III Discussion of Results , 1951 .

[159]  K. T. Ramesh,et al.  Microcompression of single-crystal magnesium , 2010 .

[160]  William D. Nix,et al.  The Role of Indentation Depth on the Measured Hardness of Materials , 1993 .

[161]  Weihua Wang,et al.  Bulk metallic glasses , 2004 .

[162]  Steven Nutt,et al.  Compression behavior of micro-scale truss structures formed from self-propagating polymer waveguides , 2007 .

[163]  J. Greer,et al.  Plastic deformation of indium nanostructures , 2011 .

[164]  P. Anderson,et al.  Transformation-induced plasticity during pseudoelastic deformation in Ni–Ti microcrystals , 2009 .

[165]  T. Nieh,et al.  Effect of strain rate on compressive behavior of a Pd40Ni40P20 bulk metallic glass , 2002 .

[166]  J. Eckert,et al.  Difference in compressive and tensile fracture mechanisms of Zr59CU20Al10Ni8Ti3 bulk metallic glass , 2003 .

[167]  W. Johnson,et al.  New features of the low temperature ductile shear failure observed in bulk amorphous alloys , 2000 .

[168]  Blythe G. Clark,et al.  Orientation-independent pseudoelasticity in small-scale NiTi compression pillars , 2008 .

[169]  A. Shpak,et al.  Inherent strength of zirconium-based bulk metallic glass , 2010 .

[170]  A. Argon,et al.  Strengthening Mechanisms in Crystal Plasticity , 2007 .

[171]  A. Minor,et al.  Incipient plasticity in metallic thin films , 2007 .

[172]  Jian Xu,et al.  Reliability of compressive fracture strength of Mg–Zn–Ca bulk metallic glasses: Flaw sensitivity and Weibull statistics , 2008 .

[173]  F. Nabarro,et al.  Dislocations in solids , 1979 .

[174]  Ken Gall,et al.  Compressive response of NiTi single crystals , 2000, Acta Materialia.

[175]  V. Vítek,et al.  Explanation of the discrepancy between the measured and atomistically calculated yield stresses in body-centred cubic metals , 2006, cond-mat/0605449.

[176]  C. Motz,et al.  Quantitative In Situ Mechanical Testing in Electron Microscopes , 2010 .

[177]  Robert J. Asaro,et al.  Toward a quantitative understanding of mechanical behavior of nanocrystalline metals , 2007 .

[178]  A. Inoue,et al.  Zr–Al–Ni Amorphous Alloys with High Glass Transition Temperature and Significant Supercooled Liquid Region , 1990 .

[179]  G. Pharr,et al.  Compressive strengths of molybdenum alloy micro-pillars prepared using a new technique , 2007 .

[180]  F. Stillinger,et al.  A Topographic View of Supercooled Liquids and Glass Formation , 1995, Science.

[181]  Amit Misra,et al.  Mechanism for shear banding in nanolayered composites , 2010 .

[182]  Reinhard Pippan,et al.  A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples , 2008 .

[183]  M. Meyers,et al.  Mechanical properties of nanocrystalline materials , 2006 .

[184]  M. Jenko,et al.  FIB damage of Cu and possible consequences for miniaturized mechanical tests , 2007 .

[185]  E. Lilleodden.  Microcompression study of Mg (0 0 0 1) single crystal , 2010 .

[186]  F. Wu,et al.  Size-dependent shear fracture and global tensile plasticity of metallic glasses , 2009 .

[187]  Blythe G. Clark,et al.  Size effect on strength and strain hardening of small-scale [111] nickel compression pillars , 2008 .

[188]  H. Espinosa,et al.  Dislocation-source shutdown and the plastic behavior of single-crystal micropillars. , 2008, Physical review letters.

[189]  K. T. Ramesh,et al.  Bulk and microscale compressive properties of a Pd-based metallic glass , 2007 .

[190]  Simon R. Phillpot,et al.  Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation , 2002, Nature materials.

[191]  O. Kraft,et al.  Plasticity in Confined Dimensions , 2010 .

[192]  Andrew M Minor,et al.  Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. , 2008, Nature materials.

[193]  G. Dehm,et al.  In situ observation of dislocation nucleation and escape in a submicrometre aluminium single crystal. , 2009, Nature materials.

[194]  A. L. Greer,et al.  Thickness of shear bands in metallic glasses , 2006 .

[195]  S. Han,et al.  Uniaxial compression of fcc Au nanopillars on an MgO substrate: The effects of prestraining and annealing , 2009 .

[196]  Huajian Gao,et al.  Materials become insensitive to flaws at nanoscale: Lessons from nature , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[197]  W. Johnson,et al.  Deformation behavior of the Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass over a wide range of strain-rates and temperatures , 2003 .

[198]  Christopher R. Weinberger,et al.  Surface-controlled dislocation multiplication in metal micropillars , 2008, Proceedings of the National Academy of Sciences.

[199]  Julia R. Greer,et al.  Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: Compression experiments and dislocation dynamics simulations , 2008 .

[200]  Ju Li,et al.  The Mechanics and Physics of Defect Nucleation , 2007 .

[201]  M. Kunz,et al.  Fabrication, structure and mechanical properties of indium nanopillars , 2010 .

[202]  T. Nieh,et al.  Strength variation and cast defect distribution in metallic glasses , 2010 .

[203]  V. Vítek,et al.  Intrinsic stacking faults in body-centred cubic crystals , 1968 .

[204]  A. Minor,et al.  Achieving the ideal strength in annealed molybdenum nanopillars , 2010 .

[205]  Ronald O. Scattergood,et al.  Ultrahigh strength and high ductility of bulk nanocrystalline copper , 2005 .

[206]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[207]  Amit Misra,et al.  Tensile behavior of 40 nm Cu/Nb nanoscale multilayers , 2008 .

[208]  H. V. Swygenhoven,et al.  Crystal rotation in Cu single crystal micropillars: In situ Laue and electron backscatter diffraction , 2008 .

[209]  Steven Nutt,et al.  Micro‐scale Truss Structures formed from Self‐Propagating Photopolymer Waveguides , 2007 .

[210]  J. Hosson,et al.  In situ TEM nanoindentation and dislocation-grain boundary interactions: a tribute to David Brandon , 2006 .

[211]  Frans Spaepen,et al.  A microscopic mechanism for steady state inhomogeneous flow in metallic glasses , 1977 .

[212]  D. Gall,et al.  High‐Temperature Tribological Behavior of CrN‐Ag Self‐lubricating Coatings , 2006 .

[213]  M. Demetriou,et al.  Cooperative shear model for the rheology of glass-forming metallic liquids. , 2006, Physical review letters.

[214]  Julia R. Greer,et al.  Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients , 2005 .

[215]  A. Ngan,et al.  Stochastic theory for jerky deformation in small crystal volumes with pre-existing dislocations , 2008 .

[216]  C. P. Frick,et al.  Strain bursts in plastically deforming molybdenum micro- and nanopillars , 2008, 0802.1843.

[217]  J. Sethna,et al.  Crackling noise , 2001, Nature.

[218]  Julia R Greer,et al.  Transition from a strong-yet-brittle to a stronger-and-ductile state by size reduction of metallic glasses. , 2010, Nature materials.

[219]  J. C. Huang,et al.  Bulk and microscale compressive behavior of a Zr-based metallic glass , 2008 .

[220]  A. Argon.  Plastic deformation in metallic glasses , 1979 .

[221]  E. Ma,et al.  Instabilities and ductility of nanocrystalline and ultrafine-grained metals , 2003 .

[222]  van der Erik Giessen,et al.  Failure stress of a disordered three-dimensional spring network , 2001 .

[223]  A. Minor,et al.  The deformation of Gum Metal through in situ compression of nanopillars , 2010 .

[224]  K. Lu,et al.  Activation energies for crystal nucleation and growth in amorphous alloys , 1991 .

[225]  Ting Zhu,et al.  Ultra-strength materials , 2010 .

[226]  Robert Danzer,et al.  Some notes on the correlation between fracture and defect statistics: Are Weibull statistics valid for very small specimens? , 2006 .

[227]  O. Senkov,et al.  Specific criteria for selection of alloy compositions for bulk metallic glasses , 2004 .

[228]  A. Ngan,et al.  Deformation of micron-sized aluminium bi-crystal pillars , 2009 .

[229]  V. Ocelík,et al.  Possible local superplasticity of amorphous metallic alloys in the catastrophic shear band under low temperature ductile shear failure , 1996 .