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Title: Strength statistics of single crystals and metallic glasses under small stressed volumes

Journal Article · · Progress in Materials Science
 [1];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

It has been well documented that plastic deformation of crystalline and amorphous metals/alloys shows a general trend of “smaller is stronger”. The majority of the experimental and modeling studies along this line have been focused on finding and reasoning the scaling slope or exponent in the logarithmic plot of strength versus size. In contrast to this view, here we show that the universal picture should be the thermally activated nucleation mechanisms in small stressed volume, the stochastic behavior as to find the weakest links in intermediate sizes of the stressed volume, and the convolution of these two mechanisms with respect to variables such as indenter radius in nanoindentation pop-in, crystallographic orientation, pre-strain level, sample length as in uniaxial tests, and others. Furthermore, experiments that cover the entire spectrum of length scales and a unified model that treats both thermal activation and spatial stochasticity have discovered new perspectives in understanding and correlating the strength statistics in a vast of observations in nanoindentation, micro-pillar compression, and fiber/whisker tension tests of single crystals and metallic glasses.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1256810
Journal Information:
Progress in Materials Science, Journal Name: Progress in Materials Science Journal Issue: C Vol. 82; ISSN 0079-6425
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (164)

Ultrahigh Strength of Dislocation-Free Ni3Al Nanocubes journal March 2012
Specimen Size Effects on Zr-Based Bulk Metallic Glasses Investigated by Uniaxial Compression and Spherical Nanoindentation journal September 2009
Metallic glasses: Gaining plasticity for microsystems journal February 2010
3-D x-ray strain microscopy in two-phase composites at submicron length scales journal March 2011
Hertzian contact of anisotropic bodies journal May 1966
Indentation induced dislocation nucleation: The initial yield point journal September 1996
Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation journal May 2003
The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape journal September 2003
Dislocation nucleation from a crack tip: An analysis based on the Peierls concept journal January 1992
Indentation size effects in crystalline materials: A law for strain gradient plasticity journal March 1998
Mechanisms controlling the durability of thermal barrier coatings journal January 2001
A nanoindentation study of serrated flow in bulk metallic glasses journal January 2003
Directional solidification and microstructures of near-eutectic Cr–Cr3Si alloys journal December 2003
Microstructures and mechanical properties of a directionally solidified NiAl–Mo eutectic alloy journal January 2005
Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients journal April 2005
Size-affected single-slip behavior of pure nickel microcrystals journal September 2005
Indentation size effect in metallic materials: Modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations journal May 2006
Indentation fracture toughness and acoustic energy release in tetrahedral amorphous carbon diamond-like thin films journal September 2006
Atomistic simulation of the deformation of gold nanopillars journal April 2007
Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys journal April 2007
Mechanical behavior of amorphous alloys journal July 2007
Sample-size effects in the yield behavior of nanocrystalline nickel journal February 2008
Stochastic nature of plasticity of aluminum micro-pillars journal May 2008
Effects of pre-strain on the compressive stress–strain response of Mo-alloy single-crystal micropillars journal October 2008
Effects of focused ion beam milling on the compressive behavior of directionally solidified micropillars and the nanoindentation response of an electropolished surface journal January 2009
Achieving the ideal strength in annealed molybdenum nanopillars journal September 2010
Indentation-induced localized deformation and elastic strain partitioning in composites at submicron length scale journal December 2010
Atomistic processes of dislocation generation and plastic deformation during nanoindentation journal February 2011
Intrinsic shear strength of metallic glass journal February 2011
Scanning transmission electron microscope observations of defects in as-grown and pre-strained Mo alloy fibers journal March 2011
Nanoindentation size effect in single-crystal nanoparticles and thin films: A comparative experimental and simulation study journal April 2011
On the shear-band direction in metallic glasses journal June 2011
Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations journal June 2011
Emergence of strain-rate sensitivity in Cu nanopillars: Transition from dislocation multiplication to dislocation nucleation journal August 2011
Variability in the yield strength of a metallic glass at micron and submicron length scales journal November 2011
Effect of solid solution elements on nanoindentation hardness, rate dependence, and incipient plasticity in fine grained magnesium alloys journal December 2011
Intrinsic and extrinsic size effects in the deformation of metallic glass nanopillars journal February 2012
Dislocation starvation and exhaustion hardening in Mo alloy nanofibers journal March 2012
Slip in directionally solidified Mo-alloy micropillars—Part II: Pillars containing defects journal June 2012
Slip in directionally solidified Mo-alloy micropillars – Part I: Nominally dislocation-free pillars journal June 2012
Size effects and strength fluctuation in nanoscale plasticity journal May 2012
Sample size matters for Al88Fe7Gd5 metallic glass: Smaller is stronger journal August 2012
Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials journal September 2012
Indentation size effect and shear transformation zone size in a bulk metallic glass in two different structural states journal November 2012
A simple stochastic model for yielding in specimens with limited number of dislocations journal April 2013
Incipient plasticity and deformation mechanisms in single-crystal Mg during spherical nanoindentation journal May 2013
Characterization of deformation anisotropies in an α-Ti alloy by nanoindentation and electron microscopy journal August 2013
Effect of ion irradiation on tensile ductility, strength and fictive temperature in metallic glass nanowires journal August 2014
Deformation mechanisms in a precipitation-strengthened ferritic superalloy revealed by in situ neutron diffraction studies at elevated temperatures journal January 2015
Characterization of dislocation structures and deformation mechanisms in as-grown and deformed directionally solidified NiAl–Mo composites journal May 2015
Stochastic behaviors in plastic deformation of face-centered cubic micropillars governed by surface nucleation and truncated source operation journal August 2015
Mechanisms of plasticity in near-theoretical strength sub-100 nm Si nanocubes journal November 2015
Formation of extended prismatic dislocation structures under indentation journal June 2016
Integration of contact size dependence and thermal activation in atomic friction journal March 2015
Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films journal November 2006
The role of dislocation walls for nanoindentation to shallow depths journal February 2009
Effects of size on the strength and deformation mechanism in Zr-based metallic glasses journal June 2011
Crystallographic orientation and size dependence of tension–compression asymmetry in molybdenum nano-pillars journal January 2012
Mixed-mode singularity and temperature effects on dislocation nucleation in strained interconnects journal April 2011
Size-dependent plasticity and fracture of a metallic glass in compression journal March 2008
Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper journal March 2004
Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation journal March 2007
Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis☆ journal January 2008
Effective elastic modulus of film-on-substrate systems under normal and tangential contact journal February 2008
Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening journal September 2008
Micro-pillar plasticity: 2.5D mesoscopic simulations journal September 2009
A Peierls perspective on mechanisms of atomicfriction journal December 2010
Indentation Schmid factor and orientation dependence of nanoindentation pop-in behavior of NiAl single crystals journal June 2011
Dislocation arrangement in small crystal volumes determines power-law size dependence of yield strength journal June 2013
Lattice rotation caused by wedge indentation of a single crystal: Dislocation dynamics compared to crystal plasticity simulations journal August 2014
Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids journal October 2015
A continuum model for dislocation dynamics in three dimensions using the dislocation density potential functions and its application to micro-pillars journal November 2015
Synthesis, characterization, and nanoindentation response of single crystal Fe–Cr–Ni alloys with FCC and BCC structures journal August 2014
Ultra-strength materials journal September 2010
Atomic-level structure and structure–property relationship in metallic glasses journal May 2011
Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect journal August 2011
Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples journal February 2007
Multidimensional contact moduli of elastically anisotropic solids journal July 2007
Compressive strengths of molybdenum alloy micro-pillars prepared using a new technique journal September 2007
A different type of indentation size effect journal November 2008
Effects of focused ion beam milling and pre-straining on the microstructure of directionally solidified molybdenum pillars: A Laue diffraction analysis journal May 2010
Size effects on strength and plasticity of vanadium nanopillars journal December 2010
The stability of Lomer–Cottrell jogs in nanopillars journal March 2011
Interface strength in NiAl–Mo composites from 3-D X-ray microdiffraction journal May 2011
Determining the activation energies and slip systems for dislocation nucleation in body-centered cubic Mo and face-centered cubic Ni single crystals journal August 2011
Influences of surface preparation on nanoindentation pop-in in single-crystal Mo journal September 2011
An explanation for the power-law scaling of size effect on strength in micro-specimens journal December 2011
Is the compression of tapered micro- and nanopillar samples a legitimate technique for the identification of deformation mode change in metallic glasses? journal May 2012
Estimation of the shear transformation zone size in a bulk metallic glass through statistical analysis of the first pop-in stresses during spherical nanoindentation journal June 2012
Size effects and ductility of Al-based metallic glass journal August 2012
Effect of tip radius on the incipient plasticity of chromium studied by nanoindentation journal January 2015
Distinguishing between slip and twinning events during nanoindentation of magnesium alloy AZ31 journal January 2016
A tale of two mechanisms: Strain-softening versus strain-hardening in single crystals under small stressed volumes journal January 2016
Deformation at the nanometer and micrometer length scales: Effects of strain gradients and dislocation starvation journal February 2007
Thin-film metallic glasses for substrate fatigue-property improvements journal June 2014
Onset of Plasticity in Gold Nanopillar Compression journal January 2007
Source Truncation and Exhaustion: Insights from Quantitative in situ TEM Tensile Testing journal September 2011
Ultrahigh Strength Single Crystalline Nanowhiskers Grown by Physical Vapor Deposition journal August 2009
Atomistic mechanisms governing elastic limit and incipient plasticity in crystals journal July 2002
Approaching the ideal elastic limit of metallic glasses journal January 2012
How thermally activated deformation starts in metallic glass journal September 2014
Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments journal July 2005
A new view of the onset of plasticity during the nanoindentation of aluminium journal August 2006
Measuring surface dislocation nucleation in defect-scarce nanostructures journal May 2015
On the correlation between microscopic structural heterogeneity and embrittlement behavior in metallic glasses journal October 2015
Ferritic Alloys with Extreme Creep Resistance via Coherent Hierarchical Precipitates journal November 2015
Tensile Strength of Whiskers journal December 1956
Plastic Deformation of Copper and Silver Whiskers journal September 1957
Thermal-expansion behavior of a directionally solidified NiAl–Mo composite investigated by neutron diffraction and dilatometry journal June 2005
Effects of focused ion beam milling on the nanomechanical behavior of a molybdenum-alloy single crystal journal September 2007
Effect of sample size on deformation in amorphous metals journal April 2008
Comment on “Effects of focused ion beam milling on the nanomechanical behavior of a molybdenum-alloy single crystal” Appl. Phys. Lett. 91, 111915 (2007) journal March 2008
Spatially resolved strain measurements in Mo-alloy micropillars by differential aperture x-ray microscopy journal August 2008
Structural heterogeneity induced plasticity in bulk metallic glasses: From well-relaxed fragile glass to metal-like behavior journal October 2013
Yield strength dependence on strain rate of molybdenum-alloy nanofibers journal June 2014
Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution journal February 2001
Indentation modulus of elastically anisotropic half spaces journal May 1993
Molecular dynamics study on compressive yield strength in Ni 3 Al micro-pillars journal June 2006
Size effects in the deformation of sub-micron Au columns journal November 2006
Stochastic theory for jerky deformation in small crystal volumes with pre-existing dislocations journal February 2008
Transition from deterministic to stochastic deformation journal May 2010
Ductile versus brittle behaviour of crystals journal January 1974
Indentation size effect in spherical and pyramidal indentations journal March 2008
Size dependence and stochastic nature of yield strength of micron-sized crystals: a case study on Ni 3 Al journal February 2006
Anomalous plastic deformation at surfaces: Nanoindentation of gold single crystals journal June 1997
Ideal shear strain of metals and ceramics journal September 2004
Determining the activation energy and volume for the onset of plasticity during nanoindentation journal February 2006
Strength differences arising from homogeneous versus heterogeneous dislocation nucleation journal February 2008
Atomistic mechanisms for bilayer growth of graphene on metal substrates journal January 2015
Temperature and Strain-Rate Dependence of Surface Dislocation Nucleation journal January 2008
Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale journal April 2008
Dislocation-Source Shutdown and the Plastic Behavior of Single-Crystal Micropillars journal May 2008
Microstructure versus Size: Mechanical Properties of Electroplated Single Crystalline Cu Nanopillars journal April 2010
Size Effects and Stochastic Behavior of Nanoindentation Pop In journal April 2011
Crossover from Localized to Cascade Relaxations in Metallic Glasses journal July 2015
Atomistic Study of Dislocation Loop Emission from a Crack Tip journal July 2004
Influence of Indenter Tip Geometry on Elastic Deformation during Nanoindentation journal July 2005
Experimental Analysis of the Elastic-Plastic Transition During Nanoindentation of Single Crystal Alpha-Silicon Nitride journal May 2012
Lattice Rotation Patterns and Strain Gradient Effects in Face-Centered-Cubic Single Crystals Under Spherical Indentation journal June 2015
Sample Dimensions Influence Strength and Crystal Plasticity journal August 2004
An Approximate Formulation of the Effective Indentation Modulus of Elastically Anisotropic Film-On-Substrate Systems journal September 2009
Deformation and Fracture Mechanisms of Bone and Nacre journal August 2011
Mechanistic Studies in Friction and Wear of Bulk Materials journal July 2014
Designing Radiation Resistance in Materials for Fusion Energy journal July 2014
The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations journal June 2010
Plasticity of Micrometer-Scale Single Crystals in Compression journal August 2009
Scale effects in convoluted thermal/spatial statistics of plasticity initiation in small stressed volumes during nanoindentation journal October 2012
The deformation behavior of ceramic crystals subjected to very low load (nano)indentations journal February 1992
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments journal June 1992
Continuous microindentation of passivating surfaces journal April 1993
Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation journal July 2004
3D x-ray microprobe investigation of local dislocation densities and elastic strain gradients in a NiAl-Mo composite and exposed Mo micropillars as a function of prestrain journal February 2010
Revelation of the effect of structural heterogeneity on microplasticity in bulk metallic-glasses journal March 2010
Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology journal January 2004
Nanoscale strength distribution in amorphous versus crystalline metals journal December 2010
Mesoscale friction anisotropy revealed by slidingless tests journal September 2011
Predicting the dislocation nucleation rate as a function of temperature and stress journal September 2011
In-situ tensile testing of single-crystal molybdenum-alloy fibers with various dislocation densities in a scanning electron microscope journal September 2011
Effective Poisson’s ratio from combined normal and lateral contacts of single crystals journal October 2011
Effects of machine stiffness on the loading–displacement curve during spherical nano-indentation journal June 2013
A stochastic model for the size dependence of spherical indentation pop-in journal September 2013
Single versus successive pop-in modes in nanoindentation tests of single crystals journal May 2016
Finite Element Studies of Homogeneous and Heterogeneous Dislocation Nucleation based on the Rice-Peierls Framework journal January 2011
Microstructures and Mechanical Properties of Directionally Solidified Intermetallic Composites journal March 2007

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