Heterogeneously randomized STZ model of metallic glasses: Softening and extreme value statistics during deformation

Abstract A nanoscale kinetic Monte Carlo (kMC) model is developed to study the deformation behavior of metallic glasses (MGs). The shear transformation zone (STZ) is adopted as our fundamental deformation unit and each nanoscale volume element (∼1 nm voxel) in the MG is considered as a potential STZ that may undergo inelastic rearrangements sampled from a randomized catalog that varies from element to element, with stress-dependent activation energies. The inelastic transformation sampled out of spatially randomized catalogs (a key characteristic of glass) is then treated as an Eshelby’s inclusion and the induced elastic field is solved in the Fourier space using the spectral method. The distinct features of our model, compared to previous work, are the introduction of randomized event catalogs for different nanoscale volume elements, repeated operations within the same element, and a “generation-dependent” softening term to reflect the internal structural change after each deformation. Simulations of uniaxial tension show the important effect of softening on the formation of shear bands, with a size-independent thickness of 18 nm. Statistical analysis of the accumulated strain at the ∼1 nm voxel level is carried out and sample size effect on the extreme value statistics is discussed.

[1]  Stéphane Roux,et al.  Extremal model for amorphous media plasticity. , 2002, Physical review letters.

[2]  Yu U. Wang,et al.  Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid , 2002 .

[3]  J. Hüsler,et al.  Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields , 2007 .

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

[5]  A. Argon.  CHAPTER 21 – MECHANICAL PROPERTIES OF SINGLE-PHASE CRYSTALLINE MEDIA: DEFORMATION AT LOW TEMPERATURES , 1996 .

[6]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  W. Jiang,et al.  The effect of compression and tension on shear-band structure and nanocrystallization in amorphous Al90Fe5Gd5: a high-resolution transmission electron microscopy study , 2003 .

[8]  Yat Li,et al.  Effect of crystallinity on the impact toughness of a La-based bulk metallic glass , 2000 .

[9]  M. Ortiz,et al.  A Finite-Deformation Constitutive Model of Bulk Metallic Glass Plasticity , 2006 .

[10]  Suzuki,et al.  Bond-orientational anisotropy in metallic glasses observed by x-ray diffraction. , 1987, Physical review. B, Condensed matter.

[11]  C. Schuh,et al.  Mesoscale modeling of amorphous metals by shear transformation zone dynamics , 2009 .

[12]  Thomas A. Weber,et al.  Hidden structure in liquids , 1982 .

[13]  John C. Mauro,et al.  Computing the Viscosity of Supercooled Liquids: Markov Network Model , 2011, PloS one.

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

[15]  Akihiko Hirata,et al.  Direct observation of local atomic order in a metallic glass. , 2011, Nature materials.

[16]  R. Reiss,et al.  Statistical Analysis of Extreme Values-with applications to insurance , 1997 .

[17]  T. Egami.  Atomic level stresses , 2011 .

[18]  Mingwei Chen,et al.  Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses , 2008, Proceedings of the National Academy of Sciences.

[19]  Weihua Wang,et al.  Carbon-nanotube-reinforced Zr52.5Cu17.9Ni14.6Al10Ti5 bulk metallic glass composites , 2002 .

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

[21]  K. T. Ramesh,et al.  Deformation and failure of Zr_57Ti_5Cu_20Ni_8Al_10 bulk metallic glass under quasi-static and dynamic compression , 2002 .

[22]  V. Vítek,et al.  Radial Distribution Function and Structural Relaxation in Amorphous Solids , 1981 .

[23]  Marin Soljacic,et al.  Probing topological protection using a designer surface plasmon structure. , 2012 .

[24]  J. F. Löffler,et al.  Deformation kinetics in Zr-based bulk metallic glasses and its dependence on temperature and strain-rate sensitivity , 2007 .

[25]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[26]  V. Bulatov,et al.  A stochastic model for continuum elasto-plastic behavior. I. Numerical approach and strain localization , 1994 .

[27]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[28]  Yunzhi Wang,et al.  Phase field modeling of defects and deformation , 2010 .

[29]  Ju Li,et al.  Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations , 2007 .

[30]  Arthur F. Voter,et al.  Introduction to the Kinetic Monte Carlo Method , 2007 .

[31]  C. Schuh,et al.  Three-dimensional shear transformation zone dynamics model for amorphous metals , 2010 .

[32]  William L. Johnson,et al.  In situ transmission electron microscopy studies of shear bands in a bulk metallic glass based composite , 2001 .

[33]  H. Neuhäuser.  Rate of shear band formation in metallic glasses , 1978 .

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

[35]  Jing Li,et al.  Nanometre-scale defects in shear bands in a metallic glass , 2002 .

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

[37]  Subra Suresh,et al.  Study of mechanical deformation in bulk metallic glass through instrumented indentation , 2001 .

[38]  Ju Li.  Modeling microstructural effects of deformation resistance and thermal conductivity , 2000 .

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

[40]  Sidney Yip,et al.  Computing the viscosity of supercooled liquids. , 2009, The Journal of chemical physics.

[41]  A. Heuer,et al.  Transmission electron microscopy of shear bands in amorphous metallic alloys , 1978 .

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

[43]  S. Roux,et al.  Mechanical noise dependent Aging and Shear Banding behavior of a mesoscopic model of amorphous plasticity , 2011, 1104.4863.

[44]  D. Rodney,et al.  Distribution of thermally activated plastic events in a flowing glass. , 2009, Physical review letters.

[45]  S. G. Mayr.  Activation energy of shear transformation zones: a key for understanding rheology of glasses and liquids. , 2006, Physical review letters.

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

[47]  F. Sciortino,et al.  Inherent Structure Entropy of Supercooled Liquids , 1999, cond-mat/9906081.

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

[49]  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.

[50]  R. Ritchie.  The conflicts between strength and toughness. , 2011, Nature materials.

[51]  P. Wolynes.  Spatiotemporal structures in aging and rejuvenating glasses. , 2008, Proceedings of the National Academy of Sciences of the United States of America.

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

[53]  Stillinger,et al.  Atomistic simulation of aging and rejuvenation in glasses , 2000, Physical review letters.

[54]  C. Pampillo.  Flow and fracture in amorphous alloys , 1975 .

[55]  A. G. Khachaturi︠a︡n.  Theory of structural transformations in solids , 1983 .

[56]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[57]  V. Vítek,et al.  An atomistic study of deformation of amorphous metals , 1983 .

[58]  D. Rodney,et al.  Modeling the mechanics of amorphous solids at different length scale and time scale , 2011, 1107.2022.

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

[60]  S. Poon,et al.  Deformation-induced nanocrystal formation in shear bands of amorphous alloys , 1994, Nature.

[61]  Philip Ball,et al.  The hidden structure of liquids. , 2014, Nature materials.

[62]  H. Bei,et al.  Softening caused by profuse shear banding in a bulk metallic glass. , 2006, Physical review letters.

[63]  W. Stobbs,et al.  The structure of shear bands in metallic glasses , 1981 .

[64]  P. Gumbsch,et al.  Atomistic modeling of mechanical behavior , 2003 .

[65]  Shin Takeuchi,et al.  Atomistic simulation and modeling of localized shear deformation in metallic glasses , 2011 .

[66]  Jun Sun,et al.  Approaching the ideal elastic limit of metallic glasses , 2012, Nature Communications.

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

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

[69]  Ju Li,et al.  Adaptive strain-boost hyperdynamics simulations of stress-driven atomic processes , 2010 .

[70]  John W. Hutchinson,et al.  Strain localization in amorphous metals , 1982 .

[71]  T. Hufnagel,et al.  Mechanical behavior of amorphous alloys , 2007 .

[72]  W. Wang,et al.  Fracture of brittle metallic glasses: brittleness or plasticity. , 2005, Physical review letters.

[73]  S. Suresh,et al.  Nanocrystallization During Nanoindentation of a Bulk Amorphous Metal Alloy at Room Temperature , 2002, Science.

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

[75]  Ju Li,et al.  Yield point of metallic glass , 2006 .

[76]  C. Su,et al.  Plane strain indentation of a Zr-based metallic glass: Experiments and numerical simulation , 2006 .