Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[1]  W. Nix,et al.  Deformation Mechanisms of the Zr40Ti14Ni10Cu12Be24 Bulk Metallic Glass , 2001 .

[2]  G. Ananthakrishna,et al.  Repeated yield drop phenomenon: a temporal dissipative structure , 1982 .

[3]  Per Bak,et al.  How Nature Works , 1996 .

[4]  Microstructural shear localization in plastic deformation of amorphous solids. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  J. Vergnol,et al.  The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy , 1987 .

[6]  Egidio Rizzi,et al.  Spatiotemporal analysis of Portevin-Le Châtelier deformation bands: theory, simulation, and experiment , 2002 .

[7]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[8]  J. F. Löffler,et al.  Temperature, Strain and Strain Rate Dependence of Serrated Flow in Bulk Metallic Glasses , 2007 .

[9]  A. L. Greer,et al.  Nanoindentation studies of shear banding in fully amorphous and partially devitrified metallic alloys , 2004 .

[10]  Bikas K. Chakrabarti,et al.  Modelling Critical and Catastrophic Phenomena in Geoscience , 2006 .

[11]  K. Jacobsen,et al.  Avalanche size scaling in sheared three-dimensional amorphous solid. , 2007, Physical review letters.

[12]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[13]  Vives,et al.  Statistics of avalanches in martensitic transformations. II. Modeling. , 1995, Physical review. B, Condensed matter.

[14]  Huajian Gao,et al.  An instability index of shear band for plasticity in metallic glasses , 2009 .

[15]  L. Kubin,et al.  Multifractal burst in the spatiotemporal dynamics of jerky flow. , 2001, Physical review letters.

[16]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality , 1998 .

[17]  T. Nieh,et al.  Effect of the nanoindentation rate on the shear band formation in an Au-based bulk metallic glass , 2007 .

[18]  Geetha Basappa,et al.  Observation of chaotic dynamics in dilute sheared aqueous solutions of CTAT. , 2000, Physical review letters.

[19]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[20]  R. Eykholt,et al.  Estimating the Lyapunov-exponent spectrum from short time series of low precision. , 1991, Physical review letters.

[21]  G. Ananthakrishna,et al.  A dynamical model for the Portevin-Le Chatelier bands , 2003 .

[22]  H. Peitgen,et al.  Functional Differential Equations and Approximation of Fixed Points , 1979 .

[23]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[24]  H. Bai,et al.  Poisson's ratio and plasticity in CuZrAl bulk metallic glasses , 2008 .

[25]  T. Ohkubo,et al.  Plasticity and microstructure of Zr–Cu–Al bulk metallic glasses , 2007 .

[26]  Peter K. Liaw,et al.  Spatiotemporally inhomogeneous plastic flow of a bulk-metallic glass , 2008 .

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

[28]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[29]  Grebogi,et al.  Plateau onset for correlation dimension: When does it occur? , 1993, Physical review letters.

[30]  Andrea J. Liu,et al.  Activated dynamics and effective temperature in a steady state sheared glass. , 2007, Physical review letters.

[31]  W. Jiang,et al.  Rate dependence of serrated flow in a metallic glass , 2003 .

[32]  Intermittent peel front dynamics and the crackling noise in an adhesive tape. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[34]  E. Ma,et al.  Cold versus hot shear banding in bulk metallic glass , 2009 .

[35]  J. Langer.  Shear-transformation-zone theory of deformation in metallic glasses , 2006 .

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

[37]  W. Johnson,et al.  Plastic deformation of metallic glasses: Size of shear transformation zones from molecular dynamics simulations , 2006 .

[38]  Itamar Procaccia,et al.  Predicting plastic flow events in athermal shear-strained amorphous solids. , 2010, Physical review letters.

[39]  G. Ananthakrishna,et al.  Chaotic flow in a model for repeated yielding , 1983 .

[40]  Christopher A. Schuh,et al.  A nanoindentation study of serrated flow in bulk metallic glasses , 2003 .

[41]  Jun Shen,et al.  Self-organized intermittent plastic flow in bulk metallic glasses , 2009 .

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

[43]  J. Eckert,et al.  "Work-Hardenable" ductile bulk metallic glass. , 2005, Physical review letters.

[44]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

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

[46]  Hidden order in crackling noise during peeling of an adhesive tape. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  A. Yavari,et al.  Unusual room-temperature compressive plasticity in nanocrystal-toughened bulk copper-zirconium glass , 2005 .

[48]  L. Kubin,et al.  Chaos in the Portevin-Le Châtelier Effect , 1997 .

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

[50]  Juyoung Kim,et al.  Rate-dependent inhomogeneous-to-homogeneous transition of plastic flows during nanoindentation of bulk metallic glasses: Fact or artifact? , 2007 .

[51]  T. Nieh,et al.  Flow serration in a Zr-based bulk metallic glass in compression at low strain rates , 2008 .

[52]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[53]  S. Poon,et al.  Critical Poisson’s ratio for plasticity in Fe–Mo–C–B–Ln bulk amorphous steel , 2006 .

[54]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[55]  G. Ananthakrishna,et al.  Current theoretical approaches to collective behavior of dislocations , 2007 .

[56]  H. S. Chen,et al.  Plastic flow and fracture of metallic glass , 1972 .

[57]  L. Kubin,et al.  Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[59]  J. Kertész,et al.  The noise spectrum in the model of self-organised criticality , 1990 .

[60]  L. Kubin,et al.  The hidden order behind jerky flow , 2002 .

[61]  S. Kok,et al.  Spatial coupling in jerky flow using polycrystal plasticity , 2003 .

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

[63]  K. T. Ramesh,et al.  Enhanced plastic strain in Zr-based bulk amorphous alloys , 2001 .

[64]  S. S. Manna.  Large-scale simulation of avalanche cluster distribution in sand pile model , 1990 .

[65]  G. Ananthakrishna,et al.  Dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: chaos, turbulence, and band propagation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  Jan Schroers,et al.  Ductile bulk metallic glass. , 2004, Physical review letters.

[67]  M. Demkowicz,et al.  Autocatalytic avalanches of unit inelastic shearing events are the mechanism of plastic deformation in amorphous silicon , 2005 .

[68]  A. Cottrell,et al.  Dislocations and plastic flow in crystals , 1953 .