Nanomechanics of slip avalanches in amorphous plasticity
Introduction
Although the plastic response of amorphous solids such as metallic glasses has been under study for some time (Cheng, Ma, 2011a, Hufnagel, Schuh, Falk, 2016, Schuh, Hufnagel, Ramamurty, 2007a), quantitative details of the elementary deformation processes at the nanoscale are still lacking. Recent compression (Antonaglia, Wright, Gu, Byer, Hufnagel, LeBlanc, Uhl, Dahmen, 2014a, Antonaglia, Xie, Schwarz, Wraith, Qiao, Zhang, Liaw, Uhl, Dahmen, 2014b, Harris, Watts, Homer, 2016, Mukai, Nieh, Kawamura, Inoue, Higashi, 2002, Sun, Pauly, Tan, Stoica, Wang, Kühn, Eckert, 2012, Wright, Schwarz, Nix, 2001) and nanoindentation (Cheng, Jiao, Ma, Qiao, Wang, 2014, Golovin, Ivolgin, Khonik, Kitagawa, Tyurin, 2001, Jiang, Atzmon, 2003, Schuh, Nieh, 2003, Schuh, Nieh, Kawamura, 2002) experiments have focused on the dynamical evolution of slip avalanches, the serrations in stress-strain behavior of a driven system. A common characteristic of serrated flow is the strain-rate sensitivity becoming more pronounced as rates are lowered (Antonaglia, Xie, Schwarz, Wraith, Qiao, Zhang, Liaw, Uhl, Dahmen, 2014b, Harris, Watts, Homer, 2016, Schuh, Nieh, Kawamura, 2002, Schuh, Hufnagel, Ramamurty, 2007a). To understand the molecular mechanisms of stress relaxation, quantitative details available from molecular simulations would be useful. However, the simulations performed to date (Albe, Ritter, Şopu, 2013, Cheng, Ma, 2011b, Sha, Wong, Pei, Branicio, Liu, Wang, Guo, Gao, 2017, Shi, Falk, 2005, Shimizu, Ogata, Li, 2007, Zhou, Zhou, Li, Chen, 2015) are constrained to strain rates higher by several orders of magnitude than those studied experimentally or treated by mechanics-based modeling.
In this work, we implement an atomistic simulation algorithm that can reach timescales in the range of experiments. We study a metallic glass model in uniaxial compression at a relatively low temperature of 0.33Tg, where Tg is the glass transition temperature, with a focus on the effects of strain rate. Our results reveal a scenario of dynamical evolution in which system deformation occurs through a series of small and large discrete stress relaxations. Even though this behavior is well known at the constitutive level, details of the individual and collective molecular processes have not been probed at low strain rate previously. By analyzing the spatial distributions of the local deviatoric strain and the non-affine atomic displacement during the evolution, we find the small avalanches to be spatially isolated processes occurring intermittently, and the large avalanches to be highly collective processes associated with the formation and subsequent evolution of a spontaneously formed shear band. The significance of avalanche size emerges naturally from visualizing the spatial and temporal correlations in local strain and atomic diffusion, as well as from the statistics on the magnitude of the stress relaxation, number of atoms involved, atom mobility and avalanche duration. Prior to the onset of yielding, only strain-rate sensitive small avalanches are observed. A large avalanche first appears at the onset of yielding. During subsequent flow, large avalanches occur intermixed with small avalanches. The regularly appearing large avalanches are associated with shear localization, just as observed in experiments (Antonaglia, Wright, Gu, Byer, Hufnagel, LeBlanc, Uhl, Dahmen, 2014a, Wright, Liu, Gu, Van Ness, Robare, Liu, Antonaglia, LeBlanc, Uhl, Hufnagel, et al., 2016) and described by an analytic mean field modeling approach (Dahmen et al., 2009). The atomistic processes during yielding and subsequent plastic flow reveal shear band formation can occur as percolation of shear transformation events at high strain rates and crack-like propagation at low strain rates. Our findings also provide nanoscale details to complement current experimental and theoretical studies, enabling a more quantitative characterization of the elementary processes of amorphous plasticity.
We begin in Section 2 with a description of the model metallic glass and a metadynamics method for atomistic simulation at a prescribed strain rate. The algorithm we implement is based on a method called ABC (autonomous basin climbing) first applied to compute the shear viscosity of supercooled liquids (Kushima et al., 2009). The saddle points along the obtained trajectory are the essential results that allow the simulation to proceed according to transition-state theory rather than Newtonian dynamics. The stress-strain curves simulated at three significantly different strain rates are presented in Section 3, each showing an elastic response up to yielding, followed by plastic flow with a series of major and minor stress drops. We give particular attention to the strain rate typical of experimental measurements. In the vicinity of yielding one sees clearly the spontaneous formation of a band-shaped region of localized shear from the local atomic strain maps. Once formed, this structural defect completely dominates the evolution of the subsequent serrated flow. In Section 4 we examine the statistical significance of the magnitude of stress relaxation, i.e. the avalanche size, as an indication of the different modes of deformation response, and also an indication of strain-rate effects. We find a natural separation between small and large avalanches that becomes a continuing theme throughout our study. The atomic-level deformations and atomic displacements are also presented which show a considerably more dominant role for the large avalanches. In Section 5 we give an interpretation of nonlinear response to the existence of a stress relaxation seen from the simulation data in various forms. In Section 6 we investigate the nanoscale processes of shear-band formation by combining mean field modeling analysis and mechanical testing experiments with the present simulation at strain rates typical of experiments or molecular dynamics simulations. In these two ranges of strain rate we find a shear band can form in a manner that can be described as crack-tip extension like and progressive percolation, respectively. Finally in Section 7 we indicate how different modeling frameworks can be unified by focusing on the nonlinear coupling between thermal and stress activations.
Section snippets
Simulation model
We model a metallic glass thin film using a two-dimensional binary Lennard–Jones (BLJ) mixture previously developed to study mechanical properties of amorphous solids (Falk and Langer, 1998). In this model there are two species referred to as ‘a’ and ‘b’. The length and energy are measured in units of the potential parameters, σab and ϵab, respectively, while time is measured in units of with m being the mass of both ‘a’ and ‘b’ particle species. The temperature is measured in
Yielding onset and serrated flow
The responses of system-level stress to uniaxial compression at three separate strain rates are shown in Fig 1(a). The curve QS (quasistatic) (Falk and Maloney, 2010) is obtained by potential energy minimization, which is effectively the limit of high strain rate (Cao, Lin, Park, 2014a, Fan, Osetskiy, Yip, Yildiz, 2013a). The other two curves correspond, respectively, to constant strain rates of 2.2 × 10 and 4.6 × 10 which are typical of conventional MD simulations and laboratory
Major and minor avalanches
Since stress relaxations (avalanches) are a natural part of the system-level behavior, their dependence on strain rate immediately becomes a subject of interest. Fig. 2 shows the statistical distribution results that suggest the avalanche size, i.e. the magnitude of the stress drop, plays a central role in characterizing the underlying molecular processes associated with the avalanches. The probability distributions of avalanche sizes P(Δσ) during steady-state flow at three strain rates are
Interpretation of nonlinear accelerated response
Throughout this work we have encountered various simulation results that suggest a natural distinction exists between small and large avalanches as measured by the magnitude of the stress relaxation. Recall in Fig. 4 we noted a threshold avalanche size, Δσc ∼ 0.1, which effectively distinguishes two regimes of stress relaxation response. In Fig. 8 we demonstrate further that the notion of a threshold Δσc is quite robust when other measures of deformation response are also taken into account.
Avalanches and shear band formation
Shear banding is a ubiquitous mode of plastic deformation that is particularly important in metallic glasses (Greer et al., 2013). We will now consider how the combination of mean-field modeling and mechanical tests with the metadynamics simulation findings can contribute to elucidating the initial stage of shear-band formation.
Implications for theoretical modeling
By probing the molecular processes associated with the onset of slip avalanches at an experimental strain rate, we have uncovered two modes of stress relaxation, a preparatory (weakening) mode of activating several minor stress relaxations, and an abrupt release mode where a major stress drop occurs suddenly. The onset of yielding is signaled by the appearance of the first major avalanche; subsequent plastic flow then proceeds through a series of small and large relaxation events. Spatial and
Acknowledgments
We thank A.S. Argon, J.S. Langer and M.L. Falk for discussions. We gratefully acknowledge support from DOE DE-NE0008450(PC), NSF CBET1336634, DOE DE-FE-0011194(KAD), NSF-DMR1042734(WJW), and DOE DE-SC0002633 and MIT-Kuwait Signature Project(SY). We especially acknowledge the Kavli Institute for Theoretical Physics for hospitality at a workshop and for support through grant NSF PHY1125915.
References (54)
- et al.
Enhancing the plasticity of metallic glasses: shear band formation, nanocomposites and nanoglasses investigated by molecular dynamics simulations
Mech. Mater.
(2013) Plastic deformation in metallic glasses
Acta Metall.
(1979)- et al.
Structural processes that initiate shear localization in metallic glass
Acta Mater.
(2009) - et al.
Strain-rate and temperature dependence of yield stress of amorphous solids via self-learning metabasin escape algorithm
J. Mech. Phys. Solids
(2014) - et al.
Atomic-level structure and structure–property relationship in metallic glasses
Prog. Mater. Sci.
(2011) - et al.
Intrinsic shear strength of metallic glass
Acta Mater.
(2011) - et al.
Serrated plastic flow during nanoindentation of a bulk metallic glass
Scr. Mater.
(2001) - et al.
Shear bands in metallic glasses
Mater. Sci. Eng.
(2013) - et al.
Competition between shear band nucleation and propagation across rate-dependent flow transitions in a model metallic glass
Acta Mater.
(2016) - et al.
Deformation of metallic glasses: recent developments in theory, simulations, and experiments
Acta Mater.
(2016)
Propagation dynamics of individual shear bands during inhomogeneous flow in a Zr-based bulk metallic glass
Acta Mater.
Effect of strain rate on compressive behavior of a Pd 40 Ni 40 P 20 bulk metallic glass
Intermetallics
A nanoindentation study of serrated flow in bulk metallic glasses
Acta Mater.
Mechanical behavior of amorphous alloys
Acta Mater.
Mechanical behavior of amorphous alloys
Acta Mater.
Atomistic origin of size effects in fatigue behavior of metallic glasses
J. Mech. Phys. Solids
A microscopic mechanism for steady state inhomogeneous flow in metallic glasses
Acta Metall.
Serrated flow and stick–slip deformation dynamics in the presence of shear-band interactions for a Zr-based metallic glass
Acta Mater.
Localized heating during serrated plastic flow in bulk metallic glasses
Mater. Sci. Eng.
Size effects on tensile and compressive strengths in metallic glass nanowires
J. Mech. Phys. Solids
Bulk metallic glasses deform via slip avalanches
Phys. Rev. Lett.
Tuned critical avalanche scaling in bulk metallic glasses
Sci. Rep.
A self-learning metabasin escape algorithm and the metabasin correlation length of supercooled liquids
Phys. Rev. E
Surface shear-transformation zones in amorphous solids
Phys. Rev. E
Strain-rate and temperature-driven transition in the shear transformation zone for two-dimensional amorphous solids
Phys. Rev. E
Understanding the mechanisms of amorphous creep through molecular simulation
Proc. Natl. Acad. Sci.
Serrated flow behaviors of a Zr-based bulk metallic glass by nanoindentation
J. Appl. Phys.
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