We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these new state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition, and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.
Since the 1970's, theories of deformation and failure of amorphous, solidlike materials have started with models in which stress-driven, molecular rearrangements occur at localized flow defects via "shear transformations." This picture is the basis for the modern theory of "shear transformation zones" (STZ's), which is the focus of this review. We begin by describing the structure of the theory in general terms and by showing several applications, specifically: interpretation of stressstrain measurements for a bulk metallic glass, analysis of numerical simulations of shear banding, and the use of the STZ equations of motion in free-boundary calculations. In the second half of this article, we focus for simplicity on what we call an "athermal" model of amorphous plasticity, and use that model to illustrate how the STZ theory emerges within a systematic formulation of nonequilibrium thermodynamics.
In a 3D model mimicking realistic Cu 64 Zr 36 metallic glass, we uncovered a direct link between the quasi-localized low-frequency vibrational modes and the local atomic packing structure. We also demonstrate that quasi-localized soft modes correlate strongly with fertile sites for shear transformations: geometrically unfavored motifs constitute the most flexible local environments that encourage soft modes and high propensity for shear transformations, whereas local configurations preferred in this alloy, i.e., the full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.liquid-like regions | heterogeneity | structure-property relationship | uncommon motifs | shear transformation zones M etallic glasses (MGs) have an inherently inhomogeneous internal structure, with a wide spectrum of atomic-packing heterogeneities (1-4). As a result, an a priori identification of structural defects that carry atomic rearrangements (strains) under imposed stimuli such as temperature and externally applied stresses has always been a major challenge (3-6). In several quasi-2D or 3D models of amorphous solids (such as jammed packings of soft spheres interacting via repulsive potentials or colloidal particles), low-frequency vibrational normal modes have been characterized, and it has recently been demonstrated that some of these modes are quasilocalized (7)(8)(9)(10)(11)(12)(13)(14). A population of "soft spots" has been identified among them in terms of their low-energy barriers for local rearrangements (13,14), correlating also with properties in supercooled liquids such as dynamic heterogeneity (15-17). However, it is not certain where the soft spots are in realistic MGs (18), in terms of an explicit correlation with local atomic packing and topological arrangements (18)(19)(20). In particular, there is a pressing need to determine whether it is possible to identify shear transformation zones, i.e., the local defects that carry inelastic deformation (21,22). Accomplishing this would permit the characterization of MG microstructure in a way that directly ties atomic configuration with mechanical response beyond the elastic regime. We will show here that there is indeed a correlation between soft modes and atoms that undergo shear transformations, and both have their structural signature in specific atomic packing environments defined in terms of coordination polyhedra (3). Fig. 1 displays the vibrational density of states (V-DOS), D(ω), calculated from the eigen-frequencies obtained by normal mode analysis of the Cu 64 Zr 36 MG prepared with a cooling rate of 10 9 K/s (Methods). The main peak stays around 14 meV and becomes only slightly narrower (or wider) when the cooling rate used to prepare the MG is slower (or faster), as seen in Fig. S1; the glasses cooled at slower rates exhibit fewer low-frequency (or low-energy) vibrational modes. The blue portion in Fig. 1 indicates the 1% lowest-frequency normal modes, which will be summed over in our calculations of the participation fraction, P i , in s...
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