Michael L. Falk

Dynamics of viscoplastic deformation in amorphous solids

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 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. {copyright} {ital 1998} {ital The American Physical Society}

Strain localization and percolation of stable structure in amorphous solids.

Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the most rapidly quenched samples higher strain rates lead to increased localization, while the more gradually quenched samples exhibit the opposite strain rate dependence. This transition coincides with the k-core percolation of atoms with quasi-crystal-like short range order. The authors infer the existence of a related microstructural length scale.

Deformation and Failure of Amorphous, Solidlike Materials

Since the 1970s, 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 (STZs), 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 stress-strain 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 review, 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.

Soft spots and their structural signature in a metallic glass.

Significance This work demonstrates a structure–property correlation in metallic glasses for the community of amorphous solids. It associates geometrically unfavored motifs, i.e., those most disordered local polyhedral packing structures in a metallic glass, with the soft spots defined from the vibrational modes and correlates them with shear transformation zones composed of atoms with large nonaffine displacements. The statistical correlation established thus ties together the heterogeneity inherent in the amorphous structure with the spatial heterogeneity in the mechanical (elastic and plastic) properties of a metallic glass. In a 3D model mimicking realistic Cu64Zr36 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.

Evaluation of the disorder temperature and free-volume formalisms via simulations of shear banding in amorphous solids.

Molecular dynamics simulations of shear band development over 1000% strain in simple shear are used to test whether the local plastic strain rate is proportional to exp(-1/chi), where chi is a dimensionless quantity related to the disorder temperature or free volume that characterizes the structural state of the glass. Scaling is observed under the assumption that chi is linearly related to the local potential energy per atom. We calculate the potential energy per atom corresponding to absolute zero disorder temperature and the energy needed to create a shear transformation zone.

Sliding behavior of metallic glass: Part I. Experimental investigations

The unlubricated sliding characteristics of zirconium-based bulk metallic glass disks have been examined in vacuum and in air using sliders made from the same material or from a hard bearing steel (52100). The pin-on-disk test system allowed collection of debris, monitoring of the friction force and, using a Kelvin probe, in situ detection of changes in the structure and chemical composition of the disk surface. Post-test characterization included microhardness testing, X-ray diffraction, SEM and EDS. Examination of worn surfaces, cross-sections and debris confirmed the importance of plastic deformation, material transfer and environmental interactions. When devitrified material was tested, sliding processes caused the near-surface material to re-amorphize. Results from sliding of bulk metallic glass specimens were compared with those from related experiments involving crystalline metals and alloys. Although bulk metallic glasses are reported to have only limited ductility in tensile tests, the friction coefficients and worn surfaces of these materials are typical of ductile materials.

Interactions between charged spherical macroions

Monte Carlo (MC) simulations were used to study the screened interactions between charged spherical macroions surrounded by discrete counterions, and to test previous theories of screening. The simulations were performed in the primitive cell of the bcc lattice, and in the spherical Wigner–Seitz cell that is commonly used in approximate calculations. We found that the Wigner–Seitz approximation is valid even at high volume fractions φ and large macroion charges Z, because the macroion charge becomes strongly screened. Pressures calculated from Poisson–Boltzmann theory and local density functional theory deviate from MC values as φ and Z increase, but continue to provide upper and lower bounds for the MC results. While Debye–Huckel (DH) theory fails badly when the bare charge is used, MC pressures can be fit with an effective DH charge, ZDH, that is nearly independent of volume fraction. As Z diverges, ZDH saturates at zψmaxRm/λ, where z is the counterion charge, Rm is the macroion radius, λ is the Bjerrum...

Sliding behavior of metallic glass: Part II. Computer simulations

t Molecular dynamics (MD) calculations were used to simulate the sliding of a two-component 2D amorphous system interacting via Lennard-Jones potentials. The friction coefficient showed a transient before reaching an average steady state value. The steady state friction coefficient was observed to decrease with an increasing sliding velocity. Mixing was observed at the sliding interface. The mixed layer grew at a rate that scaled with the square root of time. A density decrease was recorded in the region adjacent to the sliding interface. This spatially corresponded to the softer layer detected experimentally near the worn surface in a Zr 41.2 Ti 13.8 Cu 12.5 Ni 10.0 Be 22.5 bulk metallic glass alloy after sliding. Subsurface displacement profiles produced in these simulations were similar to those observed in other material systems. The Navier-Stokes equation was used to analyze the material flow pattern, with results in agreement with data obtained from simulations. This suggests that the observed subsurface displacement profile may be a generic material flow pattern under combined compression and shear.

Structural transformation and localization during simulated nanoindentation of a noncrystalline metal film

A simulation study demonstrates that localization can arise as the result of the breakdown of stable quasicrystal-like atomic configurations. Samples produced at elevated quench rates and via more energetic processes contain a lower fraction of such configurations and exhibit significantly less pronounced localization and shorter spacing between bands. In the samples produced by the lowest quench rates, localization is accompanied by the amorphization of material with initially quasicrystal-like medium range order. This result is of particular significance in light of recent experimental evidence of local quasicrystal order in the most stable of the bulk metallic glasses.

Thermal effects in the shear-transformation-zone theory of amorphous plasticity: Comparisons to metallic glass data

We extend our earlier shear-transformation-zone theory of amorphous plasticity to include the effects of thermally assisted molecular rearrangements. This version of our theory is a substantial revision and generalization of conventional theories of flow in noncrystalline solids. As in our earlier work, it predicts a dynamic transition between jammed and flowing states at a yield stress. Below that yield stress, it now describes thermally assisted creep. We show that this theory accounts for the experimentally observed strain-rate dependence of the viscosity of metallic glasses, and that it also captures many of the details of the transient stress-strain behavior of those materials during loading. In particular, it explains the apparent onset of superplasticity at sufficiently high stress as a transition between creep at low stresses and plastic flow near the yield stress. We also argue that there are internal inconsistencies in the conventional theories of these deformation processes, and suggest ways in which further experimentation as well as theoretical analysis may lead to better understanding of a broad range of nonequilibrium phenomena.