Model Metallic Glass Research Articles

Evaluating Mohr–Coulomb yield criterion for plastic flow in model metallic glasses

The yielding of metallic glasses (MGs) is generally considered to be dependent on pressure or normal stress, which is usually described by the Mohr–Coulomb yield criterion. Experimentally, the orientation of the shear band angle or fracture angles in MG is roughly 40° to 42° in uniaxial compression and 50° to 59° in uniaxial tension, both with respect to the loading direction. However, the amounts of deviation from the maximum shear stress direction (45°) under uniaxial tension and compression are quite different, which seems to be inconsistent with the Mohr–Coulomb yield criterion. Here we carried out molecular dynamics simulations to study the incipient plasticity of model Dzugutov glasses subjected to various uniaxial and biaxial stress states. The yield points are defined as the sharp rise of the population of atoms participating in non-affine deformations, in addition to the traditional offset method. The yield surfaces thus created agree well with the Mohr–Coulomb yield criterion. Furthermore, the orientations of the embryonic shear bands (instead of the fully-grown shear bands, or fracture planes) are measured, which also follow predictions based on the Mohr–Coulomb criterion. Our simulation results call for orientational measurement of incipient shear bands in experiments to critically examine the Mohr–Coulomb yield criterion in MG systems.

Compression-compression fatigue study on model metallic glass nanowires by molecular dynamics simulations

We report compression-compression fatigue simulations on model metallic-glass nanowires up to a 4% maximum compressive strain and 100 cycles using the molecular dynamics method. The distribution and irreversibility of the fatigue-induced deformations are characterized by the local shear strain and rise of the system temperature, respectively. Furthermore, the system potential energy, structural signatures in terms of icosahedral centers, and radial distribution functions are obtained to identify structural transformations during cyclic loading. No noticeable changes on the aforementioned isotropic structural signatures have been found during fatigue tests. Based on a binary view of the constituting local structures (stable clusters and floppy clusters) in metallic glasses, we attribute the irreversible deformation to inter-conversion of those floppy clusters, which leads to a constant composition of stable and floppy clusters. Finally, uniaxial compression tests were carried out on the cyclically loaded samples. The mechanical behaviors of fatigue-tested samples are rather similar to the original sample. Upon cyclic loading, unlike macroscopic samples, a metallic-glass nanowire is free of permanent structural damage, and therefore does not exhibit deteriorated mechanical behaviors. The excellent fatigue-resistance behavior of a metallic-glass nanowire might be related to its defect-free structure (no stress concentrators). It appears that defects may play a central role in fatigue damages in experimental metallic-glass systems.

Thermally-activated atomic rearrangements in elastically deformed metallic glasses

This study investigates by molecular dynamics the response of model metallic glasses to artificial atom displacements at increasing deformation degrees. Glasses are shown to contain unstable regions that spontaneously rearrange under deformation. The relative stability of such regions was measured by the length of artificial atomic displacements inducing a rearrangement. Such length scales with the amplitude of atomic thermal vibrations, which suggests for deformation-induced rearrangements a thermal activation mechanism.

Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.

Shear influence on the structural ordering in a model metallic glass

Nonequilibrium molecular dynamics simulations of a model amorphous system are performed with the aim of studying the structural transformations induced by external shear influence. We reveal that the shear drive has both positive and negative effects on the structural ordering processes. The dependence of the phase transition rate versus the strain rate at three different temperatures is found.

Cu–Zr and Cu–Zr–Al clusters: Bonding characteristics and mechanical properties

We present density functional theory (DFT) calculations results on two representative clusters (Cu 7Zr 6 and Cu 10Zr 5) and their interconnections (touching and interpenetrating). The choice of these clusters and their combinations is dictated from previous molecular dynamics (MD) simulations results on the Cu 60Zr 40 model metallic glass (MG) in which they were found to be the most abundant microstructural units. In addition, aiming in gaining inside on the experimental findings referring to properties improvement upon small Al additions in the CuZr MGs, we performed calculations for the same systems in which Al substitutional atoms were incorporated into the clusters. In all cases the electronic structures were analyzed and the corresponding bonding characteristics were deduced. Moreover, in order to reveal the electronic modifications these systems subsist under mechanical deformation, we performed non-equilibrium calculations by applying tensile solicitations and we deduced the basic alterations that are responsible for the systems’ responses. It turns out that Al has elemental bonding preference; its presence in the clusters and in their interconnections alters significantly their electronic structure by introducing new low-energy states, while significant charge transfer occurs upon mechanical deformation. The present results are in line with the available experimental findings and provide inside on the fundamental issues that are related with the improvement of the glass forming ability and of the mechanical properties in the systems that contain small Al additions.

Structure inhibited pit initiation in a Ni–Nb metallic glass

A model metallic glass Ni 50Nb 50, which would undergo a polymorphous transformation during devitrification, was selected to clarify the correlation of amorphous structure with corrosion. The electrochemical polarization behaviour, film breakdown and composition of surface film have been studied in detail by comparing the amorphous alloy with its crystalline counterparts. Interestingly, it was found that the pit initiation is inhibited greatly on amorphous sample relative to the crystallized one. The origin is thought to be related to the defective interface beneath passive film that inhibits the formation of pitting precursors in corrosion.

Icosahedral ordering in Cu60Zr40 metallic glass: Molecular dynamics simulations

The atomic structure of bulk metallic glasses has long been mysterious for the lack of long range order. Although the solute-centered cluster packing model has recently been proposed to disclose the nanoscale medium-range order (MRO), the atomic packing scheme in systems with large solute concentration remains obscure. In this work, the atomic structure of Cu60Zr40 metallic glass is investigated via molecular dynamics simulations with the Finnis–Sinclair potential. It is found that the fragments of icosahedra are dominant in the model metallic glass. The icosahedra are completely centered by solvent atoms. Extended clusters composed of two icosahedra interpenetrate and form MRO with 3–11 icosahedra. It is suggested that the structure of Cu60Zr40 metallic glass can be described by the aggregation of icosahedra.

Mesoscale modeling of amorphous metals by shear transformation zone dynamics

A new mesoscale modeling technique for the thermo-mechanical behavior of metallic glasses is proposed. The modeling framework considers the shear transformation zone (STZ) as the fundamental unit of deformation, and coarse-grains an amorphous collection of atoms into an ensemble of STZs on a mesh. By employing finite element analysis and a kinetic Monte Carlo algorithm, the modeling technique is capable of simulating glass processing and deformation on time and length scales greater than those usually attainable by atomistic modeling. A thorough explanation of the framework is presented, along with a specific two-dimensional implementation for a model metallic glass. The model is shown to capture the basic behaviors of metallic glasses, including high-temperature homogeneous flow following the expected constitutive law, and low-temperature strain localization into shear bands. Details of the effects of processing and thermal history on the glass structure and properties are also discussed.

Atomistic simulation of a NiZr model metallic glass under hydrostatic pressure

Compressive behavior of a model NiZr metallic glass under hydrostatic pressure is simulated using molecular dynamics. The equation of state obtained exhibits two distinct regimes, one at low and the other at high pressure, along with an intermediate region in between. The densification is associated with topological rearrangement of atoms at low pressure and hard-sphere-like compaction dictated by the strong interatomic repulsion at high pressure. Different from many isotropic materials, the atomic rearrangement in the metallic glass during compression is accompanied by strong local topological structure change and chemical short-range (re)ordering. The possibility of a pressure-induced phase transition is briefly discussed.

Shear induced structural ordering of a model metallic glass

We report results of nonequilibrium molecular dynamics simulations of a one-component glassy system under the influence of a shear flow, with the aim of investigating shear-induced ordering of this system. In spite of the very low temperature, the system transforms into a strained crystalline state through well defined nucleation events. Various characteristics of the observed ordering at different strain rates and temperatures are discussed. We also define and discuss the transition rates.

Ordered clusters and free volume in a Zr–Ni metallic glass

The atomic arrangement of a model metallic glass Zr2Ni was studied by extended x-ray absorption fine structure and x-ray scattering experiments combined with reverse Monte Carlo simulation imposed an additional potential constraint. By an approach to calculating the free volume (FV) on atomic level, we have found a connection between the coordination number and FV, and then revealed that the atomic structure of Zr2Ni metallic glass is essentially an association of the ordered clusters and FV. The ordered clusters about 1.5nm consist of a densely packed core (i.e., icosahedral or fcc-type packing) and the surrounding loosely packed clusters with large FV.

Surface structure and properties of NiZr model metallic glasses: A molecular dynamics simulation

A systematic study of the surface structure and properties of NiZr model metallic glasses is reported using atomistic simulations. It is found that at low temperatures below the glass transition temperatures, the surface retains the amorphous structure and the surface energy γ is significantly lower (∼50%) than that of the corresponding crystalline alloy constituents. The variation of alloy concentration has little effect on γ; but increase in cooling rate and annealing temperature can lead to large decrease in γ. At elevated temperatures, γ increases with temperature and surface melting occurs at a temperature about 30% below Tg. At all temperatures up to Tg, the surface remains atomically smooth.

Strong configurational dependence of elastic properties for a binary model metallic glass

In this work, the strong dependence of elastic properties on configurational changes in a Cu–Zr binary metallic glass assessed by molecular dynamics simulations is reported. By directly evaluating the temperature dependence and configurational potential energy dependence of elastic constants, the shear modulus dependence on the specific configurational inherent state of metallic glasses is shown to be much stronger than the dependence on Debye-Grüneisen thermal expansion.

Simulations of nanoindentation in a thin amorphous metal film

Nanoindentation was simulated in a two dimensional model metallic glass thin film using molecular dynamics. Strain localization was observed in simulations where the system was sufficiently structurally relaxed prior to deformation. Indentation simulations utilized an atomic indenter that adhered to the surface or a frictionless indenter. Boundary conditions were varied to constrain the film or allow the film to relax in-plane to examine the effect on shear band formation. The most constrained system, i.e. that with the atomic indenter and the constrained boundaries exhibited the highest hardness.

Diffusion in a model metallic glass: Heterogeneity and ageing

We report results of molecular dynamics simulations of a binary Lennard-Jones system at zero pressure in the undercooled liquid and glassy states. We first follow the evolution of diffusivity and dynamic heterogeneity with temperature and show their correlation. In a second step we follow the ageing of a quenched glass. As diffusivity decreases with ageing, heterogeneity increases. We conclude that the heterogeneity is a property of the inherent diffusion of the relaxed state. The variations with ageing time can be explained by annealing of quenched defect structures. This annealing has the same decay constants for both diffusivity and heterogeneity of both components.

Relating metallic glass mechanical properties to liquid structure

Abstract Molecular dynamics simulations indicate that the mechanical properties of a model metallic glass depend critically on the degree of supercooling attained in the liquid prior to vitrification. A well-characterized binary glass-forming system roughly analogous to ZrTi was quenched instantaneously from a series of liquid temperatures. These temperatures ranged from approximately twice that of the onset of supercooled liquid behaviour down to just above the mode-coupling temperature ( T MCT ). The low-temperature mechanical properties of these glass samples is studied in simple shear at constant strain rate while the density of the system is held constant. All the glasses exhibit an initial linear response at small strain and approached a steady-state flow regime at large strain. However, glasses obtained by quenching from supercooled liquids just above T MCT , which we will refer to as T MCT glasses, exhibit higher shear strength and modulus than glasses obtained by quenching from higher temperature liquids. The T MCT glasses also exhibit pronounced shear softening. The change in pressure during shear is markedly different in these glasses, and indicates that the T MCT glasses retain aspects of the quenched-in structure out to as much as 25% strain. The changes in pressure also indicate significant structural changes occur even during nearly linear stress–strain response.

Yield surface of a simulated metallic glass

We perform molecular simulations of multiaxial deformation in a model metallic glass using a zero-Kelvin energy minimization technique. We find that there is a pronounced asymmetry between the magnitudes of the yield stresses in tension and compression, with the uniaxial compressive strength approximately 24% higher. By exploring a variety of biaxial stress states, we probe the plane-stress yield surface and find that it is not well-described by traditional yield criteria that depend only on the maximum shear stress. In contrast, the Mohr–Coulomb criterion, which includes an additional normal stress term, is found to describe the data quite well. Finally, the simulation results are shown to compare favorably with the available experimental data.

Structural dynamics on the μs scale in molecular-dynamics simulated, deeply undercooled, glass-forming Ni 0.5Zr 0.5

Results are reported from molecular dynamics (MD) simulations on the structural dynamics in a Ni 0.5Zr 0.5 metallic-glass model. Presented are, in particular, the mean squares displacements (MSD) for Ni and Zr atoms over a time window of 0.7 μs at 700 K. They indicate a change of the system between temporarily arrested and dynamical transient phases. The former extend up to 0.3 μs. From the data, diffusion coefficients are estimated and related to those from earlier simulations for higher temperatures. Atomic chain transitions in two-centre configurations are identified as the basic mechanisms of the dynamics. For some cases, the barrier heights of the centres are calculated and the pressure effect deduced. The latter indicates an activation volume of 7×10 −30 m 3 , a value comparable to the experimental activation volume of diffusion in NiZr.

A Monte Carlo study of realistic models of metallic spin glasses

Monte Carlo simulation methods are used to study the critical behaviour of the classical Ruderman-Kittel-Kasuya-Yosida model (RKKY) metallic spin glasses both with and without the presence of weak Dzyaloshinskii-Moriya anisotropy (DM). Finite-size scaling analyses of the data for equilibrium averages and relaxation times indicate a zero-temperature critical point for the isotropic RKKY model. When the DM interaction is included, the model exhibits a phase transition at a non-zero temperature. The values of the critical exponents at this transition are close to those obtained for the three-dimensional short-range Ising spin glass and in experiments on CuMn.