Molecular dynamics simulations are performed to examine the dynamic response of amorphous solids to oscillatory shear at finite temperatures. The data were collected from a poorly annealed binary glass, which was deformed periodically in the elastic regime during several hundred shear cycles. We found that the characteristic time required to reach a steady state with a minimum potential energy is longer at higher temperatures and larger strain amplitudes. With decreasing strain amplitude, the asymptotic value of the potential energy increases but it remains lower than in quiescent samples. The transient decay of the potential energy correlates well with a gradual decrease in the volume occupied by atoms with large nonaffine displacements. By contrast, the maximum amplitude of shear stress oscillations is attained relatively quickly when a large part of the system starts to deform reversibly.
Many structural glasses feature static and dynamic mechanical properties that can depend strongly on glass formation history. The degree of universality of this history-dependence, and what it is possibly affected by, are largely unexplored. Here we show that the variability of elastic properties of simple computer glasses under thermal annealing depends strongly on the strength of attractive interactions between the glasses' constituent particles -- referred to here as glass `stickiness'. We find that in stickier glasses the stiffening of the shear modulus with thermal annealing is strongly s…
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted…
Glasses behave as solids on experimental time scales due to their slow relaxation. Growing dynamic length scales due to cooperative motion of particles are believed to be central to this slow response. For quiescent glasses, however, the size of the cooperatively rearranging regions has never been observed to exceed a few particle diameters, and the observation of long-range correlations that are signatures of an elastic solid has remained elusive. Here, we provide direct experimental evidence of long-range correlations during the deformation of a dense colloidal glass. By imposing an external…
The effects of entanglement and chain orientation on strain hardening in glassy polymers are separated by examining mixtures of chains with different lengths. Simulations show that the orientation of a molecule of a given chain length is the same in monodisperse systems and bidisperse mixtures, even when entangled and unentangled chains are mixed. In addition, the stress in mixtures is equal to the weighted average of the stresses in monodisperse systems. These results indicate that chains contribute independently to strain hardening, that chain orientation is determined by local interactions …
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only obser…
Yielding behavior in amorphous solids has been investigated in computer simulations employing uniform and cyclic shear deformation. Recent results characterise yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively…
Glasses prepared by physical vapour deposition have been shown to be remarkably more stable than those prepared by standard cooling protocols, with properties that appear to be similar to systems aged for extremely long times. When subjected to a rapid rise in temperature, ultrastable glasses anneal towards the liquid in a qualitatively different manner than ordinary glasses, with the seeming competition of different timescales and lengthscales. We numerically reproduce the phenomenology of ultrastable glass annealing with a kinetically constrained model, a three dimensional East model with so…
When amorphous solids are strained they display elastic deformation at small strain, however, beyond a critical strain they yield and begin to flow plastically. The origin of this plasticity lies in the irreversible rearrangement of particles. Such rearrangements have been shown to give rise to a long-ranged quadrupolar strain field, similar to Eshebly's spherical inclusions. However, their spatio-temporal organisation at finite temperatures and finite shear rate remains unclear. Here, we have investigated the strain field in sheared colloidal glasses. We show that the strain field in homogene…
The influence of variable-amplitude loading on the potential energy and mechanical properties of amorphous materials is investigated using molecular dynamics simulations. We study a binary mixture that is either rapidly or slowly cooled across the glass transition temperature and then subjected to a sequence of shear cycles with strain amplitudes above and below the yielding strain. It was found that well annealed glasses can be rejuvenated by small-amplitude loading if the strain amplitude is occasionally increased above the critical value. By contrast, poorly annealed glasses are relocated t…
A comparison is made between the nonlinear rheological response of bulk metallic glass formers and of colloidal dispersions. Stress-strain curves measured after switch-on of constant deformation rates are analyzed quantitatively using a schematic model of mode coupling theory generalized to homogeneous and incompressible flows. A mapping between metallic and dispersion rheology is possible when stresses are rescaled by an entropic scale, accumulated strains by geometrical factors, and rates by the intrinsic relaxation time. Exploiting this similarity and the possibility to directly observe ind…
We theoretically investigate high-pressure effects on the atomic dynamics of metallic glasses. The theory predicts compression-induced rejuvenation and the resulting strain hardening that have been recently observed in metallic glasses. Structural relaxation under pressure is mainly governed by local cage dynamics. The external pressure restricts the dynamical constraints and slows down the atomic mobility. In addition, the compression induces a rejuvenated metastable state (local minimum) at a higher energy in the free energy landscape. Thus, compressed metallic glasses can rejuvenate and the…
We consider the yielding behaviour of a model glass subjected to asymmetric cyclic shear deformation, wherein the applied strain varies between 0 and a maximum value $γ_{\rm max}$, and study its dependence on the degree of annealing of the glass and system size. The yielding behaviour of well annealed glasses (unlike poorly annealed glasses) display striking differences from the symmetric case, with the emergence of an intermediate strain regime with substantial plasticity but no yielding. The observed behaviour is satisfactorily captured by a recently proposed model. For larger system sizes, …
Metallic Glasses are prone to fail mechanically via a shear-banding instability. In a remarkable paper Johnson and Samwer demonstrated that this failure enjoys a high degree of universality in the sense that a large group of metallic glasses appears to possess a yield-strain that decreases with temperature following a $-T^{2/3}$ law up to logarithmic corrections. In this Letter we offer a theoretical derivation of this law. We show that our formula fits very well simulational data on typical amorphous solids.
We use an analogue of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static …
The effect of small-amplitude periodic shear on annealing of a shear band in binary glasses is investigated using molecular dynamics simulations. The shear band is first introduced in stable glasses via large-amplitude periodic shear, and then amorphous samples are subjected to repeated loading during thousands of cycles at strain amplitudes below the yield strain. It was found that with increasing strain amplitude, the glasses are relocated to deeper potential energy levels, while the energy change upon annealing is not affected by the glass initial stability. The results of mechanical tests …
We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $σ$ while being deformed with strain rate $\dotε$, the microscopic structural relaxation time $τ_{\rm str}$ is given by the universal relation $σ/G_\infty\dotε$ with $G_\infty$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxatio…
We describe an apparatus for performing constant strain rate deformations of polymer glasses while simultaneously measuring the segmental mobility with an optical probe reorientation method. Poly(methyl methacrylate) glasses were deformed at Tg - 19 K, for local strain rates between 3.7x10-5/s and 1.2x10-4/s. In these experiments, the mobility initially increases in the pre-yield regime, by a factor of 40 to 160, as compared to the undeformed PMMA glass. The mobility then remains constant after yield, even as the stress is decreasing due to strain softening. This is consistent with the view th…
The dynamics of structural relaxation in a model polymer glass subject to spatially-homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about $10^4$ cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics…
We investigate the stress relaxation behavior on the application of step strains to aging aqueous suspensions of the synthetic clay Laponite. The stress exhibits a two-step decay, from which the slow relaxation modes are extracted as functions of the sample ages and applied step strain deformations. Interestingly, the slow time scales that we estimate show a dramatic enhancement with increasing strain amplitudes. We argue that the system ends up exploring the deeper sections of its energy landscape following the application of the step strain.
We explore the link between soft vibrational modes and local relaxation events in polymer glasses during physical aging, active deformation at constant strain rate, and subsequent recovery. A softness field is constructed out of the superposition of the amplitudes of the lowest energy normal modes, and found to predict up to 70% of the rearrangements. Overlap between softness and rearrangements increases logarithmically during aging and recovery phases as energy barriers rise due to physical aging, while yielding rapidly rejuvenates the overlap to that of a freshly prepared glass. In the strai…
Recently, ultrastable glasses have been created through vapor deposition. Subsequently, computer simulation algorithms have been proposed that mimic the vapor deposition process and result in simulated glasses with increased stability. In addition, random pinning has been used to generate very stable glassy configurations without the need for lengthy annealing or special algorithms inspired by vapor deposition. Kinetic and mechanical stability of experimental ultrastable glasses is compared to those of experimental glasses formed by cooling. We provide the basis for a similar comparison for si…
The influence of strain amplitude, glass stability and thermal fluctuations on shear band formation and yielding transition is studied using molecular dynamics simulations. The model binary mixture is first gradually cooled below the glass transition temperature and then periodically deformed to access a broad range of potential energy states. We find that the critical strain amplitude becomes larger for highly annealed glasses within about one thousand shear cycles. Moreover, upon continued loading at a fixed strain amplitude, the yielding transition is delayed in glasses mechanically anneale…
The response of glasses to mechanical loading often leads to the formation of inhomogeneous flow patterns that strongly affect materials properties. Among them, shear bands are ubiquitous in a wide variety of materials, ranging from soft matter systems to metallic alloys. Shear banding is associated with strain localization, i.e. the deformation of the sheared glassy solid is localized in space in form of band-like structures. These structures are often precursors to catastrophic failure, implying that a proper understanding of the underlying mechanisms could lead to the design of smarter mate…
The precipitation of a glass forming solute from solution is modelled using a lattice model previously introduced to study dissolution kinetics of amorphous materials. The model includes the enhancement of kinetics at the surface of a glass in contact with a plasticizing solvent. We demonstrate that precipitation can produce a glass substantially more stable than that produced by very long time annealing of the bulk glass former. The energy of these ultra-stable amorphous precipitates is found to be dominated by residual solvent rather than high energy glass configurations.
We report a strain rate (equivalent to experimental observation time) induced glass transition in model SrCaYbMg(Li)Zn(Cu) metallic glasses at room temperature. A critical strain rate, equivalent to glass transition temperature, is found for the strain rate induced a glassy state to liquid-like viscoplastic state translation. The results show that the observation time, equivalent to temperature and stress, is a key parameter for the glass transition. A three-dimension glass transition phase diagram involved in time, temperature and stress in metallic glasses is established for understanding th…
Using coarse-grained molecular-dynamics simulations, a generic styrene-(block)-butadiene-(block)-styrene (SBS) triblock copolymer under lamellar conformation is used in order to investigate the mutual entanglement evolution when a structure of alternating glassy (S)/rubbery (B) layers is submitted to an imposed deformation. By varying the amount of loop chains between each phase, i.e. noncrossing chains, it is possible to generate different types of S/B interface definitions. A specific boundary driven tensile strain protocol has been developed in order to mimic "real" experiments and measure …
Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely col- loidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dy- namics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different beha…
By comparing the response to external strains in metallic glasses and in Lenard-Jones glasses we find a quantitative universality of the fundamental plastic instabilities in the athermal, quasistatic limit. Microscopically these two types of glasses are as different as one can imagine, the latter being determined by binary interactions, whereas the former by multiple interactions due to the effect of the electron gas that cannot be disregarded. In spite of this enormous difference the plastic instability is the same saddle-node bifurcation. As a result the statistics of stress and energy drops…
The evolution of porous structure, potential energy and local density in binary glasses under oscillatory shear deformation is investigated using molecular dynamics simulations. The porous glasses were initially prepared via a rapid thermal quench from the liquid state across the glass transition and allowed to phase separate and solidify at constant volume, thus producing an extended porous network in an amorphous solid. We find that under periodic shear, the potential energy decreases over consecutive cycles due to gradual rearrangement of the glassy material, and the minimum of the potentia…
We investigate the response of dense hard sphere glasses to a shear strain, in a wide range of pressures ranging from the glass transition to the infinite-pressure jamming point. The phase diagram in the density-shear strain plane is calculated analytically using the mean field infinite dimensional solution. We find that just above the glass transition, the glass generically yields at a finite shear strain. The yielding transition, in the mean field picture, is a spinodal point in presence of disorder. At higher densities, instead, we find that the glass generically jams at a finite shear stra…
The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the many-body Smoluchowski equation. The resulting nonlinear stress-strain (constitutive) relation is very simple, with few fitting parameters, yet contains all the microscopic physics. The theory is successfully tested against experimental data on metallic glasses, and it is able to reproduce the ubiq…
The yielding behaviour of hard sphere glasses under large amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian Dynamics simulations. Brownian motion assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in\ $G^{\prime \prime}$. At intermediate frequencies a novel, for HS glasses, double peak in $G^{\prime \prime}$ is revealed r…
Using molecular dynamics simulations, we investigate the effect of uniaxial elastostatic compression on the potential energy, structural relaxation, and mechanical properties of binary glasses. We consider the three-dimensional Kob-Andersen binary mixture, which was initially cooled from the liquid state to the glass phase with a slow rate at zero pressure. The glass was then loaded with a static stress at the annealing temperature during extended time intervals. It is found that the static stress below the yielding point induces large-scale plastic deformation and significant rejuvenation whe…
We develop a free energy framework to describe the response of glasses to applied stress. Unlike crystals, for which the free energy increases quadratically with strain due to affine displacements, for glasses, the nonequilibrium free energy decreases due to complex interplay of non-affine displacements and dissipation. We measure this free energy directly in strained colloidal glasses, and use mean-field theory to relate it to affine and nonaffine displacements. Nonaffine displacements grow with applied shear due to shear-induced loss of structural connectivity. Our mean-field model allows fo…
Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a thi…
The influence of cyclic loading and glass stability on structural relaxation and yielding transition in amorphous alloys was investigated using molecular dynamics simulations. We considered a binary mixture cooled deep into the glass phase and subjected to cyclic shear deformation where strain varies periodically but remains positive. We found that rapidly cooled glasses under asymmetric cyclic shear gradually evolve towards states with lower potential energy and finite stress at zero strain. At the strain amplitude just below a critical value, the rescaled distributions of nonaffine displacem…
Amorphous materials such as metallic, polymeric, and colloidal glasses, exhibit complex preparation-dependent mechanical response to applied shear. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate $R$ used to prepare them. The ensemble-averaged stress versus strain curve $\langleσ(γ)\rangle$ resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak at intermediate s…
In this paper we study the mechanical properties and pore structure in a three-dimensional molecular dynamics model of porous glass under athermal quasistatic shear. The vitreous samples are prepared by rapid thermal quench from a high temperature molten state. The pore structures form via solid-gas phase separation. The quiescent samples exhibit a wide range of pore topography, from inter-connected pore network to randomly distributed compact pores depending on the material density. We find the shear modulus strongly depends on the density and porosity. Under mechanical loading, the pore stru…
We study the yielding behaviour of a model glass under cyclic athermal quastistatic deformation computationally, and show that yielding is characterised by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localised. Strain localisation is accompanied by a corresponding change in the energies, and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band whereas the energies correspond to the highest possible energy minima at the given density within the s…
The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements bec…
Molecular dynamics simulations are used to investigate the effects of deformation on the segmental dynamics in an aging polymer glass. Individual particle trajectories are decomposed into a series of discontinuous hops, from which we obtain the full distribution of relaxation times and displacements under three deformation protocols: step stress (creep), step strain, and constant strain rate deformation. As in experiments, the dynamics can be accelerated by several orders of magnitude during deformation, and the history dependence is entirely erased during yield (mechanical rejuvenation). Agin…
Amorphous solids, such as metallic, polymeric, and colloidal glasses, display complex spatiotemporal response to applied deformations. In contrast to crystalline solids, during loading, amorphous solids exhibit a smooth crossover from elastic response to plastic flow. In this study, we investigate the mechanical response of binary Lennard-Jones glasses to athermal, quasistatic pure shear as a function of the cooling rate used to prepare them. We find several key results concerning the connection between strain-induced particle rearrangements and mechanical response. We show that more rapidly c…
We present results from microscopic mode coupling theory generalized to colloidal dispersions under shear in an integration-through-transients formalism. Stress-strain curves in start-up shear, flow curves, and normal stresses are calculated with the equilibrium static structure factor as only input. Hard spheres close to their glass transition are considered, as are hard spheres with a short-ranged square-well attraction at their attraction dominated glass transition. The consequences of steric packing and physical bond formation on the linear elastic response, the stress release during yield…
Surface stress and surface energy are fundamental quantities which characterize the interface between two materials. Although these quantities are identical for interfaces involving only fluids, the Shuttleworth effect demonstrates that this is not the case for most interfaces involving solids, since their surface energies change with strain. Crystalline materials are known to have strain dependent surface energies, but in amorphous materials, such as polymeric glasses and elastomers, the strain dependence is debated due to a dearth of direct measurements. Here, we utilize contact angle measur…
Mode coupling theory (MCT) has had notable successes in addressing the rheology of hard-sphere colloidal glasses, and also soft colloidal glasses such as star-polymers. Here, we explore the properties of a recently developed MCT-based schematic constitutive equation under idealized experimental protocols involving single and then double step strains. We find strong deviations from expectations based on factorable, BKZ-type constitutive models. Specifically, a nonvanishing stress remains long after the application of two equal and opposite step strains; this residual stress is a signature of pl…
The influence of thermal processing on the potential energy, atomic structure, and mechanical properties of metallic glasses is examined using molecular dynamics simulations. We study the three-dimensional binary mixture, which was first relaxed near the glass transition temperature, and then rapidly cooled deep into the glass phase. It was found that glasses prepared at higher annealing temperatures are relocated to higher energy states and their average glass structure remains more disordered, as reflected in the shape of the pair correlation function. The results of mechanical testing demon…
Non-equilibrium molecular dynamics simulations are performed to investigate the dynamic behavior of three-dimensional binary glasses prepared via an instantaneous quench across the glass transition. We found that with increasing strain amplitude up to a critical value, the potential energy approaches lower minima in steady state, whereas the amplitude of shear stress oscillations becomes larger. Below the yielding transition, the storage modulus dominates the mechanical response, and the gradual decay of the potential energy over consecutive cycles is accompanied by reduction in size of transi…
