Structural defects in amorphous solids Statistical analysis of a computer model

World beyond the nearest neighbors

The structure beyond the nearest neighbor atoms in liquid and glass is characterized by the medium-range order (MRO). In the conventional approach, the MRO is considered to result directly from the short-range order (SRO) in the nearest neighbors. To this bottom-up approach starting with the SRO, we propose to add a top-down approach in which global collective forces drive liquid to form density waves. The two approaches are in conflict with each other, and the compromise produces the structure with the MRO. The driving force to produce density waves provides the stability and stiffness to the MRO, and controls various mechanical properties. This dual framework provides a novel perspective for description of the structure and dynamics of liquid and glass.

Medium-range atomic correlation in simple liquids. II. Theory of temperature dependence

The spatial atomic correlations in liquids and glasses extend often significantly beyond the nearest neighbors. Such correlations, called the medium-range order (MRO), affect many physical properties, but their nature is not well understood. In this article the variation of the MRO with temperature is calculated based upon the concept of the atomic-level pressure, focusing on simple liquids, such as metallic liquids. It is shown that the structural coherence length that characterizes MRO follows the Curie-Weiss law with a negative Curie temperature as observed by experiment and simulation. It is also shown that the glass transition is induced by freezing of the MRO, rather than the freezing of the nearest-neighbor shell. The implications of these results are discussed.

Low-energy quasilocalized excitations in structural glasses

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

Predicting orientation-dependent plastic susceptibility from static structure in amorphous solids via deep learning

It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotationally non-invariant local structure representation that enables different predictions for different loading orientations, which is found essential for high-fidelity prediction of the propensity for stress-driven shear transformations. This novel structure representation, when combined with convolutional neural network (CNN), a powerful deep learning algorithm, leads to unprecedented accuracy for identifying atoms with high propensity for shear transformations (i.e., plastic susceptibility), solely from the static structure in both two- and three-dimensional model glasses. The data-driven models trained on samples at one composition and a given processing history are found transferrable to glass samples with different processing histories or at different compositions in the same alloy system. Our analysis of the new structure representation also provides valuable insight into key atomic packing features that influence the local mechanical response and its anisotropy in glasses.

Internally Stressed and Positionally Disordered Minimal Complexes Yield Glasslike Nonphononic Excitations

Glasses, unlike their crystalline counterparts, exhibit low-frequency nonphononic excitations whose frequencies ω follow a universal D(ω)∼ω^{4} density of states. The process of glass formation generates positional disorder intertwined with mechanical frustration, posing fundamental challenges in understanding the origins of glassy nonphononic excitations. Here we suggest that minimal complexes-mechanically frustrated and positionally disordered local structures-embody the minimal physical ingredients needed to generate glasslike excitations. We investigate the individual effects of mechanical frustration and positional disorder on the vibrational spectrum of isolated minimal complexes, and demonstrate that ensembles of marginally stable minimal complexes yield D(ω)∼ω^{4}. Furthermore, glasslike excitations emerge by embedding a single minimal complex within a perfect lattice. Consequently, minimal complexes offer a conceptual framework to understand glasslike excitations from first principles, as well as a practical computational method for introducing them into solids.

Relation Between the Defect Interactions and the Serration Dynamics in a Zr-Based Bulk Metallic Glass

For this study, the effects of thermal annealing and compressive strain rate on the complexity of the serration behavior in a Zr-based bulk metallic glass (BMG) was investigated. Here, as-cast and thermally-annealed (300 °C, 1 week) Zr52.5Cu17.9Ni14.6Al10Ti5 BMG underwent room-temperature compression tests in the unconstrained condition at strain rates of 2 × 10−5 s−1 and 2 × 10−4 s−1. The complexity of the serrated flow was determined, using the refined composite multiscale entropy technique. Nanoindentation testing and X-ray diffraction characterization were performed to assess the changes in the microstructure and mechanical properties of the BMG that occurred during annealing. The results indicated that the BMG did not crystallize during annealing in the prescribed heating condition. Nanoindentation tests revealed that annealing led to a significant increase in the depth-dependent nanoindentation hardness and Young’s modulus, which were attributed to the structural relaxation in the glass. Furthermore, both annealing and an increased strain rate resulted in a marked enhancement in the complexity of the serrated flow during compression. It was concluded that the increase in the sample entropy with increasing strain rate is related to an increase in the number of defect interactions during the serrated flow.

The Mechanical Behaviors of Polyethylene/Silver Nanoparticle Composites: an Insight from Molecular Dynamics study

This research uses molecular dynamics simulation (MD) to study the mechanical properties of pristine polyethylene (PE) and its composites which include silver nanoparticles (PE/AgNPs) at two AgNP weight fractions of 1.05 wt% and 3.10 wt%. The stress-strain distribution of the tensile process shows that the embedded AgNPs can significantly improve the Young’s modulus and tensile strength of the pristine PE, due to improvements in the local density and strength of the PE near the AgNP surface in the range of 12 Å. Regarding the effect of temperature on the mechanical properties of pristine PE and PE/AgNP composites, the Young’s modulus and the strength of the pristine PE and PE/AgNP composites decreased significantly at 350 K and 450 K, respectively, consistent with predicted melting temperature of pristine PE, which lies at around 360 K. At such temperatures as these, PE material has stronger ductility and a higher mobility of AgNPs in the PE matrix than those at 300 K. With the increase of tensile strain, AgNPs tend to be close, and the fracture of PE leads to a similarity between both the Young’s modulus and ultimate strength found for the pristine PE and those found for the PE/AgNP composites at 350 K and 450 K, respectively.

Ideality of liquid structure: A case study for metallic alloy liquids

It is difficult to characterize by experiment the structural features of liquids and glasses which lack long-range translational periodicity in the structure. Here, we suggest that the height and shape of the first peak of the structure function S(Q) carry significant information about the nature of the medium-range order and the coherence of density correlations. It is further proposed that they indicate how ideal the liquid structure is. Here, the ideal state is defined by long-range density correlations, not by structural coherence at the atomic level. The analysis is applied to the S(Q) of metallic alloy liquids determined by x-ray diffraction and simulation. The ideality index defined here may provide a common parameter to characterize structural coherence among various disparate groups of liquids and glasses.

Curie-Weiss behavior of liquid structure and ideal glass state

We present the results of a structural study of metallic alloy liquids from high temperature through the glass transition. We use high energy X-ray scattering and electro-static levitation in combination with molecular dynamics simulation and show that the height of the first peak of the structure function, S(Q) - 1, follows the Curie-Weiss law. The structural coherence length is proportional to the height of the first peak, and we suggest that its increase with cooling may be related to the rapid increase in viscosity. The Curie temperature is negative, implying an analogy with spin-glass. The Curie-Weiss behavior provides a pathway to an ideal glass state, a state with long-range correlation without lattice periodicity, which is characterized by highly diverse local structures, reminiscent of spin-glass.

Shape Stability of Metallic Nanoplates: A Molecular Dynamics Study

Metallic nanoplates have attracted widespread interests owing to their functional versatility, which relies heavily on their morphologies. In this study, the shape stability of several metallic nanoplates with body-centered-cubic (bcc) lattices is investigated by employing molecular dynamics simulations. It is found that the nanoplate with (110) surface planes is the most stable compared to the ones with (111) and (001) surfaces, and their shapes evolve with different patterns as the temperature increases. The formation of differently orientated facets is observed in the (001) nanoplates, which leads to the accumulation of shear stress and thus results in the subsequent formation of saddle shape. The associated shape evolution is quantitatively characterized. Further simulations suggest that the shape stability could be tuned by facet orientations, nanoplate sizes (including diameter and thickness), and components.

Flow units as dynamic defects in metallic glassy materials

In a crystalline material, structural defects such as dislocations or twins are well defined and largely determine the mechanical and other properties of the material. For metallic glass (MG) with unique properties in the absence of a long-range lattice, intensive efforts have focused on the search for similar 'defects'. The primary objective has been the elucidation of the flow mechanism of MGs. However, their atomistic mechanism of mechanical deformation and atomic flow response to stress, temperature, and failure, have proven to be challenging. In this paper, we briefly review the state-of-the-art studies on the dynamic defects in metallic glasses from the perspective of flow units. The characteristics, activation and evolution processes of flow units as well as their correlation with mechanical properties, including plasticity, strength, fracture, and dynamic relaxation, are introduced. We show that flow units that are similar to structural defects such as dislocations are crucial in the optimization and design of metallic glassy materials via the thermal, mechanical and high-pressure tailoring of these units. In this report, the relevant issues and open questions with regard to the flow unit model are also introduced and discussed.

Molecular Dynamics Simulation on B3-GaN Thin Films under Nanoindentation

The B3-GaN thin film was investigated by performing large-scale molecular dynamics (MD) simulation of nanoindentation. Its plastic behavior and the corresponding mechanism were studied. Based on the analysis on indentation curve, dislocation density, and orientation dependence, it was found that the indentation depths of inceptive plasticity on (001), (110), and (111) planes were consistent with the Schmid law. The microstructure evolutions during the nanoindentation under different conditions were focused, and two formation mechanisms of prismatic loop were proposed. The "lasso"-like mechanism was similar to that in the previous research, where a shear loop can translate into a prismatic loop by cross-slip; and the extended "lasso"-like mechanism was not found to be reported. Our simulation showed that the two screw components of a shear loop will glide on another loop until they encounter each other and eventually produce a prismatic dislocation loop.

An atomic-scale evaluation of the fracture toughness of silica glass

Using an atomistic technique consistent with continuum balance laws and drawing on classical fracture mechanics theory, we estimate the resistance to fracture propagation of amorphous silica. We discuss correspondence and deviations from classical linear elastic fracture mechanics theory including size dependence, rigid/floppy modes of deformation, and the effects of surface energy and stress.

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and [Formula: see text]-based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid's mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Characterization of microscopic deformation through two-point spatial correlation functions

The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.

Deformation behavior of metallic glasses with shear band like atomic structure: a molecular dynamics study

Molecular dynamics simulations were employed to investigate the plastic deformation within the shear bands in three different metallic glasses (MGs). To mimic shear bands, MG specimens were first deformed until flow localization occurs, and then the volume of the material within the localized regions was extracted and replicated. Homogeneous deformation that is independent of the size of the specimen was observed in specimens with shear band like structure, even at a temperature that is far below the glass transition temperature. Structural relaxation and rapid cooling were employed to examine the effect of free volume content on the deformation behavior. This was followed by detailed atomic structure analyses, employing the concepts of Voronoi polyhedra and "liquid-like" regions that contain high fraction of sub-atomic size open volumes. Results suggest that the total fraction of atoms in liquid-like regions is a key parameter that controls the plastic deformation in MGs. These are discussed in the context of reported experimental results and possible strategies for synthesizing monolithic amorphous materials that can accommodate large tensile plasticity are suggested.

The mechanical properties and thermal stability of ultrathin germanium nanowires

The mechanical properties of ultrathin germanium nanowires are investigated: the mechanical properties of the nanowires are severely reduced when temperature increases.

Robust scaling of strength and elastic constants and universal cooperativity in disordered colloidal micropillars

We study the uniaxial compressive behavior of disordered colloidal free-standing micropillars composed of a bidisperse mixture of 3- and 6-μm polystyrene particles. Mechanical annealing of confined pillars enables variation of the packing fraction across the phase space of colloidal glasses. The measured normalized strengths and elastic moduli of the annealed freestanding micropillars span almost three orders of magnitude despite similar plastic morphology governed by shear banding. We measure a robust correlation between ultimate strengths and elastic constants that is invariant to relative humidity, implying a critical strain of ∼0.01 that is strikingly similar to that observed in metallic glasses (MGs) [Johnson WL, Samwer K (2005) Phys Rev Lett 95:195501] and suggestive of a universal mode of cooperative plastic deformation. We estimate the characteristic strain of the underlying cooperative plastic event by considering the energy necessary to create an Eshelby-like ellipsoidal inclusion in an elastic matrix. We find that the characteristic strain is similar to that found in experiments and simulations of other disordered solids with distinct bonding and particle sizes, suggesting a universal criterion for the elastic to plastic transition in glassy materials with the capacity for finite plastic flow.

Heterogeneous shear elasticity of glasses: the origin of the boson peak

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the boson-peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the boson-peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.

Elementary excitations and crossover phenomenon in liquids

The elementary excitations of vibration in solids are phonons. But in liquids phonons are extremely short lived and marginalized. In this Letter through classical and ab initio molecular dynamics simulations of the liquid state of various metallic systems we show that different excitations, the local configurational excitations in the atomic connectivity network, are the elementary excitations in high temperature metallic liquids. We also demonstrate that the competition between the configurational excitations and phonons determines the so-called crossover phenomenon in liquids. These discoveries open the way to the explanation of various complex phenomena in liquids, such as fragility and the rapid increase in viscosity toward the glass transition, in terms of these excitations.

Atomic mechanism of flow in simple liquids under shear

Atomic correlations in a simple liquid in steady-state flow under shear stress are studied by molecular dynamics simulation. The local atomic level strain is determined through the anisotropic pair-density function. The atomic level strain has a limited spatial extension whose range is dependent on the strain rate and extrapolates to zero at the critical strain rate. A failure event is identified with altering the local topology of atomic connectivity by exchanging bonds among neighboring atoms.

Local elastic properties of a metallic glass

The nature of non-crystalline materials causes the local potential energy of a cluster of atoms or molecules to vary significantly in space. Different configurations of an ensemble of atoms in a metallic glass lead therefore to a distribution of elastic constants which also changes in space. This is totally different to their crystalline counterparts, where a long-range order exists in space and therefore a much more unified elastic modulus is expected. Using atomic force acoustic microscopy, we present data which show that the local so-called indentation modulus M indeed exhibits a wide distribution on a scale below 10 nm in amorphous PdCuSi, with ΔM/M≈30%. About 10(4) atoms are probed in an individual measurement. Crystallized PdCuSi shows a variation that is 10-30 times smaller and which is determined by the resolution of the microscope and by the polycrystalline structure of the material.

Tuning the electronic properties of boron nitride nanotube by mechanical uni-axial deformation: a DFT study

The effect of uni-axial strain on the electronic properties of (8,0) zigzag and (5,5) armchair boron nitride nanotubes (BNNT) is addressed by density functional theory calculation. The stress-strain profiles indicate that these two BNNTS of differing types display very similar mechanical properties, but there are variations in HOMO-LUMO gaps at different strains, indicating that the electronic properties of BNNTs not only depend on uni-axial strain, but on BNNT type. The variations in nanotube geometries, partial density of states of B and N atoms, B and N charges are also discussed for (8,0) and (5,5) BNNTs at different strains.

Correlation of atomic cluster symmetry and glass-forming ability of metallic glass

Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce70-xAl10Cu20Cox upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by 27Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.

Athermal shear-transformation-zone theory of amorphous plastic deformation. I. Basic principles

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.

Low-frequency dynamical heterogeneity in simulated amorphous Ni0.5Zr0.5 below its glass temperature: correlations with cage volume and local order fluctuations

From molecular dynamics simulations results are reported concerning correlations between low-frequency (lf) heterogeneous dynamics in simulated Ni0.5Zr0.5 melts at 700, 760, and 810 K, which means around the Kauzmann temperature of the model, TK approximately 750 K. A method is presented to separate lf dynamics, reflecting the slow relaxation dynamics in the vitrifying melt, and high-frequency (hf) dynamics, characteristic of the thermal fluctuations at the considered temperatures. By means of a suitable quantitative measure of the distribution of heterogeneous lf dynamics in space and time, correlation parameters are evaluated between the spatial distribution of lf dynamics and structural inhomogeneities in the thermodynamically homogeneous melt. Relevant correlations are found between lf dynamics and some involved structure quantities such as the cage volume around Ni atoms, Omega Ni, or the Theta Ni parameter which reflects the geometry of the nearest-neighbor cage around Ni atoms. Further, at 810 K there is a weak correlation between heterogeneous dynamics and fluctuations of the mean potential energy per atom and a comparable weak anticorrelation with the particle density and Ni-atom density inhomogeneities, where these three correlations decrease with decreasing temperature. The present results indicate the existence of long-living regions of enhanced Omega Ni in the structure, which may act as regions of preferential initiation of irreversible lf dynamics and slow relaxation.

Numerical tests of constitutive laws for dense granular flows

We numerically and theoretically study the macroscopic properties of dense, sheared granular materials. In this process we first consider an invariance in Newton's equations, explain how it leads to Bagnold's scaling, and discuss how it relates to the dynamics of granular temperature. Next we implement numerical simulations of granular materials in two different geometries--simple shear and flow down an incline--and show that measurements can be extrapolated from one geometry to the other. Then we observe nonaffine rearrangements of clusters of grains in response to shear strain and show that fundamental observations, which served as a basis for the shear transformation zone (STZ) theory of amorphous solids [M. L. Falk and J. S. Langer, Phys. Rev. E. 57, 7192 (1998); M.R.S. Bull 25, 40 (2000)], can be reproduced in granular materials. Finally we present constitutive equations for granular materials as proposed by Lemaître [Phys. Rev. Lett. 89, 064303 (2002)], based on the dynamics of granular temperature and STZ theory, and show that they match remarkably well with our numerical data from both geometries.

Dynamics of shear-transformation zones in amorphous plasticity: nonlinear theory at low temperatures

We use considerations of energy balance and dissipation to derive a self-consistent version of the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. The theory is generalized to include arbitrary spatial orientations of STZs. Continuum equations for elasto-plastic material and their energy balance properties are discussed.

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.

Fracture behavior of Lennard-Jones glasses

The fracture behavior of binary Lennard-Jones (LJ) glasses is studied by extensive molecular dynamics simulations. These LJ glasses represent a nonbond limit of polymer network glasses. We determine that the low strain behavior of the LJ and polymer glasses is similar. Two different LJ glasses are fractured under tensile strain without any preexisting crack. Void formation and resulting growth as strain increases is the mechanism through which the system fails. Void formation initiates at the yield strain of varepsilon (y) approximately 0.09, which is approximately the same strain at which the yielding behavior is first observed in cross-linked network models of polymer adhesives. The yield stress increased only by small amounts with increased strain rate and with increased system size (from N=30 000 atoms to 120 000 atoms). Within the ranges tested, the stress-strain behavior of these systems is independent of the temperature drop during quench and the initial molecular configuration.