Glass breaks like metal, but at the nanometer scale

Brittle and ductile yielding in soft materials

Many soft materials yield under mechanical loading, but how this transition from solid-like behavior to liquid-like behavior occurs can vary significantly. Understanding the physics of yielding is of great interest for the behavior of biological, environmental, and industrial materials, including those used as inks in additive manufacturing and muds and soils. For some materials, the yielding transition is gradual, while others yield abruptly. We refer to these behaviors as being ductile and brittle. The key rheological signatures of brittle yielding include a stress overshoot in steady-shear-startup tests and a steep increase in the loss modulus during oscillatory amplitude sweeps. In this work, we show how this spectrum of yielding behaviors may be accounted for in a continuum model for yield stress materials by introducing a parameter we call the brittility factor. Physically, an increased brittility decreases the contribution of recoverable deformation to plastic deformation, which impacts the rate at which yielding occurs. The model predictions are successfully compared to results of different rheological protocols from a number of real yield stress fluids with different microstructures, indicating the general applicability of the phenomenon of brittility. Our study shows that the brittility of soft materials plays a critical role in determining the rate of the yielding transition and provides a simple tool for understanding its effects under various loading conditions.

Criticality in the fracture of silica glass: Insights from molecular mechanics

The universality of avalanches characterizing the inelastic response of disordered materials has the potential to bridge the gap from micro to macroscale. In this study, we explore the statistics and the scaling behavior of avalanches occurring during the fracture process in silica glass using molecular mechanics. We introduce a robust method for capturing and quantifying these avalanches, allowing us to perform rigorous statistical analyses, revealing universal power laws associated with critical phenomena. The influence of an initial crack is explored, observing deviations from mean-field predictions while maintaining the property of criticality. However, the avalanche exponents in the unnotched samples are predicted correctly by the mean-field depinning model. Furthermore, we investigate the strain-dependent probability density function, its cutoff function, and the interrelation between the critical exponents. Finally, we unveil distinct scaling behavior for small and large avalanches of the crack growth, shedding light on the underlying fracture mechanisms in silica glass.

Griffith theory of physical fractures, statistical procedures and entropy production: Rosetta stone's legacy

A physical model, based on energy balances, is proposed to describe the fractures in solid structures such as stelae, tiles, glass, and others. We applied the model to investigate the transition of the Rosetta Stone from the original state to the final state with three major fractures. We consider a statistical corner-breaking model with cutting rules. We obtain a probability distribution as a function of the area and the number of vertices. Our generic results are consistent with the current state of the Rosetta Stone and, additionally, predictions related to a fourth fracture are declared. The loss of information on such heritage pieces is considered through entropy production. The explicit quantification of this concept in information theory stays examined.

Dynamics of crack front waves in three-dimensional material failure

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in three-dimensional (3D) materials. We study FW dynamics in the framework of a 3D phase-field platform that features a rate-dependent fracture energy Γ(v) (v is the crack propagation velocity) and intrinsic length scales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with dΓ(v)/dv>0, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally observed solitonic behavior. Driving in-plane FWs into the nonlinear regime, we find that they propagate slower than predicted by a linear perturbation theory. Finally, by introducing small out-of-plane symmetry-breaking perturbations, coupled in- and out-of-plane FWs are excited, but the out-of-plane component decays under pure tensile loading. Yet, including a small antiplane loading component gives rise to persistent coupled in- and out-of-plane FWs.

Universal mechanical instabilities in the energy landscape of amorphous solids: Evidence from athermal quasistatic expansion

Using numerical simulations, we study the failure of an amorphous solid under athermal quasistatic expansion starting from a homogeneous high-density state. During the expansion process, plastic instabilities occur, manifested via sudden jumps in pressure and energy, with the largest event happening via cavitation leading to the material's yielding. We demonstrate that all these plastic events are characterized by saddle-node bifurcation, during which the smallest nonzero eigenvalue of the Hessian matrix vanishes via a square-root singularity. We find that after yielding and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show subextensive system-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our paper reveals universal features in the fundamental characteristics during mechanical failure in amorphous solids under any quasistatic deformation protocol.

Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems

Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

Low bend loss femtosecond laser written waveguides exploiting integrated microcrack

We introduce the fabrication and use of microcracks embedded in glass as an optical element for manipulating light propagation, in particular for enhancing waveguide performance in silica integrated optics. By using a femtosecond laser to induce a strong asymmetric stress pattern in silica, uniform cracks with set dimensions can be created within the substrate and propagated along a fixed path. The smoothness of the resulting cleave interface and large index contrast can be exploited to enhance waveguide modal confinement. As a demonstration, we tackle the longstanding high bend-loss issue in femtosecond laser written silica waveguides by using this technique to cleave the outer edge of laser written waveguide bends, to suppress radiative bend loss. The microcrack cross section is estimated to be 15 μm in height and 30 nm in width, for the 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times$$\end{document}× 10 μm waveguides. At 1550 nm wavelength, losses down to 1 dB/cm at 10 mm bend radius were achieved, without introducing additional scattering. Both the cleave stress pattern and waveguide are fabricated with the same multiscan writing procedure, without requiring additional steps, and re-characterisation of the waveguides after 1 year confirm excellent long term performance stability.

Observation of cavitation governing fracture in glasses

Crack propagation is the major vehicle for material failure, but the mechanisms by which cracks propagate remain longstanding riddles, especially for glassy materials with a long-range disordered atomic structure. Recently, cavitation was proposed as an underlying mechanism governing the fracture of glasses, but experimental determination of the cavitation behavior of fracture is still lacking. Here, we present unambiguous experimental evidence to firmly establish the cavitation mechanism in the fracture of glasses. We show that crack propagation in various glasses is dominated by the self-organized nucleation, growth, and coalescence of nanocavities, eventually resulting in the nanopatterns on the fracture surfaces. The revealed cavitation-induced nanostructured fracture morphologies thus confirm the presence of nanoscale ductility in the fracture of nominally brittle glasses, which has been debated for decades. Our observations would aid a fundamental understanding of the failure of disordered systems and have implications for designing tougher glasses with excellent ductility.

Molecular dynamics simulations of simplified sodium borosilicate glasses: the effect of composition on structure and dynamics

The fusion of valuable material properties has led to the acceptance of sodium borosilicate (NBS) glasses for nuclear waste immobilization. Although popular, the mechanisms associated with these properties are still only partially discovered and need further exploration. Bearing this in mind, the combination of experiments, molecular dynamics (MD) simulations and the Dell, Yuan and Bray model have been used to understand the role of composition variation for structural and physical aspects of vitrified borosilicate glasses. Experiments have been conducted to evaluate the macroscopic glass parameters of density (ρ), glass transition temperature (Tg) and thermal expansion coefficient (TEC). Experimentally observed trends for ρ, Tg and TEC with composition have been found in good agreement with the MD results. MD studies also provide a microscopic understanding of the glass structure and phenomena associated with the change in the glass composition. A detailed view of local structure and medium-range connectivity for the borosilicate glasses has been explored. Owing to a large B4 population, the results showed the abundant presence of BO4-BO4 connections, we hereby omit the generally accepted "B[4] avoidance rule" for glass. The relative propensity for connecting SiO4/BO3/BO4 structural motifs is in line with the predictions made by the Dell, Yuan and Bray model. Furthermore, the effects of composition on the mechanical integrity of NBS glasses, including the elastic nature, plastic distortion, yielding, breaking stress, and brittle fracture, have been explored by MD simulations. In addition, the glass dynamics have been evaluated by diffusion coefficient and the results suggest that Na+ is likely to be more mobile in the case of NBS1 as compared to NBS2 and NBS3 due to significant disruption in the glass network introduced by a larger amount of Na2O network modifier. Also, the diffusivity was reduced with increasing B2O3 due to the altered role of Na+ ions from network modifiers to charge compensators. The combined study of experiments, MD simulations and the Dell, Yuan and Bray model establish the correlation between the microscopic structure and macroscopic properties of NBS glasses with varied composition, which might be of great scientific use for future glasses in various applications including nuclear waste immobilization.

Size-Dependent Mechanical Properties of Amorphous SiO2 Nanowires: A Molecular Dynamics Study

Uniaxial tension tests were performed for amorphous SiO2 nanowires using molecular dynamics simulation to probe the size effect on the mechanical properties and plastic deformation by varying the length of nanowires. The simulation results showed that the Young's modulus of SiO2 nanowires increased with the decrease of nanowires length due to its higher surface stress. The corresponding deformation of SiO2 nanowires during tension exhibited two periods: atomic arrangement at small strain and plastic deformation at large strain. During the atomic arrangement period, the percentage variations of atom number of 2-coordinated silicon and 3-coordinated silicon (PCN2 and PCN3) decreased, while the percentage variations of atom number of 4-coordinated silicon, 5-coordinated silicon (PCN4 and PCN5) and the Si-O bond number (PCB) rose slightly with increasing strain, as the strain was less than 22%. The situation reversed at the plastic deformation period, owing to the numerous breakage of Si-O bonds as the strain grew beyond 22%. The size effect of nanowires radius was considered, finding that the Young's modulus and fracture stress were higher for the larger nanowire because of fewer dangling bonds and coordinate defeats in the surface area. The elastic deformation occurred at a small strain for the larger nanowire, followed by the massive plastic deformation during tension. A brittle mechanism covers the fracture characteristics, irrespective of the nanowire size.

Dynamics and Properties of the Cohesive Zone in Rapid Fracture and Friction

The cohesive zone is the elusive region in which material fracture takes place. Here, the putatively singular stresses at a crack's tip are regularized. We present experiments, performed on PMMA, in which we visualize the cohesive zone of frictional ruptures as they propagate. Identical to shear cracks, these ruptures range from slow velocities to nearly the limiting speeds of cracks. We reveal that the cohesive zone is a dynamic quantity; its spatial form undergoes a sharp transition between distinct phases at a critical velocity. The structure of these phases provides an important window into material properties under the extreme conditions that occur during fracture.

Fracture toughness of a metal-organic framework glass

Metal-organic framework glasses feature unique thermal, structural, and chemical properties compared to traditional metallic, organic, and oxide glasses. So far, there is a lack of knowledge of their mechanical properties, especially toughness and strength, owing to the challenge in preparing large bulk glass samples for mechanical testing. However, a recently developed melting method enables fabrication of large bulk glass samples (>25 mm³) from zeolitic imidazolate frameworks. Here, fracture toughness (K_Ic) of a representative glass, namely ZIF-62 glass (Zn(C₃H₃N₂)_1.75(C₇H₅N₂)_0.25), is measured using single-edge precracked beam method and simulated using reactive molecular dynamics. K_Ic is determined to be ~0.1 MPa m^0.5, which is even lower than that of brittle oxide glasses due to the preferential breakage of the weak coordinative bonds (Zn-N). The glass is found to exhibit an anomalous brittle-to-ductile transition behavior, considering its low fracture surface energy despite similar Poisson’s ratio to that of many ductile metallic and organic glasses.

Metal-organic framework glasses are gaining interest, but large samples are difficult to fabricate and mechanical properties are not well understood. Here, the authors use experiments and simulations to assess fracture toughness and flexural strength of a zeolitic imidazolate framework glass.

Silica Glass Toughened by Consolidation of Glassy Nanoparticles

The brittleness of oxide glasses has dramatically restricted their practical applications as structural materials despite very high theoretical strength. Herein, using molecular dynamics simulations, we show that silica glass prepared by consolidating glassy nanoparticles exhibit remarkable tensile ductility. Because of dangling bonds at surfaces and high contact stresses, the pressure applied for consolidating glassy nanoparticles to achieve ductility is significantly lower than that required to toughen bulk glass via permanent densification. We have identified 5-fold silicon, with a higher propensity to carry out local shear deformation than 4-fold silicon, as the structural origin for the observed tensile ductility. Interestingly, the work hardening effect has been, for the first time, observed in thus-prepared silica glass, with its strength increasing from 4 GPa to ∼7 GPa upon cold work. This is due to stress-assisted relaxation of 5-fold silicon to 4-fold during cold work, analogous to transformation hardening.

Damage Accumulation in Silica Glass Nanofibers

The origin of the brittle-to-ductile transition, experimentally observed in amorphous silica nanofibers as the sample size is reduced, is still debated. Here we investigate the issue by extensive molecular dynamics simulations at low and room temperatures for a broad range of sample sizes, with open and periodic boundary conditions. Our results show that small sample-size enhanced ductility is primarily due to diffuse damage accumulation, that for larger samples leads to brittle catastrophic failure. Surface effects such as boundary fluidization contribute to ductility at room temperature by promoting necking, but are not the main driver of the transition. Our results suggest that the experimentally observed size-induced ductility of silica nanofibers is a manifestation of finite-size criticality, as expected in general for quasi-brittle disordered networks.

Microscopic dynamics and failure precursors of a gel under mechanical load

Material failure is ubiquitous, with implications from geology to everyday life and material science. It often involves sudden, unpredictable events, with little or no macroscopically detectable precursors. A deeper understanding of the microscopic mechanisms eventually leading to failure is clearly required, but experiments remain scarce. Here, we show that the microscopic dynamics of a colloidal gel, a model network-forming system, exhibit dramatic changes that precede its macroscopic failure by thousands of seconds. Using an original setup coupling light scattering and rheology, we simultaneously measure the macroscopic deformation and the microscopic dynamics of the gel, while applying a constant shear stress. We show that the network failure is preceded by qualitative and quantitative changes of the dynamics, from reversible particle displacements to a burst of irreversible plastic rearrangements.

Cavitation-Induced Fracture Causes Nanocorrugations in Brittle Metallic Glasses

Brittle metallic glasses exhibit a unique and intriguing fracture morphology of periodic nanocorrugations whose spacing and amplitude are of the order of tens of nanometers. We show through continuum simulations that they fail by spontaneous and simultaneous cavitation within multiple weak zones arising due to intrinsic atomic density fluctuations ahead of a notch tip. Dynamic crack growth would then occur along curved but narrowly confined shear bands that link the growing cavities. This mechanism involves little dissipation and also explains the formation of nanocorrugations.

Size-Dependent Brittle-to-Ductile Transition in Silica Glass Nanofibers

Silica (SiO2) glass, an essential material in human civilization, possesses excellent formability near its glass-transition temperature (Tg > 1100 °C). However, bulk SiO2 glass is very brittle at room temperature. Here we show a surprising brittle-to-ductile transition of SiO2 glass nanofibers at room temperature as its diameter reduces below 18 nm, accompanied by ultrahigh fracture strength. Large tensile plastic elongation up to 18% can be achieved at low strain rate. The unexpected ductility is due to a free surface affected zone in the nanofibers, with enhanced ionic mobility compared to the bulk that improves ductility by producing more bond-switching events per irreversible bond loss under tensile stress. Our discovery is fundamentally important for understanding the damage tolerance of small-scale amorphous structures.

Heterogeneity: The key to failure forecasting

Elastic waves are generated when brittle materials are subjected to increasing strain. Their number and energy increase non-linearly, ending in a system-sized catastrophic failure event. Accelerating rates of geophysical signals (e.g., seismicity and deformation) preceding large-scale dynamic failure can serve as proxies for damage accumulation in the Failure Forecast Method (FFM). Here we test the hypothesis that the style and mechanisms of deformation, and the accuracy of the FFM, are both tightly controlled by the degree of microstructural heterogeneity of the material under stress. We generate a suite of synthetic samples with variable heterogeneity, controlled by the gas volume fraction. We experimentally demonstrate that the accuracy of failure prediction increases drastically with the degree of material heterogeneity. These results have significant implications in a broad range of material-based disciplines for which failure forecasting is of central importance. In particular, the FFM has been used with only variable success to forecast failure scenarios both in the field (volcanic eruptions and landslides) and in the laboratory (rock and magma failure). Our results show that this variability may be explained, and the reliability and accuracy of forecast quantified significantly improved, by accounting for material heterogeneity as a first-order control on forecasting power.

Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet

We study the interaction of two collinear cracks in polymer sheets slowly growing towards each other, when submitted to uniaxial stress at a constant loading velocity. Depending on the sample's geometry-specifically, the initial distances d between the two cracks' axes and L between the cracks' tips-we observe different crack paths with, in particular, a regime where the cracks repel each other prior to being attracted. We show that the angle θ characterizing the amplitude of the repulsion-and specifically its evolution with d-depends strongly on the microscopic behavior of the material. Our results highlight the crucial role of the fracture process zone. At interaction distances larger than the process zone size, crack repulsion is controlled by the microscopic shape of the process zone tip, while at shorter distances, the overall plastic process zone screens the repulsion interaction.

Brittle to ductile transition in densified silica glass

Current understanding of the brittleness of glass is limited by our poor understanding and control over the microscopic structure. In this study, we used a pressure quenching route to tune the structure of silica glass in a controllable manner, and observed a systematic increase in ductility in samples quenched under increasingly higher pressure. The brittle to ductile transition in densified silica glass can be attributed to the critical role of 5-fold Si coordination defects (bonded to 5 O neighbors) in facilitating shear deformation and in dissipating energy by converting back to the 4-fold coordination state during deformation. As an archetypal glass former and one of the most abundant minerals in the Earth's crest, a fundamental understanding of the microscopic structure underpinning the ductility of silica glass will not only pave the way toward rational design of strong glasses, but also advance our knowledge of the geological processes in the Earth's interior.

Propagation mechanism of brittle cracks

We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as observed in experiments on the nanoscale. The appearance of these voids is responsible for roughening the crack path on small scales, in agreement with theoretical expectations. With increasing speed of propagation one observes the branching instabilities that were reported in experiments. The simulations allow understanding the phenomena by analyzing the elastic stress field that accompanies the crack dynamics.

Reduced stress concentration and enhanced fracture toughness by yielding-rehardening combination

A range of tough materials (e.g., metals and polymer solids) exhibit a characteristic mechanical behavior, that is, a combination of yielding and subsequent rehardening. We numerically investigate how the combination of these mechanical behaviors enhances resistance to crack propagation.Our system has a 2-dimensional square lattice structure where pairs of adjacent lattice points are connected by "special" bonds. An isolated bond behaves as a linear spring for small deformations, but yields at a threshold force to produce a plateau in its force-deformation curve, and then shows rehardening on further loading up to a critical force of bond-breaking; on unloading from above the yielding point, the force rapidly decreases with deformation (hysteresis). We simulate crack propagation in the entire system (the square lattice structure) from an initial crack driven by boundary loading. The threshold force for bond-yielding is varied as a simulation parameter, while the critical force for bond-breaking in the rehardening regime is fixed to 1. In other words, the substantial simulation parameter is the ratio between the yielding and breaking forces. We find that the fracture behavior drastically changes depending on the ratio: when the ratio is low, the bond-breaking energy (of a single bond) is low, but more work is required to fracture the entire system via the crack propagation. The opposite tendency between the bond-breaking energy and the fracture work is due to formation of a well-developed yielding zone around the crack tip.

Towards ultrastrong glasses

The development of new glassy materials is key for addressing major global challenges in energy, medicine, and advanced communications systems. For example, thin, flexible, and large-area glass substrates will play an enabling role in the development of flexible displays, roll-to-roll processing of solar cells, next-generation touch-screen devices, and encapsulation of organic semiconductors. The main drawback of glass and its limitation for these applications is its brittle fracture behavior, especially in the presence of surface flaws, which can significantly reduce the practical strength of a glass product. Hence, the design of new ultrastrong glassy materials and strengthening techniques is of crucial importance. The main issues regarding glass strength are discussed, with an emphasis on the underlying microscopic mechanisms that are responsible for mechanical properties. The relationship among elastic properties and fracture behavior is also addressed, focusing on both oxide and metallic glasses. From a theoretical perspective, atomistic modeling of mechanical properties of glassy materials is considered. The topological origin of these properties is also discussed, including its relation to structural and chemical heterogeneities. Finally, comments are given on several toughening strategies for increasing the damage resistance of glass products.

Shear thinning and local melting of colloidal crystals

Phenomena such as shear thinning and thickening, occurring when complex materials are exposed to external forces, are generally believed to be closely connected to changes in the microstructure. Here, we establish a direct and quantitative relation between shear thinning in a colloidal crystal and the surface area of the locally melted region by dragging a probe particle through the crystal using optical tweezing. We show that shear thinning originates from the nonlinear dependence of the locally melted surface area on the drag velocity. Our observations provide unprecedented quantitative evidence for the intimate relation between mechanical properties and underlying changes in microscopic structure.

Evidence of deep water penetration in silica during stress corrosion fracture

We measure the thickness of the heavy water layer trapped under the stress corrosion fracture surface of silica using neutron reflectivity experiments. We show that the penetration depth is 65-85   Å, suggesting the presence of a damaged zone of ∼100   Å extending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results.

Contribution of spatially and spectrally resolved cathodoluminescence to study crack-tip phenomena in silica glass

A current controversy over the nature of fracture in silica glass is revisited in the light of additional experimental evidence obtained by cathodoluminescence (CL) spectroscopy in the immediate crack-tip zone of two different types of silica glass. The Letter describes the dual experimental output obtained by monitoring optically active oxygen defects in silica glass, as follows: (i) analysis of local crack-tip stoichiometry (i.e., lattice defect population); and, (ii) spatially resolved stress analysis ahead of the crack tip based on a piezo-spectroscopic (PS) approach. CL experiments provided us with direct access to crack-tip stress fields, thus unfolding some missing detail about the complex mechanochemical interactions occurring at the crack tip in silica glass.

Void deformation and breakup in shearing silica glass

We study shear deformation and breakup of voids in silica glass using molecular dynamics simulations. With an increase in the shear strain, two kinds of defects--threefold-coordinated silicon and nonbridging oxygen atoms--appear as spherical voids deform elastically into ellipsoidal shapes. For shear strains epsilon>15%, nanocracks appear on void surfaces and voids deform plastically into a threadlike structure. Nanocracks are nucleated by the migration of threefold-coordinated Si and nonbridging O on -Si-O-Si-O- rings. For epsilon>40%, the threadlike structures break up into several fragments.

Breakdown of linear elastic fracture mechanics near the tip of a rapid crack

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities (0.2-0.8c(s)), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be nonunique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the r(-1/2) divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.

Crack propagation through phase-separated glasses: effect of the characteristic size of disorder

We perform fracture experiments on nanoscale phase-separated glasses and measure crack surface roughness by atomic force microscopy. The ability of tuning the phase domain size by thermal treatment allows us to test thoroughly the predictions of crack front depinning models about the scaling properties of crack surface roughness. It appears that, in the range of validity of these depinning models developed for the fracture of brittle materials, our experimental results show a quantitative agreement with theoretical predictions: Beyond the characteristic size of disorder, the roughness of crack surfaces obeys the logarithmic scaling early predicted by Ramanathan, Ertaş, and Fisher [Phys. Rev. Lett. 79, 873 (1997)].

Interaction of voids and nanoductility in silica glass

Multimillion-to-billion-atom molecular dynamics simulations are performed to investigate the interaction of voids in silica glass under hydrostatic tension. Nanometer size cavities nucleate in intervoid ligaments as a result of the expansion of Si-O rings due to a bond-switching mechanism, which involves bond breaking between Si-O and bond formation between that Si and a nonbridging O. With further increase in strain, nanocracks form on void surfaces and ligaments fracture through the growth and coalescence of ligament nanocavities in a manner similar to that observed in ductile metallic alloys.

Statistics of fracture surfaces

We analyze the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the distribution to an analysis based on the structure functions. For length scales delta larger than a characteristic scale Lambda that corresponds to a material heterogeneity size, we find that the distribution of the height increments Deltah=h(x+delta)-h(x) is Gaussian and monoaffine, i.e., the scaling of the standard deviation sigma is proportional to delta(zeta) with a unique roughness exponent. Below the scale Lambda we observe a deviation from a Gaussian distribution and a monoaffine behavior. We discuss for the latter, the relevance of a multiaffine analysis and the influences of the discreteness resulting from material microstructures or experimental sampling.

Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics

We investigate the scaling properties of postmortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular, a roughness exponent zeta approximately 0.75 in homogeneous glass and zeta approximately 0.4 in glassy ceramics. The ranges of length scales over which these two scalings are observed are shown to be below and above the size of the process zone, respectively. A model derived from linear elastic fracture mechanics in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect the damage screening occurring for length scales below the size of the process zone.

A nanoscale mechanism of fatigue in ionic solids

We employ periodic density functional theory to explore the effect of cyclic tensile loading on the behavior of alumina in the threshold region of crack formation. We find evidence for nanoscale fatigue when the alumina lattice is subjected to uniaxial tensile loading and unloading and tensile stresses normal to the applied load. It is possible that such atomic-scale fatigue impacts the durability of ceramics, since the highly ionic bonding requires near-ideal lattice structures in order to maintain cohesive strength.

Atomistic characterization of three-dimensional lattice trapping barriers to brittle fracture

We present a detailed account of an atomistic study of three-dimensional lattice trapping barriers to brittle fracture in Si. By means of a prototypical interatomic potential model, we map out the molecular details of the evolution of atomically sharp cracks in the (111) cleavage plane with straight crack fronts along the and directions, respectively. The thermally activated processes of bond rupturing along the crack front are quantitatively characterized using a reaction pathway sampling scheme. The calculated minimum energy paths reveal a mechanism of kink-pair formation and migration in facilitating the crack front advancement. We show that the physical origin of directional anisotropy in cleavage crack propagation can be attributed to a difference in the kink-pair formation energy for different crack orientations. The effects of interatomic potentials are delineated by comparing the Stillinger–Weber model with an environment-dependent model.

Local waiting time fluctuations along a randomly pinned crack front

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, P(v) alpha v-eta with eta=2.55+/-0.15, for velocities v larger than the average front speed <v>. The burst size distribution is also a power law, P(S) alpha S-gamma with gamma=1.7+/-0.1. Above a characteristic length scale of disorder Ld approximately 15 microm, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H=0.66.

Dynamics of wing cracks and nanoscale damage in glass

We investigate initiation, growth, and healing of wing cracks in confined silica glass by molecular dynamics simulations. Under dynamic compression, frictional sliding of precrack surfaces nucleates nanovoids which evolve into nanocrack columns at the precrack tip. Nanocrack columns merge to form a wing crack, which grows via coalescence with nanovoids in the direction of maximum compression. Lateral confinement arrests the growth and partially heals the wing crack. Growth and arrest of the wing crack occur repeatedly, as observed in dynamic compression experiments on brittle solids under lateral confinement.

Optimum information in crackling noise

The crackling noise due to scratching superhard nanocomposite coatings was investigated by using a simple stick-slip model. The optimum information extracted from statistical analysis, in terms of the Akaike information criterion, is in good agreement with real tests. As a nanocomposite coating approaches an optimal performance, the acoustic emission energy follows a power-law distribution and its behavior is likely to be independent of microscopic and macroscopic details. The results imply that a peculiar deformation behavior, due to the competition between different deformation mechanisms such as dislocation pile-ups in nanocrystalline grains and grain sliding-grain rotation within amorphous boundaries, plays a vital role in the nanostructure with superhardness.

Void formation and roughening in slow fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Postmortem analysis of the resulting fracture surfaces of ductile and brittle materials on the microm-mm and the nm scales, respectively, reveals self-affine cracks with anomalous scaling exponent zeta approximately = 0.8 in 3 dimensions and zeta approximately = 0.65 in 2 dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2 dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.

Branching mechanism of intergranular crack propagation in three dimensions

We investigate the process of slow intergranular crack propagation by the finite element method model and show that branching is induced by partial arresting of a crack front owing to the geometrical randomness of grain boundaries. A possible scenario for the branching instability of crack propagation in a disordered continuous medium is also discussed.

Fracture of brittle metallic glasses: brittleness or plasticity

We report a brittle Mg-based bulk metallic glass which approaches the ideal brittle behavior. However, a dimple structure is observed at the fracture surface by high resolution scanning electron microscopy, indicating some type of "ductile" fracture mechanism in this very brittle glass. We also show, from the available data, a clear correlation between the fracture toughness and plastic process zone size for various glasses. The results indicate that the fracture in brittle metallic glassy materials might also proceed through the local softening mechanism but at different length scales.

Crack roughness and avalanche precursors in the random fuse model

We analyze the scaling of the crack roughness and of avalanche precursors in the two-dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents (zeta, zeta(loc) ) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as s(0) approximately L(D) , with a universal fractal dimension D , the distribution exponent tau differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value tau=5/2 .

Roughening of fracture surfaces: the role of plastic deformation

Post mortem analysis of fracture surfaces of ductile and brittle materials on the microm-mm and the nm scales, respectively, reveal self-affine cracks with anomalous scaling exponent zeta approximately 0.8 in three dimensions and zeta approximately 0.65 in two dimensions. Attempts to use elasticity theory to explain this result failed, yielding exponent zeta approximately 0.5 up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the void positions are positively correlated to yield exponents higher than 0.5.

Fracture of silicate glasses: ductile or brittle?

Atomic force microscopy is used to investigate the possibility of cavity formation during crack growth in silicate glasses. Matching areas on both fracture surfaces were mapped and then compared. For silica glass, and soda-lime-silicate glass, the fracture surfaces matched to a resolution of better than 0.3 nm normal to the surface and 5 nm parallel to the surface. We could find no evidence for cavity formation in our study and suggest that completely brittle fracture occurs in glass.