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 non-unique, 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 is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability at a fraction of the wave speed.
This paper explores the global Mode I fracture energy of a carbon fiber composite subject to a biaxial stress state at a crack tip, specifically in which one stress component is compressive and parallel to the crack. Based on an experimental technique previously coined as The Gap Test and Bazant's Type II Size Effect Law, it is found that there is a monotonic decrease in the Mode I fracture energy as the crack parallel compressive stress increases. Compared to the nominal value of fracture energy, where no crack parallel compression is applied, the fracture energy is observed to decrease by up…
We study the dynamics of cracks in brittle materials when the velocity of the crack is comparable to the sound velocity by means of lattice simulations. Inertial and damped dynamics are analyzed. It is shown that dissipation strongly influences the shape of the crack. While inertial cracks are highly unstable, dissipation can stabilize straight cracks. Our results can help to explain recent experiments on PMMA.
Numerous measurements showed that the crack tip opening angle (CTOA) is nearly constant upon stable ductile fracture in Al alloys which widely used in modern transportation industry. The atomic structure of the very tip of a crack front has remained unknown, however. We have carried out a first-principles density functional theory study to reveal the precise alignment of atoms near the crack tip in single-crystalline Al. The calculations demonstrate that the CTOA increases with the opening displacement, thus the observed constant CTOA in millimeter scale is an entirely plastic effect during du…
In this study, we report the mechanical properties and fracture mechanism of pre-cracked and defected InSe nanosheet samples using molecular dynamics (MD) simulations. We noticed that the failure of pre-cracked and defected InSe nanosheet is governed by brittle type fracture. Armchair directional bonds exhibit a greater resistance for crack propagation relative to the zigzag directional ones. Thus, fracture strength of the pre-cracked sheet is slightly higher for zigzag directional loading than that for armchair. We evaluated the limitation of the applicability of Griffith's criterion for sing…
A dynamic crack will travel in a straight path up to a material-dependent critical speed beyond which its path becomes erratic. Predicting this critical speed and discovering the origin of this instability are two outstanding problems in fracture mechanics. We recently discovered a simple scaling model based on an effective elastic modulus that gives successful predictions for this critical speed by transforming the nonlinear crack dynamics problem into a linear elasticity representation. We now show that a simple atomic picture based on broken-bond relaxation at the dynamic crack tip provides…
The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects a R-curve behavior associated to a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.
In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.
Crack-tip stress evaluation has always been a problem in the frame of classical elasticity theory. Peridynamics has been shown to have great advantages in dealing with crack problems. In the present study, we present a peridynamic crack-tip stress evaluation method for multi-scale Griffith crack subject to tensile loading. The bond-based peridynamics is used to calculate the displacement field. Non-local deformation gradient definition from non-ordinary state-based peridynamics is used for stress calculation. Besides, a scale factor is introduced for evaluating crack-tip stress of multi-scale …
A series of experimental results on the in-plane fracture of a fiber reinforced laminated composite panel is analyzed using the variational multi-scale cohesive method (VMCM). The VMCM results demonstrate the influence of specimen geometry and load distribution on the propagation of large scale bridging cracks in the fiber reinforced panel. Experimentally observed variation in fracture resistance is substantiated numerically by comparing the experimental and VMCM load-displacement responses of geometrically scaled single edge-notch three point bend (SETB) specimens. The results elucidate the s…
A planar crack generically segments into an array of "daughter cracks" shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We investigate facet propagation and coarsening using in-situ microscopy observations of fracture surfaces at different stages of quasi-static mixed-mode crack propagation and phase-field simulations. The results demonstrate that the bifurcation from propagating planar to segmented crack front is strongly subcritical, reconciling previous theoretical predictions of line…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis allows to extend the link to the nominal strength of structures. We show that a Family-Vicsek scaling leads to the classical size effect of linear elastic fracture mechanics. On the contrary, in the case of an anomalous scaling, there is a smooth transition from the case of no size effect, for small structure sizes, to a power law size effect which appears we…
In this paper, we'll answer several abstract, formal questions about the nature of crack growth and nucleation. Bringing a field theory point of view to fracture illuminates things in what I hope will be an entertaining way. Formally, what is the crack nucleation rate? Fracture is an instability of elastic theory under tension. For thermally nucleated cracks, there is an analogy with supercooled liquids. Here the crack nucleation rate can be thought of as an imaginary part of the free energy - giving the decay rate of the metastable, stretched material. As an amusing consequence, we can formal…
This work presents a critical overview of the effects of different aspects of model formulation on crack path selection in quasi-static phase field fracture. We consider different evolution methods, mechanics formulations, fracture dissipation energy formulations, and forms of the irreversibility condition. The different model variants are implemented with common numerical methods based on staggered solution of the phase-field and mechanics sub-problems via FFT-based solvers. These methods mix standard approaches with novel elements, such as the use of bound-constrained conjugate gradients for…
We use classical molecular dynamics (MD) simulations to investigate the mechanical properties of pre-cracked, nano-porous single layer MoS2 (SLMoS2) and the effect of interactions between cracks and pores. We found that the failure of pre-cracked and nano-porous SLMoS2 is dominated by brittle type fracture. Bonds in armchair direction show a stronger resistance to crack propagation compared to the zigzag direction. We compared the brittle failure of Griffith prediction with the MD fracture strength and toughness and found substantial differences that limit the applicability of Griffith criteri…
Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is challenging. In this work, we propose a thermo-mechanical phase-field fracture model, which is based on a thermodynamically consistent derivation. The influence of different coupling terms such as damage-informed thermomechanics and heat conduction and temperature-dependent fracture properties, as well as different phase-field fracture formulations, are discuss…
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the regularized crack. The key novelty is the combination of a strain energy split with a partial rank-I relaxation in the vicinity of the diffuse interface. The former is necessary to account for physically meaningful crack kinematics like crack closure, the latter ensures the mechanical jump conditions throughout the diffuse region. The model is verified by a co…
The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In this investigation, this problem is revisited in view of the recent progresses on the phase field approach to brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model,…
We show that the delivery of fracture work to the tip of an advancing planar crack is strongly reduced by surface phonon emission, leading to forbidden ranges of crack speed. The emission can be interpreted through dispersion of the group velocity, and Rayleigh and Love branches contribute as well as other high frequency branches of the surface wave dispersion relations. We also show that the energy release rate which enters the Griffith criterion for the crack advance can be described as the product of the continuum solution with a function that only depends on the lattice geometry and descri…
Fracture is the ultimate source of failure of amorphous carbon (a-C) films, however it is challenging to measure fracture properties of a-C from nano-indentation tests and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions on fracture of a-C. Systematic large-scale K-field controlled atomic-scale simulations of crack propagation are performed for a-C samples with densities of $ρ=2.5, \, 3.0 \, \text{ and } 3.5~\text{g/cm}^{3}$ created by liquid quenches for a range of quench rates $\dot{T}_q = 10 - 1000~\te…
Fractoluminescence experiments are performed on two kinds of silicate glasses. All the light spectra collected during dynamic fracture reveal a black body radiator behaviour, which is interpreted as a crack velocity-dependent temperature rise close to the crack tip. Crack velocities are estimated to be of the order of 1300 m.s$^{-1}$ and fracture process zones are shown to extend over a few nanometers.
The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and …
In this work we present the design of a new test geometry inspired by the Tapered Double Cantilever Beam (TDCB) specimen that is shown to provide an improved characterization of the fracture properties of brittle solids. First, we show that our new design results in an exponential increase of the specimen compliance with crack length, leading to an extremely stable crack growth during the test. We determine an analytical description of this behavior, which provides a simple procedure to extract the fracture energy without depending on finite element calculations. Validation tests are done on p…
The widespread use of sodium aluminosilicate glass in many engineering applications due to its mechanical and optical properties (transparency, dielectric, etc.), has become common in recent years. However, glass, a brittle material, has its vulnerability to fracture. Processes such as heat treatment (heat tempering) or chemical strengthening through ion-exchange have been used to create residual stress profiles on the glass, in a bid to improve its fracture strength. However, failure still occurs, which is mostly catastrophic and expensive to repair. Therefore understanding, predicting, and e…
The relation between fracture surface morphology and the three-dimensional structure of crack fronts is investigated through direct observation of brittle cracks in gels. A key notion in this investigation is the discontinuity of the crack front, whose advancement creates the fracture surface. We discuss the significance of our findings in the studies of general three-dimensional brittle fractures.
Stress-strain plots based on nanoindentation load-depth curves reflected cracking phenomenon. A transition from ductile to brittle fracture was observed on increasing the depth or load of indenter penetration. A new approach with shape factors in the fracture studies based on radial crack branching and micro-cracking was done. Hardness and modulus plots were fitted with polynomials. The coefficients were varied to obtain different hardness and modulus responses.
The extent to which time-dependent fracture criteria affect the dynamic behavior of fracture in a discrete structure is discussed in this work. The simplest case of a semi-infinite isotropic chain of oscillators has been studied. Two history-dependent criteria are compared to the classical one of threshold elongation for linear bonds. The results show that steady-state regimes can be reached in the low subsonic crack speed range where it is impossible according to the classical criterion. Repercussions in terms of load and crack opening versus velocity are explained in detail. A strong qualita…
Water molecules play a fundamental role in the physics of slow crack propagation in glasses. It is commonly understood that, during stress-corrosion, water molecules that move in the crack cavity effectively reduce the bond strength at the strained crack tip and, thus, support crack propagation. Yet the details of the environmental condition at the crack tip in moist air are not well determined. In a previous work, we reported direct evidence of the presence of a 100 nm long liquid condensate at the crack tip in fused silica glass during very slow crack propagation (10^-9 to 10^-10 m/s). These…
We investigate the fracture of Li-ion battery cathodic particles using a thermodynamically consistent phase-field approach that can describe arbitrarily complex crack paths and captures the full coupling between Li-ion diffusion, stress, and fracture. Building on earlier studies that introduced the concept of electrochemical shock, we use this approach to quantify the relationships between stable or unstable crack propagation, flaw size, and C-rate for 2D disks and 3D spherical particles. We find that over an intermediate range of flaw sizes, the critical flaw size for the onset of crack propa…
Reviewing work done in collaboration with Jennifer Hodgdon, we derive the most general crack growth law allowed by symmetry for mixed-mode three-dimensional fracture. We do so using the system developed in condensed matter physics to derive new laws that emerge on long length and time scales. In our derivation, we provide a symmetry interpretation for the three modes of fracture, we rederive the law giving the crack growth direction in two dimensional fracture, and we derive a growth law appropriate for three dimensional simulations. We briefly discuss related work subsequent to ours, incorpor…
Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a tot…
Brittle fracture is one of the important failure modes of Single-Walled Carbon Nanotube (SWNT) due to mechanical loading. In this paper, the fracture resistance of zigzag SWNTs with preexisting defects is calculated using fracture mechanics concepts based on atomistic simulations. The problem of unstable crack growth at finite temperature, presumably caused by lattice trapping effect, is circumvented by computing the strain energy release rate through a series of displacement-controlled tensile loading of SWNTs (applied through moving the outermost layer of atoms at one end at constant strain …
In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental meas…
To clarify effects of crack speed and cross-link density on fracture energy of acrylamide gels, we evaluated the roughness of the fracture surface and measured the fracture energy taking into account the roughness. The fracture energy increases linearly with crack speed $V$ in a fast crack speed region, and the increasing rate of fracture energy with $V$ decreases with increasing cross link density in the gels. In a slow crack speed region the fracture energy depends on crack speed more strongly than in the fast crack speed region. This indicates that a qualitative change exists in fracture pr…
We present a generalised framework for resolving the electrochemistry-diffusion interface and modelling hydrogen transport near a crack tip. The adsorption and absorption kinetics are captured by means of Neumann-type generalised boundary conditions. The diffusion model includes the role of trapping, with a constant or evolving trap density, and the influence of the hydrostatic stress. Both conventional plasticity and strain gradient plasticity are used to model the mechanical behaviour of the solid. Notable differences are found in the estimated crack tip hydrogen concentrations when comparin…
Since crack propagation in oxide materials at low crack velocities is partly determined by chemical corrosion, proper knowledge of the crack tip chemistry is crucial for understanding fracture in these materials. Such knowledge can be obtained only from in situ studies because the processes that occur in the highly confined environment of the crack tip are very different from those that take place at free surfaces, or that can be traced post mortem. We report the occurrence of hydrous liquid condensate between the two fracture surfaces in the vicinity of the tip of tensile cracks in silica. Ob…
In this review article we consider the crack growth resistance ofmicrometer and submicrometer sized samples from the fracture mechanics point of view. Standard fracture mechanics test procedures were developed for macroscale samples, and reduction of the specimen dimensions by three to five orders of magnitude has severe consequences. This concerns the interpretation of results obtained by micro and nanomechanics, as well as the life time and failure prediction of micro and nano devices. We discuss the relevant fracture mechanics length scales and their relation to the material specific struct…
It is the purpose of this short paper to show that the well known Griffiths theory of brittle fracture can be re-interpreted as a simple case of a modified Hamiltonian, and corresponds to a stationary action solution using the Euler-Lagrange equations. In this derivation it is still necessary to employ the equivalence with Irwins stress intensity factor approach to obtain the Griffith-Irwin equation. It is then shown that if physics of fracture is modelled using a simplified crack tip stress wave unloading model, then the Griffith-Irwin relationship can be derived in a single process, which is…
We present an intuitive physical picture for fractures in nacre-type stratified materials via scaling arguments: strain distributions around a fracture are rather different depending on directions and size of fractures. We thus observe that viscoelastic effects are important for parallel fractures. These effect are taken into account via the simplest viscoelastic model for weakly cross-linked polymer. Within a certain limit, we find a trumpet crack shape similar to that in certain polymers and make predictions for the fracture energy of certain stratified materials in this mode.
We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in 2 space dimensions) of one macro and one micro crack, and demonstrate that their interaction results in a {\em large} and {\em rapid} velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the …
Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the square root stress singularity remains valid during the plastic deformation, while the dislocation density is proportional to the stress intensity factor and distributed as the square root of the distance from the crack tip. The analytical solution for the angular distribution of the dislocation density is found.
This paper has been withdrawn by the authors due to new available results. A revised version, that incorporates the new results, will be submitted later.
The propagation front of a crack generates large strain gradients and it is therefore a strong source of gradient-induced polarization (flexoelectricity). Herein, we demonstrate that, in piezoelectric materials, a consequence of flexoelectricity is that crack propagation will be helped or hindered depending on whether it is parallel or antiparallel to the piezoelectric polar axis. This means that the theory of fracture physics can no longer assume mechanical symmetry in polar materials. The discovery of fracture asymmetry also has practical repercussions for the electromechanical fatigue of fe…
A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields at time $t$ are determined by the crack path at a {\bf retarded time} $t-τ_d$, where the delay time $τ_d$ scales with the ratio of $\ell_{nl}$ and the typical wave speed $c_{nl}$ within the nonlinear zone. The resulting equation is shown to agree with known results in the quasi-static regime. As a first application in the fully dynamic regime, an approximate…
We have measured the velocity of a running crack in brittle single crystal silicon as a function of energy flow to the crack tip. The experiments are designed to permit direct comparison with molecular dynamics simulations; therefore the experiments provide an indirect but sensitive test of interatomic potentials. Performing molecular dynamics simulations of brittle crack motion at the atomic scale we find that experiments and simulations disagree showing that interatomic potentials are not yet well understood.
Monolayer antimonene has drawn the attention of research communities due to its promising physical properties. But mechanical properties of antimonene is still largely unexplored. In this work, we investigate the mechanical properties and fracture mechanisms of two stable phases of monolayer antimonene -- the $α$ antimonene ($α$-Sb) and the $β$ antimonene ($β$-Sb), through molecular dynamics (MD) simulations. Our simulations reveal that stronger chiral effect results in a greater anisotropic elastic behavior in $β$-antimonene than in $α$-antimonene. In this paper we focus on crack-tip stress d…
We present a continuum theory which describes the fast growth of a crack by surface diffusion. This mechanism overcomes the usual cusp singularity by a self-consistent selection of the crack tip radius. It predicts the saturation of the steady state crack velocity appreciably below the Rayleigh speed and tip blunting. Furthermore, it includes the possibility of a tip splitting instability for high applied tensions.
A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are taken into account. Two different mechanism of crack propagation, a first order phase transition and surface diffusion are considered, and we discuss different loading modes. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique.
We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of exper…
The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip deformation mechanisms under mode-I loading based on classical interatomic potentials yield contradicting predictions. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a ma…
The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite eleme…
