Eran Bouchbinder, Ariel Livne, Jay Fineberg
This paper has been withdrawn by the authors due to new available results.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.
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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.
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.
We propose a minimal nonlinear model of brittle crack propagation by considering only the motion of the crack-tip atom. The model captures many essential features of steady-state crack velocity and is in excellent quantitative agreement with many-body dynamical simulations. The model exhibits lattice-trapping. For loads just above this, the crack velocity rises sharply, reaching a limiting value well below that predicted by elastic continuum theory. We trace the origin of the low limiting velocity to the anharmonicity of the potential well experienced by the crack-tip atom.
Taking into account stress fluctuations due to thermal noise, we study thermally activated irreversible crack growth in disordered media. The influence of material disorder on sub-critical growth of a single crack in two-dimensional brittle elastic material is described through the introduction of a rupture threshold distribution. We derive analytical predictions for crack growth velocity and material lifetime in agreement with direct numerical calculations. It is claimed that crack growth process is inhibited by disorder: velocity decreases and lifetime increases with disorder. More precisely…
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…
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 …
Crack tip kinematics reveal the cohesive zone structure in brittle hydrogel fracture
本研究利用显微学方法探测脆性水凝胶裂纹尖端的小尺度屈服区，直接测量并确定了通过内聚力丧失耗散大部分能量的区域尺度和结构，为脆性材料破坏机制提供了新见解。
Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertina-like folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petal-like tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations and simple theories. In particular, we describe the tran…
The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that dive…
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,…
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 …
Hydrogen-induced fast fracture in a 1.5 GPa dual-phase steel
本研究通过实验揭示1.5 GPa双相钢在氢预充下的氢脆机制，提出氢致快速断裂模型，阐明氢扩散与裂纹速度对脆性断裂的协同作用。
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…
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 study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.
The purpose of this paper is to fill the gap between the classical treatment of brittle fracture mechanics and the new idea of considering the crack evolution as a free discontinuity problem. Griffith and Irwin criterions of crack propagation are studied and transformed in order to be no longer dependent on any prescription of the geometry of the crack during its evolution. The inequality contained in theorem 6.1. represents the link between generalized Irwin and Griffith criterions of brittle crack propagation. The physical meaning of this inequality is explained in the last section. Further …
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 s…
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…
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…
High-fidelity fracture mechanics simulations of multiple microcracks interaction via physics-based models quickly become computationally expensive as the number of microcracks increases. This work develops a Graph Neural Network (GNN) based framework to simulate fracture and stress evolution in brittle materials due to multiple microcracks' interaction. The GNN framework is trained on the dataset generated by XFEM-based fracture simulator. Our framework achieves high prediction accuracy on the test set (compared to an XFEM-based fracture simulator) by engineering a sequence of GNN-based predic…
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…
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.
Many studies have confirmed that cracks in brittle materials branch when the crack speed exceeds a certain threshold velocity, but the value of that threshold is not understood. Almost all theoretical calculations overestimate the threshold by factors of two or more. We show that thermal noise can reduce the threshold by a substantial amount, and we propose that this effect can account for the discrepancy.
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 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 force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure inside a microscopic process zone and macroscopic linear elasticity. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissi…
Process zone at the tip of a propagating crack engendered by the stress-induced local phase transition of the second order is studied theoretically. We show that the zone can only exist within a certain domain of the phase diagram at one side of the phase transition line depending upon the sign of the striction constant. We obtain the boundary of this domain and establish its dependence upon the crack velocity. We show the existence of a critical crack velocity above which the zone cannot exist. We report the overcritical solution for the order parameter describing the incipient process zone, …
The breakup of glass and alumina plates due to planar impacts on one of their lateral sides is studied. Particular attention is given to investigating the spatial location of the cracks within the plates. Analysis based on a phenomenological model suggests that bifurcations along the cracks' paths are more likely to take place closer to the impact region than far away from it, i. e., the bifurcation probability seems to lower as the perpendicular distance from the impacted lateral in- creases. It is also found that many observables are not sensitive to the plate material used in this work, as …
A comparison of phase field models of brittle fracture incorporating strength: I -- Mixed-mode loading
本文系统比较了三种考虑强度的脆性断裂相场模型在II型、III型及混合模式加载下的裂纹扩展预测能力，证实完全形核方法最可靠，并揭示了其他方法在强度面处理和断裂韧性预测上的不足。
Unravelling the mechanisms underlying crack initiation in additively manufactured steel
研究增材制造钢裂纹萌生机制，结合多模态技术观察裂纹尖端塑性三维演变，发现锻造钢与增材制造合金在裂纹尖端塑性表现不同，揭示抗断裂能力受其空间演变控制，为提高损伤容限提供机理框架。
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.
Finite element analysis of stress about a blunt crack tip, emphasizing finite strain and phenomenological and mechanism-based strain gradient plasticity (SGP) formulations, is integrated with electrochemical assessment of occluded-crack tip hydrogen (H) solubility and two H-decohesion models to predict hydrogen environment assisted crack growth properties. SGP elevates crack tip geometrically necessary dislocation density and flow stress, with enhancement declining with increasing alloy strength. Elevated hydrostatic stress promotes high-trapped H concentration for crack tip damage; it is impe…
Most monolithic brittle materials are vulnerable to the failure by cracks because of a lack of intrinsic toughening mechanisms, such as the plasticity in the vicinity of the crack front. As a result, most of the efforts to mitigate the sudden failure of brittle ceramics have been focused on developing the extrinsic toughening mechanisms that hinder crack propagation behind the tip, such as the fiber bridging. In this work, we experimentally demonstrate that the intrinsic toughening arises even in the brittle monolithic ceramic material such as diamond-like carbon (DLC) when its external dimens…
Crack initiation emerges due to a combination of elasticity, plasticity, and disorder, and it is heavily dependent on the material's microstructural details. In this paper, we investigate brittle metals with coarse-grained, microstructural disorder that could originate in a material's manufacturing process, such as alloying. As an investigational tool, we consider crack initiation from a surface, ellipsoidal notch: As the radius of curvature at the notch increases, there is a dynamic transition from notch-induced crack initiation to bulk-disorder crack nucleation. We perform extensive and real…
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…
Phase-field analysis for brittle fracture in ferroelectric materials with flexoelectric effect
针对铁电材料脆性断裂力电耦合作用复杂的问题，构建含多序参量、考虑应变梯度与挠曲电效应的扩展相场模型，揭示初始极化方向对裂纹扩展的影响机制，为复杂铁电结构力电失效研究提供工具。
Size effects in the toughening of brittle materials by heterogeneities: a non-linear analysis of front deformations
扩展Gao和Rice理论至二阶，预测扰动裂纹前沿的I型应力强度因子分布，揭示韧性异质性对材料增韧的尺寸依赖性及宏观R曲线行为。
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…
In situ elucidation of mechanisms governing crack transition to plasticity arrest
研究通过原位实验揭示冷加工AA-5052合金裂纹在低驱动力下混合模式传播，并在裂纹尖端过程区扩展时转变为塑性主导裂纹，通过能量分区和过程区扩展实现阻滞。
The aim of the paper is to propose a paradigm shift for the variational approach of brittle fracture. Both dynamics and the limit case of statics are treated in a same framework. By contrast with the usual incremental approach, we use a space-time principle covering the whole loading and crack evolution. The emphasis is given on the modelling of the crack extension by the internal variable formalism and a dissipation potential as in plasticity, rather than Griffith's original approach based on the surface area. The new formulation appears to be more fruitful for generalization than the standar…
Observing the crack tip behaviour at the nanoscale during fracture of ceramics
本研究通过透射电镜原位观察陶瓷裂纹尖端纳米尺度行为，发现相变增韧机制在纳米层面促进裂纹偏转，将断裂抗力提高约50%，连接了原子与连续介质断裂视角。
We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which being described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a plastic process zone. We show that such a model leads to a two-phase crack propagation: a first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanica…
High angular resolution electron backscatter diffraction (HR-EBSD) was coupled with focused ion beam (FIB) slicing to characterize the shape of the plastic zone in terms of geometrically necessary dislocations (GNDs) in W single crystal in 3 dimensions. Cantilevers of similar size with a notch were fabricated by FIB and were deformed inside a scanning electron microscope at different temperatures (21$^{\circ}$C, 100$^{\circ}$C and 200$^{\circ}$C) just above the micro-scale brittle-to-ductile transition (BDT). J-integral testing was performed to analyse crack growth and determine the fracture t…
We report results on the interrelation between driving force, roughness exponent, branching and crack speed in a finite element model. We show that for low applied loadings the crack speed reaches the values measured in the experiments, and the crack surface roughness is compatible with logarithmic scaling. At higher loadings, the crack speed increases, and the crack roughness exponent approaches the value measured at short length scales in experiments. In the case of high anisotropy, the crack speed is fully compatible with the values measured in experiments on anisotropic materials, and we a…
Slow strain rates tests (SSRT) were conducted on hydrogen-containing specimens of PH13-8Mo maraging stainless steel. Hydrogen-assisted subcritical quasi-cleavage cracking was shown to take place during SSRT, thus accelerating material failure. Fractographic analysis showed that quasi-cleavage is composed of flat brittle areas and rougher areas. Using cross-sectional electron backscatter diffraction (EBSD) analysis of a secondary subcritically grown crack, we observed brittle cracks propagated across martensite blocks ahead the main crack tip. These cracks were stopped at high-angle boundaries.…
Nanoscale crack propagation in clay with water adsorption through reactive MD modeling
采用反应性 MD 模拟叶蜡石与钙基蒙脱石吸水后的 I/II 型纳米裂纹扩展，揭示水分子氢键、裂纹尖端钝化及 Si-O 键断裂主导机制，并确定临界断裂参数。
Various fields such as mechanical engineering, materials science, etc., have seen a widespread use of linear elastic fracture mechanics (LEFM) at the continuum scale. LEFM is also routinely applied to the atomic scale. However, its applicability at this scale remains less well studied, with most studies focusing on non-linear elastic effects. Using a harmonic (snapping spring) nearest-neighbor potential which provides the closest match to LEFM on a discrete lattice, we show that the discrete nature of an atomic lattice leads to deviations from the LEFM displacement field during energy minimiza…
Atomistic Indicators of the Ductile-to-Brittle Transition in Polycrystalline Tungsten: Temperature and Rhenium Effects on Crack-Tip Plasticity
该研究通过分子动力学模拟，探究温度和铼含量对多晶钨裂纹尖端塑性的影响，揭示了高应变速率下韧脆转变的原子级指标，为理解体心立方金属的断裂行为提供了依据。
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence di…
The slow advance of a crack in sodo-silicate glasses was studied at nanometer scale by in situ and real time atomic force microscopy (AFM) in a well controlled atmosphere. An enhanced diffusion of sodium ions in the stress gradient field at the submicrometric vicinity of the crack tip was revealed through several effects: growth of nodules in AFM height images, changes in the AFM tip/sample energy dissipation. The nodules patterns revealed a dewetting phenomenon evidenced by 'breath figures'. Complementary chemical micro-analyses were done. These experimental results were explained by a two-st…
Crack advance from short or long pre-cracks is predicted by the progressive failure of a cohesive zone in a strain gradient, elasto-plastic solid. The presence of strain gradients leads to the existence of an elastic zone at the tip of a stationary crack, for both the long crack and the short crack cases. This is in sharp contrast with previous asymptotic analyses of gradient solids, where elastic strains were neglected. The presence of an elastic singularity at the crack tip generates stresses which are sufficiently high to activate quasi-cleavage. For the long crack case, crack growth resist…
Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions. Systematic experimental measurements and numerical simulations are presented against an asymptotic prediction for the crack trajectory developing in solids with small voids (of circular and elliptical shape). The experiments also cover the dynamic regime, where new features involving crack kinking and roughness of the fracture surface occur.
The quantitative characterisation of crack tip loads is fundamental in fracture mechanics. Although the potential influence of higher order terms on crack growth and stability is known, classical studies solely rely on first order stress intensity factors. We calculate higher order Williams coefficients using an integral technique based on conjugate work integrals and study the convergence with increasing crack tip distance. We compare the integral method to the state-of-the-art fitting method and provide results for higher-order terms with several crack lengths, external forces, and sizes for…
A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force and a tip splitting instability above a critical driving force.
Despite their recent success, machine learning (ML) models such as graph neural networks (GNNs), suffer from drawbacks such as the need for large training datasets and poor performance for unseen cases. In this work, we use transfer learning (TL) approaches to circumvent the need for retraining with large datasets. We apply TL to an existing ML framework, trained to predict multiple crack propagation and stress evolution in brittle materials under Mode-I loading. The new framework, ACCelerated Universal fRAcTure Emulator (ACCURATE), is generalized to a variety of crack problems by using a sequ…
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.
This investigation demonstrates a way to innovatively modify the ferritic microstructure at a local scale, particularly at the failure prone area such as Charpy V-notch (CVN) root. Tensile pre-strain (PS) up to 6 percent and 12 percent were employed before annealing (An) the samples at 650°C for 15 minutes. Ferrite grain size increased sharply and gradually (along the distance ahead of the notch root) within the microstructurally modified region in 6-12 percent pre-strained and annealed samples, respectively. Critical strain which promotes strain induced boundary migration (SIBM), was found to…
Influence of temperature and crack-tip speed on crack propagation in elastic solids
本研究将裂纹尖端键断裂建模为应力辅助热激活过程，揭示温度降低和裂尖速度升高会增大有效裂纹扩展能，并解释其对粘合裂纹更显著，理论得到PDMS相关实验支持。
A damage mechanics model for quasi brittle materials based on the structured deformation theory
在不可逆过程热力学框架内，采用结构变形理论构建了适用于准脆性材料的损伤模型，引入Mohr-Coulomb准则与硬化软化函数描述应力应变演化，并通过Kupfer混凝土数据库验证。
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