Origin of crack tip instabilities

Nature, 2008

When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack 1 . The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen 2 . The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front 1,3 . The physical interplay of multiple length scales makes brittle fracture a complex 'multi-scale' phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known 1 , and significant advances have been made recently in understanding their origin 4,5 . Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally 6,7 .

International Journal of Fracture, 2006

A discrete two-dimensional square-cell lattice with a steady propagating crack is considered. The lattice particles are connected by massless bonds, which obey a piecewise-linear doublehumped stress-strain relation. Initially, Hooke's law is valid as the first stable branch of the forceelongation diagram; then, as the elongation becomes critical, the transition to the other branch occurs. Further, when the strain reaches the next critical value, the bond breaks. This transition is assumed to occur only in a line of the breaking bonds; the bonds outside the crack line are assumed to be in the initial branch all the time. The formulation relates to the crack propagation with a 'damage zone' in front of the crack. An analytical solution is presented that allows to determine the crack speed as a function of the far-field energy release rate, to find the total speed-dependent dissipation, and to estimate the role of the damage zone. The analytical formulation and the solution present a development of the previous ones for L. I. Slepyan (B) the crack and localized phase transition dynamics in linear and bistable-bond lattices.

Phys Rev E, 2004

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 dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the cracks tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.

Physical Review Letters, 2001

We address the role of material heterogeneities on the propagation of a slow rupture at laboratory scale. With a high speed camera, we follow an in-plane crack front during its propagation through a transparent heterogeneous Plexiglas block. We obtain two major results. First, the slip along the interface is strongly correlated over scales much larger than the asperity sizes. Second, the dynamics is scale dependent. Locally, mechanical instabilities are triggered during asperity depinning and propagate along the front. The intermittent behavior at the asperity scale is in contrast with the large scale smooth creeping evolution of the average crack position. The dynamics is described on the basis of a Family-Vicsek scaling.

Physical Review Letters, 2013

We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two dimensionless variables, between dynamics ruled by continuum fracture mechanics and crackling dynamics. Selection of the latter by the loading, microstructure and specimen parameters is formulated in terms of scaling laws on the power spectrum of crack velocity. This analysis defines the experimental conditions required to observe crackling in fracture. Beyond failure problems, the results extend to a variety of situations described by models of the same universality class, e.g. the dynamics in wetting or of domain walls in amorphous ferromagnets.

Physical Review E, 2004

We address the interaction of fast moving cracks in stressed materials with microcracks on their way, considering it as one possible mechanism for fluctuations in the velocity of the main crack (irrespective whether the microcracks are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in two space dimensions) of one macrocrack and one microcrack, and demonstrate that their interaction results in a large and rapid velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the crack tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.

Journal of The Mechanics and Physics of Solids, 2001

Wave conÿgurations for modes I and II of crack propagation in an elastic triangular-cell lattice are studied. [Mode III was considered in Part I of the paper: Slepyan, L.I. Feeding and dissipative waves in fracture and phase transition. I. Some 1D structures and a square-cell lattice. J. Mech. Phys. Solids 49 (2001) 469.] A general solution incorporates a complete set of the feeding and dissipative waves. The solution is based on the wave dispersion dependences obtained in an explicit form. Also some general properties and the long-wave asymptotes of the corresponding Green function are found. This results in the determination of the wavenumbers and modes. The macrolevel-associated solutions exist as the sub-Rayleigh crack speed regime for both modes and as a shear-longitudinal wave-speed intersonic regime for mode II only. In particular, it is shown that any intersonic crack speed is possible, whereas only the speed (shear wave speed multiplied by √ 2) corresponds to a positive energy release in the cohesive-zone-free homogeneous-material model. This is a manifestation of the fact that the local energy release in the lattice is not connected with the singularity of the macrolevel ÿeld. Microlevel solutions, corresponding to a nonzero feeding wavenumber, exist for both modes, at least from the energy point of view, for any, sub-and super-Rayleigh, intersonic and supersonic crack speed regimes. In particular, in the super-Rayleigh regime, a high-frequency wave delivers energy to the crack, while the macrolevel wave carries energy away from the crack.

Physical Review Letters, 1999

Using Eshelby's energy-momentum tensor, it is shown that the elastic configurational force acting on a moving crack tip does not necessarily point in the direction of crack propagation. A generalization of Griffith's approach that takes into account this fact is proposed to describe dynamic crack propagation in two dimensions. The model leads to a critical velocity below which motion proceeds in a pure opening mode, while above it, it does not. The possible relevance of this instability to recent experimental observations is discussed. [S0031-9007 08705-0] PACS numbers: 62.20.Mk, 46.05. + b, 46.50. + a, 81.40.Np

Journal of The Mechanics and Physics of Solids, 2001

In the lattice structure considered here, crack propagation is caused by feeding waves, carrying energy to the crack front, and accompanied by dissipative waves carrying a part of this energy away from the front (the di erence is spent on the bond disintegration). The feeding waves di er by their wavenumber. A zero feeding wavenumber corresponds to a macrolevel-associated solution with the classical homogeneous-material solution as its long-wave approximation. A non-zero wavenumber corresponds to a genuine microlevel solution which has no analogue on the macrolevel. In the latter case, on the crack surfaces and their continuation, the feeding wave is located behind (ahead) the crack front if its group velocity is greater (less) than the phase velocity. Dissipative waves, which appear in both macrolevel-associated and microlevel solutions, are located in accordance with the opposite rule. (Wave dispersion is the underlying phenomenon which allows such a wave conÿguration to exist.) In contrast to a homogeneous material model, both these solutions permit supersonic crack propagation. Such feeding and dissipative waves and other lattice phenomena are characteristic of dynamic phase transformation as well. In the present paper, mode III crack propagation in a square-cell elastic lattice is studied. Along with the lattice model, some simpliÿed one-dimensional structures are considered allowing one to retrace qualitatively (with no technical di culties) the main lattice phenomena.

Arxiv preprint arXiv:0911.0173, 2009

Cracks are the major vehicle for material failure and often exhibit rather complex dynamics. The laws that govern their motion have remained an object of constant study for nearly a century. The simplest kind of dynamic crack is a single crack that moves along a straight line. We first briefly review the current understanding of this "simple" object. We then critically examine the assumptions of the classic, scale-free theory of dynamic fracture and note when it works and how it may fail if certain assumptions are relaxed. Several examples are provided in which the introduction of physical scales into this scale-free theory profoundly affects both a crack's structure and the resulting dynamics.