Cracks Cleave Crystals

The problem of finding what direction cracks should move is not completely solved. A commonly accepted way to predict crack directions is by computing the density of elastic potential energy stored well away from the crack tip, and finding a direction of crack motion to maximize the consumption of this energy. I provide here a specific case where this rule fails. The example is of a crack in a crystal. It fractures along a crystal plane, rather than in the direction normally predicted to release the most energy. Thus, a correct equation of motion for brittle cracks must take into account both energy flows that are described in conventional continuum theories and details of the environment near the tip that are not.Comment: 6 page

Some exact results for the velocity of cracks propagating in non-linear elastic models

We analyze a piece-wise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the perpendicular direction. The velocity of the crack is a function of the value of the applied strain. We find analytically the value of the propagation velocity close to the Griffith threshold, and close to the strain of uniform breakdown. Contrary to the case of perfectly harmonic behavior up to the fracture point, in the piece-wise linear elastic model the crack velocity is lower than the sound velocity, reaching this limiting value at the strain of uniform breakdown. We complement the analytical results with numerical simulations and find excellent agreement.Comment: 9 pages, 13 figure

Front Propagation up a Reaction Rate Gradient

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fl uctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the front velocity depe ndence on bulk particle density, showing that the velocity indeed diverge s in the infinite density limit. The form in which diffusion is impleme nted, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence

Supersonic crack propagation in a class of lattice models of Mode III brittle fracture

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.Comment: 4 pages, 3 figure

Propagating mode-I fracture in amorphous materials using the continuous random network (CRN) model

We study propagating mode-I fracture in two dimensional amorphous materials using atomistic simulations. We used the continuous random network (CRN) model of an amorphous material, creating samples using a two dimensional analogue of the WWW (Wooten, Winer & Weaire) Monte-Carlo algorithm. For modeling fracture, molecular-dynamics simulations were run on the resulting samples. The results of our simulations reproduce the main experimental features. In addition to achieving a steady-state crack under a constant driving displacement (which had not yet been achieved by other atomistic models for amorphous materials), the runs show micro-branching, which increases with driving, transitioning to macro-branching for the largest drivings. Beside the qualitative visual similarity of the simulated cracks to experiment, the simulation also succeeds in explaining the experimentally observed oscillations of the crack velocity

Spontaneous decay of excited atomic states near a carbon nanotube

Spontaneous decay process of an excited atom placed inside or outside (near the surface) a carbon nanotube is analyzed. Calculations have been performed for various achiral nanotubes. The effect of the nanotube surface has been demonstrated to dramatically increase the atomic spontaneous decay rate -- by 6 to 7 orders of magnitude compared with that of the same atom in vacuum. Such an increase is associated with the nonradiative decay via surface excitations in the nanotube.Comment: 8 pages, 3 figure

Vortex-type elastic structured media and dynamic shielding

The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortextype nature of the structured media. The related homogenised effective behavior is obtained analytically and it has been implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.Comment: 24 pages, 13 figure

Discrete models of dislocations and their motion in cubic crystals

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their cores and profiles. Dislocation loops and dipoles are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.

Feeding and dissipative waves in fracture and phase transition.

Abstract 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 4

Analysis of dynamic damage propagation in discrete beam structures

In the last decade, signicant theoretical advances were obtained for steady-state fracture propagation in spring-mass lattice structures, that also revealed surprising fracture regimes. Very few articles exist, however, on the dynamic fracture processes in lattices composed of beams. In this paper we analyse a failure (feeding) wave propagating in a beam-made lattice strip with periodically placed point masses. The fracture occurs when the strain of the supporting beam reaches the critical value. The problem reduces to a Wiener-Hopf equation, from which the complete solution is obtained. Two cases are considered when the feeding wave transmits into the intact structure as a sinusoidal wave(s) or only as an evanescent wave. For both cases, a complete analysis of the strain inside the structure is presented. We determine the critical level of the feeding wave, below which the steady-state regime does not exist, and its connections to the feeding wave parameters and the failure wave speed. The accompanied dynamic effects are also discussed. Amongst much else, we show that the switch between the two considered regimes introduces a rapid change in the minimum energy required for the failure wave to propagate steadily. The failure wave developing under an incident sinusoidal wave is remarkable due to the fact that there is an upper bound of the domain where the steady-state regime exists. In the present paper, only the latter is examined; the alternative regimes are considered separately