Propagating solitary waves along a rapidly moving crack front

International Journal of Fracture, 2003

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack's propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a `crack front'). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially `massless' cracks acquire inertia.

Philosophical Magazine B, 1998

The classical theory of fracture mechanics states that a crack propagating in an unbounded body should smoothly accelerate until it reaches the Rayleigh wave speed. We introduce here a general approach for solving the equation of motion of the crack tip. We show that the loading conditions and the geometry of the con® guration do not produce inertial e ects. The equation of motion of a propagating crack is always a ® rst-order di erential equation.

Journal of The Mechanics and Physics of Solids, 2020

Crack front waves: a 3D dynamic response to a local perturbation of tensile and shear cracks,

Journal of the Mechanics and Physics of Solids, 2000

Willis and Movchan [Willis, J.R., Movchan, A.B., 1995. Dynamic weight functions for a moving crack I. Mode I loading. J. Mech. Phys. Solids 43, 319.] devised weight functions for a dynamic mode I fracture, within the singular crack model, using a ®rst order perturbation of in-plane crack motion from the 2D results. Ramanathan and Fisher [Ramanathan, S., Fisher, D.S., 1997. Dynamics and instabilities of planar tensile cracks in heterogeneous media. Phys. Rev. Lettr. 79, 877.] reformulated the Willis-Movchan's result in terms of crack growth at constant fracture energy, thereby con®rming the existence of a crack front wave. Such a wave, as a propagating mode local to the moving crack front, was seen in the non-perturbative numerical simulations based on a cohesive zone fracture model, equivalent to growth at constant fracture energy. In this paper, the result of Ramanathan and Fisher, given in the wavenumber±frequency domain, is recast in the wavenumber±time domain to analyze fracture propagation within ®rst-order perturbations for the singular crack model. This allows application of a spectral numerical methodology and is shown to be consistent with the known 2D results. Through analysis of a single spatial mode of crack shape, the propagating crack front wave and its resonance are demonstrated. Crack propagation through a randomly heterogeneous zone, and growth of disorder with propagation distance, are also examined.

International Journal of Fracture, 1983

This paper considers cracks of a fixed size and shape which exist in an unbounded linear elastic body. The crack faces are assumed to suffer a sudden disturbance, which results in a shock wave emanating from the region of the crack into the body. The geometry and physics are assumed such as to give rise to problems governed by the equations of two-dimensional elastodynamics. For a crack of finite length, two approaches are utilized to find the shape of the wave front which will propagate into a body with homogeneous material properties. For a semi-infinite crack an analogous problem is solved, but in this case for a body with nonhomogeneous cylindrically symmetric material properties. The paper concludes with a heuristic discussion of the corresponding situation within the framework of three-dimensional elastodynamics.

International Journal of Engineering Science, 1978

steady state solutions have been considered for crack propagation in media with spatially varying elastic moduli when the crack propagates in a plane where the elastic moduli are constant. Some solutions for transient crack propagation in infinite media and for cracks in displacement loaded strips are reviewed in . To date, no consideration has been given to crack propagation in variable moduli media when the crack moves in the direction of the modulus variation. As a first step we consider here steady state crack propagation in media where the moduli vary exponentially. Steady state conditions are assumed because a definite result can be obtained and a possible interpretation made of the results to distinguish between the effects of inertia for crack propagation in directions of either increasing or decreasing moduli. The particular exponential variation is chosen because this is the only variation which will allow a steady state for which the displacement field is a function of time only through x = x, -Vt, where x is the moving co-ordinate associated with the crack tip. One other limitation must be mentioned, we assume the medium to have constant elastic wave speeds, again this seems a necessary condition for the steady state solution to exist. We begin in Section I by considering anti-plane deformation. The analysis is much simpler in this case and it is possible to treat the transient crack problem also, this is done in Appendix A, both to verify our analysis of the steady state situation and also to demonstrate how the steady state is achieved from the corresponding initial value problem. In Section 2 we treat the much more complicated problem plane strain situation and derive results for the steady state only. These results mimic those of the anti-plane problem. A full discussion of these is given in the discussion section, perhaps they give an indication of the extremes of behaviour possible for crack propagation in materials with varying elastic properties.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Journal of Applied Mechanics and Technical Physics, 1974

An experimental investigation is made of interaction between longitudinal and Rayleigh waves and a growing crack. It is shown that stress waves can be used effectively to change the direction of a growing crack and to slow it down. The change in the trajectory of the growth of the crack is due to changes in the state of stress at its apex. The angle of deviation of the crack depends on the angle of attack of the wave and on the state of stress at the apex. An expression is given for determining the angle of deviation of a crack.

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.

International Journal of Engineering Science, 2012

This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solid with microstructures subject to antiplane loading applied on the crack surfaces. The loading is moving with the same constant velocity as that of the crack tip. We assume subsonic regime, that is the crack velocity is smaller than the shear wave velocity. The material behaviour is described by the indeterminate theory of couple stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the material as well as for the strong size effects arising at small scales and observed when the representative scale of the deformation field becomes comparable with the length scale of the microstructure, such as the grain size in a polycrystalline or granular aggregate.