Interaction between stress waves and a growing crack

The Journal of the Acoustical Society of America, 2008

Diffraction effects and features of acoustic wave propagation in elastic media with microcrack were investigated in detail for pulse probing signals. The crack's plane was oriented across the direction of longitudinal ultrasonic wave incidence so that the detection of such a crack with so "inconvenient" spatial location is difficult enough by using traditional acoustic techniques. By using laser interferometer, the set of instantaneous pictures of acoustic field on the specimen's surface, corresponding to different time moments was obtained what allowed investigating and visualizing of acoustic field propagation and diffraction effects on the crack's top in dynamics. Using numerical modeling of diffraction processes of acoustic waves by the crack's edge and top for pulse signals the origin of V-like structures on the snapshots of acoustic fields was explained and analyzed.

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 Fracture, 1986

Acoustical Physics, 2005

The interrelated elastic and inelastic fast and slow effects of acoustic wave interaction with cracks are discussed from a unified point of view. Special attention is given to the dissipative manifestations of the presence of cracks and to the effects of the symmetrically time-reversible slow dynamics observed for acoustically activated cracks. These effects can be more pronounced than the conventionally discussed nonlinear elastic effects (such as higher harmonic generation). Taking into account the main geometric features of cracks, a thermoelastic mechanism is proposed to consistently interpret the experimental data. Consequences of the results of these studies for seismics are discussed, and the possibilities of using the observed effects for nonlinear acoustic diagnostics of cracks are discussed.

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.

1997

The optical method of caustics for measuring the dynamic stress intensity factor in a transient process is investigated in this study. The transient full-field solutions of a propagating crack contained in an infinite medium subjected to step-stress wave and ramp-stress wave loadings are used to establish the exact equations of the initial and caustic curves. The results of the stress

Mathematics and Mechanics of Solids, 2019

In this study, we investigate the dynamics of (damaged) materials with a nonlinear microstructure (microcracks in frictional contact) using a discontinuous Galerkin method. Although the propagation of a plane wave is associated with a complex phenomenon and the stress field loses its homogeneity, the loading pulse has an overall front wave at each moment. Thus, a macroscopic behavior can be extracted and compared with reference solutions based on analytical formulas deduced from the effective (static) elasticity models of a cracked solid. The influences of the mesh and of the microcrack pattern have been tested to choose an optimal numerical setting. We analyzed the sensitivity of the damaged pulse with respect to microcrack density, wavelength, and microcrack orientation. For small values of crack density parameter, the theoretical formula and the computed speed of the damaged pulse are very close, but for larger values there is an important gap between them. For large ratios of wa...

Geophysical Prospecting, 1974

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.

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.

International Journal of Engineering Science, 1970

The problem of the diffraction of normally indicent longitudinal and antiplane shear waves on a Griffith crack located in an infinite, isotropic elastic medium is considered. A Fredholm integral equation of the second kind is derived in each case for the determination of diffracted field. From the integral equation an asymptotic development of the solution is obtained which is valid for wavelength long compared to the crack length. For wavelengths comparable with the size of the crack the integral equation is solved numerically. The stress and the displacement fields in the vicinity of the crack as well as the radiation field at points far away from the crack are computed for a range of values of the frequency.

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.

Europhysics Letters (EPL), 1995

We report experimental evidence that the velocity of a crack, in brittle materials, can be considered as a control parameter which determines several properties of the crack dynamics. Above a critical speed the crack develops an instability associated with a strong sound emission and a strong increase of the surface roughness. Both phenomena seem to be two efficient mechanisms which allow the crack to dissipate energy.

Review of Progress in Quantitative Nondestructive Evaluation, 1992

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.