Interaction of elastic waves with a Griffith crack (original) (raw)
Related papers
Acta Mechanica, 2004
Stresses are determined in the vicinity of a propagating finite crack having a constant velocity in a non-homogeneous elastic layer sandwiched between two dissimilar elastic half-planes. The selfequilibrated system of pressure is applied to the crack surfaces. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. In order to solve the equations, the differences in the crack surface displacements are expanded in a series of functions that are equal to zero outside the crack. The unknown coefficients in the series are solved by the Schmidt method. The stress intensity factors are calculated numerically for a crack in a non-homogeneous layer between a half-plane made of epoxy resin and a half-plane made of aluminum.
International Journal of the Society of Materials Engineering for Resources
Stresses around a propagating finite crack having a constant velocity in an elastic layer sandwiched between two elastic half-planes are determined. The self-equilibrated system of pressure is applied to the crack surfaces. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. In order to solve the equations, the differences of the crack surface displacements are expanded in a series of functions that are equal to zero outside of the crack. The unknown coefficients in the series are solved using the Schmidt method. The stress intensity factors are calculated numerically for a crack in a layer made of epoxy resin sandwiched between two half-planes made of aluminum.
Diffraction of P-Waves by Edge Crack in an Infinitely Long Elastic Strip
JSME International Journal Series A, 2006
The in-plane problem relating to the elastodynamic response of edge crack in an infinitely long elastic strip is analyzed. Fourier transform is used to reduce the mixed boundary value problem to Fredholm integral equation of second kind which was solved numerically to calculate the stress intensity factor at the tip of the crack. Stress intensity factor for various geometry parameters and frequency has been plotted to show the effect of strip width on stress intensity factor. Also normal stress at distant points from the crack has been evaluated numerically and plotted for various parameters.
Journal of the Mechanics and Physics of Solids
We investigate diffraction of reduced traction shear waves applied at the faces of a stationary crack in an elastic solid with microstructure, under antiplane deformation. The material behaviour is described by the indeterminate theory of couple stress elasticity and the crack is rectilinear and semi-infinite. The full-field solution of the crack problem is obtained through integral transforms and the Wiener-Hopf technique. A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack, localized waves irradiating from the cracktip with, possibly, super-Rayleigh speed and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission. Dynamic stress intensity factors are presented, which generalize to Elastodynamics the corresponding results already obtained in the static framework. The correction brings out the important role of wave diffraction on stress concentration.
A semi-analytical approach in the high-frequency diffraction by cracks
Mechanics Research Communications, 2011
In the problem of high-frequency diffraction by cracks in linear elastic materials we propose a numerical method which is based on a separation of the oscillating (GTD) solution and a certain slowly varying function. This technique, described in literature for regular (Fredholm) integral equations, is applied here to hyper-singular equations arising in diffraction by thin cracks in elastic media. The algorithm proposed is efficient for both high and moderate frequencies.
Scattering of a flexural wave by a finite straight crack in an elastic plate
Journal of Sound and Vibration, 1995
The diffraction of flexural waves by a short straight crack in an elastic thin plate is considered. The vibrations of the plate are described by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of existence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposition method. It leads to infinite systems of algebraic equations for the coefficients. The truncation method is proved to be applicable to these systems due to the special choice of the polynomials. A physical interpretation of numerical and asymptotic results obtained for the directivity of the scattered wave and for the stress intensity coefficients near the ends of the crack is suggested.
Diffraction of an Elastic Wave by a Rough Crack Edge
AIP Conference Proceedings, 2003
It is of importance in ultrasonic NDE to know how crack roughness effects the quality of inspection. Rough crack face was modeled in the past as a mosaic of large triangles using the Kirchhoff approximation. On the other hand, until now rough crack edge was modeled only under assumption of small perturbation. In this paper, in the spirit of the triangular facet model we model rough crack edge as a polygonal line and then apply the Isakovich approach which was developed for scatter from rough surfaces and is also based on the Kirchhoff approximation. For simplicity, we deal with a planar crack.
A spatiotemporal picture of the acoustic field of elastic-wave diffraction at the edge of a crack
Russian Journal of Nondestructive Testing, 2008
With a Doppler ultrasonic laser interferometer, we have visualized the features of the spatiotemporal structure of the acoustic field near a crack with a small width of opening and a spatial location not allowing its detection by traditional techniques of acoustic nondestructive testing. The obtained result can be used in development of new techniques to detect cracks and microcracks of different kinds by nondestructive testing of products and units.
International Journal of Solids and Structures, 1997
The transient response for diffraction of an incident horizontally polarized shear wave by a finite crack in an unbounded elastic solid is investigated in this study. In analyzing this problem, an infinite number of diffracted waves generated by two crack tips must be taken into account that will make the analysis extremely difficult. An alternative methodology different from the conventional superposition method is used to construct the reflected and diffracted fields. The complete solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are the problems for applying exponentially distributed (in the Laplace transform domain) traction and screw dislocation on the crack faces and along the crack tip line, respectively. The exact transient closed form solutions of dynamic stress intensity factor for two crack tips are obtained and expressed in very simple and compact formulations. Each term in the formulations has its own physical meaning. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted waves. Numerical results of both tips for different incident angles are evaluated which indicate that the dynamic stress intensity factors will oscillate near the correspondent static values after the first three waves have passed the specified crack tip. Some discrepancies of the numerical results compared with available solutions are discussed in detail.