Direct and Inverse Methods for Scattering by Cracks at High Frequencies

Further results are presented for the direct problem of scattering of high-frequency waves by cracks in elastic solids. Results for a penny-shaped crack, obtained on the basis of geometrical diffraction theory, are compared with experimental data. For simple crack geometries a hybrid method, whereby the crack-opening displacement is computed by ray theory, and the scattered field is subsequently obtained by the use of a representation theorem, is tested by comparison with exact results. The simple form of the far-field high-frequency solutions to the direct scattering problem suggests the application of Fourier-type integrals to solve the inverse problem. Two different inversion integrals are discussed. The inversion method is checked by applying it to the scattered field of a flat elliptical crack, for which an analytical expression is derived. Some computational technicalities are discussed, and numerical results are presented

Measurements of Local Surface Wave Speeds by a Dual-Probe Laser Interferometer

In a recent paper Huang and Achenbach [1] have reported the development of a dual-probe laser interferometer. In addition to the usual advantages of a laser interferometer such as no contact and point detection, the dual-probe interferometer measures the same signal at two points along its propagation path. Hence the instrument is particularly useful for the measurement of surface wave speed and attenuation. Such measurements provide valuable information on the near-surface material properties as well as the condition of the surface

Analytical Treatment of Polar Backscattering from Porous Composites

Polar backscattering from a fiber-reinforced composite which contains regions of porosity, consists of several components. Roughly speaking these components can be attributed to effects of finite beam width, to the structuring of the material and to the existence of porosity. The backscatter amplitude strongly depends on the polar and the azimuthal angles, which together define the position of the transducer. It has been shown experimentally that the backscatter amplitude shows a steep peak when the incident beam is normal to the fiber direction [l]–[4]

Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space

This is the pre-peer reviewed version of the following article: Arias, I.; Achenbach, J. Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space. "International journal for numerical methods in engineering", Agost 2004, vol. 60, núm. 13, p. 2131-2146, which has been published in final form at http://www3.interscience.wiley.com/journal/109060861/abstractA simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two-dimensional wave propagation problems in elastic half-spaces. The proposed method exploits the knowledge of the far-field asymptotic behaviour of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution involving the same boundary integrals that form the original BEM system. The method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary element scheme is discussed in some detail. The formulation is then validated for a free Rayleigh pulse travelling on a half-space and successfully tested for a benchmark problem with a known approximation to the analytical solution.Peer ReviewedPostprint (author’s final draft

Crack-Tip Diffraction in a Transversely Isotropic Solid

Crack diffraction in a transversely isotropic material is analyzed. The solution is given for the diffracted field generated by incidence of a plane time-harmonic wave on a semi- infinite crack located in a plane normal to the axis of symmetry of the material. The exact solution is obtained by Fourier integral methods and the Wiener-Hopf technique. The diffraction coefficients have been used in the context of the geometrical theory of diffraction to compute high-frequency scattering by a crack of finite length. Applications to scattering by delamina- tions in a medium of periodic layering have been considered for the case that the wavelength and the crack length are of the same order of magnitude, but both are much larger than the larger layer thickness

Scattering by Surface-Breaking and Sub-Surface Cracks

This paper is concerned with exact solutions and approximate solutions in the high-frequency domain for scattering of time-harmonic waves by surface-breaking cracks and cracks which are located near a free surface. Both incident surface waves and incident body waves have been considered. The high-frequency approximate solutions are generally based on elastodynamic ray theory. Some approximate solutions based on the Kirchhoff approximation have been included for comparison

Interaction of laser generated ultrasonic waves with wedge-shaped samples

Wedge-shaped samples can be used as a model of acoustic interactions with samples ranging from ocean wedges, to angled defects such as rolling contact fatigue, to thickness measurements of samples with non-parallel faces. We present work on laser generated ultrasonic waves on metal samples; one can measure the dominant Rayleigh-wave mode, but longitudinal and shear waves are also generated. We present calculations, models, and measurements giving the dependence of the arrival times and amplitudes of these modes on the wedge apex angle and the separation of generation and detection points, and hence give a measure of the wedge characteristics