Frequency Dependence of Ultrasonic Wave Scattering from Cracks

Studies of spectral analysis of the scattered longitudinal and shear waves from crack-like flaws in solids were carried out in the region of ka ≥ 1. Experimental data are analyzed and compared to two new theories developed recently for elastic wave-diffraction from cracks. These theories relate the amplitude spectra of scattered L and S waves to crack parameters such as size, orientation, surface roughness, etc. On the development of the interpretation obtained from phase spectral information the scattered phase from spherical cavities was calculated from exact theory and compared to experimental data

Models for the Frequency Dependence of Ultrasonic Scattering from Real Flaws

My objective is to help develop a quantitative working model for a typical nondestructive testing system. Specifically, our objective is to relate the parameters which characterize a defect s~ch as size, orientation, and shape to the ultrasonic scattering field parameters such as amplitude, frequency, scattering angle, and polarization or mode conversion. In Fig. 1 is shown a flat surface sample immersed in liquid containing a real flaw a certain distance below the surface; i.e., in the bulk of the material. Sound waves propagate through the liquid and for the simplest case the wave front enters such that only incident longitudinal waves are present. The waves .at the flaw are scattered, and also mode converted; the scattered wave, which will now be both shear and longitudinal will be reconverted back to a longitudinal wave once leaving the solid body and picked up by a receiver oriented at some angle

Diffraction of Ultrasonic Waves by Elliptical Cracks in Metals

Ultrasonic spectrum analysis is used to study the frequency and angular behavior of diffracted longitudinal waves from elliptical cracks with arbitrary orientation in diffusion bonded titanium alloy. The aspect ratio of the cracks (ratio of major to minor axis) ranged from 1 to 8 and the bandwidth of the input signal was such that the scattering diameter was ka ≥ l. The experimental data are analyzed based on a recently developed elastodynamic diffraction theory (by Achenbach et al.). Some of the key parameters of the scattering data are identified to address the inverse problem

Elastic Wave Scattering from Griffith Cracks

To model elastic wave scattering from fatigue cracks in metals, studies were conducted of wave scattering from artificial cracks using ultrasonic spectroscopy. The cracks are of two dimensional planar strips oriented at various angles and embedded in diffusion bonded titanium alloy. The crack is assumed to behave as a Griffith crack and expressions (derived by Achenbach) to describe diffracted field of elastic waves are used to analyze experimental results

Identification of Flaws from Scattered Ultrasonic Fields as Measured at a Planar Surface

Ultrasonic wave scattering from ellipsoidal and cylindrical cavities embedded in titanium was measured and analyzed with a newly designed signal processing system. Using an immersion system and samples with flat faces, the range for waves incident, at certain polar and azimuthal angles,was determined for both L-L and L-S scattering. Attempts were made to define key parameters from both amplitude and phase spectra for characterizing cavities. Results are compared to predictions of Born approximations (developed by Krumhansl et al. at Cornell) and to experimental results taken by a contact system . A new (Keller type) theory for crack-like defects which includes mode conversion will also be presented

Vortices and Polynomials

The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical vortices on the line. Stationary and uniformly translating vortex configurations with vortices of the same strength but positive or negative orientation are given by the zeros of the Adler-Moser polynomials, which arise in the description of rational solutions of the Korteweg-de Vries equation. For quadupole background flow, vortex configurations are given by the zeros of polynomials expressed as wronskians of Hermite polynomials. Further new solutions are found in this case using the special polynomials arising the in the description of rational solutions of the fourth Painleve equation.Comment: 17 pages, minor revisions and references adde

Ultrasonic Characterization of Rough Cracks

It has been reported before that frequency and angular information from ultrasonic scattering can be used to characterize smooth artificial defects in metals. In this study ultrasonic measurements from fractured and smooth penny-shaped cracks of the same size were carried out. Experimental procedures included the use of broad band and narrow band ultrasonic signals. From angular and frequency dependence of ultrasonic scattering measurements the size, shape, orientation and rms roughness of the fractured surface have been estimated. Ultrasonic measurements of these parameters have been compared to the actual parameters of the defect